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[ "<title>Introduction</title>", "<p id=\"Par3\">Despite a national effort to curb opioid addiction and fatal overdoses, excessive opioid prescribing continues to vary substantially over well-defined geographic areas^{##UREF##0##1##}. One promising way to attack this problem involves notifying physicians by mail when one of their patients has a fatal opioid overdose and urging them to reduce opioid prescriptions to safeguard other patients. For example, an initial notification study found the intervention led to an approximately 10% reduction in morphine milligram equivalents (MMEs) dispensed, fewer new patients started on opioids, and a decrease in high-dose opioid prescriptions 1 to 4 months after receipt of the letter^{##REF##30093595##2##}. A follow-up study reported positive spillover effects on benzodiazepine prescription practices^{##REF##35994260##3##}, a demonstration that the letters improved safe prescription practices for a broader range of scheduled drugs. A separate study showed the effects of these notifications on prescription practices persisted for up to 1 year^{##REF##36607639##4##}. Notifications may have a lasting impact on patient safety and potentially could reduce the risk of future overdose. Overall, these studies provide evidence that notification of patients’ fatal overdose, a low-cost solution that is easily scalable, may have several positive effects.</p>", "<p id=\"Par4\">There might be ways to improve such letters to ensure robust, safe prescription practices. One potential approach is to incorporate planning prompts—sometimes referred to as implementation intentions or If/when-then plans—into these letters^{##REF##36607639##4##–##UREF##2##6##}. Planning prompts are mental rules that describe events meant to bring about concrete actions in specific situations: If (or when) situation S occurs, then engage in behavior B. For example, physicians who receive a notification of a patient’s fatal overdose would be prompted to carry out a concrete plan of action that would be triggered by a specific set of circumstances (e.g., when their patients present with pain).</p>", "<p id=\"Par5\">With the incorporation of planning prompts into these letters, physicians may be more likely to take concrete steps to modify their prescription practices and to reduce the risk of future overdose. For example, a physician might better use the information in the letter, if the letter guidance urges them to implement steps at the visit, such as discussing alternative pain management strategies or consulting with a pain management or addiction specialist for evaluation and care.</p>", "<p id=\"Par6\">We hypothesize that the incorporation of planning prompts into notifications will further enhance the effectiveness of the communication, lead to even lower doses and fewer opioid orders, and possibly reduce overdose risk.</p>", "<p id=\"Par7\">To test this hypothesis, we conducted a decedent-clustered randomized trial to compare the effectiveness of standard notification letters to those that incorporate If/when-then plans in Los Angeles County, where the standard letter is mandated by the County Board of Supervisors. We conjecture that If/when-then plain text in the letters will bridge the gap between physicians’ intentions and actions; this will result in improved prescription practices.</p>", "<p id=\"Par8\">The trial’s comparison of the effectiveness of a standard notification letter to one that incorporates If/when-then plans will provide insight into not only which letter leads to reduced dose and frequency of opioid orders but will also identify whether certain physicians, such as those who have more patient deaths, benefit the most from the more effective letter. Our trial aims to advance the design of effective interventions to improve patient safety and reduce the risk of future overdose.</p>" ]

[ "<title>Methods</title>", "<p id=\"Par26\">The trial protocol contains details regarding the intervention, power calculations, randomization, inclusion criteria, and statistical approach (see Supplement). All study procedures were ethically compliant and reviewed and approved by the University of Southern California’s Institutional Review Board (IRB) prior to trial implementation (UP-19-00172). As part of this approval, we were granted a waiver of informed consent and a full waiver of HIPAA authorization. Participants were not compensated.</p>", "<title>Intervention</title>", "<p id=\"Par27\">This cluster randomized controlled trial compares two versions of a personal notification of a patient’s fatal overdose designed to reduce Schedule II-IV prescriptions and opioid dosages. Trial participants were Schedule II-IV prescribers to individuals who died of an overdose between late October 18, 2018 and late May 21, 2020 in Los Angeles County, where opioids were a contributing or primary cause. We received decedent demographics and toxicology information from the Los Angeles County Department of Medical Examiner-Coroner. The contributing cause of death was determined by the Medical Examiner’s judgment. The decedent’s gender was obtained from a government-issued ID and, therefore, self-reported. Clinician gender was also self-reported, and retrieved via license search on the Department of Consumer Affairs site^{##UREF##4##11##}. Gender was not considered in the study design. We received a waiver of consent, which does not allow us to report disaggregated, individual-level data for gender, or any other demographic characteristic. The Medical Examiner staff downloaded prescriber names for each decedent through the State of California Department of Justice’s CURES online portal^{##UREF##5##12##}; data was maintained on a secure, electronic database with restricted access by the Los Angeles Department of Medical Examiner-Coroner. Prescribers were grouped into decedent clusters and randomized to receive a standard letter or comparator.</p>", "<p id=\"Par28\">The standard letter (see Supplementary Methods S##SUPPL##0##1##) was used in Doctor et al.^{##REF##30093595##2##}. Both letters informed prescribers of their patient’s opioid-related overdose, provided guidance on judicious prescription practices, and directed the prescriber to CURES. Both letters were also signed by the Los Angeles County Chief Medical Examiner-Coroner and one of the Los Angeles, Pasadena, or Long Beach Public Health Officers as determined by the prescriber’s practice location. The comparator letter, however, included an If/when-then plan that advised the clinician to keep the letter’s recommendations close when their next patient presents with pain (see Supplementary Methods S##SUPPL##0##2##). The If/when-then plan specifies a contingent action. Letters were sent to prescribers on a monthly basis between April 4, 2019 and July 8, 2020.</p>", "<p id=\"Par29\">California pharmacies that dispense controlled substances are legally required to submit weekly reports to CURES. We accessed this data in collaboration with the research unit and program manager of CURES; per decedent, we notified administrators that clinician prescriptions would be prospectively analyzed post-randomization and letter receipt. We provided CURES with prescriber names to retrieve all Schedule II-IV prescriptions from October 1, 2017 to August 31, 2021. CURES replaced personal identifiers with randomized digit IDs for transfer to the University of Southern California.</p>", "<title>Power calculations</title>", "<p id=\"Par30\">Power was calculated with the statistical computing language R clusterPower package. We assumed a mean of 5.5 prescribers per decedent^{##REF##30093595##2##}, and a coefficient of variation of 1.22. This limited the number of prescribers per decedent at the 99th percentile to 20. Relative to the intraclass correlation of 0.05–0.15^{##REF##11180309##13##} found for most clinician process measures, we used a more conservative estimate of 0.20. Using the Taylor method for variance inflation due to unequal clusters and given a two-tailed test with a 5% Type 1 error rate, we had 80% power to detect a 50% reduction in mean MME or DME (<italic>σ</italic> = 140) with 103 decedents per study arm.</p>", "<title>Inclusion and exclusion criteria</title>", "<title>Decedents</title>", "<p id=\"Par31\">Decedents were included in the randomization if they died of an opioid-related overdose in Los Angeles County from October 18, 2018 to May 21, 2020, and received a legitimate Schedule II–IV prescription from a clinician verified by CURES within the 12 months prior to their death.</p>", "<title>Prescribers</title>", "<p id=\"Par32\">Prescribers were included if they (1) were located and practicing in LA County, (2) had scheduled drug prescribing privileges and, (3) prescribed a Schedule II–IV drug within the 12 months prior to a patient’s death where opioids were the primary or a contributing cause.</p>", "<title>Randomization</title>", "<p id=\"Par33\">Decedents who died of an opioid-related overdose in Los Angeles County from October 18, 2018 to May 21, 2020, and received a CURES-verified Schedule II-IV prescription, were randomized to the comparator or standard letter. Decedent randomization was stratified by whether the decedent was prescribed a benzodiazepine in the year prior to death. For each of the 2 combinations of stratification levels, the principal investigator and lead analyst created a list of decedents. We used random.org’s list randomizer to randomize decedent clusters to a numbered list. The first half of the list was randomized to the standard arm, and the second half of the list was randomized to the comparator arm. If the number of decedents was not divisible by 2, the last decedents on the randomly numbered list were assigned by a ½ probability lottery on random.org. The randomization process was repeated for new prescribers each monthly cycle. Prescribers with multiple decedents received multiple letters. Their experimental condition did not change after the first letter, ensuring they received the same letter repeatedly.</p>", "<title>Measures</title>", "<p id=\"Par34\">In addition to opioids, we analyzed benzodiazepines for potential spillover effects. Opioid and benzodiazepine prescriptions dispensed in the 52 weeks prior to a prescriber’s letter sent date were included in the pre-intervention period. Opioid and benzodiazepine prescriptions dispensed 4–52 weeks after the letter sent date were included in the post-intervention period. The first 4 weeks of follow-up were washed out to avoid contamination from undispensed prescriptions ordered before letter receipt. In the case of prescribers with multiple decedents, the first decedent’s letter sent date defined the pre- and post-intervention periods.</p>", "<title>Outcomes</title>", "<p id=\"Par35\">We used the Centers for Disease Control for MME conversion factors and guidelines (Supplemental Table ##SUPPL##0##S4a##)^{##UREF##6##14##}. We converted benzodiazepines to diazepam milligram equivalents (DME) based on information provided by Borrelli et al.^{##REF##34949119##15##}. (Supplemental Table ##SUPPL##0##S4b##). Our primary outcomes were the change in total weekly MME and DME dispensed pre- to post-intervention between study arms. Per-prescription average daily MME and DME were calculated by multiplying the prescription strength by the number of units prescribed per day and the conversion factor (i.e., strength*(quantity/days)*conversion factor)^{##REF##34949119##15##}. This was summed per clinician per week.</p>", "<p id=\"Par36\">We log-transformed total weekly MME and DME to ensure normality. We confirmed normality with quantile-quantile (q-q) plots. Pre-intervention outliers were detected using Tukey’s fences^{##UREF##7##16##}, which is 1.5 times the interquartile range plus or minus quartiles three and one, respectively.</p>", "<p id=\"Par37\">Our exploratory outcomes were the difference in the likelihood of an opioid prescription greater than or equal to 50 MME and the difference in the likelihood of an opioid prescription greater than 90 MME. We also tested the difference in the probability of a new patient receiving an opioid or benzodiazepine prescription pre- to post-intervention between study arms. To test patient safety associated with spillover effects, we assessed pre-to-post-intervention mean DME drop-offs greater than 20%.</p>", "<title>Statistical analysis</title>", "<p id=\"Par38\">Statistical analyses were executed using SAS version 9.4, STATA software version 16, and R version 4.3.2^{##UREF##8##17##}. We used a multilevel regression with left censoring to account for observations without any opioid or benzodiazepine prescriptions^{##UREF##9##18##}. We regressed log MME and DME on the study arm (comparator vs. standard letter), the study period (pre-intervention vs. post-intervention), and the interaction between the study arm and the study period. To control for differences in decedent and prescriber behavior, we included a random intercept for the prescriber nested within the decedent. Model 1 is the effect of time (<italic>β</italic>₁) study arm (<italic>β</italic>₂), and the interaction between time and study arm (β₃) on <italic>Y</italic> for the prescriber and prescription, where <italic>Y</italic> is uncensored, latent weekly log MME or log DME. The coefficients are a [100*(1 − exp(<italic>β</italic>)] change in uncensored MME and DME per-level increase. is the random intercept for prescriber nested within the decedent, with mean 0 and variance . Due to prescriber outliers in the standard letter group, we calculated trimmed pre-intervention means for Table ##TAB##2##3## and Table ##TAB##3##4## that resulted in the smallest difference between letter groups, which was 9% and 7% for opioid and benzodiazepine prescribers, respectively. We calculated adjusted post-intervention means to obtain the difference-in-difference in pre- to post-weekly MME and DME between the standard and comparator study arms. 95% confidence intervals were bootstrapped using 2000 repetitions of 12,000 randomly selected observations.</p>", "<p id=\"Par39\">We evaluated exploratory outcomes using mixed-effects, logistic regressions to test whether patients with prescribers randomized to the comparator letter were less likely to receive an opioid prescription greater than or equal to 50 MME or greater than 90 MME post-intervention and the probability of a new patient receiving an opioid or benzodiazepine prescription post-intervention. We calculated the per-clinician percent change in mean DME pre-to-post intervention and used logistic regression to test whether greater than 20% drop-offs were higher among clinicians in the comparator arm, controlling for the proportion of new users and opioid coprescriptions.</p>", "<p id=\"Par40\">We conducted two post hoc analyses. The first added a three-way interaction between study arm, time, and number of decedents to Model 1 to test whether high-frequency prescribers with multiple decedents were more amenable to repeat comparator letter exposure. The second assessed whether letter efficacy decreased over time by including two fixed interaction terms between the study arm, the study start (weeks 4–22), and the study end (weeks 23–52). We compared study-start and study-end coefficients using an equality of regression coefficients test^{##UREF##10##19##}. Boxplots and corresponding legends were generated using the R officer, cowplot, rvg, and ggplot2 packages^{##UREF##11##20##}.</p>", "<title>Reporting summary</title>", "<p id=\"Par41\">Further information on research design is available in the ##SUPPL##2##Nature Portfolio Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<title>Opioids sample</title>", "<p id=\"Par9\">Figure ##FIG##0##1## shows the sample progression. The Los Angeles Medical Examiner-Coroner examined 316 fatal accidental opioid-related overdoses from late October 2018 to late May 2020 in Los Angeles County. Of these, 236 decedents (74.7%) received at least one CURES-documented scheduled drug from 541 prescribers in the 12 months prior to their death. Thirty-one prescribers (5.73%) had no opioid prescription during the study period and were removed. Three decedents (1.27%) received Scheduled II–IV prescriptions from these prescribers only and were also removed. Since we assigned each prescriber to a cluster by his or her first decedent, this resulted in a final analytic sample of 219 first-decedents and 510 clinicians.</p>", "<p id=\"Par10\">There was no difference in decedent age, sex, race, or cause of death between study arms (Table ##TAB##0##1##). There was a small difference (<italic>P</italic> = 0.025) in prescriber professional practice between study arms (Table ##TAB##1##2##). On average, decedents received prescriptions from 2.40 (<italic>σ</italic> = ± 2.25) prescribers, with a range of 1–13. Four hundred sixty-nine prescribers (91.96%) had one decedent. Forty-one prescribers (8.04%) had more than one decedent and received a letter for each. The average number of decedents per prescriber (corresponding to letters sent) was 1.20 (<italic>σ</italic> = ± 0.40). The number of prescribers who had more than one decedent did not differ by study arm in the analytic sample (<italic>χ</italic>² = 1.21, <italic>P</italic> = 0.271).</p>", "<title>Morphine milligram equivalents (MMEs)</title>", "<p id=\"Par11\">Of the 1,538,821 prescriptions dispensed during the study, 559,658 (36.37%) were for an opioid. Logarithm-transformed MME normalized the distribution (Supplementary Fig. ##SUPPL##0##S1a##, b). Table ##TAB##2##3## shows the change in average total weekly MME pre-to-post intervention between study arms. In the comparator arm, the average weekly MME decreased from 157.81 (95% CI: 153.85, 161.76) pre-intervention to 77.05 (95% CI: 75.12, 78.98) post-intervention, compared to 157.70 (95% CI: 153.45, 161.96) and 103.16 (95% CI: 100.34, 105.98) in the standard arm. The difference in average weekly MME pre-to-post intervention was −80.76 (95% CI: −82.92, −78.60) in the comparator arm and −54.55 (95% CI: −56.05, −53.04) in the standard arm. The difference in average weekly MME pre-to-post intervention between study arms was −26.21 (95% CI: −29.63, −22.86), corresponding to a 12.85% (95% CI: 6.83%, 18.49%; <italic>P</italic> &lt; 0.001) greater decrease in MME among prescribers randomized to the comparator letter (Supplementary Table ##SUPPL##0##S1a##).</p>", "<p id=\"Par12\">To evaluate if outlier clinicians played a role in study effects, Fig. ##FIG##1##2## shows the clinician-level total log MME distribution pre-to-post intervention between study arms among clinicians with one decedent and more than one decedent. Pre-intervention, the dependent variable did not differ by study arm (<italic>t</italic> = 0.83, <italic>P</italic> = 0.406), or among clinicians with one versus multiple decedents (<italic>t</italic> = −0.61, <italic>P</italic> = 0.544). The number of outliers also did not differ by study arm (<italic>χ</italic>² = 1.42, <italic>P</italic> = 0.233) or number of decedents (<italic>χ</italic>² = 0.48, <italic>P</italic> = 0.759) (Supplementary Table ##SUPPL##0##S2a##).</p>", "<title>Exploratory opioid outcomes</title>", "<p id=\"Par13\">Prescribers in the comparator arm were less likely to prescribe an opioid to a new patient post-intervention, but not significantly (<italic>β</italic> = −0.09; [95% CI: −0.19, 0.01]; <italic>P</italic> = 0.07). There was also no significant difference in the odds of a patient receiving a prescription of at least 50 MME (<italic>β</italic> = −0.01; [95% CI: −0.12, 0.11]; <italic>P</italic> = 0.894). Clinicians randomized to the comparator letter had significantly lower odds (<italic>β</italic> = −0.18; [95% CI: −0.34, −0.02]; <italic>P</italic> = 0.027) of a patient receiving a medication greater than 90 MME compared to those who received the standard letter.</p>", "<title>Post-hoc morphine milligram equivalent analyses</title>", "<p id=\"Par14\">There was no difference in the study-start and study-end coefficients (<italic>β</italic> = −0.06 [95% CI: −0.16, 0.04]; <italic>P</italic> = 0.224), indicating that the effect persisted over time. There was a significant three-way interaction between study arm, time, and number of decedents, translating to a 31.41% ([95% CI: 11.38%, 46.91%]; <italic>P</italic> = 0.004) greater decrease in total weekly MME for prescribers who received multiple comparator letters (Supplementary Table ##SUPPL##0##S3a##).</p>", "<title>Benzodiazepine sample</title>", "<p id=\"Par15\">Thirteen clinicians (2.40%) did not prescribe a benzodiazepine during the study period and were removed from the analysis (Fig. ##FIG##2##3##). One decedent (0.42%) received scheduled prescriptions from these prescribers and was also removed. The final analytic sample was 528 clinicians and 220 first-decedents.</p>", "<p id=\"Par16\">Relative to opioid prescribers, decedents received scheduled prescriptions from a slightly higher number of clinicians who prescribed a benzodiazepine (<italic><underline>X</underline></italic> = 2.44, <italic>σ</italic> = ± 2.27; range: 1–13). Benzodiazepine prescribers received an average of 1.21 (<italic>σ</italic> = ± 0.42) letters. Forty-one (7.77%) prescribers had more than one decedent. The number of decedents did not vary by study arm (<italic>χ</italic>² = 1.29, <italic>P</italic> = 0.256).</p>", "<title>Diazepam milligram equivalents (DME)</title>", "<p id=\"Par17\">Three hundred eighty-four thousand seven hundred sixty-eight (25%) dispensed scheduled prescriptions for a benzodiazepine. Log transforming DME normalized the distribution (Supplementary Fig. ##SUPPL##0##S1c##, d). Average weekly DME decreased from 51.47 (95% CI: 49.83, 53.11) pre-intervention to 30.16 (95% CI: 29.27, 31.05) post-intervention in the comparator arm and from 54.36 (95% CI: 52.90, 55.82) to 43.71 (95% CI: 42.49, 44.92) in the standard arm (Table ##TAB##3##4##). The difference in pre-to-post-intervention average weekly DME was −21.31 (95% CI: −21.98, −20.64) in the comparator arm and −10.65 (95% CI: −10.95, −10.35) in the standard arm. The difference-in-difference in average weekly DME was −10.66 (95% CI: −12.27, −9.04). This corresponds to an 8.32% ([95% CI: 2.34, 13.93]; <italic>P</italic> &lt; 0.01) greater decrease in DME (Supplementary Table ##SUPPL##0##S1b##).</p>", "<p id=\"Par18\">To evaluate if outliers contributed to the effect, Fig. ##FIG##3##4## shows the pre-to-post intervention clinician-level logarithm transformed DME distribution by study arm and number of decedents. There were no differences by study arm in log DME (<italic>t</italic> = 1.50, <italic>P</italic> = 0.133). Pre-intervention log DME was slightly higher among clinicians with more than one decedent (<italic>t</italic> = −5.28, <italic>P</italic> &lt; 0.001). The number of outliers also did not differ by study arm (χ² = 3.65, <italic>P</italic> = 0.125) or number of decedents (<italic>χ</italic>² = 0.09, <italic>P</italic> = 1.0) (Supplementary Table ##SUPPL##0##S2b##).</p>", "<title>Exploratory benzodiazepine outcomes</title>", "<p id=\"Par19\">Prescribers in the comparator arm were not less likely to prescribe a benzodiazepine to a new patient post-intervention (<italic>β</italic> = 0; [95% CI: −0.09, 0.09]; <italic>P</italic> = 0.962). Comparator arm clinicians did not have higher odds of reducing DME by more than 20% (<italic>β</italic> = −0.14; [95% CI: −0.54, 0.26]; <italic>P</italic> = 0.488).</p>", "<title>Post-hoc diazepam milligram equivalent analyses</title>", "<p id=\"Par20\">There was no difference in the study-start and study-end coefficients (<italic>β</italic> = −0.06 [95% CI: −0.15, 0.04]; <italic>P</italic> = 0.229), indicating that the effect persisted over time. The three-way interaction between study arm, time, and number of decedents was significant (Supplementary Table ##SUPPL##0##S3b##); prescribers who received multiple comparator letters had a 56.05% ([95% CI: 45.04%, 64.85%]; <italic>P</italic> &lt; 0.001) greater reduction in total weekly DME.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par21\">We sought to determine whether the addition of If/when-then plans could bridge the gap between physicians’ intentions and actions in notifications of a fatal overdose in a physician’s practice. Our findings suggest that If/when-then plans may reduce opioid prescription intensity and frequency, thereby reducing future risk. A moderator analysis showed that the If/when-then plan was more effective relative to the standard letter for prescribers who received multiple letters. These were persons with multiple deaths in their practice. There was also evidence of spillover to more judicious benzodiazepine prescribing. A safety analysis showed that study arms did not differ in the number of clinicians demonstrating a 20% reduction in filled benzodiazepine prescriptions. The If/when-then plan may have helped prescribers with complex or difficult patients to implement skills that promote safe prescription practices. Alternatively, the prescribers with multiple deaths may have lacked skills and benefited from a letter that carefully outlined steps to improve prescription safety.</p>", "<p id=\"Par22\">The intervention is scalable. Forty-nine of the 50 U.S. states operate prescription drug monitoring programs, and every county in the U.S. has a medical examiner or coroner. These interventions could easily operate out of the medical examiner’s office almost anywhere in the U.S. This intervention has the benefit of helping clinicians learn of deaths in their practice that they might not otherwise learn about. This creates a more balanced sample from which they can draw inferences about their patients’ outcomes. The intervention is low-cost and requires only minimal changes to routine administrative tasks in the medical examiner’s office. A downside to the intervention is that it cannot reach all clinicians, but only those with a death in their practice. Those clinicians with a death in their practice are, however, in greatest need of receiving the intervention.</p>", "<p id=\"Par23\">Doctor et al. ^{##REF##30093595##2##} compared a letter notifying clinicians of a death in their practice to a no-treatment control group. Morphine milligram equivalents in prescriptions filled by patients of letter recipients versus no intervention controls decreased by 9.7% (95% CI: 6.2 to 13.2%; <italic>P</italic> &lt; 0.001)^{##REF##30093595##2##}. The current paper compared a modified letter to the active treatment in Doctor et al. 2018, which resulted in a 12.9% decrease in morphine milligram equivalent prescriptions filled. The new letter appears even more effective than the letter in Doctor et al. (2018). From the standpoint of psychological mechanisms, the plan may have provided a simple way to take contingent action at pain-related visits. Our results are in line with previous research that shows If/when-then plans are effective in other environments^{##REF##20424044##7##–##REF##19864187##9##}.</p>", "<p id=\"Par24\">This study has several strengths. It is a randomized concealment design^{##UREF##3##10##} that avoids standard pitfalls that come with trial enrollment, attrition, and non-response. The study also used unobtrusive measures (California’s Controlled Substance Utilization Review and Evaluation System 2.0 [CURES]), which lowered the potential for reactivity. Despite the strengths of our study, there are several limitations to consider. First, our study was conducted in Los Angeles County, and while it is the largest County in the United States, the results may not be generalizable to other populations or geographic regions. Additionally, our sample size was limited, and our study only examined the short-term effects of the intervention. Finally, we were unable to examine the effects of the intervention on patient outcomes, such as overdose rates or other adverse events.</p>", "<p id=\"Par25\">In conclusion, our study provides evidence that If/when-then plans as additions to fatal overdose notification letters moderate physician prescription practices. Further research is needed to confirm the results, examine the long-term effects of the intervention, and explore its potential effects on patient outcomes.</p>" ]

[]

[ "<p id=\"Par1\">Prior work has demonstrated that personalized letters are effective at reducing opioid and benzodiazepine prescribing, but it is unclear whether If/when-then planning prompts would enhance this effect. We conducted a decedent-clustered trial which randomized 541 clinicians in Los Angeles County to receive a standard (<italic>n</italic> = 284), or comparator (<italic>n</italic> = 257) version of a letter with If/when-then prompts. We found a significant 12.85% (6.83%, 18.49%) and 8.32% (2.34%, 13.93%) decrease in the primary outcomes morphine (MME) and diazepam milligram equivalents (DME), respectively. This study confirms the benefit of planning prompts, and repeat letter exposure among clinicians with poor patient outcomes. Limitations include lack of generalizability and small sample size. Clinicaltrials.gov registration: NCT03856593.</p>", "<p id=\"Par2\">A personalized letter from the Medical Examiner-Coroner in Los Angeles County has proven effective at reducing opioid and benzodiazepine prescribing. Here the authors show that the introduction of if/when-then planning prompts in to the letter further reduced opioid prescribing by 12.85% and benzodiazepine prescribing by 8.32%; they were most effective for clinicians with multiple patient deaths due to accidental opioid-related overdose.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41467-023-44573-5.</p>", "<title>Acknowledgements</title>", "<p>This study was supported by the National Institutes on Aging (P30AG024968; PI: Dr. Jason Doctor, University of Southern California). The funding agency had no role in the design and conduct of the study, collection, management, analysis, or interpretation of the data; preparation, review, or approval of the paper; or decision to submit the paper for publication.</p>", "<title>Author contributions</title>", "<p>M.K. and E.P.S. had full access to all of the data in the study and took responsibility for the integrity of the data and the accuracy of the data analysis. Concept and design: J.N.D., N.J.G. and J.L. Acquisition, analysis, or interpretation of data: J.N.D., M.K., N.J.G., J.L., T.K.K. and E.P.S. Drafting of the paper: J.N.D., M.K., E.P.S. and N.J.G. Critical revision of the manuscript for important intellectual content: J.N.D., M.K., N.J.G., J.L., T.K.K. and E.P.S. Statistical analysis: M.K., E.P.S. and J.N.D. Obtained funding: J.N.D. Administrative, technical, or material support: T.K. and J.N.D. Supervision: T.K. and J.N.D.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par42\"><italic>Nature Communications</italic> thanks Robert Dunne and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.</p>", "<title>Data availability</title>", "<p>The datasets generated and/or analyzed during the current study involve third-party data from the California Department of Justice and are not publicly available as they contain protected health information, posing participant confidentiality and privacy concerns. Data may be available jointly through the Department of Justice and the corresponding author (J.N.D.) through a signed Data Use Agreement. Requests should be submitted to [email protected]; allow 30 days for a response to your request.</p>", "<title>Code availability</title>", "<p>All code used for data management, descriptive analyses, model fitting, and plotting is publicly available on a GitHub repository at LA-Letters-Code/ at main · epstewart111/LA-Letters-Code · GitHub. We have also used Zenodo to assign a DOI to the repository: 10.5281/zenodo.10263890. The license used to generate the code is the Schaeffer Center for Health Policy and Economics, University of Southern California.</p>", "<title>Competing interests</title>", "<p id=\"Par43\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Opioid Prescriber CONSORT diagram.</title><p>CONSORT diagram for clinicians who prescribed an opioid during the study period.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Clinician-level Opioid Prescribing.</title><p>Boxplots showing median log MME, the interquartile range, and outliers pre-to-post intervention between study arms among clinicians with one versus multiple decedents.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Benzodiazepine Prescriber CONSORT diagram.</title><p>CONSORT diagram for clinicians who prescribed a benzodiazepine during the study period.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Clinician-level Benzodiazepine Prescribing.</title><p>Boxplots showing median log DME, the interquartile range, and outliers pre-to-post intervention between study arms among clinicians with one versus multiple decedents.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Decedent characteristics^{##UREF##0##1##}</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th colspan=\"5\">Randomization group</th></tr><tr><th>Characteristic^a</th><th>Comparator (<italic>N</italic> = 109)</th><th>Standard (<italic>N</italic> = 127)</th><th>Statistic^e</th><th>Two-sided <italic>P</italic> value</th></tr></thead><tbody><tr><td>Age, (±σ)</td><td>40.76 (13.13)</td><td>40.02 (13.92)</td><td><italic>t</italic> = −0.42</td><td>0.674</td></tr><tr><td colspan=\"5\"><bold>Gender</bold>^{<bold>b</bold>}</td></tr><tr><td>Female</td><td>32 (29.36%)</td><td colspan=\"3\">29 (22.83%)</td></tr><tr><td>Male</td><td>77 (70.64%)</td><td>98 (76.38%)</td><td><italic>χ</italic>² = 1.30</td><td>0.253</td></tr><tr><td colspan=\"5\"><bold>Race</bold></td></tr><tr><td>Hispanic</td><td>33 (30.28%)</td><td colspan=\"3\">26 (20.47%)</td></tr><tr><td>White</td><td>61 (55.96%)</td><td>80 (62.99%)</td><td><italic>χ</italic>² = 3.04</td><td>0.219</td></tr><tr><td>Other/missing</td><td>15 (13.76%)</td><td colspan=\"3\">21 (16.54%)</td></tr><tr><td colspan=\"5\"><bold>Cause of death</bold></td></tr><tr><td>Opioid^c prescription only</td><td>37 (33.94%)</td><td colspan=\"3\">34 (26.77%)</td></tr><tr><td>Heroin only</td><td>13 (11.93%)</td><td colspan=\"3\">25 (19.69%)</td></tr><tr><td>Opioid prescription and heroin</td><td>49 (44.95%)</td><td>48 (37.8%)</td><td><italic>χ</italic>² = 5.92</td><td>0.116</td></tr><tr><td>Other/missing^d</td><td>10 (9.17%)</td><td colspan=\"3\">20 (15.75%)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Prescriber characteristics</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"2\">Characteristic^a</th><th colspan=\"2\">Randomization group</th><th rowspan=\"2\">Statistic^b</th><th rowspan=\"2\">Two-sided <italic>P</italic> value</th></tr><tr><th>Comparator (<italic>n</italic> = 257)</th><th>Standard (<italic>n</italic> = 284)</th></tr></thead><tbody><tr><td colspan=\"5\"><bold>Gender</bold></td></tr><tr><td>Male</td><td>99 (38.52%)</td><td colspan=\"3\">104 (36.62%)</td></tr><tr><td>Female</td><td>27 (10.51%)</td><td colspan=\"3\">29 (10.21%)</td></tr><tr><td>Declined to disclose</td><td>58 (22.57%)</td><td>67 (23.59%)</td><td><italic>χ</italic>2 = 0.27</td><td>0.966</td></tr><tr><td>Missing</td><td>73 (28.40%)</td><td colspan=\"3\">84 (29.58%)</td></tr><tr><td colspan=\"5\"><bold>Professional practice</bold></td></tr><tr><td>Medical doctor (MD)</td><td>172 (66.93%)</td><td colspan=\"3\">194 (68.31%)</td></tr><tr><td>Doctor of osteopathy (DO)</td><td>20 (7.78%)</td><td colspan=\"3\">12 (4.23%)</td></tr><tr><td>Nursing (NP/FNP/DNP)</td><td>23 (8.95%)</td><td>39 (13.73%)</td><td><italic>χ</italic>2 = 11.13</td><td>0.025</td></tr><tr><td>Physician assistant (PA)</td><td>20 (7.78%)</td><td colspan=\"3\">28 (9.86%)</td></tr><tr><td>Other</td><td>22 (8.56%)</td><td colspan=\"3\">11 (3.87%)</td></tr><tr><td colspan=\"5\"><bold>Primary specialty</bold></td></tr><tr><td>Emergency medicine</td><td>31 (12.06%)</td><td colspan=\"3\">37 (13.03%)</td></tr><tr><td>Internal medicine</td><td>44 (17.12%)</td><td colspan=\"3\">43 (15.14%)</td></tr><tr><td>Psychiatry</td><td>21 (8.17%)</td><td colspan=\"3\">22 (7.75%)</td></tr><tr><td>Family medicine</td><td>22 (8.56%)</td><td>20 (7.04%)</td><td><italic>χ</italic>2 = 1.18</td><td>0.947</td></tr><tr><td>Other</td><td>41 (15.95%)</td><td colspan=\"3\">45 (15.85%)</td></tr><tr><td>Missing</td><td>98 (38.13%)</td><td colspan=\"3\">117 (41.20%)</td></tr><tr><td colspan=\"5\"><bold>Race/Ethnicity</bold></td></tr><tr><td>Asian/Pacific Islander</td><td>21 (8.17%)</td><td>14 (4.93%)</td><td/><td/></tr><tr><td>Non-Hispanic White</td><td>18 (7.00%)</td><td>20 (7.04%)</td><td/><td/></tr><tr><td>Other</td><td>12 (4.67%)</td><td>23 (8.10%)</td><td><italic>χ</italic>2 = 5.02</td><td>0.285</td></tr><tr><td>Declined to disclose</td><td>132 (51.36%)</td><td colspan=\"3\">139 (48.94%)</td></tr><tr><td>Missing</td><td>74 (28.79%)</td><td colspan=\"3\">88 (30.99%)</td></tr><tr><td colspan=\"5\"><italic>Location</italic></td></tr><tr><td>Los Angeles City</td><td>240 (93.39%)</td><td colspan=\"3\">259 (91.20%)</td></tr><tr><td>Long Beach or Pasadena City</td><td>17 (6.61%)</td><td>25 (8.80%)</td><td><italic>χ</italic>2 = 0.902</td><td>0.342</td></tr><tr><td colspan=\"5\"><bold>No. of decedents</bold></td></tr><tr><td>&gt;1</td><td>16 (6.23%)</td><td colspan=\"3\">25 (8.80%)</td></tr><tr><td>1</td><td>241 (93.77%)</td><td>259 (91.20%)</td><td><italic>χ</italic>2 = 1.28</td><td>0.258</td></tr><tr><td>No. of decedents, (±<italic>σ</italic>)</td><td>1.07 (0.27)</td><td>1.10 (0.32)</td><td>t = 1.16</td><td>0.248</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Adjusted mean total weekly morphine milligram equivalents (MMEs) dispensed between study arms. Values in parentheses are 95% CIs with 9% trimmed means</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"2\">Parameter</th><th colspan=\"2\">Randomization group</th></tr><tr><th>Comparator</th><th>Standard</th></tr></thead><tbody><tr><td>Prescribers followed</td><td>241</td><td>269</td></tr><tr><td>Pre-intervention</td><td>157.81 (153.85, 161.76)</td><td>157.70 (153.45, 161.96)</td></tr><tr><td>Post-intervention^a</td><td>77.05 (75.12, 78.98)</td><td>103.16 (100.34, 105.98)</td></tr><tr><td>Increment (pre- to post-)</td><td>−80.76 (−82.92, −78.60)</td><td>−54.56 (−56.05, −53.04)</td></tr><tr><td>Difference in increment</td><td colspan=\"2\">−26.21 (−29.63, −22.86)</td></tr><tr><td>Two-sided <italic>P</italic> value</td><td colspan=\"2\">&lt;0.001</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Adjusted mean total weekly diazepam milligram equivalents (DMEs) dispensed between study arms. Values in parentheses are 95% CIs with 7% trimmed means</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"2\">Parameter</th><th colspan=\"2\">Randomization group</th></tr><tr><th>Comparator</th><th>Standard</th></tr></thead><tbody><tr><td>Prescribers followed</td><td>251</td><td>277</td></tr><tr><td>Pre-intervention</td><td>51.47 (49.83, 53.11)</td><td>54.36 (52.90, 55.82)</td></tr><tr><td>Post-intervention^a</td><td>30.16 (29.27, 31.05)</td><td>43.71 (42.49, 44.92)</td></tr><tr><td>Increment (pre- to post-)</td><td>−21.31 (−21.98, −20.64)</td><td>−10.65 (−10.95, −10.35)</td></tr><tr><td>Difference in increment</td><td colspan=\"2\">−10.66 (−12.27, −9.04)</td></tr><tr><td>Two-sided <italic>P value</italic></td><td colspan=\"2\">0.007</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>" ]

[ "<table-wrap-foot><p>OTC over the counter, n number of clinicians.</p><p>^aCounts of less than 10 were censored in accordance with the State of California Department of Justice’s CURES policy.</p><p>^bOne decedent’s missing gender was deduced using first name.</p><p>^cSupplemental Table ##SUPPL##0##4a## contains opioid types.</p><p>^dOther are multi-causal deaths that in addition to opioids, included alcohol/ethanol, non-opioid Schedule II–IV prescriptions (e.g., benzodiazepines, anticonvulsants, muscle relaxants, and barbiturates), and/or illicit drugs (e.g., methamphetamine, cocaine, MDMA, and ketamine).</p><p>^eTwo-sample <italic>t</italic>-test for continuous traits. Chi-square test for categorical variables.</p></table-wrap-foot>", "<table-wrap-foot><p>^aCounts of less than 10 were censored in accordance with the State of California Department of Justice’s CURES policy.</p><p>^bTwo-sample <italic>t</italic>-test for continuous traits. Chi-square test for categorical variables.</p></table-wrap-foot>", "<table-wrap-foot><p>^aPredicted MME using coefficients from censored, mixed linear model (Table ##SUPPL##0##S1a##) testing the two-sided hypothesis that change in pre-to-post MME does not differ by study arm.</p></table-wrap-foot>", "<table-wrap-foot><p>^aPredicted DME using coefficients from censored, mixed linear model (Table ##SUPPL##0##S1b##) testing two-sided hypothesis that change in pre-to-post DME does not differ by study arm.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41467_2023_44573_MOESM1_ESM.pdf\"><caption><p>Supplementary Information</p></caption></media>", "<media xlink:href=\"41467_2023_44573_MOESM2_ESM.pdf\"><caption><p>Peer Review File</p></caption></media>", "<media xlink:href=\"41467_2023_44573_MOESM3_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Sepsis refers to the life-threatening organ dysfunction induced by a dysregulated host response to infection^{##REF##26903338##1##} and is considered a major cause of health loss. In 2017, an estimated 48.9 million incident cases of sepsis were recorded worldwide, and 11.0 million sepsis-related deaths were reported, representing 19.7% of all global deaths^{##REF##31954465##2##}. In patients suspected of having sepsis, initial appropriate antibiotic treatment results in a favorable outcome and a significant decrease in the mortality rate^{##REF##33722641##3##,##REF##14699463##4##}. However, in order to select the optimum initial antimicrobial treatment, the early identification of pathogenic microorganisms is critical. To address this problem, we previously reported the development of a novel rapid, easy, cost-effective method of identifying a broad range of pathogenic bacteria (&gt; 100 bacterial species) using a real-time polymerase chain reaction (PCR)-based system; we named this novel method the Tm mapping method^{##REF##26218169##5##–##REF##34090356##7##}.</p>", "<p id=\"Par3\">In the treatment of sepsis, it is difficult to judge the best timing to stop antibiotic treatment or even whether a given antibiotic treatment is actually appropriate. To make accurate judgments, we need biomarkers that strictly reflect the severity of sepsis. The biomarkers currently used to reflect the severity of sepsis include procalcitonin, presepsin, and C-reactive protein (CRP) levels; the body temperature (BT); and the white blood cell (WBC) count^{##REF##33198109##8##}. However, while these biomarkers are correlated with the severity of sepsis to some extent, they do not always accurately reflect the severity at a particular point in time. For example, procalcitonin cannot reliably differentiate sepsis from other non-infectious causes of systemic inflammatory response syndrome in critically ill adult patients^{##REF##17317602##9##}, and presepsin concentrations increase with age and kidney dysfunction, so their interpretation might be altered in elderly patients or those with an impaired renal function^{##REF##24076253##10##}. Thus, there is still no truly reliable biomarker of sepsis.</p>", "<p id=\"Par4\">The fluctuations in the biomarkers mentioned above are due to host defenses against microbial infection. In the present study, as a novel biomarker to accurately judge the severity of sepsis, we suggest “the number of bacteria in a blood sample”, which is not a result of the host defense but direct information about the pathogen itself. The quantitative detection of a specific type of bacteria in a clinical sample (e.g. <italic>Borrelia burgdorferi</italic>^{##REF##10325354##11##}, <italic>Porphyromonas gingivalis</italic>^{##REF##10835003##12##}, <italic>Mycobacterium tuberculosis</italic>^{##REF##9650945##13##}, <italic>Streptococcus pneumoniae</italic>^{##REF##11526140##14##}, <italic>Mycoplasma ovipneumoniae</italic>^{##REF##25649947##15##}, <italic>Staphylococcus aureus</italic>^{##REF##17881553##16##}, <italic>Enterococcus faecalis</italic>^{##REF##17881553##16##}, and <italic>pneumococcal pneumonia</italic>^{##REF##19433527##17##}, etc.) has been reported previously. However, the quantitative detection of unknown bacteria in a clinical sample is quite difficult technically. In fact, there have been no reports of methods to accurately quantify unknown pathogenic bacteria in a clinical sample.</p>", "<p id=\"Par5\">If the bacterial species are unknown, a broad range of bacteria can be detected using bacterial universal primers targeting highly conserved regions in the bacterial 16S ribosomal RNA (rRNA) gene^{##REF##2095137##18##}. The main problem associated with bacterial universal PCR is the achievement of the sensitive and reliable detection of bacteria without any bacterial DNA contamination. This is because the reagents used in the PCR process, especially stock solution of the thermostable DNA polymerase^{##REF##10790092##19##–##REF##2087233##22##}, are usually contaminated with trace amounts of bacterial DNA. Whenever pathogenic bacteria are present in very small quantities, bacterial DNA contamination becomes a major problem. Since even low-copy-number contamination will be amplified with bacterial universal PCR, there are bound to be issues with obtaining low detection limits in a clinical sample.</p>", "<p id=\"Par6\">To address this, we developed a eukaryote-made thermostable DNA polymerase that is free from bacterial DNA contamination^{##REF##21775543##23##}. Using this thermostable DNA polymerase, the sensitive and reliable detection of bacteria is feasible, making the quantitative detection of a small amount of bacteria in a clinical sample possible.</p>", "<p id=\"Par7\">One more problem in the quantitative detection of unknown bacteria is the variation of the 16S rRNA operon copy number in genomes among bacterial species. Quantification results using bacterial universal primer do not reflect actual bacterial concentrations unless adjusted according to the pathogen’s 16S rRNA operon copy number. Our quantification method is based on the melting temperature (Tm) mapping method for rapidly identifying the dominant bacteria in a clinical sample^{##REF##26218169##5##}. In the novel quantification method, quantification results can be adjusted according to the 16S rRNA operon copy number of the pathogen identified by the Tm mapping method.</p>", "<p id=\"Par8\">We herein report the development of a novel rapid identification and quantification method of unknown bacteria in a clinical sample using a real-time PCR system. We also report the importance of the number of bacteria in a septic blood sample compared to other current biomarkers.</p>" ]

[ "<title>Methods</title>", "<title>Clinical specimens</title>", "<p id=\"Par29\">Whole-blood samples (2 mL each) were randomly collected from patients with suspected sepsis. All procedures were performed under a protocol approved by the Ethics Committee at the University of Toyama, and written informed consent was obtained from all patients. The methods were carried out in accordance with the approved guidelines.</p>", "<title>Isolation of bacterial genomic DNA from whole blood</title>", "<p id=\"Par30\">A total of 2 mL of venous blood was collected in EDTA-2K tubes (BD Biosciences Japan, Tokyo, Japan). The blood samples were then centrifuged at 100×<italic>g</italic> for 5 min to spin down the red blood cells, and the resulting supernatant fraction (500 μL) with buffy coat was used. The supernatant with buffy coat was centrifuged again at 20,000×<italic>g</italic> for 10 min, and 400 μL of the supernatant fraction was carefully removed in order to not disturb the pellets. Next, 1 mL of molecular-grade distilled water (water deionized and sterilized for molecular biology; Nacalai Tesque, Inc., Kyoto, Japan) was added to the pellets, and the mixture was gently turned upside down several times, and subsequently centrifuged at 20,000×<italic>g</italic> for 5 min. Finally, 1 mL of the supernatant fraction was again carefully removed in order to not disturb the pellets. DNA was isolated from the pellets using a DNA extraction kit (QIAamp UCP Pathogen Mini Kit; Qiagen, Germany). To lyse bacterial cell walls thoroughly and obtain consistent high detection sensitivity, we modified the supplier’s protocols (mechanical pre-lysis protocol and spin protocol) as follows: Step 1, Add 100 μL of molecular-grade distilled water (water deionized and sterilized for molecular biology; Nacalai Tesque, Inc.) to a tube containing a bacterial pellet, or as a negative control for DNA extraction, add 200 μL of molecular-grade distilled water to an empty tube; then, mix with a vortex mixer for 10 s, and spin it down briefly in a microcentrifuge. Step 2, Transfer the sample from Step 1 into a fresh Pathogen Lysis Tube (S) containing small beads to assist in lysing bacteria; then, add 400 μL of Buffer ATL (containing Reagent DX), and mix the sample with a vortex mixer for 10 min at maximum speed. Step 3, Add 40 μL of Proteinase K and mix the sample by pipetting up and down several times, and then incubate the sample at 56 °C for 10 min. Step 4, Add 200 μL of Buffer APL2 to the sample, mix with a vortex mixer for 10 min at maximum speed, and then incubate the sample at 70 °C for 10 min. Step 5, Briefly spin the tube (Pathogen Lysis Tube (S)) to remove droplets from the inside of the lid. Step 6, Transfer 740 μL of the supernatant from Step 5 into a fresh 1.5-mL microcentrifuge tube, taking care to not transfer any of the small beads in doing so. Step 7, Add 300 μL of ethanol to the lysate. Close the cap, and mix thoroughly by pulse-vortex mixing for 15–30 s.</p>", "<p id=\"Par31\">We conducted the remaining steps of the procedure in accordance with the supplier’s instructions, but during the final elution step, we added 50 μL of Buffer AVE (elution buffer) incubated at room temperature for 10 min and then centrifuged the sample at full speed for 1 min to elute the DNA. We repeated the elution step again, so the final amount of eluted DNA solution was 100 μL.</p>", "<title>PCR assays</title>", "<p id=\"Par32\">The following is a nested PCR procedure (first PCR: 30 cycles → dilute 100-fold → second, nested PCR: 35 cycles). The Rotor-Gene Q (Qiagen) was used for the amplification, real-time detection of the target DNA, and Tm value analysis of the amplified products. All PCR assays were performed as single-tube assays (no multiplex PCR). We used 1.5-mL PCR-clean Eppendorf tubes that were RNase- and DNase-free (Eppendorf, Germany), 0.2-mL PCR tubes (Qiagen) for the first PCR, and 0.1-mL Strip Tubes and Caps (Qiagen) for the second (nested) PCR.</p>", "<p id=\"Par33\">All oligonucleotide primers for Tm mapping identification and quantification were designed using a multiple alignment software program (ClustalX) and synthesized by Life Technologies Japan, Ltd. (Tokyo, Japan). Bacterial universal primers were designed to universally amplify the seven regions of the bacterial 16S ribosomal RNA gene (16S rDNA). The primers were as follows: Region 1 primers (forward 1a: 5′-AGAGTTTGATCATGGCTCAG-3′, forward 1b: 5′-AGAGTTTGATCCTGGCTCAG-3′, reverse: 5′-CGTAGGAGTCTGGACCGT-3′, amplicon size: 338 bp. For the first PCR, forward 1a and 1b are equally mixed together, but for the second PCR, only forward 1a is used), Region 2 primers (forward: 5′-GACTCCTACGGGAGGCA-3′, reverse: 5′-TATTACCGCGGCTGCTG-3′, amplicon size: 199 bp), Region 3 primers (forward: 5′-AGCAGCCGCGGTAATA-3′, reverse: 5′-GGACTACCAGGGTATCTAATCCT-3′, amplicon size: 287 bp), Region 4 primers (forward: 5′-AACAGGATTAGATACCCTGGTAG-3′, reverse: 5′-AATTAAACCACATGCTCCACC-3′, amplicon size: 181 bp), Region 5 primers (forward: 5′-TGGTTTAATTCGATGCAACGC-3′, reverse: 5′-GAGCTGACGACAGCCAT-3′, amplicon size: 120 bp), Region 6 primers (forward: 5′-TTGGGTTAAGTCCCGC-3′, reverse: 5′-CGTCATCCCCACCTTC-3′, amplicon size: 109 bp), and Region 7 primers (forward: 5′-GGCTACACACGTGCTACAAT-3′, reverse: 5′-CCGGGAACGTATTCACC-3′, amplicon size: 166 bp).</p>", "<p id=\"Par34\">The first PCR primer set was the same as the Region 1 forward primer (forward 1a and 1b are equally mixed together) and the Region 7 reverse primer. The second PCR primer set for quantification was the same as the Region 3 primers.</p>", "<p id=\"Par35\">During the first PCR procedure, the PCR reaction mixture (20 µL) contained 10 µL of DNA template in 200 µM of each dNTP (CleanAmp™ Hot Start dNTP Mix, Sigma-Aldrich, USA) filtered using an Amicon Ultra 50K centrifugal filter (Merck Millipore, Germany), 50 mM KCl, 2.25 mM MgCl₂, 10 mM Tris–HCl (pH 8.3), 0.3 µM of each primer, 1 × EvaGreen (Biotium Inc., CA, USA), and 1.0 units (0.5 µL) of eukaryote-made thermostable DNA polymerase supplemented with stock buffer solution. The generation of eukaryote-made thermostable DNA polymerase using <italic>Saccharomyces cerevisiae</italic> has been described previously^{##REF##21775543##23##}. In place of 10 µL of DNA template, the PCR reaction mixture contained 10 µL of DNA extracted from 3 serially diluted concentrations (2500 cells/10 µL = 50,000 cells/mL of whole blood, 250 cells/10 µL = 5000 cells/mL of whole blood, and 12.5 cells/10 µL = 250 cell/mL of whole blood, counted using flow cytometry method) of <italic>E. coli</italic> (ATCC 25922) as quantification standards in quantitative real-time PCR, or 10 µL of molecular-grade distilled water (water deionized and sterilized for molecular biology; Nacalai Tesque, Inc.) as a negative control for the PCR step.</p>", "<p id=\"Par36\">Each sample was incubated for 5 min at 95 °C to activate the Hot Start dNTPs and then was denatured for 10 s at 94 °C, annealed for 10 s at 57 °C, extended for 30 s at 72 °C and subjected to fluorescence acquisition for 2 s at 82 °C for 30 cycles. The PCR product was diluted 100-fold with molecular-grade distilled water (water deionized and sterilized for molecular biology; Nacalai Tesque, Inc.) and then used as a template for the second (nested) PCR procedure.</p>", "<p id=\"Par37\">For the second (nested) PCR procedure, the PCR reaction mixture (20 µL) contained 10 µL of DNA template of the diluted first PCR product in 200 µM of each dNTP (CleanAmp™ Hot Start dNTP Mix; Sigma-Aldrich) filtered using an Amicon Ultra 50K centrifugal filter (Merck Millipore), 50 mM KCl, 2.5 mM MgCl₂, 10 mM Tris–HCl (pH 8.3), 0.25 µM of each primer, 1 × EvaGreen (Biotium, Inc.), and 1.0 units (0.5 µL) of eukaryote-made thermostable DNA polymerase supplemented with stock buffer solution. The 7 samples used to amplify Regions 1 to 7 were incubated for 5 min at 95 °C to activate the Hot Start dNTPs and then denatured for 10 s at 94 °C, annealed for 10 s at 57 °C, extended for 10 s at 72 °C, and subjected to fluorescence acquisition for 2 s at 82 °C for 35 cycles. To quantify bacteria in a sample, the threshold cycle (Ct) values amplified by Region 3 primers in the second PCR were analyzed using the Rotor-Gene Q software program. The seven PCR amplicons were then analyzed to obtain the Tm values. If no amplification was observed by the 35th cycle of all 7 secondary PCRs, we defined the sample as containing no bacteria.</p>", "<title>The melting temperature (Tm) value analysis</title>", "<p id=\"Par38\">For the Tm value analysis, the resulting 7 amplicons were heated at 95 °C for 10 s and then cooled at 72 °C for 90 s. A post-PCR Tm value analysis was performed from 72  to 95 °C, increasing at 0.5 °C/step. The data profile was subsequently analyzed using the Rotor-Gene Q software program, and the Tm values were identified. Finally, the dominant bacteria in a sample were identified using the Tm mapping method.</p>", "<title>Quantification of bacterial concentration in a blood sample</title>", "<p id=\"Par39\">We conducted quantitative real-time PCR for the relative quantification of bacteria in blood samples. In every test, the standard curve was formed by Ct values (region 3 amplicon) of three serially diluted quantification standards (<italic>E. coli</italic> DNA) with known concentrations measured by flow cytometry. The blood bacterial concentrations were measured using the standard curve and finally adjusted according to the 16S ribosomal RNA operon copy number of pathogenic bacteria identified by the Tm mapping method.</p>", "<title>Culture-based biochemical identification of bacteria</title>", "<p id=\"Par40\">A total of 20 mL of whole blood samples (for one aerobic blood culture bottle and one anaerobic blood culture bottle, respectively) were collected simultaneously with 2 mL of whole blood sample for Tm mapping method from the same puncture site. The whole-blood samples were then analyzed according to standard methods used by the Clinical Laboratory Center (certified ISO15189) at Toyama University Hospital. The blood culture procedures were performed using the BacT/ALERT 3D system (bioMerieux, Inc., Mercy-l’Etoile, France). Positive blood culture bottles were subcultured onto sheep blood agar, chocolate agar, and BTB lactose-contained agar. Moreover, as a result of microscopic examination, added appropriate media if necessary. Then, they were incubated aerobically or anaerobically until sufficient growth was present to proceed with testing (usually 18–24 h). The specific identification methods differed according to the organism, although they involved the MicroScan WalkAway system (Siemens Healthcare Diagnostics, IL, USA), RapID ANA II (Thermo Fisher Scientific, UK), and various latex agglutination and biochemical spot tests.</p>" ]

[ "<title>Results</title>", "<title>The rapid identification and quantification method workflow</title>", "<p id=\"Par9\">The workflow of the rapid identification and quantification method for unknown pathogenic bacteria developed in our laboratory is shown in Fig. ##FIG##0##1##. This method consists of five major steps.</p>", "<p id=\"Par10\">First, bacterial DNA is extracted directly from a clinical sample (2 mL of a whole blood sample, etc.) as a template for PCR. Three quantification standards (<italic>Escherichia coli</italic> DNA solutions) with different known concentrations (the number of bacteria/mL) measured by flow cytometry are also prepared in advance. Step two involves nested PCR using the seven bacterial universal primer sets; these primers can detect almost all species of bacteria. In order to achieve accuracy in this PCR step, we developed a eukaryote-made thermostable DNA polymerase which is free from bacterial DNA contamination^{##REF##21775543##23##}. This eukaryote-made thermostable DNA polymerase is a recombinant polymerase manufactured using eukaryotic (yeast) host cells. Employing this DNA polymerase in bacterial universal PCR, sensitive and reliable detection of bacteria without false-positive results is feasible, thereby making it possible for PCR to identify and quantify bacterial isolates directly from patient samples. After the nested PCR procedure is performed, seven (or fewer) PCR amplicons are obtained. In step three, the seven Tm values are acquired by analyzing the amplicons. Step four involves mapping the seven Tm values in two dimensions. The plot creates a unique species-specific shape, known as the Tm mapping shape. By comparing the Tm mapping shape to the shapes in the database, the bacterial isolates can be rapidly identified. We named this novel method the “Tm mapping method” and described it in detail previously^{##REF##26218169##5##}. In step five, the bacterial concentration is measured in conversion as <italic>E. coli</italic> using the standard curve formed by Ct values (region 3 amplicon) of the three different quantification standards (<italic>E. coli</italic> DNA) with known concentrations. Finally, the bacterial concentration is corrected according to the 16S ribosomal RNA operon copy number (Supplemental Table ##SUPPL##0##S1##) of the bacteria rapidly identified by the Tm mapping method. As a result, identification and quantification results of pathogenic bacteria in a clinical sample can be obtained within four hours of sample collection.</p>", "<title>Establishment of the quantification method</title>", "<p id=\"Par11\">The first step in developing the quantification method is to reduce the loss of bacterial cells as much as possible during the isolation of bacteria from whole blood samples. To isolate bacteria from red blood cells, the blood sample is slightly centrifuged (100×<italic>g</italic>, 5 min) to spin down the red blood cells only, and the resulting supernatant fraction with buffy coat (500 μL) is used. In this step, the distribution of bacteria (<italic>E. coli</italic>, <italic>S. aureus</italic>, <italic>K. pneumoniae</italic> and <italic>P. aeruginosa</italic>) in plasma is almost unchanged after low-speed centrifugation (Fig. ##FIG##1##2##A). After pelletization of the supernatant fraction with buffy coat, to maintain constant (maximize) DNA extraction efficiency regardless of bacterial species, we use not only Proteinase K but also small beads that assist in lysing bacterial cell walls thoroughly (see the Method section).</p>", "<p id=\"Par12\">The second step involves the performance of accurate quantitative real-time PCR of bacteria in a blood sample. The primer designs are shown in Fig. ##FIG##1##2##B, and using region 3 amplicon, the quantification analysis is performed. In this step, it is necessary to eliminate the adverse effect of the base sequence differences between the primers and bacterial target regions, which affect the Ct values. As a countermeasure for this problem, we use mixed 1st PCR forward primers (Fig. ##FIG##1##2##C). Regarding the 16S bacterial conserved region targeted by the 1st PCR forward primer, there are mainly two kinds of base sequences among bacterial species (AGAGTTTGATC<underline>A</underline>TGGCTCAG or AGAGTTTGATC<underline>C</underline>TGGCTCAG). We generated standard curves by an analysis of serial dilution of <italic>E. coli</italic> DNA using the primers as follows: 1st PCR forward primer with no mismatch against <italic>E. coli</italic> (AGAGTTTGATC<underline>A</underline>TGGCTCAG), 1st PCR forward primer with one mismatch against <italic>E. coli</italic> (AGAGTTTGATC<underline>C</underline>TGGCTCAG), a mix of both 1st PCR forward primers (no mismatch : one mismatch = 1 : 1). The 1st PCR reverse primer is the same in all cases. The quantification result using the 1st PCR forward primer with one mismatch was around 25% (PCR amplification efficiency/cycle = 62%, Ct difference = 1.2) lower than when using the 1st PCR forward primer with no mismatch. In contrast, the quantification result using the mixed 1st PCR forward primers was almost the same as when using the 1st PCR forward primer with no mismatch. Moreover, in the 2nd PCR, we purposely use the region 3 amplicon to quantify bacteria. This is because the base sequences of the region 3 primers are the almost completely conserved among all bacterial species and does not affect the Ct values. As a result, we concluded that, when using the mixed 1st PCR forward primers and the region 3 primers, accurate quantitative real-time PCR of bacteria is feasible, regardless of bacterial species.</p>", "<p id=\"Par13\">In the third step, for sensitive and accurate quantification of a small number of bacteria, we adopted the nested PCR method. In addition, to eliminate adverse effects on quantification due to primer-dimer formation, we set the temperature for fluorescence acquisition to 82 °C instead of the conventional 72 °C. With this ingenuity, the hydrogen bonds of the primer dimers are dissociated and broken, allowing the accurate quantification of only the target bacterial amplicons. To confirm the quantitative accuracy of the nested PCR method compared with conventional one-time quantitative PCR, we evaluated the regression lines generated by serial dilution of a known amount of <italic>E. coli</italic> DNA (Fig. ##FIG##1##2##D). As a result, the linear correlation between the Ct values and the logarithm of <italic>E. coli</italic> count/PCR tube (R² value) was &gt; 0.99. The nested PCR method was found to be more accurate than the conventional one-time quantitative PCR method for quantifying a small number of bacteria (1.0 to 10.0 <italic>E. coli</italic>/PCR tube). The limit of quantification for the nested PCR method was 1.0 genomic DNA of <italic>E. coli</italic>/PCR tube, and a wider linear dynamic range (1.0 to 4.1 × 10⁵ genomic DNA of <italic>E. coli</italic>/PCR tube) was established. Using this reliable range, the blood bacterial concentrations in conversion as <italic>E. coli</italic> are measured and finally corrected according to the 16S ribosomal RNA operon copy number of the pathogen. The measurement error of this quantification method is around ± 5% (Supplemental Table ##SUPPL##0##S2##).</p>", "<title>Identification and quantification of pathogenic bacteria in septic blood samples</title>", "<p id=\"Par14\">To evaluate the utility of the rapid method for identifying and quantifying pathogenic bacteria, we first tried to identify and quantify bacteria in blood samples of five healthy controls (Table ##TAB##0##1##) using the results of conventional blood culture, body temperature (BT, °C), WBC, CRP, presepsin, blood urea nitrogen (BUN), and creatinine (Cr). As a result, no bacteria were detected in the blood samples of any healthy controls (5 out of 5 controls), and those blood cultures showed no bacterial growth. In this case, “0 bacteria/mL of blood” means “ &lt; 20 bacteria (calculated as <italic>E. coli</italic>)/mL of blood” based on the limit of detection (LOD) of this method.</p>", "<p id=\"Par15\">We subsequently identified and quantified pathogenic bacteria in septic blood samples (and a healthy control sample) and then examined the time-dependent changes in the number of bacteria, BT, WBC, CRP, presepsin, and IL-6 values before and 24 and 72 h after antibiotic treatment (Fig. ##FIG##2##3##). Regarding the identification, to assess the suitability of the Tm mapping method, we established the interpretative criteria based on the Difference Value^{##REF##26218169##5##} (Supplemental Table ##SUPPL##0##S3##).<list list-type=\"bullet\"><list-item><p id=\"Par16\">Case 1 (Fig. ##FIG##2##3##A): A 76-year-old woman was diagnosed with sepsis associated with urinary tract infection. The Tm mapping result (Difference Value = 0.29) was <italic>E. coli</italic>, and 2 days later, the blood culture result and urine culture result were also consistent with <italic>E. coli</italic>. Before antibiotic treatment, the number of <italic>E. coli</italic> was 1,320/mL. Meropenem (<italic>E. coli</italic> isolates were susceptible to meropenem) was then administered systemically. At 24 h after antibiotic treatment, the number of <italic>E. coli</italic> had decreased to 260/mL, although the other current biomarkers had increased, except for IL-6. At 72 h after antibiotic treatment, bacteria were no longer detected in the blood.</p></list-item><list-item><p id=\"Par17\">Case 2 (Fig. ##FIG##2##3##B): An 88-year-old woman was diagnosed with sepsis associated with retrograde cholangitis. The Tm mapping result (Difference Value &gt; 0.5) was polymicrobial infection, which means the causative bacteria could not be identified, and 2 days later, the blood culture result was found to be <italic>Klebsiella oxytoca</italic>, <italic>Haemophilus influenzae</italic>, and <italic>S. pneumoniae</italic>. The blood bacterial concentration was thus calculated in conversion as <italic>E. coli</italic>. Before antibiotic treatment, the number of bacteria was 175,280/mL. Cefepime (<italic>K. oxytoca</italic> and <italic>H. influenzae</italic> isolates were susceptible to cefepime. <italic>S. pneumoniae</italic> isolates were intermediate to cefepime) was then administered systemically. At 24 h after antibiotic treatment, the number of bacteria had decreased to 31,460/mL, although the WBC, CRP, and presepsin values had increased. At 72 h after antibiotic treatment, the number of bacteria had decreased to 2,060/mL.</p></list-item><list-item><p id=\"Par18\">Case 3 (Fig. ##FIG##2##3##C): A 94-year-old woman was diagnosed with sepsis associated with urinary tract infection. The Tm mapping result (Difference Value = 0.19) was <italic>E. coli</italic>, and 2 days later, the blood culture result and the urine culture result were also consistent with <italic>E. coli</italic>. Before antibiotic treatment, the number of <italic>E. coli</italic> was 3600/mL. Tazobactam/piperacillin (<italic>E. coli</italic> isolates were susceptible to tazobactam/piperacillin) was then administered systemically. At 24 h after antibiotic treatment, the number of <italic>E. coli</italic> had decreased to 2100/mL, although the CRP value had increased. At 72 h after antibiotic treatment, bacteria were no longer detected in the blood, although the BT and presepsin values had increased.</p></list-item><list-item><p id=\"Par19\">Case 4 (Fig. ##FIG##2##3##D): An 84-year-old woman was diagnosed with sepsis associated with postoperative wound infection after the spine surgery. The Tm mapping result (Difference Value = 0.28) was <italic>S. dysgalactiae</italic>, and 2 days later, the blood culture result was also consistent with <italic>S. dysgalactiae</italic>. Before antibiotic treatment, the number of <italic>S. dysgalactiae</italic> was 2,660/mL. Tazobactam/piperacillin (<italic>S. dysgalactiae</italic> isolates were susceptible to tazobactam/piperacillin) was then administered systemically. At 24 h after antibiotic treatment, the number of <italic>S. dysgalactiae</italic> had decreased to 300/mL, although the CRP value had increased. At 72 h after antibiotic treatment, the number of <italic>S. dysgalactiae</italic> had decreased to 20/mL, although the BT had increased.</p></list-item><list-item><p id=\"Par20\">Case 5 (Fig. ##FIG##2##3##E): An 81-year-old woman was diagnosed with sepsis associated with urinary tract infection. The Tm mapping result (Difference Value = 0.48) was <italic>Enterobacter aerogenes</italic>, and 2 days later, the blood culture result and the urine culture result were also consistent with <italic>E. aerogenes</italic> (two strains). Before antibiotic treatment, the number of <italic>E. aerogenes</italic> was 41,090/mL. Tazobactam/piperacillin (<italic>E. aerogenes</italic> isolates were susceptible to tazobactam/piperacillin) was then administered systemically. At 24 h after antibiotic treatment, the number of <italic>E. aerogenes</italic> had decreased to 19,145/mL, although the WBC, CRP, and presepsin values had increased. At 72 h after antibiotic treatment, the number of <italic>E. aerogenes</italic> had decreased to 70/mL, although the CRP and presepsin values had increased.</p></list-item><list-item><p id=\"Par21\">Healthy Control (Fig. ##FIG##2##3##F): A 44-year-old woman who does not have any illnesses including infectious diseases and participated in this study as a volunteer. No bacteria were detected in the blood using the Tm mapping method and blood culture, and both CRP and IL-6 were below the detection sensitivity. Furthermore, BT, WBC, and Presepsin were each within the normal range. There was almost no daily variation in each biomarker.</p></list-item></list></p>" ]

[ "<title>Discussion</title>", "<p id=\"Par22\">In the present study, we developed a novel rapid method for identifying and quantifying unknown pathogenic bacteria in a clinical sample within four hours of sample collection (Japanese patent No. 7023465 and international patent application No. PCT/JP2018/023597). As the main technology of this method, the Tm mapping method can quickly identify more than 160 species registered in the database^{##REF##26218169##5##} without a blood culture (Japanese patent No. 4590573 and international patent No. WO2007/097323). In this study, the protocol for the Tm mapping method was modified slightly to perform accurate quantification of bacteria (e.g. up to 30 cycles for 1st PCR so that PCR amplification does not saturate and affect quantification, etc.), but this modification did not affect the identification results (Supplemental Table ##SUPPL##0##S4##). The most important point of this study is that the novel method can be used to determine the number of bacteria in a clinical sample as a novel biomarker of infectious diseases.</p>", "<p id=\"Par23\">To precisely measure the number of bacteria in a clinical sample, in addition to some technical ingenuities described in the Results section, bacterial DNA contamination-free PCR is essential. To perform bacterial DNA contamination-free PCR, not only the eukaryote-made thermostable DNA polymerase^{##REF##21775543##23##} we developed (Japanese patent No. 5583602 and international patent No. WO2010/082640) but also the contamination-free PCR tubes, distilled water, primers, DNA extraction kit, and appropriate experimental environment are indispensable. We achieved bacterial DNA contamination-free PCR with this method and did not detect any contamination during the DNA extraction and PCR steps.</p>", "<p id=\"Par24\">However, another major problem is bacterial DNA contamination of vacuum blood collection tubes (Supplemental Fig. ##SUPPL##0##S1##). We evaluated the contamination state of commercially available vacuum blood collection tubes, and bacterial DNA (i.e. dead bacteria) was detected in 8 tubes out of 10. While the number of bacteria differed among tubes, the average number was 65 bacteria/blood collection tube, which would hamper attempts to detect a small number of bacteria in a clinical sample accurately. To address this problem, we developed a bacterial DNA contamination-free vacuum blood collection tube (OP-BF0205-1) in cooperation with Nipro Corporation (Osaka, Japan). As a result, no bacteria were detected in any (10 tubes out of 10) of Nipro′s vacuum blood collection tubes (Supplemental Fig. S1). Of note, this blood collection tube is not commercially available at present, and consultation required for ordering.</p>", "<p id=\"Par25\">Through five cases of sepsis patients, we showed that the number of bacteria is a novel useful biomarker that more sensitively reflects the therapeutic effect than currently available biomarkers (BT, WBC, CRP, presepsin, and IL-6). Since the number of bacteria can change greatly over a short period of time, the time-dependent changes in the number of bacteria would be particularly useful for monitoring therapeutic effects. Since the current biomarkers reflect the host's immune response to microorganisms, they will inevitably cause a time-lag. Indeed, the current biomarkers showed an increasing trend at 24 h after antibiotic administration, even though the antibacterial treatment was effective, and the number of bacteria in the blood was decreasing.</p>", "<p id=\"Par26\">The number of bacteria referred to in the novel method is the total number of bacteria in both the plasma and buffy coat, i.e. the total number of bacteria floating in the blood and bacteria phagocytosed by leukocytes. By including the buffy coat, the detection sensitivity is increased. We experimentally confirmed the quantitative ratio of bacteria floating in septic blood to bacteria phagocytosed by leukocytes as around 1:10 (data not shown). Phagocytosis by leukocytes indicates that the bacteria in the buffy coat is a pathogen. Conversely, to determine contamination, it is sufficient to confirm the absence of bacteria in the buffy coat despite the presence of bacteria in the plasma. Another advantage of including the buffy coat is that the number of bacteria fluctuates greatly in a short period of time, reflecting therapeutic effects. As a biomarker of sepsis, the number of bacteria changes every hour due to competition between the speed at which bacteria proliferate and the speed at which bacteria are phagocytosed and destroyed by leukocytes. If the antibacterial treatment is effective, bacterial proliferation stops, and phagocytosis by leukocytes becomes dominant, reducing the number of bacteria in septic blood.</p>", "<p id=\"Par27\">By using the bacterial universal PCR and the established bacterial DNA contamination-free PCR, we were able to rapidly detect the absence of bacteria (below the limit of detection) in a sample. We already showed that there were no bacteria detected in the blood samples of five healthy controls (Table ##TAB##0##1##). For example, in the case of fever of unknown origin, rapid diagnosis of the absence of bacteria is useful because treatment is completely different depending on whether it is bacterial or not. Furthermore, using the rapid method of identifying and quantifying pathogenic bacteria, we reported that most (approximately 90%) cases with suspected sepsis in our hospital were aseptic, results that were also clinically useful.</p>", "<p id=\"Par28\">In conclusion, our novel method enables the identification and quantification of bacteria in a clinical sample within four hours of whole-blood collection. Based on the number of bacteria in a blood sample, we were able to estimate the severity of microbial infection accurately. Furthermore, using the time-dependent changes in the number of bacteria, we were able to monitor the therapeutic effect accurately. As a result, the number of bacteria may provide clues to decide the better timing to stop antibiotic treatment. This method for the rapid identification and quantification of bacteria may change our approach to medical care.</p>" ]

[]

[ "<p id=\"Par1\">Sepsis is life-threatening organ dysfunction and is considered a major cause of health loss. However, since the current biomarkers of sepsis reflect the host’s immune response to microorganisms, they would inevitably cause a time-lag. This means that there is still no truly reliable biomarker of sepsis. In the present study, we developed a novel method for identifying and quantifying unknown pathogenic bacteria within four hours of sample collection. The most important point of this study is that the novel method can be used to determine the number of bacteria in a sample as a novel biomarker of infectious diseases. Indeed, based on the number of bacteria, we were able to accurately estimate the severity of microbial infection. Furthermore, using the time-dependent changes in the number of bacteria, we were able to monitor the therapeutic effect accurately. The rapid identification and quantification of bacteria may change our approach to medical care.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-50864-0.</p>", "<title>Acknowledgements</title>", "<p>This research was supported by AMED under Grant Number JP19im0210217, JSPS KAKENHI Grant Number 21H02825 to H.N., and JSPS KAKENHI Grant Number 18H02728 to I.K.</p>", "<title>Author contributions</title>", "<p>A.M and H.N. developed the method of quantifying pathogenic bacteria in a patient sample. H.N. wrote the manuscript. A.M. and H.N. designed, and A.M. performed the experiments. H.N., M.M., H.T. and H.M. developed the eukaryote-made thermostable DNA polymerase. T.U., M.W., Y.H., Y.M., A.T., A.H., Y.Y. and I.K. contributed to the development of the method of quantifying pathogenic bacteria in a patient sample. I.K. contributed to the design of experiments and supervised the overall project. All authors read and edited the manuscript.</p>", "<title>Data availability</title>", "<p>All data generated or analyzed during this study are included in this published article and its supplementary information files.</p>", "<title>Competing interests</title>", "<p id=\"Par41\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Workflow of the novel rapid method for identifying and quantifying unknown pathogenic bacteria in sepsis within four hours of whole-blood collection. *This figure conceptually shows the workflow of the novel method, and the individual values in the figure have no meaning.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Establishment of the quantification method. (<bold>A</bold>) Distribution of bacteria (CFU/mL) in saline after low-speed centrifugation. The bacterial concentration in the upper half and the lower half were examined after low-speed centrifugation (100×<italic>g</italic>, 5 min). A total of 2 mL of bacterial suspension (<italic>E. coli</italic>, <italic>S. aureus</italic>, <italic>K. pneumoniae</italic> and <italic>P. aeruginosa</italic>) in saline was centrifuged, and the colony-forming unit (CFU) value was measured in the upper and lower half (1 mL each). The figure shows the ratio (%) of each half. Error bars indicate triplicate testing. (<bold>B</bold>) The primer designs. Nested PCR is performed using seven bacterial universal primer sets, and then the seven PCR amplicons (Tm values) are obtained. The pathogenic bacteria are identified using the seven Tm values of region 1 to 7 amplicons, and the bacterial concentration is measured using the region 3 amplicon alone. (<bold>C</bold>) Standard curves generated using three different primers. We generated standard curves by conducting an analysis of serial dilutions of <italic>E. coli</italic> DNA using primers as follows: 1st PCR forward primer with no mismatch against <italic>E. coli</italic>, 1st PCR forward primer with one mismatch against <italic>E. coli</italic>, and a mix of both 1st PCR forward primers (no mismatch : one mismatch = 1: 1). The 1st PCR reverse primer was the same in all cases. These results indicated that the quantification result using the 1st PCR forward primer with 1 mismatch was around 25% lower than that using the 1st PCR forward primer with no mismatch. In contrast, the quantification result using the mixed 1st PCR forward primers was almost the same as that using the 1st PCR forward primer with no mismatch. Error bars indicate triplicate testing. (<bold>D</bold>) The comparison of the regression lines generated by serial dilution of a known amount of <italic>E. coli</italic> DNA using conventional PCR method and nested PCR method. The regression lines calculated for the datum points are shown. The linear correlation between the Ct values and the logarithm of the number of <italic>E. coli</italic>/PCR tube (R² value) was &gt; 0.99. Error bars indicate triplicate testing.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Time-dependent changes of the number of bacteria, BT, WBC, CRP, Presepsin and IL-6 in sepsis patients before antibiotic treatment and 24 and 72 h after. (<bold>A</bold>) Case 1: A 76-year-old woman was diagnosed with sepsis associated with urinary tract infection. The Tm mapping result (Difference Value = 0.29) was <italic>E. coli</italic>, and 2 days later, the blood culture result and urine culture result were also consistent with <italic>E. coli</italic>. Meropenem (<italic>E. coli</italic> isolates were susceptible to meropenem) was then administered systemically. Error bars indicate triplicate testing. (<bold>B</bold>) Case 2: An 88-year-old woman was diagnosed with sepsis associated with retrograde cholangitis. The Tm mapping result (Difference Value &gt; 0.5) was polymicrobial infection, and 2 days later, the blood culture result was found to be <italic>Klebsiella oxytoca</italic>, <italic>Haemophilus influenzae</italic>, and <italic>S. pneumoniae</italic>. The blood bacterial concentration was thus calculated in conversion as <italic>E. coli</italic>. Cefepime (<italic>K. oxytoca</italic> and <italic>H. influenzae</italic> isolates were susceptible to cefepime. <italic>S. pneumoniae</italic> isolates were intermediate to cefepime) was then administered systemically. Error bars indicate triplicate testing. (<bold>C</bold>) Case 3: A 94-year-old woman was diagnosed with sepsis associated with urinary tract infection. The Tm mapping result (Difference Value = 0.19) was <italic>E. coli</italic>, and 2 days later, the blood culture result and the urine culture result were also consistent with <italic>E. coli</italic>. Tazobactam/piperacillin (<italic>E. coli</italic> isolates were susceptible to tazobactam/piperacillin) was then administered systemically. Error bars indicate triplicate testing. (<bold>D</bold>) Case 4: An 84-year-old woman was diagnosed with sepsis associated with postoperative wound infection after the spine surgery. The Tm mapping result (Difference Value = 0.28) was <italic>S. dysgalactiae</italic>, and 2 days later, the blood culture result was also consistent with <italic>S. dysgalactiae</italic>. Tazobactam/piperacillin (<italic>S. dysgalactiae</italic> isolates were susceptible to tazobactam/piperacillin) was then administered systemically. Error bars indicate triplicate testing. (<bold>E</bold>) Case 5: An 81-year-old woman was diagnosed with sepsis associated with urinary tract infection. The Tm mapping result (Difference Value = 0.48) was <italic>Enterobacter aerogenes</italic>, and 2 days later, the blood culture result and the urine culture result were also consistent with <italic>E. aerogenes</italic> (2 types of mutant strains). Tazobactam/piperacillin (<italic>E. aerogenes</italic> isolates were susceptible to tazobactam/piperacillin) was then administered systemically. Error bars indicate triplicate testing. (<bold>F</bold>) Healthy Control: A 44-year-old woman who does not have any illnesses including infectious diseases and participated in this study as a volunteer. No bacteria were detected in the blood using the Tm mapping method and blood culture. Error bars indicate triplicate testing.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>The identification and quantification results of bacteria in blood samples of five healthy controls.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Healthy controls</th><th align=\"left\" colspan=\"2\">Identification results</th><th align=\"left\" rowspan=\"2\">Quantification results (mL of blood)</th><th align=\"left\" colspan=\"6\">Laboratory data</th></tr><tr><th align=\"left\">Conventional culture method</th><th align=\"left\">Tm mapping method</th><th align=\"left\">BT (℃)</th><th align=\"left\">WBC (µ/L)</th><th align=\"left\">CRP (mg/L)</th><th align=\"left\">BUN (mg/dL)</th><th align=\"left\">Cr (mg/dL)</th><th align=\"left\">Presepsin (ng/mL)</th></tr></thead><tbody><tr><td align=\"left\">1</td><td align=\"left\">No culture growth</td><td align=\"left\">None detected</td><td align=\"left\">0*</td><td char=\".\" align=\"char\">36.2</td><td align=\"left\">8540</td><td char=\".\" align=\"char\">1.0</td><td align=\"left\">14</td><td char=\".\" align=\"char\">0.90</td><td align=\"left\">159</td></tr><tr><td align=\"left\">2</td><td align=\"left\">No culture growth</td><td align=\"left\">None detected</td><td align=\"left\">0*</td><td char=\".\" align=\"char\">36.9</td><td align=\"left\">6810</td><td char=\".\" align=\"char\">7.5</td><td align=\"left\">16</td><td char=\".\" align=\"char\">0.78</td><td align=\"left\">206</td></tr><tr><td align=\"left\">3</td><td align=\"left\">No culture growth</td><td align=\"left\">None detected</td><td align=\"left\">0*</td><td char=\".\" align=\"char\">36.3</td><td align=\"left\">5370</td><td char=\".\" align=\"char\">0.1</td><td align=\"left\">21</td><td char=\".\" align=\"char\">0.62</td><td align=\"left\">130</td></tr><tr><td align=\"left\">4</td><td align=\"left\">No culture growth</td><td align=\"left\">None detected</td><td align=\"left\">0*</td><td char=\".\" align=\"char\">36.5</td><td align=\"left\">6760</td><td char=\".\" align=\"char\">0.8</td><td align=\"left\">13</td><td char=\".\" align=\"char\">0.72</td><td align=\"left\">119</td></tr><tr><td align=\"left\">5</td><td align=\"left\">No culture growth</td><td align=\"left\">None detected</td><td align=\"left\">0*</td><td char=\".\" align=\"char\">36.1</td><td align=\"left\">7430</td><td char=\".\" align=\"char\">0.2</td><td align=\"left\">12</td><td char=\".\" align=\"char\">1.05</td><td align=\"left\">189</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p><italic>BT</italic> body temperature,<italic> WBC</italic> white blood cells,<italic> CRP</italic> C-reactive protein,<italic> BUN</italic> blood urea nitrogen,<italic> Cr</italic> creatinine.</p><p>*A quantification result of “0 bacteria/mL of blood” means “ &lt; 20 bacteria (calculated as <italic>E. coli</italic>)/mL of blood” based on the limit of detection (LOD) of this method.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Akio Miyakoshi and Hideki Niimi.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41598_2023_50864_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"41598_2023_50864_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"41598_2023_50864_Fig3_HTML\" id=\"MO3\"/>" ]

[ "<media xlink:href=\"41598_2023_50864_MOESM1_ESM.docx\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">The ecological network approach has entailed a remarkable advance in the study of mutualistic plant-pollinator interactions^{##REF##19628856##1##–##REF##19739366##3##}. Among other topics, ecological networks have been used to assess the consequences of habitat fragmentation and disturbance^{##UREF##1##4##,##UREF##2##5##}, the impact of alien plant invasions^{##UREF##3##6##,##REF##23486435##7##} or in the conservation of endangered plants^{##UREF##4##8##}.</p>", "<p id=\"Par3\">Adaptations to nocturnal pollination are widespread among flowering plants^{##REF##29562117##9##}. Yet, network studies of plant-pollinator interactions have paid little attention to nocturnal pollinators, except in a few noteworthy papers^{##REF##23486435##7##,##UREF##5##10##–##REF##32396782##13##}. Nocturnal pollinators include insects (beetles^{##UREF##7##14##}, bees^{##UREF##8##15##}, moths^{##REF##25914438##16##,##UREF##9##17##}), as well as vertebrates (bats^{##REF##19789175##18##}, rodents^{##REF##18723860##19##}, other micromammals^{##UREF##10##20##}). While some of these nocturnal pollinators (e.g., bats) may be of limited geographical or taxonomic importance^{##REF##19789175##18##}, others are very widespread. In particular, moths are spread worldwide^{##REF##25914438##16##,##UREF##9##17##} and undoubtedly the most diversified group of nocturnal pollinators; just the two largest families of macro-moths (Macroheterocera) are more diverse than all Papilionoidea (Noctuidae and Geometridae, ca. 35,000 and 21,000 species, respectively)^{##UREF##11##21##}. Therefore, leaving nocturnal moths out of plant-pollinator networks neglects a huge component of the architecture of biodiversity.</p>", "<p id=\"Par4\">Building accurate ecological networks is crucial to properly understand the structure and dynamics of complex ecological systems^{##REF##19739366##3##,##UREF##12##22##,##REF##20532234##23##}. Mutualistic networks based exclusively on diurnal flower visitors violate two fundamental requirements of community studies: sampling must be designed to avoid temporal bias and to achieve taxonomic independence^{##REF##20532234##23##}. In the case of plant-pollinator networks, taxonomic and temporal constrictions are unavoidably linked, because most nocturnal insects visiting flowers belong to exclusively night-active taxa. Thus, neglect of nocturnal moths could severely influence fundamental properties of networks such as nestedness, modularity and phylogenetic structure, derived properties such as robustness to extinctions, and their implications for conservation and restoration of ecosystem services^{##UREF##5##10##,##UREF##6##12##,##UREF##13##24##}. Two alternative scenarios are conceivable when considering nocturnal moths in plant-pollinator networks^{##UREF##6##12##}. First, nocturnal moths could be connected to the most linked plants of the network by preferential attachment. In this scenario, pollinators are more likely to interact with plants already visited by many species, potentially because they are more abundant, provide better resources, or are more attractive^{##UREF##14##25##,##REF##18589522##26##}. This scenario likely causes no major changes in network structure, besides increased network dimension and nestedness. Alternatively, nocturnal moths may adjust to the traditional concept of pollination syndromes, in which nocturnal moths should preferentially visit phalaenophilous plants -those with tubular white flowers and nocturnal floral anthesis, nectar secretion and odour emission at dusk or night^{##UREF##15##27##}. In this latter scenario, nocturnal moths may conform distinct modules^{##REF##18056808##28##} within the combined network (i.e., diurnal and nocturnal visits), which may increase modularity and decrease network nestedness.</p>", "<p id=\"Par5\">To date only a few works have considered nocturnal pollinators in mutualistic networks, either alone^{##REF##32396782##13##,##UREF##16##29##–##REF##34992227##31##} or in combination with diurnal pollinators^{##REF##23486435##7##,##UREF##5##10##–##UREF##6##12##}. Several of these studies reported that some nocturnal pollinators formed specific modules^{##REF##23486435##7##,##UREF##6##12##}, but other nocturnal pollinators were part of mixed modules^{##UREF##6##12##}. Devoto et al<italic>.</italic>^{##UREF##5##10##} reported similar properties of nocturnal and combined networks, but they did not perform a comparison between them. In sum, previous research highlights the important but overlooked role that nocturnal pollinators may have in pollination networks, and the complementarity between diurnal and nocturnal pollinators. However, to date, no formal comparison of the extent to which adding nocturnal pollinators to diurnal networks modifies network structure has been performed.</p>", "<p id=\"Par6\">Here, we assemble the combined plant-pollinator networks from three high-mountain sites located in the Iberian Peninsula to assess the changes in network properties when nocturnal moths are considered. Studying plant-pollinator networks in high-mountain environments is relevant because they are key for preserving the functionality of these fragile ecosystems^{##UREF##18##32##}. We address the following specific questions: (1) Do nocturnal moths preferentially interact with phalenophilous plants or do they visit the most linked plants in the network by preferential attachment? and (2) Are general network properties modified by the addition of the nocturnal moths?</p>" ]

[ "<title>Methods</title>", "<title>Study sites</title>", "<p id=\"Par7\">Three typical high mountain plant communities were chosen along a latitudinal and climatic gradient in the Iberian Peninsula: Picos de Europa (N Spain, Atlantic climate, 2050 m a.s.l.), Sierra de Guadarrama (central Spain, continental Mediterranean climate, 2210 m a.s.l.) and Sierra Nevada (S Spain, Mediterranean climate, 2850 m a.s.l.) (Fig. ##FIG##0##1##). These sites represented equivalent altitudinal vegetation belts above treeline, although their absolute elevation differed due to the contrasting climatic conditions of the three mountain ranges (see Santamaría et al.^{##UREF##18##32##} and Lara-Romero et al<italic>.</italic>^{##UREF##19##33##} for further details).</p>", "<title>Sampling protocol</title>", "<p id=\"Par8\">Diurnal and nocturnal plant-flower visitor networks (hereafter, plant-pollinator networks) were built for each site during the flowering season of 2010 (Picos de Europa) and 2011 (Sierra de Guadarrama and Sierra Nevada). To build the diurnal networks, interactions between plants and floral visitors were recorded along diurnal transects at each site, where all insects contacting the reproductive structures of the flowers were recorded. The sampled area differed between sites from 500 × 250 m in Picos de Europa to 150 × 100 m in Sierra Nevada and 100 × 60 m in Sierra de Guadarrama. These differences were dependent on the small-scale heterogeneity of vegetation. The transects were evenly distributed throughout the study area. The length of the transects varied depending on the size of the study area. Diurnal transects were performed from 10 to 18 h on sunny days with mild wind conditions for pollinator activity. Species vouchers were captured and identified to species or morphospecies level. Sampling involved 2–6 people during 5 to 7 weeks from June to August for a total of 9679, 3278 and 11,754 recorded visits in Picos de Europa, Sierra de Guadarrama and Sierra Nevada, respectively (see Santamaría et al<italic>.</italic>^{##UREF##18##32##} and Lara-Romero et al<italic>.</italic>^{##UREF##19##33##} for further details).</p>", "<p id=\"Par9\">Nocturnal plant-pollinator networks were built for each site by trapping moths using light traps and analysing their pollen loads. Light traps consisted of a UV light surrounded by three white triangular sheets. Moths landing on the sheets were immediately trapped and stored in individual vials with a small piece of tissue and some drops of ethyl acetate. This procedure was essential to avoid pollen loss or pollen transfer among individuals, thus allowing a reliable estimation of plant-moth interactions and pollen loads. Three (four in Sierra de Guadarrama) trapping sessions were carried out along the flowering period, about one week apart and around the flowering peak. The sampling period each night was from dusk to about 01:00 am (ca. 3–3.5 h). To minimize the intrinsic limitations of light traps, such as the attraction of moths from relatively large distances or variation in their attraction ability to different species^{##UREF##5##10##,##UREF##20##34##,##UREF##21##35##}, traps were located at the central area of each study site.</p>", "<title>Pollen extraction and identification</title>", "<p id=\"Par10\">For identification purposes, a pollen reference collection was compiled at each site. Flowers of each entomophilous plant species were harvested and pollen was collected, stained with basic fuchsine and fixed in microscope slides^{##UREF##22##36##}. Pollen pictures were taken with a reflex camera (Canon 450D) coupled to a phase contrast microscope (Olympus Bx51). To build a reference pollen key, pollen size and ornamentation for each plant species was recorded by using ImageJ^{##UREF##23##37##}.</p>", "<p id=\"Par11\">Moths were mounted and pollen loads were collected by rubbing small fuchsine jelly cubes around the head and mouthparts^{##UREF##22##36##}. Cubes were melted and mounted on slides, and pollen grains were counted in the microscope. Then, the pollen grains were compared to the pollen reference key and identified to species. The only exception were two closely related <italic>Sedum</italic> species with indistinguishable pollen grains, that were classified as the same morphospecies^{##UREF##5##10##} (see Table ##SUPPL##0##S2##). To avoid a potential bias by heterospecific pollen transport^{##UREF##5##10##}, an interaction was only scored when an individual nocturnal moth carried three or more pollen grains of that particular plant species.</p>", "<title>Data analysis</title>", "<p id=\"Par12\">We assembled three qualitative (i.e., presence-absence) interaction networks per site: one considering exclusively diurnal visits (hereafter, diurnal network), one considering exclusively nocturnal visits (hereafter, nocturnal network) and one considering both diurnal and nocturnal visits (hereafter combined network). Assembly of all networks was qualitative to avoid the difficulties in comparing quantitative interactions obtained with different sampling methodologies^{##UREF##6##12##} (see also Discussion “<xref rid=\"Sec11\" ref-type=\"sec\">Caveats and further developments</xref>” section). Interaction and species sampling completeness for diurnal and nocturnal networks were calculated following Chacoff et al<italic>.</italic>^{##REF##21815890##38##} with the R-package vegan version 2.4–5^{##UREF##24##39##}. To obtain the expected asymptotic richness of species and interactions, this method uses the non-parametric Chao 2 estimator that is particularly appropriate for small sample sizes^{##REF##21815890##38##,##REF##19449706##40##}.</p>", "<p id=\"Par13\">We assessed whether nocturnal moths preferentially attached to the plants already showing the highest number of links in the diurnal network, by performing a <italic>t</italic>-test that compared differences in the diurnal degree (number of links) rank between plants with and without nocturnal moths. In the case of a tie, the average rank was assigned to the plant species involved.</p>", "<p id=\"Par14\">Fifteen network properties of diurnal and combined networks (Table ##TAB##0##1##) were assessed using the R-packages bipartite version 2.08^{##UREF##25##41##} and vegan version 2.4–5^{##UREF##24##39##}. Pollinator, plant, and total nestedness were measured using NODF^{##UREF##26##42##}. Bipartite modularity (<italic>Q</italic>) and number of modules were estimated using the DIRTLPAwb+algorithm^{##REF##26909160##43##}. In the combined networks, module composition was checked to identify the existence of modules consisting only of nocturnal moths. To assess the significance of NODF and Q we used Z-test against a fixed–fixed null distribution derived from 500 random networks (for NODF) and 100 networks (for Q) with the same number of plants, pollinators and interactions as the observed networks. The estimation of network robustness was based on species extinction curves, in which the proportion of \"secondary extinctions\" caused by the accumulation of random \"primary extinctions\" among their mutualistic partners is represented^{##REF##21699640##44##}. We used the function <italic>second.extinct</italic> in the bipartite package in R^{##UREF##25##41##} to simulate species extinction curves, averaging from 100 repetitions. Then, we calculated two values for each network: (i) robustness to pollinator extinction (R₅₀ A), i.e., the minimum fraction of primary extinctions of pollinators that causes ≥ 50% of secondary extinction of plants and (ii) robustness to plant extinction (R₅₀ P), i.e., the minimum fraction of primary extinctions of plants that causes ≥ 50% of secondary extinction of pollinators^{##UREF##27##45##,##UREF##28##46##}. We then calculated the percentage change in all these network descriptors after adding the nocturnal interactions to the diurnal networks (Table ##TAB##0##1##).</p>", "<p id=\"Par15\">To address whether the network structure was modified by the addition of the nocturnal moths or whether the lack of these nocturnal pollinators could be simply considered a case of undersampling (i.e., it is equivalent to improve the sampling of diurnal networks), we focused on eight network properties (Table ##TAB##1##2##). We assessed how these properties were affected when a random set of diurnal pollinators was substituted by a set of nocturnal moths using an approach inspired in how data resampling influences network properties^{##UREF##29##47##,##UREF##30##48##}. Assuming that <italic>n</italic> is the number of nocturnal interactions and <italic>d</italic> is the number of diurnal interactions, we randomly subsampled the diurnal network starting from 10% of diurnal interactions and subsequently adding sets of 10% of interactions until we reached <italic>d</italic>-<italic>n</italic> interactions (Fig. ##FIG##1##2##). Each random subsampling was replicated 100 times and the average value and the confidence intervals for each network property were calculated at each subsampling level. This gradient of subsampling ended with the total diurnal network, which was compared to an alternative network (100 random replicates) with <italic>d</italic> interactions consisting of the <italic>n</italic> nocturnal interactions added to the subsampling with <italic>d-n</italic> interactions. This comparison aimed to discern any disparities in network properties when introducing <italic>n</italic> diurnal interactions versus <italic>n</italic> nocturnal interactions to a network characterized by <italic>d</italic>-<italic>n</italic> interactions. Our expectation was that if the presence of nocturnal moths modified network properties, deviations from the trends observed in the subsampled diurnal network would become evident (as depicted in Fig. ##FIG##1##2##). To ascertain the significance of these deviations, we considered a departure to be significant when the confidence interval of a network metric value for the resampled diurnal network, which encompasses nocturnal interactions (black dot in Fig. ##FIG##1##2##), did not overlap with the equivalent value for the complete diurnal network (last grey dot in Fig. ##FIG##1##2##).</p>" ]

[ "<title>Results</title>", "<p id=\"Par16\">A total of 132 nocturnal moths (Picos de Europa), 168 (Sierra de Guadarrama) and 118 (Sierra Nevada) were captured. Three or more pollen grains were found in 20%, 29% and 15% of the moths. Overall, nocturnal moths interacted with 33 plant species and four of the latter only showed nocturnal interactions (see Appendix ##SUPPL##0##S1## and ##SUPPL##0##S2## in Supporting Information). To our knowledge, we provide the first evidence of interactions with nocturnal moths for Gentianaceae and Plantaginaceae. Nocturnal networks were considerably smaller than diurnal networks, comprising 13–16 moth species, 10–21 plant species, and 20–34 interactions, with matrix sizes ranging from 208 to 680 (Appendix ##SUPPL##0##S1## in Supplementary Information). Diurnal networks comprised 102–120 animal species, 17–92 plant species, 315–1136 interactions, and had matrix sizes ranging from 1734 to 11,040 (Table ##TAB##0##1##).</p>", "<p id=\"Par17\">Eighty-five per cent of the plant species visited by nocturnal moths showed a diurnal syndrome. In Sierra de Guadarrama and Sierra Nevada, eleven plant species attracted both diurnal and nocturnal pollinators, whereas in Picos de Europa only eight plant species did (Tables ##SUPPL##0##S1##, ##SUPPL##0##S2##, ##SUPPL##0##S3## and Appendix ##SUPPL##0##S1## in the Supplementary Information). No significant differences in diurnal degree rank were found between the plants that interacted with nocturnal moths and those with only diurnal visits in any of the sites (Picos de Europa: <italic>t</italic>₉₃ = − 1.915, <italic>P</italic> = 0.742; Sierra de Guadarrama: <italic>t</italic>₁₆ = − 0.195, <italic>P</italic> = 0.848; Sierra Nevada: <italic>t</italic>₃₃ = − 1.311, <italic>P</italic> = 0.199). Nocturnal moths interacted with plants of very different degree, from highly to scarcely connected and even with plants with no diurnal visits (Fig. ##FIG##2##3## and Appendix ##SUPPL##0##S2## in Supplementary Information).</p>", "<p id=\"Par18\">The combined networks showed higher asymmetry and modularity than diurnal networks, with a few exceptions, including the modularity in the combined network from Guadarrama (Table ##TAB##0##1##). Diurnal and combined networks were significantly modular compared to random networks (<italic>Z</italic>-test: all <italic>P</italic> &lt; 0.01). Nocturnal moths and the plants visited by them were not grouped in specific modules except in Picos de Europa (see Figure ##SUPPL##0##S1##of Appendix ##SUPPL##0##S2## in Supplementary Information). In Sierra Nevada, the addition of nocturnal moths increased the number of modules from five to seven. Both diurnal and combined networks were significantly nested (<italic>Z</italic>-test: all <italic>P</italic> &lt; 0.01) in all study sites, excepting the diurnal network in Picos de Europa (<italic>P</italic> = 0.205). Combined networks showed lower nestedness, connectivity for pollinators, connectivity for plants (except in Sierra de Guadarrama) as well as lower total connectivity and connectance (Table ##TAB##0##1##).</p>", "<p id=\"Par19\">The resampling of the diurnal network indicated a gradual increase in connectance, web asymmetry, NODF, connectivity and robustness (Figs. ##FIG##3##4##, ##FIG##4##5##), as well as a gradual decrease in modularity (Fig. ##FIG##3##4##). Against these general trends, replacing <italic>n</italic> diurnal interactions by <italic>n</italic> nocturnal interactions entailed a significant break in the trend of all network properties (Figs. ##FIG##3##4##, ##FIG##4##5##; Table ##TAB##1##2##). Connectance, NODF, connectivity, robustness to the extinction of plant species decreased after adding the nocturnal interactions, while asymmetry and modularity increased (Figs. ##FIG##3##4##, ##FIG##4##5##; Table ##TAB##1##2##). Robustness to the extinction of pollinator species differed among networks (Figs. ##FIG##3##4##, ##FIG##4##5##; Table ##TAB##1##2##). It decreased in Picos de Europa, increased in Sierra de Guadarrama and did not differ significantly in Sierra Nevada (Figs. ##FIG##3##4##, ##FIG##4##5##; Table ##TAB##1##2##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par20\">The addition of nocturnal moths had a relevant effect on the overall architecture of the three high mountain plant-pollinator networks. Moths modified network properties by decreasing connectance, nestedness, connectivity and robustness to plant extinction and by increasing web asymmetry and modularity. Our results indicate that disregarding the nocturnal component of plant-pollinator networks may cause changes in network properties different from those expected from random undersampling of diurnal pollinators and lead to a misinterpretation of plant-pollinator networks. It is remarkable that the addition of this nocturnal component did not conform well to any of the two expected scenarios: nocturnal moth pollinators were not preferentially connected to the most linked plants of the network and were grouped into a single nocturnal module only in one network. These results highlight the potential consequences of underestimating the role of nocturnal moths as pollinators in natural ecosystems.</p>", "<title>Nocturnal moths visited a random sample of plant species in most networks</title>", "<p id=\"Par21\">None of the three networks studied showed preferential attachment of nocturnal moths to the most linked plants. Only in one network, moths met the expectations of the pollination syndrome concept and conformed to a particular nocturnal module. Thus, these results did not adjust to any of the two initially set scenarios. In networks with a heterogeneous distribution of links per species, new randomly recorded species are assumed to preferentially attach to the most linked species^{##UREF##14##25##,##REF##18056808##28##} but this is not always true^{##REF##28921857##49##}. Syndrome-related modules have been found in several mutualistic networks^{##REF##21699640##44##,##UREF##31##50##} including two plant-pollinator networks in which both diurnal and nocturnal pollinators have been included^{##REF##23486435##7##,##UREF##6##12##}. Nevertheless, the extent to which network modules match plant pollination syndromes is variable^{##UREF##6##12##}, and increases with increasing specialization of the interactions^{##UREF##32##51##,##UREF##33##52##}. In this study, the absence of a nocturnal module in two out of three networks is unsurprising because generalist pollination interactions are expected to be the rule in harsh and variable environments such as high mountain ecosystems^{##UREF##34##53##,##UREF##35##54##}.</p>", "<p id=\"Par22\">Our study warns against a naïve inference of pollinators from floral traits. A small, but not trivial, number of plant species showed a large mismatch between expected and actual pollinators. For example, plants with expected nocturnal moth pollination, such as <italic>Silene boryi</italic> and <italic>S. ciliata</italic>, were visited both by diurnal and nocturnal insects (Appendix ##SUPPL##0##S1##). Diurnal visitation of species with phalaenophilous syndrome are well known in <italic>Silene</italic>^{##REF##17204083##55##,##REF##26070638##56##} and, more generally, have been reported in desert^{##UREF##36##57##}, temperate^{##UREF##37##58##,##UREF##38##59##} and tropical ecosystems^{##UREF##6##12##}. For instance, in a plant-pollinator network from the Neotropics, flowers with nocturnal anthesis that remained open during the day were important connectors of the diurnal and nocturnal components^{##UREF##6##12##}. More interestingly, some plant species apparently adapted to diurnal pollinators were also visited by nocturnal moths^{##REF##32396782##13##,##UREF##39##60##}. The most striking case were <italic>Linaria</italic> species, for which a bee, bee-fly and butterfly syndrome had been described^{##REF##24142920##61##}. These results, together with those of previous nocturnal networks^{##REF##23486435##7##,##UREF##5##10##,##REF##28783730##11##,##UREF##16##29##}, are unveiling overlooked nocturnal visitors for many flowering plants and call for future work to determine the contribution of nocturnal pollinators to plant reproduction. This invites a reconsideration of currently accepted levels of plant specialization^{##UREF##40##62##}.</p>", "<title>Addition of nocturnal moths modified network properties, including modularity and robustness</title>", "<p id=\"Par23\">The addition of a moderate number of interactions and species of nocturnal moths resulted in changes in most of the analysed network properties. Some network studies have previously targeted neglected groups nocturnal pollinators^{##REF##23486435##7##,##UREF##5##10##,##UREF##6##12##,##REF##32396782##13##,##UREF##16##29##}. For instance, Walton et al.^{##REF##32396782##13##} detected a higher complexity (higher linkage density and interaction diversity) in the nocturnal pollination network than in the diurnal networks in an agro-ecosystem. However, this is the first study assessing in a comprehensive way the differences in structural properties of networks with and without neglected groups of pollinators. Given the absence of previous studies that follow a similar approach, we decided to compare these results with the general trends obtained in studies testing subsampling effects on network properties. In general, the values of all metrics increase with increasing sampling effort, except for binary modularity and connectance that decrease^{##UREF##29##47##,##REF##26476103##63##} (but see Rivera-Hutinel et al.^{##REF##22919906##64##}). Our results strikingly departed from these trends in two ways. First, the addition of nocturnal moth pollinators led to opposite changes in trend for modularity and nestedness to those reported for subsampling. Second, the magnitude of the changes in most properties was higher than the usually reported for subsampling^{##UREF##29##47##,##REF##26476103##63##,##REF##22919906##64##}. This suggests that adding nocturnal pollinators (1) has consequences on network connectance that cascade to other network properties and (2) is not equivalent to better sampling of diurnal networks.</p>", "<p id=\"Par24\">Current wisdom is that mutualistic networks are robust^{##UREF##14##25##,##REF##15615687##65##,##REF##12881488##66##} and that robustness is reliably assessed in incompletely sampled networks^{##REF##22919906##64##}. However, our results indicate that neglecting nocturnal moths can lead to an overestimation of network robustness. In evolutionary terms, this adds complexity to the arguments for the evolution of generalized pollination systems^{##REF##21815890##38##,##UREF##41##67##,##REF##21560672##68##}.</p>", "<title>Caveats and further developments</title>", "<p id=\"Par25\">Our results highlight the importance of including nocturnal pollinators in plant-pollinator networks. Ideally, nocturnal pollinators should be added using the same sampling methods as those used for diurnal networks. While this is, in principle, feasible, exceptions may arise, such as when integrating different studies into a single plant-pollinator network^{##UREF##6##12##}.The main potential caveat of combining diurnal and nocturnal networks obtained using different methods is that it can lead to biases. Certainly, comparisons of visit- and pollen-based networks indicate that pollen-transport networks are smaller and more specialized compared with their respective visitation networks^{##REF##32396782##13##,##UREF##42##69##–##REF##26336181##71##} (but see Jędrzejewska-Szmek and Zych^{##UREF##44##72##} and Walton et al<italic>.</italic>^{##REF##32396782##13##}). However, in terms of network metrics such as nestedness, modularity, and connectance (evaluated in this study), the results of these comparisons lack clear patterns^{##UREF##44##72##–##REF##29203872##76##}. This diversity of results aligns better with “noise” than with a consistent bias due to differences in sampling methods. On the other hand, the few existing studies combining pollen and flower visitor networks^{##UREF##6##12##,##REF##19379135##73##,##REF##37035419##75##} have shown higher connectivity and nestedness compared to visitor-only networks^{##REF##19379135##73##,##REF##37035419##75##}. If the addition of nocturnal interactions would simply introduce a bias in network parameters, we would expect the combined network parameters to be biased in the same direction shown by the comparative studies of visit vs. pollen networks. However, our results show a change in the opposite direction. This allows us to be confident that our results are unbiased with respect to the sampling protocols used. Nevertheless, we acknowledge that combining networks constructed using different sampling techniques entails interpretation challenges and we encourage further studies to assess the generality of our findings.</p>", "<p id=\"Par26\">A second caveat, inherent to any sample methodology, could be sample completeness. Interaction and species sampling completeness were lower in the nocturnal networks, compared to the diurnal ones, especially for interactions (Table ##SUPPL##0##S4## of Appendix ##SUPPL##0##S3## in Supplementary Information). In any case, species sampling completeness of the combined networks revealed that, on average, more than 50% of both plant and pollinators could be detected for all the study sites (Table ##SUPPL##0##S5## of Appendix ##SUPPL##0##S3## in Supplementary Information), which compares favorably with the only estimate of species completeness performed for nocturnal networks^{##REF##28783730##11##}. Species completeness was greater than interaction completeness in the nocturnal networks, as shown by previous studies on pollination and dispersal networks^{##REF##21815890##38##,##UREF##45##77##}. This lower interaction completeness in the nocturnal networks (especially in Sierra Nevada) may respond to several factors such as a low sampling effort and a possible inflated expected richness computed by the Chao 2 estimator, that considers singletons and doubletons to estimate the number of undetected interactions^{##REF##21815890##38##,##REF##19449706##40##}. This may be particularly important in the nocturnal networks studied, in which most moths were rare (they fell in the light traps only once) and they bore pollen from one or two plant species. Although we could expect small network sizes for the nocturnal side of high mountain pollination networks and in turn low sampling efforts, only further research will reveal the actual frequency of nocturnal interactions. Recently, a multi-level approach has been used to study diurnal and nocturnal networks^{##UREF##6##12##}. Here, we suggest exploring the change in network properties by subsampling of the diurnal network with the addition of the nocturnal network. In sum, these results call for new studies combining diurnal and nocturnal pollination by integrating analysis approaches that consider different sampling efforts.</p>", "<p id=\"Par27\">Building nocturnal plant-pollinator networks is challenging. Based on our experience and previous works on nocturnal moth species inventories, we can draw some methodological advice. (1) For a complete assessment of species diversity, at least 5–10 days of sampling will yield high percentages of the expected species (e.g., Beck and Linsenmair^{##UREF##20##34##}). (2) Immediate hand-sampling at the light source and careful individual packing are necessary to avoid pollen contamination among specimens. (3) Although it is usually assumed that moth visits to flowers are particularly concentrated on twilight and first night hours, light traps should be ideally set during the whole night because shorter sessions could miss species with different flight times^{##UREF##20##34##}. (4) As with the sampling of diurnal pollination networks^{##REF##20100244##78##,##REF##29311619##79##}, nocturnal sampling should be conducted throughout the flowering season, especially in ecosystems with high seasonality. (5) Nocturnal moths from different families may be differently attracted to light^{##UREF##21##35##}, and thus the combination of light traps with other sampling techniques like bait traps may be appropriate^{##UREF##46##80##}.</p>", "<p id=\"Par28\">In a more applied perspective, combined networks will provide fundamental information about the role of nocturnal pollinators^{##UREF##5##10##,##UREF##6##12##,##UREF##16##29##} and will contribute to assess the effects of increasing threats that affect this group, such as increasing light pollution^{##REF##28783730##11##,##REF##25914438##16##,##REF##29215778##81##}. Ultimately, these threats may jeopardize ecosystem services provided by nocturnal pollinators by disrupting their interactions with plants^{##REF##28783730##11##,##REF##25914438##16##}. The present study indicates that ignoring nocturnal pollinators leads to an underestimation of functional and phylogenetic diversity. Since plant diversity closely depends on functional diversity of pollinators^{##UREF##47##82##}, information on the dynamics of nocturnal moth assemblages and their role on plant-pollinator networks structure is crucial for a reliable monitoring of the conservation status of plant communities^{##UREF##9##17##,##REF##29215778##81##}. Consequently, neglect of nocturnal interactions may provide a distorted view of the structure of pollination networks.</p>" ]

[]

[ "<p id=\"Par1\">Although the ecological network approach has substantially contributed to the study of plant-pollinator interactions, current understanding of their functional structure is biased towards diurnal pollinators. Nocturnal pollinators have been systematically ignored despite the publication of several studies that have tried to alleviate this diurnal bias. Here, we explored whether adding this neglected group of pollinators had a relevant effect on the overall architecture of three high mountain plant-pollinator networks. Including nocturnal moth pollinators modified network properties by decreasing total connectivity, connectance, nestedness and robustness to plant extinction; and increasing web asymmetry and modularity. Nocturnal moths were not preferentially connected to the most linked plants of the networks, and they were grouped into a specific “night” module in only one of the three networks. Our results indicate that ignoring the nocturnal component of plant-pollinator networks may cause changes in network properties different from those expected from random undersampling of diurnal pollinators. Consequently, the neglect of nocturnal interactions may provide a distorted view of the structure of plant-pollinator networks with relevant implications for conservation assessments.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-49944-y.</p>", "<title>Acknowledgements</title>", "<p>We thank P. Jordano and C.F. Dormann for help with analysis of some netwoks properties; J. Cerca, M. Correia, L. de Soto, R. García-Camacho, R. Milla, N. Rodríguez, A.L. Teixido, G. Escribano-Ávila, P. Quintana-Ascencio, and R. Torices for help in the field; M. Cantero and D. Galisteo for pollen identification; M. Bravo, M. Carles-Tolrá, L. Castro, M. Cerny, X. Espadaler, D. Gibbs, D. Gutiérrez, M.A. Marcos, A.I. Martínez, V. Michelsen, C. Ornosa, F.J. Ortiz, M. Pollet, A. Pont, H.-P. Tschorsnig and J.L. Yela for insect identification; J. Lorite and H. Nava for plant identification and the staff of the three national parks for permits. This study was supported by the project URJC-CM-2007-CET-1620 from the Rey Juan Carlos University and the Regional Government of Madrid (LGB, MM and SS), project 014/2009 from the Spanish Autonomous Authority for National Parks (LGB, MM and SS), and project LIMITES: CGL2009-07229 from the Spanish Ministry of Science and Innovation (JMI, CLR and JML). CLR, JML and YG were supported by a FPI fellowship (Spanish Ministry of Science and Innovation). CLR was supported by a Juan de la Cierva Incorporación postdoctoral fellowship (Ministerio de Ciencia, Innovación y Universidades: IJC2019-041342-I). YG had additional support from a grant from the Swedish Research Council (VR 2016–04508). JML had additional support from Juan de la Cierva Formación postdoctoral fellowship (Ministerio de Ciencia e Innovación: FJC2020-046353-I).</p>", "<title>Author contributions</title>", "<p>The order of autorship is alphabetical. This is an equal contribution paper. Y.G., L.G.B., J.M.I., C.L.R., M.M., J.M.L. and S.S. substantially contributed to field work, data analysis and writing, and ideas were discussed in several joint meetings.</p>", "<title>Data availability</title>", "<p> The data used on this research are openly available at the following Zenodo link: <ext-link ext-link-type=\"uri\" xlink:href=\"https://zenodo.org/records/10391505\">https://zenodo.org/records/10391505</ext-link>.</p>", "<title>Competing interests</title>", "<p id=\"Par29\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Study sites. Spatial locations of the three sample sites in the Iberian Peninsula.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Testing for changes in network properties. Hypothetical example of the change in a network property as new interactions are added. Grey dots represent the trend of the network property as a function of the percentage of diurnal interactions added. The black dot represents the addition of nocturnal instead of diurnal interactions. The bifurcation at 100% sampling completeness shows the expected break produced when adding nocturnal instead of diurnal interactions. Notice that in this example the number of nocturnal interactions added represents 4% of the number of total diurnal interactions recorded. Because of this, the bifurcation point is drawn at 96% completeness.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Number of diurnal and nocturnal interactions per plant species. Number of interactions of the different plant species in the diurnal networks (grey bars) and number of interactions added by nocturnal moths (black bars).</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Subsampling network properties. Subsampling performed for each network property. The dots indicate the mean values, and the error bars the 95% confidence intervals. In some cases, the width of the dot is larger than the error bars. The grey line indicates the different subsamples of the diurnal networks. The black circle indicates the addition of the <italic>n</italic> nocturnal interactions to the resampled diurnal network, built by removing <italic>n</italic> diurnal interactions from the <italic>d</italic> diurnal interactions and adding the <italic>n</italic> nocturnal interactions. Notice that the subsampling <italic>d</italic>-<italic>n</italic> differs among sites (98% for Picos de Europa, 96% for Sierra Nevada, 89% for Sierra de Guadarrama) due to different size of the nocturnal network.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Subsampling robustness. Subsampling performed for robustness to the extinction of animals (R₅₀ A) and robustness to the extinction of plants (R₅₀ P). The dots indicate the mean values, and the error bars the 95% confidence intervals. In some cases, the width of the dot is larger than the error bars. The grey line indicates the trend of the different subsamples of the diurnal networks. The grey dots depict the robustness values corresponding to the resampled diurnal networks. The black dots indicate the robustness value after the addition of the <italic>n</italic> nocturnal interactions to the resampled diurnal network with <italic>d-n</italic> diurnal interations. Notice that the subsampling <italic>d</italic>-<italic>n</italic> differs among sites (98% for Picos de Europa, 96% for Sierra Nevada, 88% for Sierra de Guadarrama) due to different sizes of the nocturnal networks.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Properties of the diurnal (D) and combined (C: diurnal plus nocturnal) networks.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Network property</th><th align=\"left\" colspan=\"3\">Picos de Europa</th><th align=\"left\" colspan=\"3\">Sierra de Guadarrama</th><th align=\"left\" colspan=\"3\">Sierra Nevada</th></tr><tr><th align=\"left\">D</th><th align=\"left\">C</th><th align=\"left\">Obs. (%)</th><th align=\"left\">D</th><th align=\"left\">C</th><th align=\"left\">Obs. (%)</th><th align=\"left\">D</th><th align=\"left\">C</th><th align=\"left\">Obs. (%)</th></tr></thead><tbody><tr><td align=\"left\">No. of animals (A)</td><td align=\"left\">120</td><td align=\"left\">136</td><td char=\".\" align=\"char\">11.8</td><td align=\"left\">102</td><td align=\"left\">116</td><td char=\".\" align=\"char\">12.0</td><td align=\"left\">115</td><td align=\"left\">128</td><td char=\".\" align=\"char\">10.2</td></tr><tr><td align=\"left\">No. of plants (P)</td><td align=\"left\">92</td><td align=\"left\">95</td><td char=\".\" align=\"char\">32.</td><td align=\"left\">17</td><td align=\"left\">17</td><td char=\".\" align=\"char\">0</td><td align=\"left\">32</td><td align=\"left\">34</td><td char=\".\" align=\"char\">5.9</td></tr><tr><td align=\"left\">Matrix size (A x P)</td><td align=\"left\">11,040</td><td align=\"left\">12,920</td><td char=\".\" align=\"char\">14.5</td><td align=\"left\">1734</td><td align=\"left\">1972</td><td char=\".\" align=\"char\">12.1</td><td align=\"left\">3712</td><td align=\"left\">4352</td><td char=\".\" align=\"char\">14.7</td></tr><tr><td align=\"left\">No. of interactions (i)</td><td align=\"left\">1136</td><td align=\"left\">1158</td><td char=\".\" align=\"char\">1.9</td><td align=\"left\">315</td><td align=\"left\">349</td><td char=\".\" align=\"char\">9.7</td><td align=\"left\">543</td><td align=\"left\">563</td><td char=\".\" align=\"char\">3.6</td></tr><tr><td align=\"left\">Web asymmetry</td><td align=\"left\">0.132</td><td align=\"left\">0.177</td><td char=\".\" align=\"char\">25.4</td><td align=\"left\">0.714</td><td align=\"left\">0.742</td><td char=\".\" align=\"char\">3.8</td><td align=\"left\">0.565</td><td align=\"left\">0.580</td><td char=\".\" align=\"char\">2.6</td></tr><tr><td align=\"left\">Connectivity A (i/A)</td><td align=\"left\">9.467</td><td align=\"left\">8.515</td><td char=\".\" align=\"char\">− 11.1</td><td align=\"left\">3.088</td><td align=\"left\">3.009</td><td char=\".\" align=\"char\">− 2.6</td><td align=\"left\">4.722</td><td align=\"left\">4.398</td><td char=\".\" align=\"char\">− 7.3</td></tr><tr><td align=\"left\">Connectivity P (i/P)</td><td align=\"left\">12.348</td><td align=\"left\">12.189</td><td char=\".\" align=\"char\">− 1.3</td><td align=\"left\">18.529</td><td align=\"left\">20.529</td><td char=\".\" align=\"char\">9.7</td><td align=\"left\">16.969</td><td align=\"left\">16.559</td><td char=\".\" align=\"char\">− 2.5</td></tr><tr><td align=\"left\">Connectivity total (i/[A + P])</td><td align=\"left\">5.358</td><td align=\"left\">5.013</td><td char=\".\" align=\"char\">− 6.9</td><td align=\"left\">2.647</td><td align=\"left\">2.644</td><td char=\".\" align=\"char\">− 0.1</td><td align=\"left\">3.694</td><td align=\"left\">3.475</td><td char=\".\" align=\"char\">− 6.3</td></tr><tr><td align=\"left\">Connectance (i/[A x P])</td><td align=\"left\">0.103</td><td align=\"left\">0.090</td><td char=\".\" align=\"char\">− 14.4</td><td align=\"left\">0.182</td><td align=\"left\">0.179</td><td char=\".\" align=\"char\">− 1.7</td><td align=\"left\">0.148</td><td align=\"left\">0.129</td><td char=\".\" align=\"char\">− 14.7</td></tr><tr><td align=\"left\">NODF</td><td align=\"left\">37.053</td><td align=\"left\">32.929</td><td char=\".\" align=\"char\">− 12.5</td><td align=\"left\">36.410</td><td align=\"left\">33.739</td><td char=\".\" align=\"char\">− 7.9</td><td align=\"left\">40.205</td><td align=\"left\">34.337</td><td char=\".\" align=\"char\">− 17.1</td></tr><tr><td align=\"left\">NODF A</td><td align=\"left\">32.090</td><td align=\"left\">28.292</td><td char=\".\" align=\"char\">− 13.4</td><td align=\"left\">36.058</td><td align=\"left\">33.500</td><td char=\".\" align=\"char\">− 7.6</td><td align=\"left\">39.370</td><td align=\"left\">33.752</td><td char=\".\" align=\"char\">− 16.7</td></tr><tr><td align=\"left\">NODF P</td><td align=\"left\">45.518</td><td align=\"left\">42.461</td><td char=\".\" align=\"char\">− 7.2</td><td align=\"left\">49.746</td><td align=\"left\">45.462</td><td char=\".\" align=\"char\">− 9.4</td><td align=\"left\">51.243</td><td align=\"left\">42.803</td><td char=\".\" align=\"char\">− 19.7</td></tr><tr><td align=\"left\">Modularity Q</td><td align=\"left\">0.267</td><td align=\"left\">0.279</td><td char=\".\" align=\"char\">4.3</td><td align=\"left\">0.324</td><td align=\"left\">0.323</td><td char=\".\" align=\"char\">− 0.3</td><td align=\"left\">0.275</td><td align=\"left\">0.281</td><td char=\".\" align=\"char\">2.1</td></tr><tr><td align=\"left\">Robustness (R₅₀ A)</td><td align=\"left\">0.925</td><td align=\"left\">0.926</td><td char=\".\" align=\"char\">0.1</td><td align=\"left\">0.951</td><td align=\"left\">0.957</td><td char=\".\" align=\"char\">− 0.6</td><td align=\"left\">0.948</td><td align=\"left\">0.953</td><td char=\".\" align=\"char\">0.5</td></tr><tr><td align=\"left\">Robustness (R₅₀ P)</td><td align=\"left\">0.880</td><td align=\"left\">0.842</td><td char=\".\" align=\"char\">− 4.5</td><td align=\"left\">0.7065</td><td align=\"left\">0.706</td><td char=\".\" align=\"char\">− 8.4</td><td align=\"left\">0.781</td><td align=\"left\">0.765</td><td char=\".\" align=\"char\">− 2.1</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Comparison of network descriptors and robustness for the diurnal network with 100% completeness and the resampled diurnal and nocturnal network.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" colspan=\"2\">Picos de Europa</th><th align=\"left\" colspan=\"2\">Sierra de Guadarrama</th><th align=\"left\" colspan=\"2\">Sierra Nevada</th></tr><tr><th align=\"left\">Diurnal</th><th align=\"left\">Diurnal+Nocturnal</th><th align=\"left\">Diurnal</th><th align=\"left\">Diurnal+Nocturnal</th><th align=\"left\">Diurnal</th><th align=\"left\">Diurnal+Nocturnal</th></tr></thead><tbody><tr><td align=\"left\">Connectance</td><td char=\".\" align=\"char\">0.103</td><td align=\"left\">0.087 (0.087, 0.087)</td><td char=\".\" align=\"char\">0.182</td><td align=\"left\">0.167 (0.167, 0.168)</td><td char=\".\" align=\"char\">0.148</td><td align=\"left\">0.127 (0.126, 0.127)</td></tr><tr><td align=\"left\">Web asymmetry</td><td char=\".\" align=\"char\">0.132</td><td align=\"left\">0.171 (0.171, 0.172)</td><td char=\".\" align=\"char\">0.714</td><td align=\"left\">0.734 (0.733, 0.735)</td><td char=\".\" align=\"char\">0.565</td><td align=\"left\">0.575 (0.574, 0.576)</td></tr><tr><td align=\"left\">Connectivity total (i/[A + P])</td><td char=\".\" align=\"char\">5.358</td><td align=\"left\">4.907 (4.905, 4.910)</td><td char=\".\" align=\"char\">2.647</td><td align=\"left\">2.466 (2.459, 2.472)</td><td char=\".\" align=\"char\">3.694</td><td align=\"left\">3.393 (3.388, 3.398)</td></tr><tr><td align=\"left\">NODF total</td><td char=\".\" align=\"char\">37.053</td><td align=\"left\">32.370 (32.328, 32.411)</td><td char=\".\" align=\"char\">36.410</td><td align=\"left\">31.604 (31.453, 31.756)</td><td char=\".\" align=\"char\">40.205</td><td align=\"left\">33.362 (33.258, 33.466)</td></tr><tr><td align=\"left\">Modularity Q</td><td char=\".\" align=\"char\">0.267</td><td align=\"left\">0.281 (0.281, 0.282)</td><td char=\".\" align=\"char\">0.324</td><td align=\"left\">0.343 (0.341, 0.345)</td><td char=\".\" align=\"char\">0.275</td><td align=\"left\">0.290 (0.289, 0.291)</td></tr><tr><td align=\"left\">R₅₀ A</td><td char=\".\" align=\"char\">0.925</td><td align=\"left\">0.923 (0.922, 0.924)</td><td char=\".\" align=\"char\">0.951</td><td align=\"left\">0.955 (0.955, 0.956)</td><td char=\".\" align=\"char\">0.948</td><td align=\"left\">0.947 (0.946, 0.948)</td></tr><tr><td align=\"left\">R₅₀ P</td><td char=\".\" align=\"char\">0.880</td><td align=\"left\">0.846 (0.845, 0.848)</td><td char=\".\" align=\"char\">0.765</td><td align=\"left\">0.707 (0.705, 0.709)</td><td char=\".\" align=\"char\">0.781</td><td align=\"left\">0.762 (0.760, 0.764)</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p>“P” denotes plant species, “A” denotes animal species and “i” denotes interactions in the networks, “Obs. (%)” is the percentage of change when nocturnal pollinators are added to the diurnal network.</p></table-wrap-foot>", "<table-wrap-foot><p>The latter was constructed by extracting <italic>n</italic> diurnal interactions and adding <italic>n</italic> nocturnal interactions to the diurnal network, where <italic>n</italic> represents the total number of nocturnal interactions sampled in each study site. The resampled diurnal and nocturnal network depicts, for each network descriptor, the average value and the 95% confidence intervals. “P” denotes plant species, “A” denotes animal species and “i” denotes interactions in the networks.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41598_2023_49944_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"41598_2023_49944_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"41598_2023_49944_Fig3_HTML\" id=\"MO3\"/>", "<graphic xlink:href=\"41598_2023_49944_Fig4_HTML\" id=\"MO4\"/>", "<graphic xlink:href=\"41598_2023_49944_Fig5_HTML\" id=\"MO5\"/>" ]

[ "<media xlink:href=\"41598_2023_49944_MOESM1_ESM.docx\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par3\">Rice is a crucial food crop that sustains over half of the world’s population. However, global climate change is expected to lead to a 51% reduction in rice cultivation and production in the next century. In South and Southeast Asia, drought is a common problem during the growing season, particularly in rainfed environments. This affects around 23 million hectares of rice production areas in Asia^{##UREF##0##1##}. Drought stress can harm different stages of rice growth, but it is particularly harmful during the vegetative and reproductive stages, resulting in a significant decline in grain yield^{##UREF##1##2##}. Grain yield per plant (SPY), a complex quantitative trait, is regulated by polygenes. It is directly impacted by yield-component traits like panicle number, seed weight, and seed number. Additionally, yield-related traits such as biomass, harvest index, plant architecture, adaptation, and resistance to biotic and abiotic stresses can indirectly influence grain yield^{##REF##27066031##3##}. However, due to the constant drought conditions, unstable rice production has severe social and economic impacts. Developing rice varieties with better grain yield and quality under both non-stress and drought-stress conditions is necessary to mitigate the challenges caused by drought.</p>", "<p id=\"Par4\">To address the above challenges, several major and minor QTLs associated with grain yield under drought stress conditions (<italic>qDTYs</italic>) have been identified in rice such as <italic>qDTY</italic>_{<italic>1</italic>.<italic>1</italic>}^{##REF##22008150##4##,##UREF##2##5##}<italic>, qDTY</italic>_{<italic>2.1</italic>}^{##REF##24885990##6##}, <italic>qDTY</italic>_{<italic>2.2</italic>}^{##UREF##3##7##}, <italic>qDTY</italic>_{<italic>2.3</italic>} and <italic>qDTY</italic>_{<italic>12</italic>.<italic>1</italic>}^{##REF##23442150##8##}<italic>, qDTY</italic>_{<italic>3.1</italic>} and <italic>qDTY</italic>_{<italic>6.1</italic>}^{##UREF##4##9##,##UREF##5##10##}, <italic>qDTY</italic>_{<italic>4.1</italic>}, <italic>qDTY</italic>_{<italic>9.1</italic>} and <italic>qDTY</italic>_{<italic>10.1</italic>}^{##REF##23667521##11##}. A research study found that 16 drought grain yield QTLs were present across all chromosomes with the exception of 5, 7, and 8^{##REF##25205576##12##}. However, a meta-QTL analysis identified 14 MQTLs on seven chromosomes (1, 2, 3, 4, 8, 10, and 12) with a 4–28% effect on drought grain yield^{##UREF##6##13##}. Introgression of prominent QTLs (<italic>qDTY</italic>_{<italic>1.1</italic>}, <italic>qDTY</italic>_{<italic>2.1</italic>}, <italic>qDTY</italic>_{<italic>2.2</italic>}<italic>, qDTY</italic>_{<italic>3.1</italic>}, <italic>qDTY</italic>_{<italic>3.2</italic>}<italic>, qDTY</italic>_{<italic>6.1</italic>}, and <italic>qDTY</italic>_{<italic>12.1</italic>}) into high-yielding but drought-susceptible mega varieties including IR64, MTU1010, TDK1-<italic>Sub1</italic>, Savitri, Swarna-<italic>Sub1</italic>, Samba Mahsuri, and Vandana imparted better yield advantage and consistent effects in multiple environments under drought stress in different genetic backgrounds^{##UREF##7##14##–##REF##30796339##18##}. Marker-aided <italic>qDTY</italic> pyramiding in Indian elite rice varieties (Sahbhagi dhan, DRR Dhan 42, CR Dhan 801, Naveen, and PB 44) showed significantly superior performance under reproductive stage drought stress conditions^{##REF##33390645##19##–##REF##35069617##23##}. Improved cultivars with either single or different combinations of <italic>qDTYs</italic> have already been released in many countries^{##REF##32753648##16##}.</p>", "<p id=\"Par5\">Recent advancements in high-throughput genotyping technologies have greatly improved the process of crop trait mapping through NGS-based methods such as QTL-seq, MutMap, Indel-Seq, or BSR-Seq^{##REF##22586469##24##–##REF##29685733##27##}. This has led to the faster development of new crop varieties. Genome-wide association studies (GWAS) have effectively identified favorable alleles associated with important agronomic traits in crops such as rice^{##UREF##10##28##,##REF##33442955##29##}. Whole-genome sequencing of diverse accessions has also made it easier to identify significant marker-trait associations, QTLs, QTNs, candidate genes, and superior haplotypes for targeted traits. A new approach called haplotype-assisted forward/backward breeding also has emerged, where superior haplotypes are identified and combined to create tailor-made varieties for crop improvement programs^{##REF##30701663##30##–##REF##33980871##32##}. A haplotype refers to a set of closely linked DNA variations within a gene that tend to be inherited together. Earlier, haplotype and phenotype (<italic>haplo-pheno)</italic> analysis was utilized to explore the relationship between haplotypes and phenotypic traits. If the average phenotypic performance of the group of individuals with a particular haplotype is significantly higher than those with other haplotypic groups, it is considered as the superior haplotype^{##REF##32455481##33##}. In rice, superior haplotypes have been identified for traits such as grain yield and quality, low glycaemic index, and deep-water rice^{##REF##30701663##30##,##REF##33980871##32##,##REF##30002253##34##}. Similarly, the <italic>haplo-pheno</italic> analysis identified superior haplotypes for three genes present in 17 genotypes of 292 pigeon pea reference set associated with drought component traits^{##REF##32455481##33##}. This approach can broaden the existing genetic pool for developing high-yielding, climate-smart crop varieties.</p>", "<p id=\"Par6\">This study aimed to determine the genes and superior haplotypes associated with the single plant yield trait in rice under drought stress. A haplotype diversity analysis was conducted on 95 genes that affect drought tolerance in rice, using a panel of 3K-RG genotypes. Furthermore, a candidate gene-based association study was conducted on a panel of 399 genotypes, selected from the 3K-RG panel, to investigate the relationship between these genes and drought tolerance.</p>" ]

[ "<title>Methods</title>", "<title>Plant materials</title>", "<p id=\"Par30\">The study used a panel of 399 genotypes from the 3K-RG panel, representing very early (60–70 days), early (71–80 days), and mid-early (80–100 days) duration genotypes from various sub-population groups, including <italic>basmati, aus, admix, indica</italic>, and <italic>japonica</italic>. The panel was analyzed for haplotype diversity and covers most <italic>O. sativa</italic> groups collected from various geographical regions across 55 rice-growing countries worldwide (Supplementary Data ##SUPPL##2##2##).</p>", "<title>Haplotype analysis of drought-responsive genes</title>", "<p id=\"Par31\">In our study, we implemented a comprehensive approach to identify genes associated with drought tolerance in rice. We first selected major genes known to be involved in drought tolerance from the RiceFun database^{##REF##29220485##59##}. Additionally, we conducted extensive literature mining to identify additional functionally characterized genes associated with drought responsiveness. As a result, a total of 95 genes were considered for haplotype analysis (Supplementary Data ##SUPPL##2##1##). A subset of 399 rice genotypes from the 3K-RG panel was used for the haplotype analysis of the 95 selected drought-responsive genes. For haplotype analysis, full-length sequences of the selected genes were downloaded from the 3K rice whole-genome database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://snp-seek.irri.org/_download.zul\">https://snp-seek.irri.org/_download.zul</ext-link>) and aligned to the Nipponbare reference genome using the BWA tool^{##UREF##15##60##}. After the alignment, variant calling was done using Genome Analysis Toolkit (GATK)^{##REF##20644199##61##}. The identified variants were later utilized for haplotype analysis using Haploview software^{##UREF##16##62##}. The Circos tool was used to visualize the relative distribution of genes &gt;2 haplotypes in the 3K subset^{##REF##19541911##63##}.</p>", "<title>Drought-tolerance phenotyping</title>", "<p id=\"Par32\">Experiments were conducted at the International Rice Research Institute (IRRI) South Asia Hub, located in Hyderabad, India at a latitude of 17° 32′ and longitude of 78° 16′, and an altitude of 540 m above sea level. 30-day-old seedlings of genotypes from the 3K-RG panel were transplanted in the main field, spaced 20 × 15 cm apart, and fertilized with a dose of 120–60–40 (N:P:K) kg/ha during two crop seasons (DS, 2019 and DS, 2020). The plots were arranged in an augmented RCBD design with 10 checks, which consisted of both drought-tolerant and susceptible varieties. The drought-tolerant checks included Vandana, Dular, Sahbhagi Dhan, DRR dhan 44, CR Dhan 801, Bahuguni Dhan1, Bahuguni Dhan 2, and Sukha Dhan 2, while MTU1010 and IR64 served as susceptible checks.</p>", "<p id=\"Par33\">An established protocol for drought phenotyping was used^{##UREF##17##64##}. To ensure synchronization between drought stress and flowering, staggered sowing, and transplantation were implemented, creating a 10-day interval between the three sets to align their flowering times for effective drought stress imposition. Irrigation of the drought plots was stopped one month after transplantation, and soil moisture content was measured using perforated PVC pipes inserted 1.0 m into the soil. Flood irrigation and drainage were applied when IR 64 plants showed leaf-rolling symptoms. Standard agronomic practices were followed, and grain yield per plant was recorded from five randomly chosen plants in each plot.</p>", "<title>Candidate gene-based association analysis</title>", "<p id=\"Par34\">Association analysis was performed using 95 selected genes to identify significant marker–trait associations (MTAs) in response to SPY. The LD decay was determined using 600K SNPs, and it was observed to occur at 50-kb with a threshold <italic>r</italic>² value of 0.2. Candidate gene prediction was performed within 50-kb upstream and 50-kb downstream regions of the genes. A <italic>Q</italic>-matrix was derived from ADMIXTURE software with <italic>K</italic> = 5 and included in association analysis^{##UREF##18##65##}. Candidate gene-based GWAS (c-GWAS) analysis was performed using the GAPIT R package with three statistical models: mixed linear model (MLM), compressed MLM model (CMLM), and multiple loci MLM (MLMM)^{##REF##16380716##66##–##REF##22706313##68##}. MTAs that surpassed the <italic>p</italic>-value threshold of <italic>p</italic> ≤ 0.005 and were common in all the models were considered as significant SNPs associated with the trait. The resulting significantly associated candidate genes were further used for <italic>haplo-pheno</italic> analysis.</p>", "<title>Haplo-pheno analysis</title>", "<p id=\"Par35\">To identify the robust donors having superior haplotypes of the key drought genes we have combined data of DS (dry season) of 2019 and 2020 for the best linear unbiased prediction (BLUP) analysis. The average BLUP values of SPY from both years were utilized for the haplo-pheno analysis.</p>", "<p id=\"Par36\">Haplo-pheno analysis was performed to associate the identified haplotypes of the selected genes with superior drought tolerance phenotypes. Haplotypes present in less than three accessions and heterozygous SNPs were removed from the analysis. The genotypes were then categorized based on haplotype groups, and superior haplotypes were identified using the phenotypic data of the individuals in each haplotype group. Haplotype-wise means of the single plant yield data were compared to define superior haplotypes. Duncan’s multiple range test (DMRT) was used to test the statistical significance among the mean of haplotype groups using the Agricolae package in R^{##UREF##19##69##}. Groups with different letters in the graphs indicated significant differences among the groups at a <italic>p</italic> &lt; 0.05 level of significance.</p>", "<title>Whole genome resequencing (WGRS) and variant identification</title>", "<p id=\"Par37\">To validate the identified superior haplotypes, a total of eight varieties, including four drought-tolerant (DRR Dhan 42, DRR Dhan 44, DRR Dhan 46, and Sahbhagi dhan) and four drought-susceptible (Naveen, BPT 5204, DRR Dhan 48 and Swarna) were sequenced. The sequencing was done using Illumina Nova-Seq 6000 with 150 bp × 2 paired-end reads at 25× coverage, generating an average of 5 GB data per sample. Reads containing adapter sequences or stretches of ambiguous bases and those with low-quality scores were removed from the raw data, and reads with a Phred quality score ≥30 were retained. FASTQC was used to check GC content and duplicate reads, and the results were collectively visualized using multiQC^{##UREF##20##70##}. The reference-based sequence assembly was performed using the BWA-MEM tool with Platinum standard Nipponbare reference genome IRGSP1.0^{##REF##24280374##71##}. Duplicate reads were removed and sorted according to coordinates using Picard tools. Mapping quality was checked for mapping percentage and genome coverage using Qualimap^{##UREF##21##72##}. GATK 4.2.6.1 was used to call variants with SNP depth ≥10, and a genotypic call rate of 90%, and the variant file was saved in the VCF format. The obtained VCF format file was used to extract genetic variants of the candidate genes with superior haplotypes. The sequence of each variety was extracted using the fasta alternate reference maker command in the GATK toolkit. The gene sequence of each variety was checked for multiple sequence alignment for better visualization of variants. The haplotypes for each of the varieties were extracted and visualized with flapjack 1.22.04.2^{##UREF##22##73##}. SIFT (<ext-link ext-link-type=\"uri\" xlink:href=\"http://sift.jcvi.org/www/SIFT_seq_submit2.html\">http://sift.jcvi.org/www/SIFT_seq_submit2.html</ext-link>) a web-based tool that predicts whether amino acid substitution affects protein function and structure based on sequence homology and the physical properties of amino acids was employed to discover functional mutations. The predicted SIFT score ranges from 0 to 1. The amino acid substitution is predicted to be damaging if the score is &lt;0.05 and tolerated if the score is &gt;0.05.</p>", "<title>Meta-analysis and co-expression network of the associated genes</title>", "<p id=\"Par38\">The expression data of the selected genes at various anatomical and developmental stages were obtained from Genevestigator software^{##UREF##23##74##} and co-expression analysis was performed using the Affymetrix Rice Genome Array platform. A co-expression network was created using the condition search tools and the perturbations profile in Genevestigator. The top 10 positively co-expressed genes were displayed in a circular plot with a Pearson correlation coefficient (PCC) score.</p>", "<title>Statistics and reproducibility</title>", "<p id=\"Par39\">Single plant yield (SPY) data were recorded over two crop seasons in 399 accessions. Matured panicles were collected, and the corresponding yield in grams was calculated for each accession in three biological replicates. For GWAS, MTAs that surpassed the <italic>p</italic>-value threshold of <italic>p</italic> ≤ 0.005 and were common in all three models were considered as significant SNPs associated with the trait. Duncan’s multiple range test (DMRT) was used to test the statistical significance among the mean of haplotype groups using the Agricolae package in R^{##UREF##20##70##}. Groups with different letters in the graphs indicated significant differences among the groups at a <italic>p</italic> &lt; 0.05 level of significance.</p>", "<title>Reporting summary</title>", "<p id=\"Par40\">Further information on research design is available in the ##SUPPL##5##Nature Portfolio Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<title>Haplotype analysis of 95 drought-responsive genes across the 3K-RG panel</title>", "<p id=\"Par7\">A haplotype analysis was conducted on 95 genes known to play a role in drought tolerance, using a panel of 3K-RG (Supplementary Data ##SUPPL##2##1##). These genes were chosen from various mapping studies and omics approaches in the public domain. The analysis revealed 2158 haplotypes, ranging from 1 to 274 haplotypes per gene. It was found that <italic>OsHSP17.0</italic>, <italic>OsMTN4</italic>, <italic>OsDREB1F</italic>, <italic>OsDHODH1</italic>, <italic>OsDSG1</italic>,<italic>OsCAF1G</italic>, and <italic>wdl1</italic> have only one haplotype each, while the <italic>OsAbF2/OsAREB8</italic> gene had the highest diversity with 274 haplotypes (Supplementary Data ##SUPPL##0##1##). The frequency and distribution of genes &gt;2 haplotypes in the subset panel of 3K-RG are shown in Fig. ##FIG##0##1##. Each gene’s haplotype was analyzed to identify structural variations in the coding regions and their potential relationship to phenotypic traits.</p>", "<title>Phenotyping of the subset panel</title>", "<p id=\"Par8\">To study the impact of drought on the yield of individual plants, a subset of 399 genotypes from the 3K-RG panel was selected to represent a wide range of diversity (Supplementary Data ##SUPPL##2##2##). This subset was then evaluated for yield under drought conditions in two crop seasons [Dry Season (DS) 2019 and Dry Season (DS) 2020] (Supplementary Fig. ##SUPPL##0##1##). The analysis using restricted maximum likelihood (REML) revealed a significant difference in yield among genotypes (<italic>σ</italic>^{<italic>2</italic>}<italic>g</italic>) under both seasons and conditions (Supplementary Table ##SUPPL##0##1##). As expected, the average yield of the subset under drought conditions was lower than that under normal conditions in both seasons.</p>", "<p id=\"Par9\">The SPY of 399 genotypes under stress conditions ranged from 0.6 to 16.8 g with higher variability than normal conditions (4.0–35.8 g). This variability was more significant under stress conditions (GCV 40.39% in DS, 2019 and 51.25% in DS, 2020) than under normal conditions (21.87% GCV in DS, 2019 and 18.83% GCV in DS, 2020). Repeatability for SPY was high (over 60%) in both normal and stress conditions, with a range of 67.62–77.52% and 76.245–77.17%, respectively. The percentage of the genetic advance of means (GAM) was also high in all conditions and seasons, but more so under stress conditions.</p>", "<title>GWAS identifies candidate genes associated with yield under drought stress</title>", "<p id=\"Par10\">Candidate gene-based GWAS (c-GWAS) was conducted to identify genetic markers associated with yield under drought stress in rice. A total of 0.6 million SNPs in 95 genes were analyzed, leading to the identification of 69 Marker Trait Associations (MTAs) associated with yield (Supplementary Fig. ##SUPPL##0##2## and Supplementary Data ##SUPPL##2##3##). These MTAs were distributed across all the chromosomes, except 4, 5, and 7, and explained between 2.00% and 4.48% of the phenotypic variation. The highest number of MTAs was found on chromosome 1 (25), while the lowest number was found on chromosomes 6, 9, and 10 (1 each). The candidate genes located in the vicinity of the significant signal were analyzed for known molecular functions, and several of them, such as <italic>OsDREB1C</italic>, <italic>OsDREB1F</italic>, <italic>OsNAC10</italic>, and <italic>ZFP182</italic> were responsible for specific DNA-binding transcription factor activity. These transcription factors are important in controlling the expression of a variety of genes associated with drought tolerance. Additionally, other genes were found to be involved in binding processes and catalytic activities, such as <italic>OsGSK1</italic>, <italic>OsMT1a</italic>, <italic>OsDIL1,</italic> and <italic>OsHSP23.7</italic> (Supplementary Fig. ##SUPPL##0##3##).</p>", "<p id=\"Par11\">Expression patterns of the targeted genes revealed that these genes were prominently expressed in reproductive tissues (Supplementary Fig. ##SUPPL##0##4a##, ##SUPPL##0##b##). In particular, <italic>OsGSK1</italic>, <italic>OsDSR2</italic>, <italic>OsNAC10</italic>, <italic>GF14c</italic>, and <italic>OsHSP23.7</italic> displayed high expression levels in the spikelet and panicle. Moreover, <italic>ASR3</italic>, <italic>OsSRO1c</italic>, <italic>OsNAC10</italic>, and <italic>OsMT1a</italic> had an expression pattern that was consistent across the developmental stages but was enhanced during the reproductive stage, suggesting they may have a vital role in drought stress responses. Additionally, a co-expression network of the selected genes gave insight into the functional aspect of genes that are positively co-expressed. The top 10 co-expressed were identified with Pearson’s correlation coefficient and visualized on circular plots (Supplementary Fig. ##SUPPL##0##5##). For <italic>OsDSG1</italic>, genes positively co-expressed were zinc finger family proteins and WD40-repeat family proteins (Supplementary Fig. ##SUPPL##0##5a##) while in the case of <italic>OsSRO1c</italic>, most of the co-expressed genes are transcription factors (Supplementary Fig. ##SUPPL##0##5b##). <italic>OsWAK89b</italic> and NAC transcription factor was found to be co-expressed with <italic>OsDERF1</italic> (Supplementary Fig. ##SUPPL##0##5c##). Similarly, <italic>OsDSR2</italic> was found to be co-expressed with kinesin motor-containing protein (Supplementary Fig. ##SUPPL##0##5d##).</p>", "<title>Superior haplotypes of associated genes for drought responsiveness</title>", "<p id=\"Par12\">The haplotype analysis across the 16 associated genes uncovered a wide range of haplotype diversity. The number of haplotypes identified varied significantly, with <italic>OsDREB1F</italic> exhibiting the lowest number of haplotypes (1), while <italic>ASR3</italic> displayed the highest number of haplotypes (91). The major haplotypes were highly prevalent, with some, including <italic>OsDREB1F</italic>-H1, exhibiting a frequency as high as 100%. This indicates that major haplotypes are likely to be common in the population and may play an important role in determining the genetic makeup of the organisms. On the other hand, the minor haplotypes were found to have a low frequency, with some as low as 0.75% (<italic>ASR3-</italic>H88) (Supplementary Data ##SUPPL##3##4##). These haplotypes are likely to be rare in the population and have a significant impact during reproductive stage drought stress tolerance.</p>", "<p id=\"Par13\">Haplo-pheno analysis was performed to identify the genes responsible for yield under drought stress by comparing the average yield of groups with different haplotypes. We identified superior haplotypes for only seven out of the 16 associated genes. For instance, among the 14 haplotypes identified for <italic>OsDIL1</italic>, H22 was identified as the superior haplotype (Fig. ##FIG##1##2##). Similarly, for the genes <italic>OsGSK1</italic>-H4, <italic>OsDSR2</italic>-H3, <italic>ASR3</italic>-H88, <italic>DSM3</italic>-H4, <italic>ZFP182</italic>-H4, and <italic>OsDREB1C</italic>-H3 were determined to be the most favorable haplotypes (Supplementary Fig. ##SUPPL##0##6##). Notably, we found that lines possessing superior haplotypes exhibited a significantly higher yield (8.5–62.5%) as compared to lines without superior haplotypes (Table ##TAB##0##1##).</p>", "<title>Identification of genotypes carrying superior haplotypes</title>", "<p id=\"Par14\">Our discovery of superior haplotypes has enabled us to identify the most promising genotypes from a subset panel, which can be utilized in a haplotype-based breeding program to design drought-tolerant plants. Across all genotypes with superior haplotypes, the average plant yield ranged from 3.8 to 6.5 g (Table ##TAB##0##1##). In order to assess how genetic variation can influence the response of a subpopulation to drought stress we have compared haplotype frequencies across subpopulations. Haplotype frequency of the 7 associated genes showed substantial differences among the subpopulation (Supplementary Data ##SUPPL##2##5##). We found that the superior haplotype for the associated genes was present only in the indica and aus subpopulations, while none of the superior haplotypes was present in the Japonica subpopulation (Supplementary Table ##SUPPL##0##2##). This result further affirms that indica varieties are better adapted to survive in drought conditions. Identifying novel haplotypes can provide important insight into the genetics of the sub-population and can help researchers gain a better understanding of evolutionary processes. In addition, we have identified accessions that carry multiple superior haplotypes, which would significantly expedite the process of customizing rice development for yield under drought stress. Notably, we have identified genotypes with two distinct combinations of superior haplotypes for genes, which result in different phenotypes depending on the specific combination of superior haplotypes utilized. For example, the DONDRADAO: <italic>IRIS_313-11411</italic> genotype from Brazil and CHANDINA: <italic>IRIS_313-9917</italic> from Sri Lanka have superior haplotypes for two gene combinations for the SPY trait: <italic>OsDREB1C</italic>-H3, <italic>ZFP182</italic>-H4, and <italic>DSM3</italic>-H4 (Supplementary Table ##SUPPL##0##3##). The combinations of identified superior haplotypes governing the foremost drought component trait SPY in the current study could be deployed to develop drought-tolerant rice cultivars through a haplotype-based breeding approach (Fig. ##FIG##2##3##).</p>", "<title>Validation of superior haplotypes in drought-tolerant rice varieties</title>", "<p id=\"Par15\">The validation of superior haplotypes was performed by conducting whole genome re-sequencing (WGRS) using the Nova Seq Illumina platform on eight known rice varieties (four drought-tolerant and four drought-susceptible). The average depth of coverage ranged from 16-fold to 45-fold, with a mean genome coverage of 91% (as depicted in Supplementary Table ##SUPPL##0##4##). Through our analysis, we compared the superior/favorable haplotypes to the inferior/unfavorable haplotypes along with drought-tolerant and susceptible varieties of the five identified genes. However, for two of the seven genes, <italic>OsGSK1</italic> and <italic>OsDSR2</italic>, the superior haplotypes were present in a large proportion of the genotypes (47% and 13%, respectively), so we did not consider them for further analysis and performed validation on only five genes (Table ##TAB##1##2##). Interestingly, for the <italic>OsDREB1C</italic> gene, the reported superior haplotype (H3 with the haplotype sequence—GAAAG), was present in all the resistant varieties (DRR Dhan 42, DRRDhan 44, DRR Dhan 46, PSBRc 68, and PSBRc 82) except Sahbhagi Dhan and Aus 299. Conversely, the unfavorable haplotype (H1 with the haplotype sequence—GAAAA) was observed in all drought-susceptible varieties, and it was linked to reduced yield under reproductive stage drought stress. This superior haplotype was observed to be absent in drought-susceptible rice varieties but was selectively bred in drought-tolerant varieties through domestication and modern breeding practices. The haplotypic differences for the <italic>OsDREB1C</italic> gene are presented in Fig. ##FIG##3##4##. For the other four genes, we did not find any correlation between resistant and susceptible varieties.</p>", "<title>In silico structural analysis of the candidate genes</title>", "<p id=\"Par16\">The impacts of nonsynonymous single nucleotide polymorphisms (nsSNPs) were assessed in order to study the structural changes in the candidate genes. SIFT scores were used to evaluate the effects of the nsSNPs on protein structure for each gene. As a result, only one SNP at position 1434870 (A/T) in the <italic>OsDREB1C</italic> gene was discovered to have a functional mutation. When analyzing the protein structure, this specific mutation with a SIFT score of 0.00 caused the replacement of methionine for lysine at the 25th amino acid position resulting in a deleterious effect. The remaining four missense mutations, on the other hand, were not found to result in any substantial structural alterations and were deemed tolerable (Supplementary Data ##SUPPL##2##6##). The superimposed model of the translated protein sequences representing the unfavorable (H1) and favorable haplotypes(H3), as predicted by SWISS-MODEL, indicates that the mutation has no significant impact on the protein structure. Further, in order to select the superior haplotype for the <italic>OsDREB1C</italic> gene, KASP (kompetitive allele-specific PCR) primer has been designed. The details of the primer are supplied in Supplementary Data ##SUPPL##2##7## for easy inclusion into breeding programs, enabling its efficient use. Similarly, for other genes, we could not find any deleterious effect nsSNPs.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par17\">Haplotype-based breeding has the potential to solve issues in modern agriculture by using superior alleles from target genes to create new traits. Genetic variation in the diversity panels can significantly increase genetic gain in this integrative pre-breeding approach. Haplotype analysis of key genes to identify trait-associated variations revealed superior haplotypes for heat stress and fertility, grain cooking, and eating quality^{##REF##33547986##35##,##REF##29222496##36##}. In addition, sequencing-based mapping strategies can also help us to identify superior haplotypes for different traits to facilitate tailor-made crop plants <italic>via</italic> haplotype-based breeding^{##REF##30701663##30##}.</p>", "<p id=\"Par18\">Although the successful cloning of functional genes in rice stands as a notable achievement, the challenge lies in the slow translation of these discoveries into concrete progress in molecular breeding. A substantial challenge exists in accessing the original donors for integration into these programs. The primary objective of this study is to narrow this gap by identifying superior or alternative haplotypes suitable for integration into molecular breeding programs. The main focus of our current study employing c-GWAS is to specifically uncover superior haplotypes of already cloned and functionally characterized genes reported in the literature through various studies (GWAS, overexpression/silencing, or omics experiments). We shortlisted 95 major drought tolerance genes from the RiceFun database, to determine the genes and superior haplotypes associated with the single plant yield trait in rice under drought stress.</p>", "<p id=\"Par19\">The present study analyzed the haplotype diversity of 95 key drought-responsive genes in 399 diverse genotypes from the 3K-RG panel. Results showed significant variation among the genotypes for the SPY across the environments, indicating a high level of segregation. The study also found that drought stress has a major influence on creating variation in the genotypes and that the degree of drought tolerance differs among the accessions. Repeatability estimates were high for all seasons and similar in stress and non-stress environments, suggesting that similar results would be obtained if the trial will be repeated under similar conditions. Further, association studies were conducted to detect genetic variants and underlying candidate genes associated with the agronomically important trait SPY.</p>", "<p id=\"Par20\">c-GWAS is a powerful approach that uses the correlation between genetic variants and trait differences based on linkage disequilibrium (LD) to study the genetic mechanism of complex traits^{##UREF##12##37##,##REF##20089441##38##}. We studied the association of SPY, which is known to be regulated by various indirect and direct traits with drought stress conditions^{##REF##18343712##39##,##REF##23218902##40##}. Our study identified 69 strongly associated MTAs in 16 candidate genes with significant Phenotypic Variance Explained (PVE) for SPY under reproductive stage drought conditions on chromosomes 1, 2, 3, 6, 8, 9,10, 11, and 12. GO annotation revealed that the 16 genes identified involve different molecular functions such as sequence-specific DNA-binding transcription factor activity, protein binding, catalytic activity, kinase activity, nucleic acid binding, and lipid-binding activity (Supplementary Fig. ##SUPPL##0##3##). These genes have been reported to play a role in processes such as floral development, stress signaling transduction, grain yield under drought conditions, wax accumulation, and drought tolerance at the vegetative and reproductive stages^{##REF##17690841##41##–##REF##23686450##45##}.</p>", "<p id=\"Par21\">Out of the 69 MTAs identified, 25 showing the strongest association signal with 4.48% PVE were found in the 50-kb region of the <italic>LOC_Os01g10840</italic> gene on chromosome 1, which encodes a glycogen synthase kinase gene involved in abiotic stress tolerance. 16 MTAs were present within the 50-kb flanking region of the <italic>LOC_Os11g47809</italic> gene, which belongs to the metallothionein-like protein family. There were 6 MTAs within the <italic>LOC_Os3g60560</italic> (<italic>ZFP182</italic>), a C₂H₂ type zinc finger protein that plays a critical role in abiotic stress tolerance (Supplementary Data ##SUPPL##2##3##). The MTAs identified in this study were also compared to previously identified QTLs using the QTL Annotation Rice Online (Q-TARO) database. Interestingly, two SNPs (S1_35970278 and S9_286465239) present within the candidate loci of <italic>OsDSR2</italic> and <italic>OsDSG1</italic> were found to be co-localized with previously identified major <italic>qDTY</italic> QTLs (<italic>qDTY</italic>_{<italic>1.1</italic>} and <italic>qDTY</italic>_{<italic>9.1</italic>})^{##REF##22008150##4##,##UREF##14##46##}, and three SNPs (S1_42747553; S6_182471138; S8_264245022) were found to be in the vicinity of <italic>qDTY</italic>_{<italic>1.1</italic>}<italic>, qDTY</italic>_{<italic>6.3</italic>}, and <italic>qDTY</italic>_{<italic>8.1</italic>}, respectively^{##REF##30796339##18##,##REF##29085383##47##} (Supplementary Table ##SUPPL##0##5##). <italic>OsDSR2</italic> is a member of the <italic>DUF966</italic> gene family and negatively regulates brassinosteroid signaling, playing a role in stress signal-transduction pathways and flower development^{##REF##24247850##48##}. The <italic>OsDSG1</italic> gene encodes a U-box E3 ubiquitin ligase and positively regulates cell elongation or division in different organs^{##REF##28013174##49##}. The colocalized MTAs identified in our study with the previously reported QTLs and the superior haplotypes of the candidate genes might prove helpful in future rice breeding programs for increasing grain yield under drought conditions. Furthermore, c-GWAS analysis using the drought susceptibility index (DSI) data provided further support to our findings, as our observations revealed a significant overlap between the identified MTAs and the genes associated with drought tolerance. This remarkable overlap reinforces the consistency of our results and is in line with the findings obtained from GWAS analysis using SPY data (Supplementary Data ##SUPPL##2##8##). These results highlight the consistency and significance of these genes in relation to drought tolerance, highlighting their potential to enhance plant productivity under challenging conditions.</p>", "<p id=\"Par22\">In c-GWAS analysis, out of 69 MTAs, only three MTAs were found to be falling directly within the genic regions (<italic>OsSRO1c</italic>, <italic>GF14c</italic>, and <italic>OsMT1a</italic>). To explore the involvement of other genes along with our candidate genes we explored all the genes present in the 50 kb region other than the cloned and functionally characterized candidate genes that we have used in the present study. As a result, 302 genes were found in the vicinity of the region. Out of these 302, only 32 genes (16 previously identified in the present study and 16 additional genes reported in the new analysis) were cloned or functionally characterized based on the <italic>Ricefun</italic> database. <italic>Haplo-pheno analysis</italic> of 16 additional new genes revealed that only two genes, <italic>ZFP15</italic> (H3) and <italic>OsPRP3</italic> (H14), exhibited superior haplotypes. <italic>ZFP15</italic>, is a C₂H₂-type zinc finger protein and plays a significant regulatory role in spike development. However, it is not associated with abiotic stress responses as previously reported^{##REF##16172918##50##}. <italic>OsPRP3</italic> encodes for flower-specific Proline-rich protein (PRP), is involved in cell wall assembly during flower maturation, and has also been shown to contribute to cold stress tolerance in rice^{##REF##19830390##51##}. However, for most of these genes, there was no variation observed in the 3K-RG panel, as indicated in Supplementary Table ##SUPPL##0##6##. Our findings provide strong support and validation, underscoring the significance of the identified genes with superior haplotypes in shaping the genetic landscape of drought stress response in rice. These insights shed light on the potential role of these associated genes and underscore their importance in future breeding and improvement programs.</p>", "<p id=\"Par23\">Scanning gene expression profiles at different development stages helps to establish the link between a gene’s expression and its biological function, including its role in variations in phenotype^{##REF##27092161##52##}. Combining GWAS with co-expression analysis improves the validation of MTAs and understanding of the molecular framework regulating traits of interest^{##REF##30413654##53##}. We found that <italic>OsHSP23.7</italic> was highly expressed in spikelets and most of the developmental stages, of which stem elongation and mature grain stage were the two best matches, suggesting its critical role throughout the life cycle of the rice plant. <italic>OsNAC10</italic> was highly expressed in the root and at the dough and mature grain stage, suggesting that <italic>OsNAC10</italic> is involved in drought tolerance and high grain yield <italic>via</italic> root growth^{##REF##20335401##43##}. Interestingly, the NAC transcription factor gene (<italic>LOC_Os11g03310</italic>) and <italic>OsWAK89b</italic> (<italic>LOC_Os09g38834</italic>) were co-expressed with the <italic>OsDERF1</italic>. <italic>OsWAK</italic> has been previously reported to control panicle number and grain yield^{##REF##28400567##54##}. Similarly, <italic>OsSRO1c</italic> was found to be co-expressed with transcription factors such as C₂H₂, zinc finger protein, GRAM domain-containing protein, and NAC domain-containing proteins, which is consistent with its role as a transactivator. <italic>OsDSG1</italic> was also found to be co-expressed with zinc finger-like protein-encoding genes. The role of zinc fingers in regulating plant architecture and grain yield has already been established in rice and other crops^{##REF##22693960##55##}. Although co-expression profiling does not capture all functional interactions and further evidence is required to validate and understand the co-expression network, these data provide informative clues about genes contributing to the same biological process associated with grain yield. In the future, integrating genetic, genomic, transcriptomic, proteomic, metabolic, and phenotypic data through a systems biology approach will provide a more comprehensive understanding of the associations between genotype and phenotype in plants.</p>", "<p id=\"Par24\">Phenotypic validation of 16 candidate genes associated with drought tolerance in a subset of 399 rice genotypes identified superior haplotypes for seven genes (<italic>OsGSK1</italic>, <italic>OsDSR2, OsDREB1C</italic>, <italic>ASR3</italic>, <italic>DSM3</italic>, <italic>ZFP182</italic>, and <italic>OsDIL1</italic>) for drought responsiveness. Among these genes, <italic>OsGSK1</italic> is a glycogen synthase kinase gene that improves tolerance to abiotic stress, while <italic>OsDIL1</italic> encodes a lipid transfer protein that aids in drought tolerance at vegetative and reproductive stages^{##REF##17690841##41##,##REF##23686450##45##}. <italic>OsDSR2</italic>, a member of the SRO (SIMILAR TO <italic>RCD</italic> ONE) family acts as a negative regulator of BR-signaling and increases sensitivity to salt and drought stress when overexpressed^{##REF##24247850##48##}. <italic>DSM3</italic>, a member of the <italic>OsITPK</italic> family, plays a crucial role in stress response, and maintaining an optimal expression level is essential for enhancing drought and salt tolerance in rice^{##REF##22038091##56##}. <italic>ASR3</italic> on the other hand, is involved in maintaining higher photosynthetic activity during cold and drought stress and influencing plants’ hormone and sugar status, at various growth and developmental stages during the plant life cycle^{##REF##23620302##57##}. <italic>OsDREB1C</italic> regulates photosynthesis and nitrogen utilization in response to drought stress, while <italic>ZFP182</italic>, a C₂H₂ type of zinc finger protein, promotes multiple stress tolerance by regulating ABA-induced antioxidant defense response in plants^{##REF##22693960##55##,##REF##35862527##58##}.</p>", "<p id=\"Par25\">To further validate our findings and gain insight into the genetic factors contributing to drought tolerance in rice, we conducted whole-genome re-sequencing on four drought-tolerant and four drought-susceptible released varieties. Our analysis focused on non-synonymous SNPs and InDels within the 5’UTR, CDS, and 3’UTR regions in the five identified genes.’ By comparing the most favorable and unfavorable haplotypes across drought-tolerant and susceptible varieties, we sought to identify the association of superior haplotypes with higher yield under reproductive stage drought stress. Additionally, we conducted a literature search to identify potential donors that have been previously utilized in conventional breeding and QTL mapping studies^{##REF##25205576##12##}.</p>", "<p id=\"Par26\">The results revealed the consistent presence of superior/favorable haplotype H3 of the <italic>OsDREB1C</italic> gene in all drought-tolerant varieties except in Sahbhagi dhan and Aus 299, which possessed the H1 haplotype. However while looking into the parentage information, we noted that each drought-tolerant variety exhibited different immediate parentage and lacked shared lineage, suggesting potential genetic differences among them (Supplementary Table ##SUPPL##0##7##). However, the common superior haplotype (H3) present in the five selected genotypes reflected that there may have been some common great-grand parentage during the course of the development of these lines. This uniformity in haplotype distribution suggests that this specific haplotype could be a key determinant of drought tolerance in these varieties. The genotypes Sahbhagi dhan and Aus 299 were found to lack the superior haplotype of the <italic>OsDREB1C</italic> gene (H3) reflecting the presence of some other superior haplotype of any other genes not identified in the present study. This suggests that donors of <italic>OsDREB1C</italic> might have been used in previous drought tolerance breeding programs for improving drought tolerance and enhancing grain yield in these modern varieties. This finding aligns with recent research highlighting the crucial role of the <italic>OsDREB1C</italic> gene in increasing grain yield by up to 40% while reducing the growth duration time in rice^{##REF##35862527##58##}.</p>", "<p id=\"Par27\">Interestingly we have not found any superior haplotypes of the other four genes <italic>ASR3</italic>, <italic>DSM3</italic>, <italic>ZFP182</italic>, and <italic>OsDIL1</italic> in the selected seven drought-tolerant lines and as expected in the susceptible lines. The genes and their superior haplotypes identified in the present study are novel and based on our validation results, it was noted that these genes are never being utilized in the drought breeding programs. This further reflects the importance of the identification of novel superior haplotypes to be deployed in breeding programs to develop climate-resilient drought-tolerant varieties. We found that the genotype (Chandina) carrying superior haplotypes for <italic>OsDREB1C</italic> and <italic>DSM3</italic> gene could be a potentially important target that can be utilized in breeding programs to enhance grain yield under drought stress.</p>", "<p id=\"Par28\">We have also noted that the number of accessions used for <italic>haplo-pheno</italic> analysis in certain cases (<italic>DSM3</italic> and <italic>ASR3</italic> genes) was limited to three individuals in the superior haplotype group. Although based on the statistical analysis minimum of three individuals are required to analyze the datasets. However, the presence of background effects from other loci can influence the results. Therefore, to ensure more reliable conclusions, it is imperative to define a group with &gt;5 individuals with minimum variance within the same group should be cut-off to start the analysis. Such analysis in the future will effectively reduce background noise from other loci. Furthermore, these findings also emphasize that these genes are novel and have not been utilized in any breeding programs for developing drought-tolerant varieties, representing the untapped potential for enhancing the performance of these varieties. Therefore, incorporating these superior haplotypes into breeding programs holds great promise for further improving drought tolerance in rice cultivars. Genotypes carrying superior haplotypes for these genes displayed higher levels of drought tolerance, as evidenced by their ability to maintain higher yields in drought conditions compared to genotypes with unfavorable haplotypes.</p>", "<p id=\"Par29\">Our finding highlights the critical role of five genes (as represented in Fig. ##FIG##2##3##) in conferring drought tolerance in rice plants. These identified haplotypes hold promise for continued exploration and prospective utilization in breeding programs aimed at strengthening drought tolerance in rice. However, further functional validation of these haplotypes is required to establish their suitability as potential targets for genome editing to enhance drought tolerance. Overall, our data provide valuable insights into the genetic basis of drought tolerance in rice and present a potential strategy for enhancing rice production in water-limited environments.</p>" ]

[]

[ "<p id=\"Par1\">Haplotype-based breeding is an emerging and innovative concept that enables the development of designer crop varieties by exploiting and exploring superior alleles/haplotypes among target genes to create new traits in breeding programs. In this regard, whole-genome re-sequencing of 399 genotypes (landraces and breeding lines) from the 3000 rice genomes panel (3K-RG) is mined to identify the superior haplotypes for 95 drought-responsive candidate genes. Candidate gene-based association analysis reveals 69 marker-trait associations (MTAs) in 16 genes for single plant yield (SPY) under drought stress. Haplo-pheno analysis of these 16 genes identifies superior haplotypes for seven genes associated with the higher SPY under drought stress. Our study reveals that the performance of lines possessing superior haplotypes is significantly higher (p ≤ 0.05) as measured by single plant yield (SPY), for the <italic>OsGSK1</italic>-H4, <italic>OsDSR2-</italic>H3, <italic>OsDIL1-</italic>H22<italic>, OsDREB1C</italic>-H3, <italic>ASR3-</italic>H88, <italic>DSM3-</italic>H4 and <italic>ZFP182</italic>-H4 genes as compared to lines without the superior haplotypes. The validation results indicate that a superior haplotype for the DREB transcription factor (<italic>OsDREB1C</italic>) is present in all the drought-tolerant rice varieties, while it was notably absent in all susceptible varieties. These lines carrying the superior haplotypes can be used as potential donors in haplotype-based breeding to develop high-yielding drought-tolerant rice varieties.</p>", "<p id=\"Par2\">Using a subset of 399 genotypes from the 3000 rice genomes panel, genotypes carrying superior haplotypes were identified for five genes associated with yield under drought stress that hold potential for the development of high-yield drought-tolerant varieties in rice.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s42003-024-05769-7.</p>", "<title>Acknowledgements</title>", "<p>The authors express sincere thanks to the Department of Biotechnology (DBT), Government of India for financial support under the project ‘Development of superior haplotype-based near-isogenic lines (Haplo-NILs) for enhanced genetic gain in rice’ grant (BT/PR32853/AGill/103/1159/2019) and DBT-RA program in Biotechnology and Life Sciences for financial support to V.P.V. This work has been undertaken as part of the ICAR-IRRI collaborative research project. IRRI is a member of the CGIAR Consortium.</p>", "<title>Author contributions</title>", "<p>P.S. and V.K.S. conceived the idea and supervised the study. Preeti.S. performed most of the analysis. Preeti.S., V.P.V., K.T.S., P.S., and V.K.S., interpreted the results and wrote the manuscript. K.T.S. and B.P. performed GWAS analysis. K.T.S., A.G., and Preeti.S. helped in analyzing WGRS data. P.J.P. analyzed phenotypic data. V.P.V. and C.V. contributed toward phenotypic data generation. U.M.S., S.K., and A.K. edited the MS. All authors read and approved the final manuscript.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par41\"><italic>Communications Biology</italic> thanks Showkat Ganie, Vlatko Galic, Jianlong Xu, and Daisuke Ogawa for their contribution to the peer review of this work. Primary Handling Editor: David Favero.</p>", "<title>Data availability</title>", "<p>The WGRS sequencing data generated in this study are available in the SRA public repository under the bioproject accession number PRJEB70241. Sequence data used in this article can be found under the following accession numbers: ERR12304009 (DRR Dhan 42), ERR12303753(DRR Dhan 44), ERR12305485 (DRR Dhan 46), ERR12305492(Naveen), ERR12305489 (Swarna), ERR12305486 (BPT 5204), ERR12305487 (DRR Dhan 48), and ERR12305488 (Sahbhagi Dhan). Data supporting the findings of this work are available within the paper and its Supplementary Information Files. The source data behind the graphs in different figures in the paper are provided in Supplementary Data ##SUPPL##4##9##. The genetic materials that support the findings of this study are available from the corresponding authors upon request.</p>", "<title>Competing interests</title>", "<p id=\"Par42\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Haplotype diversity in the drought-responsive genes.</title><p>The frequency and relative distribution of drought-responsive genes carrying &gt;2 haplotypes in subset panel of 3K rice genomes are represented in the Circos diagram. The outermost circle represents 12 rice chromosomes (Chr 01–Chr 12) in different colors, and the inner two circles represent the number of haplotypes and their frequency distribution. The histogram displays the number of haplotypes obtained for each gene. The bubbles represent the frequencies of each haplotype particular to the gene. The range of haplotype frequencies is represented by different colors as indicated.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Haplotype analysis of the <italic>OsDIL1</italic> gene associated with the trait across the subset panel.</title><p><bold>A</bold> Haplotypic variation in the <italic>OsDIL1</italic> gene associated with single plant yield trait (SPY) in the subset panel. <bold>B</bold> Phenotypic evaluation of the subset panel (<italic>n</italic> = 399) in field conditions under non-stress and drought stress conditions. <bold>C</bold> Violin plot showing variation in SPY trait in rice accessions significant at <italic>p</italic>-value &lt; 0.05. Different alphabets denote significant differences between haplotypes. The median is depicted by the horizontal line in the box. Note: Haplotype variation reflects only those haplotypes that are used in haplo-pheno analyses. The violin plot uses an orange color to depict the distribution of the superior haplotype, while the green color is employed to represent the distribution of the remaining haplotypes associated with the <italic>OsDIL1</italic> gene.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Tailor-made rice with superior haplotypes for developing high-yielding drought-tolerant varieties.</title><p><bold>A</bold> Representative rice plant carrying inferior haplotype combination (<italic>OsDREB1C-H1</italic>, <italic>ASR3-H89</italic>, <italic>OsDIL1</italic>-H1, <italic>DSM3</italic>-H2, and <italic>ZFP182</italic>-H20). <bold>B</bold> Superior haplotype combination (<italic>OsDREB1C-H3</italic>, <italic>ASR3-H88</italic>, <italic>OsDIL1</italic>-H22, <italic>DSM3</italic>-H4, and <italic>ZFP182</italic>-H4) for SPY trait under reproductive stage drought stress. New breeding lines can be developed by introgressing superior haplotype combinations through haplotype-based breeding. SPY single plant yield.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Validation of the superior haplotypes in drought-tolerant rice varieties for the <italic>OsDREB1C</italic> gene.</title><p><bold>A</bold> Haplotypic variation of <italic>OsDREB1C</italic> gene in 3K-subset. <bold>B</bold> Subpopulation- wise distribution of haplotypes in the subset and violin plot showing variation in SPY trait in rice accessions significant at p-value &lt; 0.05. The violin plot uses an orange color to depict the distribution of the superior haplotype, while the green color is employed to represent the distribution of the remaining haplotypes associated with the <italic>OsDREB1C</italic> gene. <bold>C</bold> Gene structure and haplotype sequence variation of the <italic>OsDREB1C</italic> gene. Four drought-susceptible (DS) and seven drought-tolerant (DT) varieties of rice were examined for haplotypic variation between the superior/favorable (H3) and the unfavorable (H1) haplotypes. DT drought tolerant lines, DS drought susceptible lines. Figure created using Biorender (<ext-link ext-link-type=\"uri\" xlink:href=\"https://biorender.com/\">https://biorender.com/</ext-link> accessed on 16 August 2023).</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Average performance in terms of single plant yield (g) of the genotypes possessing superior haplotypes in comparison to another group of haplotype.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Gene</th><th><italic>Os_ID</italic></th><th>Total no. of haplotypes</th><th>SH</th><th>Average performance of individuals with SH</th><th>Range of average performance of haplotypic groups other than SH group</th><th>Top performing three donors possessing SH</th></tr></thead><tbody><tr><td><italic>OsGSK1</italic></td><td><italic>Os01g0205700</italic></td><td>4</td><td><bold>H4</bold></td><td>H4-4.2 g^a</td><td>H3-3.2 g^b - H2-3.9 g^a</td><td><p>Da Nuo</p><p>IH Pen Shim Ming</p><p>Deng Deng Qi</p></td></tr><tr><td><italic>OsDSR2</italic></td><td><italic>Os01g0839200</italic></td><td>3</td><td><bold>H3</bold></td><td>H3-3.8 g^a</td><td>H1-3.1 g^b - H2-3.4 g^a,b</td><td><p>Lalka (lal dhan)</p><p>Da Nuo</p><p>India dular</p></td></tr><tr><td><italic>OsDREB1C</italic></td><td><italic>Os06g0127100</italic></td><td>6</td><td><bold>H3</bold></td><td>H3-5.2 g^a</td><td>H5-2.9 g^b - H6-3.1g^b</td><td><p>Chandina</p><p>Hodarawala</p><p>Merle</p></td></tr><tr><td><italic>ASR3</italic></td><td><italic>Os02g0543000</italic></td><td>32</td><td><bold>H88</bold></td><td>H88-6.5 g^a</td><td>H99-2.7 g^bc - H130-5.2^ab</td><td><p>Lal taura</p><p>Aus 359</p><p>Sada aus</p></td></tr><tr><td><italic>DSM3</italic></td><td><italic>Os03g0230500</italic></td><td>4</td><td><bold>H4</bold></td><td>H4-5.5 g^a</td><td>H2-3.3 g^b - H5-4.2 g^ab</td><td><p>Chandina</p><p>L10833</p><p>IR28</p></td></tr><tr><td><italic>ZFP182</italic></td><td><italic>Os03g0820300</italic></td><td>16</td><td><bold>H4</bold></td><td>H4- 4.7 g^a</td><td>H14-2.6 g^ab - H8-4.0 g^ab</td><td><p>ARC 18533</p><p>Salsi</p><p>Napdai</p></td></tr><tr><td><italic>OsDIL1</italic></td><td><italic>Os10g0148000</italic></td><td>14</td><td><bold>H22</bold></td><td>H22- 4.5 g^a</td><td>H21-1.7 g^b - H9-4.0^ab</td><td><p>T. kaug pao</p><p>Nam Sa-Gui 19</p><p>E Zi 96</p></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Validation of superior haplotypes on known drought-tolerant and susceptible varieties.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Gene</th><th>Chromosome</th><th>Total no. of haplotypes</th><th>Superior haplotype</th><th>Accessions with SH</th><th>Superior haplotype sequence</th><th colspan=\"7\">Drought-tolerant varieties</th><th colspan=\"4\">Drought-susceptible varieties</th></tr><tr><th/><th/><th/><th/><th/><th/><th>DRR Dhan 44</th><th>DRR Dhan 42</th><th>DRR Dhan 46</th><th>Sahbhagi Dhan</th><th>PSBRc 82</th><th>PSBRc 68</th><th>Aus 299</th><th>Naveen</th><th>Swarna</th><th>DRR Dhan 48</th><th>BPT5204</th></tr></thead><tbody><tr><td><italic>OsDREB1C</italic></td><td>6</td><td>4</td><td>H3</td><td>5</td><td>GAAAG</td><td>GAAAG (H3)</td><td>GAAAG (H3)</td><td>GAAAG (H3)</td><td>GAAAA (H1)</td><td>GAAAG (H3)</td><td>GAAAG (H3)</td><td>^aGAAAA (H1)</td><td>^aGAAAA (H1)</td><td>^aGAAAA (H1)</td><td>^aGAAAA (H1)</td><td><p>^aGAAAA</p><p>(H1)</p></td></tr><tr><td><italic>ASR3</italic></td><td>2</td><td>32</td><td>H88</td><td>3</td><td>T–A--TA------T–A</td><td>^bT–A--TA–C------A</td><td>^bT–A--TA-C------A</td><td>^bT–A--TA–C------A</td><td>^bT–A--TA–C------A</td><td><p>^aT-A--TA---G--TT</p><p>(H99)</p></td><td>^bT–A--TA–CGG–ATT</td><td><p>^aT–A--TA--GG—TT</p><p>(H112)</p></td><td>^bT–A--TA–C------A</td><td>^bT–A--TA–C------A</td><td>^bT–A--TA–C------A</td><td>^bT–A--TA–C------A</td></tr><tr><td><italic>DSM3</italic></td><td>3</td><td>4</td><td>H4</td><td>3</td><td>GGGAAAGT</td><td><p>^aGATAAAAT</p><p>(H2)</p></td><td>^aGATAAAAT (H2)</td><td>^aGATAAAAT (H2)</td><td>^aGATAAAAT (H2)</td><td>^bA/GT/GAATACA/G</td><td><p>^aGGGAAACGT</p><p>(H3)</p></td><td><p>^aGGGAAACGT</p><p>(H3)</p></td><td>^aGATAAAAT (H2)</td><td>^aGATAAAAT (H2)</td><td>^aGATAAAAT (H2)</td><td>^aGATAAAAT (H2)</td></tr><tr><td><italic>ZFP182</italic></td><td>3</td><td>16</td><td>H4</td><td>10</td><td>A----A–C CGG--T</td><td>^bA----A–C–CGGT–T</td><td>^bA----A–C–CGGT–T</td><td>^bA----A–C–CGGT–T</td><td>^bA----A–C–CGGT–T</td><td><p>^aA-TA-A-C-CGG—T</p><p>(H8)</p></td><td><p>^aA-----A-C-C----–</p><p>(H1)</p></td><td><p>A----A–C–C–G—T</p><p>(H2)</p></td><td>^bA----A–C–CGGT–T</td><td>^bA----A–C–CGGT–T</td><td>^bA----A–C–CGGT–T</td><td>^bA----A–C–CGGT–T</td></tr><tr><td><italic>OsDIL1</italic></td><td>10</td><td>14</td><td>H22</td><td>3</td><td>T–ACGAAG–TGC</td><td>^bTTACGAAGAT–C</td><td>^bTTACGAAGAT–C</td><td>^bTTACGAAGAT-C</td><td>^bTTACGAAGAT-C</td><td><p>^aT-ACGAAGA-GC</p><p>(H24)</p></td><td><p>^aT-ACGAAGA-GC</p><p>(H24)</p></td><td><p>^aTT–CAGGG---C</p><p>(H24)</p></td><td>^bTTACGAAGAT–C</td><td>^bTTACGAAGAT–C</td><td>^bTTACGAAGAT–C</td><td>^bTTACGAAGAT–C</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM5\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM6\"></supplementary-material>" ]

[ "<table-wrap-foot><p>Duncan’s analysis was employed to test statistical significance at <italic>P</italic> &lt; 0.05. Means followed by different letter for each haplotype groups are significantly differenct. <italic>Haplo-pheno</italic> analysis of only those haplotype groups was performed in which at least three genotypes were present. <italic>SH</italic> Superior haplotype.</p></table-wrap-foot>", "<table-wrap-foot><p>^aThese genotypes possess other alternate haplotypes than the superior haplotype identified for the gene of interest.</p><p>^bHaplotype not present in the subset panel.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Preeti Singh, Krishna T. Sundaram, Vishnu Prasanth Vinukonda.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"42003_2024_5769_Fig1_HTML\" id=\"d32e559\"/>", "<graphic xlink:href=\"42003_2024_5769_Fig2_HTML\" id=\"d32e774\"/>", "<graphic xlink:href=\"42003_2024_5769_Fig3_HTML\" id=\"d32e1102\"/>", "<graphic xlink:href=\"42003_2024_5769_Fig4_HTML\" id=\"d32e1541\"/>" ]

[ "<media xlink:href=\"42003_2024_5769_MOESM1_ESM.pdf\"><caption><p>Supplementary Information</p></caption></media>", "<media xlink:href=\"42003_2024_5769_MOESM2_ESM.pdf\"><caption><p>Description of Additional Supplementary Files</p></caption></media>", "<media xlink:href=\"42003_2024_5769_MOESM3_ESM.xlsx\"><caption><p>Supplementary Data 1-3 and 5-8</p></caption></media>", "<media xlink:href=\"42003_2024_5769_MOESM4_ESM.xlsx\"><caption><p>Supplementary Data 4</p></caption></media>", "<media xlink:href=\"42003_2024_5769_MOESM5_ESM.xlsx\"><caption><p>Supplementary Data 9</p></caption></media>", "<media xlink:href=\"42003_2024_5769_MOESM6_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Eyelid abnormalities can occur in various ophthalmic disorders, including Graves’ orbitopathy (GO), ptosis, and orbital tumors. For patients with eyelid abnormalities, it is necessary to evaluate the morphology and position of the eyelids. Various metrics, such as margin–reflex distance 1 (MRD1), MRD2, palpebral fissure height (PFH), and eyelid length, are currently being used to objectively assess the shape and condition of the eyelids^{##REF##2487216##1##,##REF##6398935##2##}. MRD1 and MRD2 are conventional methods used to measure the vertical length of the eyelids. Upper and lower eyelid lengths are measured with the aid of digital images and software, which provide comprehensive information about the size and curvature of the eyelids. However, manually measuring parameters of the eyelid morphology has the drawback of being less consistent and reproducible. In addition, most of these metrics only capture the linear aspect of the eyelid contour, making it difficult to directly assess the morphology of curved eyelids. The concept of the mid-pupil lid distance (MPLD) has been used in various studies to compare the curvature of the eyelid between different patients^{##REF##22197435##3##–##REF##23138202##6##}. However, when measuring the MPLD, it is necessary to establish a standardized horizontal line passing through the pupil. This requirement can sometimes lead to inconsistent outcomes.</p>", "<p id=\"Par3\">In order to overcome the disadvantages of manual eyelid measurements, there have been attempts to automatically or semi-automatically evaluate eyelid morphology through digital image analysis^{##REF##28391655##7##–##UREF##0##9##}. However, semi-automatic measurements, similar to manual measurements, may introduce variability in the segmentation process. Automated measurements have the advantage of allowing consistent measurements through automated segmentation. However, if there is a low-contrast transition in the image, errors may occur during the edge detection process. Recently, neural networks (NNs) have been utilized in various fields of ophthalmology for image analysis^{##REF##37005981##10##,##UREF##1##11##}. NNs are not as limited by image contrast, and this limitation can be overcome by accurately detecting edges through the learning process. Additionally, they can also significantly reduce the time required for evaluation. Deep learning techniques have been reported as feasible in eyelid image analysis for the automated measurement of eyelid parameters^{##REF##36915314##12##–##REF##33827341##15##}. If these NN techniques are designed to automatically and accurately establish the reference line, they will be able to provide more consistent and accurate measurements of the curved eyelid contour. In addition, the use of NNs to analyze eyelid images may be an effective approach for detecting outliers or abnormal areas, which provide immediate information on eyelid abnormalities.</p>", "<p id=\"Par4\">In this study, we aimed to evaluate the clinical usefulness and reliability of a NN-based automated eyelid measurement system. We determined whether the contour of the eyelids could be measured using the intercanthal distance, which connects both canthi and is automatically established by the NNs as a reference line instead of the midpupillary line. Furthermore, we investigated whether the NN could effectively provide comprehensive information for detecting eyelid abnormalities during automated measurements.</p>" ]

[ "<title>Methods</title>", "<p id=\"Par18\">The protocol was approved by the Institutional Review Board of Chung-Ang University Hospital (IRB No. 2303-014-19461). The requirement for informed consent was waived due to the retrospective nature of the study. The study was conducted in accordance with the principles of the Declaration of Helsinki. Consent for publication has been obtained from the individual depicted in the illustration featured in this manuscript.</p>", "<title>Image collection</title>", "<p id=\"Par19\">The study was conducted retrospectively using electronic medical records from January 2010 to February 2023, with a specific focus on outpatient ophthalmology visits at Chung-Ang University Hospital. A total of 100 patients with a normal eyelid morphology, 100 patients with eyelid retraction due to GO, and 100 patients with eyelid ptosis were included in the study. Normal controls were subjects who visited our clinic for reasons such as dry eye syndrome, cataract, or a regular check-up for retinal examination. Patients with unclear diagnoses or those whose pupillary reflex was not visible in facial photographs were excluded from the study. Patients who had undergone previous upper or lower eyelid surgery were also excluded. Demographic information, such as age and gender, was recorded.</p>", "<p id=\"Par20\">The facial photographs were taken by a single examiner in the same room under identical conditions using a 12.3-megapixel automated digital camera (Nikon D90, Nikon, Tokyo, Japan). The aperture, shutter speed, and exposure time were determined based on external lighting conditions. Subjects were instructed to relax and focus on the center of the camera lens in the primary gaze position. A circular marker with a diameter of 9.0 mm was placed on the subjects’ forehead before the image was taken to provide a reference scale in millimeters per pixel. The images were then transferred to a personal computer and saved as JPG files (1200 × 797 pixels, 24-bit, RGB).</p>", "<title>Manual measurement of eyelid parameters</title>", "<p id=\"Par21\">Quantitative measurements of eyelid parameters were performed with patient photographs using ImageJ software version 1.46 (National Institutes of Health, Bethesda, MD, USA; <ext-link ext-link-type=\"uri\" xlink:href=\"http://rsbweb.nih.gov/ij/\">http://rsbweb.nih.gov/ij/</ext-link>). The following parameters were measured and analyzed: MRD1, which is the vertical distance between the upper eyelid margin and the corneal light reflex; MRD2, which is the vertical distance between the lower eyelid margin and the corneal light reflex; upper eyelid length, which is the curvilinear length of the upper eyelid between the medial and lateral canthus; lower eyelid length, which is the curvilinear length of the lower eyelid between the medial and lateral canthus. The measurements were performed by two of the authors (Y.S.N., and J.K.L.) independently. The average values of all parameters were used for data analysis. Among the eyelids of both eyes, the left eyelid or the eyelid with more severe symptoms was selected for comparison of automated and manual measurement.</p>", "<title>Automated measurement of eyelid parameters</title>", "<p id=\"Par22\">An automated measurement system based on NNs was developed to measure MRD1 and MRD2, as well as the lengths of the upper and lower eyelids (Fig. ##FIG##3##4##). First, the system divided the original image of the subjects into three images, each showing the left eye, right eye, or circular marker. The left and right eye images were obtained by vertically splitting the original image in half. The marker image was obtained by cropping the area between 1/4 and 3/4 of the original image’s width. Next, the three images were resized to a square image of 512 × 512 pixels. To prevent distortion caused by resizing, the system maintained the original width-to-height ratio and filled any remaining areas with zero padding. Then, the left and right eye images were fed into three NN models (DeepLab V3+)^{##UREF##2##18##}, with each model responsible for outputting the segments of the sclera, cornea, and light reflex. Therefore, they were individually trained to segment the sclera, cornea, and light reflex. One additional DeepLab V3 + model was used for marker segmentation. The diameter of the segmented marker was then used to convert the pixel length of the sclera, cornea, and light reflex into their respective actual lengths in millimeters (mm).</p>", "<p id=\"Par23\">After image segmentation, each segment was overlaid by the system for the length measurement process. In the first step, the length of the outer boundary of the cornea was measured. The horizontal endpoints of the segmented sclera were used as reference points to differentiate between the upper and lower eyelids. In this study, we measured the length of the eyelids using the perimeter of a virtual quadrant instead of directly measuring the pixel perimeter. which was performed when the pixels on the eyelid formed a corner (Supplementary Fig. ##SUPPL##0##S1##). Using a proportionality equation, the actual length of the eyelids could also be calculated. The midpoint of the light reflex layer was used to calculate the vertical distance between the upper and lower eyelids. The diameter of the marker was used to calculate MRD1 and MRD2 with proportional equations. The results were then compared with manually measured values.</p>", "<title>Automated detection of eyelid abnormalities</title>", "<p id=\"Par24\">The system divided the eyelid margin into 360 degrees (1-degree intervals). First, a horizontal line was added by connecting pixels on the lateral and medial canthi. Then, an orthogonal line was drawn by connecting a pixel on the light reflex with the horizontal line (Fig. ##FIG##4##5##). As a result, we could obtain four partitions by drawing two lines. Additional partitions could be obtained by dividing each partition equally, based on the given degree intervals. Our system then measures the distance from the point where the intercanthal line intersects with the vertical line passing through the pupil light reflex to the eyelid margin for each segment. In this study, the corresponding degree segment was considered abnormal if the length was outside the 95% range of the normal distribution for 300 subjects.</p>", "<p id=\"Par25\">Additionally, any subject who had at least one abnormal segment of 360 degrees was classified as an abnormal subject. The verification performance for abnormal subjects could be improved by reducing the degree interval. Therefore, an optimal trade-off between the degree interval and the verification performance could be achieved. In this study, we determined the ratio of identified abnormal subjects to true cases by varying the degree interval as follows: 90.0, 45.0, 22.5, 15.0, 11.3, 5.6, 2.8, and 1.4; for simplicity, we defined each degree interval as having 4, 8, 16, 24, 32, 64, 128, and 256 partitions, respectively.</p>", "<p id=\"Par26\">To train DeepLab V3 + for image segmentation, 724 images were used. These images included the left and right eye, pupil reflex, and marker of the subjects. For the two eye images, we applied left–right augmentation to improve the accuracy of the learning process. These images were randomly divided into training, validation, and test sets with ratios of 0.6, 0.2, and 0.2, respectively. The hyperparameters were set as follows: a batch size of 32, 30 epochs, AdamW optimizer, and a learning rate of 1e−3. We assessed the performance of DeepLab V3 + using the mean Intersection over union (mIoU) metric. We conducted all the experiments using the PyTorch (version 1.10.1) library and a computer system equipped with a GeForce RTX 3090 24 GB GPU (NVIDIA, Santa Clara, CA, USA).</p>", "<title>Statistical analysis</title>", "<p id=\"Par27\">Data are represented as the mean value with standard deviation. We performed analysis of variance (ANOVA) to analyze demographic characteristics such as age and gender, as well as quantitative measurements including MRD1, MRD2, upper eyelid length, and lower eyelid length. The difference between automated and manual measurements was assessed by Wilcoxon rank-sum test and paired t-test. The ICC was calculated to assess the agreement between manual and automated measurements. ICC values below 0.40 were categorized as 'poor', and values in the range of 0.40–0.60, 0.60–0.75, and 0.75–1.00 were characterized as 'fair', 'good', and 'excellent', respectively. Bland–Altman plots were used to visualize the discrepancies between manual and automated measurements. The 95% confidence intervals for the mean difference and limits of agreement (LOA) are shown on the plot. All statistical analyses were performed using R software (version 4.2.2). A <italic>p</italic>-value of &lt; 0.05 was considered statistically significant.</p>" ]

[ "<title>Results</title>", "<p id=\"Par5\">The average age of the 300 subjects was 50.5 ± 18.6 years, and 204 (68.0%) of them were female. In subgroup comparison, the average age of the ptosis group was the highest at 63.9 ± 13.3 years, whereas the average age of the GO group was the lowest at 37.6 ± 12.1 years. The GO group had a significantly higher proportion of females compared with that in the normal group (<italic>p</italic> &lt; 0.001) and the ptosis group (<italic>p</italic> = 0.047). However, there was no significant difference between the normal and ptosis groups (<italic>p</italic> = 0.596) (Table ##TAB##0##1##).</p>", "<p id=\"Par6\">We compared the values for 300 individuals obtained from both manual measurement and the proposed automated measurement system. The average values of MRD1, MRD2, upper eyelid length, and lower eyelid length were 3.2 ± 1.7 mm, 6.0 ± 1.4 mm, 32.9 ± 6.1 mm, and 29.0 ± 5.6 mm, respectively, when measured using the automated system and 3.0 ± 1.5 mm, 5.8 ± 1.3 mm, 31.5 ± 4.2 mm, and 28.4 ± 3.4 mm, respectively when measured manually. The average values obtained from the automated system were consistently higher than those obtained from manual measurement (Table ##TAB##1##2##).</p>", "<p id=\"Par7\">The values obtained from both manual and automated measurements generally showed good agreement for all eyelid parameters of the subjects. The intraclass correlation coefficient (ICC) values indicated excellent correlation, with values of 0.972 for MRD1 and 0.937 for MRD2. However, the lengths of the upper and lower eyelids showed slightly lower values at 0.803 and 0.737, respectively (Fig. ##FIG##0##1##).</p>", "<p id=\"Par8\">The average differences and 95% limits of agreement for the values of all subjects obtained from manual and automated measurements were as follows: average difference of MRD1 = 0.214 mm (range: 0.178–0.250), average difference of MRD2 = 0.271 mm (range: 0.227–0.315), average difference of upper eyelid length = 1.396 mm (range: 1.052–1.740), and average difference of lower eyelid length = 0.548 mm (range: 0.169–0.927) (Fig. ##FIG##1##2##). The 95% limits of agreement for these measurements were narrow, indicating a high level of agreement between the values obtained from manual and automated measurements. All measured parameters exhibited statistically significant and strong correlations.</p>", "<p id=\"Par9\">In subgroup analysis, both MRD1 and MRD2 consistently showed excellent agreement with ICC values of 0.9 or higher. On the other hand, the lengths of the upper and lower eyelids showed good agreement with ICC values of 0.747 and 0.772 in the normal control group and fair agreement with ICC values ranging from 0.553 to 0.650 in the ptosis and GO groups. The mean differences for MRD1 and MRD2 were 0.223 mm (range: 0.173–0.272) and 0.211 mm (range: 0.126–0.295), respectively, in the normal control group, 0.032 mm (range: − 0.018–0.082) and 0.251 mm (range: 0.173–0.330), respectively, in the ptosis group, and 0.388 mm (range: 0.320–0.455) and 0.351 mm (range: 0.284–0.417), respectively, in the GO group. These values were all less than 0.5 mm. The mean differences for the upper and lower eyelid lengths ranged from − 0.407 to 2.825 mm. The largest differences were observed in the GO group, with values of 2.633 mm and 2.825 mm, respectively (Supplementary Tables ##SUPPL##0##S1##–##SUPPL##0##S3##).</p>", "<p id=\"Par10\">By evaluating the verification performance based on 4, 8, 16, 24, 32, 64, and 128 partitions, we obtained the ratio of identified abnormal subjects (Fig. ##FIG##2##3##). The ratio of identified abnormal subjects could be interpreted as the sensitivity of the test given that the number of identified abnormal subjects represents the number of true positives, whereas the total number of abnormal subjects is equal to the sum of the number of true positives and false negatives. The specificity of this test is always 100% because there are no false positive cases. Experimental results showed a sensitivity value above 0.8 from 24 partitions (15-degree intervals). However, the slope decreased from 32 partitions, indicating that the conventional 24 partitions could provide a good balance between test simplicity and verification performance.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par11\">In our study, we developed an automated eyelid measurement system based on NNs to quantitatively measure eyelid parameters, such as MRD1 and MRD2. We confirmed the accuracy of our system by comparing the data with those obtained from manual measurement. Current image measurement programs require a segmentation process, which can be either manual or semi-automated. However, this process often leads to problems such as interobserver variability, reduced reproducibility, and time consumption. We compared the results of a conventional image measurement method and an automated measurement method. The results showed a high degree of consistency between the two methods. Furthermore, the automated measurement method took only a few seconds and required no operator intervention.</p>", "<p id=\"Par12\">Previous studies that performed deep learning-based image analysis of eyelid morphology have reported ICCs ranging from 0.934 to 0.971 for the MRDs of patients with ptosis^{##REF##34844503##14##}. For patients with GO, ICCs of 0.989 for MRD1 and 0.964 for MRD2 have been reported^{##REF##36915314##12##}. Our results also demonstrated that the proposed automated measurement system exhibited a high level of agreement with the manual measurement method for MRD1 and MRD2 in the overall group and individual subgroups (normal, ptosis, and GO), with ICC values exceeding 0.92. On the other hand, the agreement levels for both the length of the upper eyelid and the length of the lower eyelid were slightly lower (ranging from fair to good) compared with those for MRD1 or MRD2. This could possibly be attributed to the curvature of the eyelids. In our NN-based algorithm, pixels are linear; however, actual lengths have curves. Therefore, a slight error may have been introduced during the conversion process. In our study, we measure the lengths of both the upper and lower eyelids based on the pixel perimeter. However, using the pixel perimeter directly for length measurement may result in significant errors due to the square shape of a pixel; actual eyelids have a curved shape. Therefore, instead of using the pixel perimeter directly, we considered the quadrant perimeter to improve the accuracy of our measurements. This approach is important considering that relying solely on the pixel perimeter can result in significant differences in automated eyelid measurements compared with manual eyelid measurements. Moreover, an approach using three-dimensional reconstruction can improve the accuracy of length measurement by considering the curvature more precisely.</p>", "<p id=\"Par13\">Based on the mean measurements, we found that our program yielded slightly high values for MRD1, MRD2, upper eyelid length, and lower eyelid length compared with those obtained from manual measurements. Although the exact reason for this discrepancy remains uncertain, it may be caused by differences in measurement strategies. The length based on the line connecting the center of the neighboring pixel was shorter than the length based on our approach using quadrants. Additionally, the agreement between the automated and manual measurements was higher in the normal group but lower in the ptosis or GO group. A possible explanation for this observation is the difficulty of performing accurate measurements for subjects with ptosis or GO. Patients with ptosis or GO have eyelid margins that are more uneven and curved than those of normal patients. These characteristics make it difficult to obtain accurate measurements.</p>", "<p id=\"Par14\">In contrast to MPLD measurements performed in previous studies to assess the shape of curved eyelids^{##REF##25933190##5##,##REF##28011464##16##,##REF##25357046##17##}, we measured the distance from the midpoint of the intercanthal line to the eyelid margin. Our rationale for this method is twofold. First, when subjects do not maintain primary gaze, the pupil light reflex may not align with the center, potentially compromising the objectivity of the results. Second, when assessing the eyelid shape exclusively, measuring from the midpoint of the intercanthal line has important implications. As NNs can clearly define the two points on each canthus that form the intercanthal line, the intercanthal line would be more easily and objectively established as the reference line. This line is expected to yield more consistent values compared with those obtained using the horizontal midpupillary line. However, with this approach, the intercanthal line often does not form a straight line, with the lateral canthus typically positioned slightly higher, resulting in an inclined line. To address this, we rotated the inclined intercanthal line to make it aligned horizontally using simple mathematics. Furthermore, when using this approach for measurements, the distances from the pupil, MRD1, and MRD2, are not included.</p>", "<p id=\"Par15\">The conventional approach of dividing the eyelids (360 degrees) into 15-degree intervals (24 partitions) has been used to characterize the entire eyelid contour; however, the exact rationale has not been provided^{##REF##22197435##3##}. In order to achieve precise evaluation, this study aimed to determine the most accurate eyelid segmentation approach for detecting abnormalities in the eyelids. The minimum number of divisions was determined to be 24 partitions, which is consistent with the traditional method using 15-degree intervals. This number may be considered the most appropriate for evaluating abnormal eyelid shapes in our study.</p>", "<p id=\"Par16\">Our study has several limitations. First, the sample size consisted of only 300 subjects. Moreover, the selection process was not completely random. Ideally, it would be beneficial to include a wide range of diseases and a larger sample size of subjects. A random selection from a larger pool, which would reflect the overall distribution of diseases, could yield more informative results. Another limitation is that length measurement was based on the corneal light reflex due to camera flash, which is not applicable when the MRD1 value is negative. Additional research is needed to automatically and accurately estimate the location of the pupil center, which can serve as a reference instead of relying on the light reflex.</p>", "<p id=\"Par17\">In conclusion, we proposed an automated NN-based measurement system that could provide a straightforward and precise method for measuring MRD1 and MRD2, as well as detecting morphological abnormalities in the eyelids. Similar to MPLD measurement, measuring the distance from the midpoint of the intercanthal line to the eyelid margin was also useful in evaluating the shape of curved eyelids. Furthermore, eyelid segmentation showed that the meaningful detection of abnormalities could be achieved with 24 partitions. This novel system may be used to provide comprehensive information to detect eyelid abnormalities by adopting it for other eyelid-related diseases during automated measurements. Our developed system could be implemented in portable devices such as cameras or smartphones for potential clinical use. Alternatively, it could be integrated into existing medical devices or used as a standalone application for wider accessibility. Further studies will be needed for clinical applications in the future.</p>" ]

[]

[ "<p id=\"Par1\">The purpose of this study was to assess the clinical utility and reliability of an automated eyelid measurement system utilizing neural network (NN) technology. Digital images of the eyelids were taken from a total of 300 subjects, comprising 100 patients with Graves’ orbitopathy (GO), 100 patients with ptosis, and 100 controls. An automated measurement system based on NNs was developed to measure margin–reflex distance 1 and 2 (MRD1 and MRD2), as well as the lengths of the upper and lower eyelids. The results were then compared with values measured using the manual technique. Automated measurements of MRD1, MRD2, upper eyelid length, and lower eyelid length yielded values of 3.2 ± 1.7 mm, 6.0 ± 1.4 mm, 32.9 ± 6.1 mm, and 29.0 ± 5.6 mm, respectively, showing a high level of agreement with manual measurements. To evaluate the morphometry of curved eyelids, the distance from the midpoint of the intercanthal line to the eyelid margin was measured. The minimum number of divisions for detecting eyelid abnormalities was determined to be 24 partitions (15-degree intervals). In conclusion, an automated NN-based measurement system could provide a straightforward and precise method for measuring MRD1 and MRD2, as well as detecting morphological abnormalities in the eyelids.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51838-6.</p>", "<title>Acknowledgements</title>", "<p>This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2021R1A2C1011351) and Institute of Information &amp; Communications Technology Planning &amp; Evaluation (IITP) grant funded by the Korean government (MSIT) (2021-0-01341, Artificial Intelligence Graduate School Program (Chung-Ang University)). The funding organization had no role in the design or conduct of this research. The authors would like to thank Subin Jang for statistical analysis.</p>", "<title>Author contributions</title>", "<p>J.L. and J.K.L. designed the project, devised the main conceptual ideas, and analyzed the data. T.S. collected the data and developed the algorithm. Y.N. wrote the manuscript. J.K.L. revised the manuscript.</p>", "<title>Data availability</title>", "<p>Datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par28\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Correlation between the proposed automated measurement system and manual technique. (<bold>a</bold>) MRD1, (<bold>b</bold>) MRD2, (<bold>c</bold>) upper eyelid length (<bold>d</bold>) lower eyelid length.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Bland Altman plots comparing the proposed automated measurement system and manual technique. MD, mean difference; LOA, limit of agreement.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Experimental results evaluating the verification performance based on 4, 8, 16, 24, 32, 64, 128, and 256 partitions.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Eyelid segmentation.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Eyelid segmentation. (<bold>a</bold>) 4 partitions (90.0-degree intervals), (<bold>b</bold>) 16 partitions (22.5-degree intervals), (<bold>c</bold>) 24 partitions (15.0-degree intervals), and (<bold>d</bold>) 32 partitions (11.3-degree intervals).</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Characteristics of subjects.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Variables</th><th align=\"left\">Total</th><th align=\"left\">Normal</th><th align=\"left\">Ptosis</th><th align=\"left\">Graves’ orbitopathy</th><th align=\"left\" rowspan=\"2\"><italic>p</italic>-value</th></tr><tr><th align=\"left\">(N = 300)</th><th align=\"left\">(N = 100)</th><th align=\"left\">(N = 100)</th><th align=\"left\">(N = 100)</th></tr></thead><tbody><tr><td align=\"left\">Age (years)</td><td align=\"left\">50.5 ± 18.6</td><td align=\"left\">50 ± 19.3</td><td align=\"left\">63.9 ± 13.3</td><td align=\"left\">37.6 ± 12.1</td><td align=\"left\"> &lt; 0.001*</td></tr><tr><td align=\"left\">Sex</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"> &lt; 0.001**</td></tr><tr><td align=\"left\"> Male, n (%)</td><td align=\"left\">96 (32.0%)</td><td align=\"left\">44 (44.0%)</td><td align=\"left\">34 (34.0%)</td><td align=\"left\">18 (18.0%)</td><td align=\"left\"/></tr><tr><td align=\"left\"> Female, n (%)</td><td align=\"left\">204 (68.0%)</td><td align=\"left\">56 (56.0%)</td><td align=\"left\">66 (66.0%)</td><td align=\"left\">82 (82.0%)</td><td align=\"left\"/></tr><tr><td align=\"left\">MRD1 (mm)^#</td><td align=\"left\">3.0 ± 1.5</td><td align=\"left\">3.1 ± 0.8</td><td align=\"left\">1.4 ± 0.6</td><td align=\"left\">4.4 ± 1.3</td><td align=\"left\"> &lt; 0.001*</td></tr><tr><td align=\"left\">MRD2 (mm)^#</td><td align=\"left\">5.8 ± 1.3</td><td align=\"left\">5.8 ± 1.1</td><td align=\"left\">5.1 ± 1.2</td><td align=\"left\">6.4 ± 1.2</td><td align=\"left\"> &lt; 0.001*</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Comparison of neural network-based and manual measurements of eyelids.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Variables</th><th align=\"left\">Neural network (N = 300)</th><th align=\"left\">Manual (N = 300)</th><th align=\"left\"><italic>p</italic>-value</th></tr></thead><tbody><tr><td align=\"left\">MRD1</td><td char=\".\" align=\"char\">3.2 ± 1.7</td><td char=\".\" align=\"char\">3.0 ± 1.5</td><td align=\"left\"> &lt; 0.001*</td></tr><tr><td align=\"left\">MRD2</td><td char=\".\" align=\"char\">6.0 ± 1.4</td><td char=\".\" align=\"char\">5.8 ± 1.3</td><td align=\"left\"> &lt; 0.001**</td></tr><tr><td align=\"left\">Upper eyelid length</td><td char=\".\" align=\"char\">32.9 ± 6.1</td><td char=\".\" align=\"char\">31.5 ± 4.2</td><td align=\"left\"> &lt; 0.001*</td></tr><tr><td align=\"left\">Lower eyelid length</td><td char=\".\" align=\"char\">29.0 ± 5.6</td><td char=\".\" align=\"char\">28.4 ± 3.4</td><td align=\"left\">0.005**</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p>MRD1, margin–reflex distance 1; MRD2, margin–reflex distance 2.</p><p>*ANOVA, pairwise t-test.</p><p>**chi-square test.</p><p>^#measured by ImageJ.</p></table-wrap-foot>", "<table-wrap-foot><p>MRD1, margin–reflex distance 1; MRD2, margin–reflex distance 2.</p><p>* Wilcoxon rank-sum test.</p><p>**Paired t-test.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41598_2024_51838_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"41598_2024_51838_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"41598_2024_51838_Fig3_HTML\" id=\"MO3\"/>", "<graphic xlink:href=\"41598_2024_51838_Fig4_HTML\" id=\"MO4\"/>", "<graphic xlink:href=\"41598_2024_51838_Fig5_HTML\" id=\"MO5\"/>" ]

[ "<media xlink:href=\"41598_2024_51838_MOESM1_ESM.pdf\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Unmanned Aerial Vehicles (UAVs) are widely used in a variety of scenarios due to their abilities of high flexibility, high productivity, ease of maneuverability, and adapting to hazardous environments. The increasing complexity of flight environments requires UAVs to have the ability to interact with highly dynamic and strongly real-time space operating environments, which put forward new demands for UAVs’ autonomy and safety. UAVs detect and determine whether there is a potential conflict in the future period through the sensors so that they can maintain a certain safe distance from the dynamic/static obstacles in the airspace, and thus plan an ideal flight path from the starting point to the target point and avoid conflicts.</p>", "<p id=\"Par3\">Unlike civil aircraft, UAVs usually perform tasks in lower airspace. There are many static obstacles in lower airspace such as buildings, trees, and dynamic aircraft. Flight conflict is a state when the distance between two aircraft in the direction of horizontal, longitudinal, or vertical is less than a specific interval resulting in the aircraft being at risk^{##UREF##0##1##}. UAVs are required to have autonomous environment sensing, collision threat estimation, avoidance path planning, and maneuver control. These abilities are referred to as Sense And Avoid (SAA). Airspace environment sensing in UAV SAA refers to the detection and acquisition of various static/moving, cooperative/non-cooperative targets in the flying space, based on the onboard sensors or data links carried by the UAV, and evaluating the environmental situation and the degree of collision threat^{##UREF##1##2##}. As shown in Fig. ##FIG##0##1##, SAA is an important safety guarantee for future UAV airspace integration applications and is also an important sign of autonomy and intelligence of UAVs^{##UREF##2##3##}.</p>", "<p id=\"Par4\">For UAVs, the ability of SAA is extremely important. The ability of path planning in the avoidance function of UAVs is an important foundation for the basis for them to complete the flight task. Complex flight environments put forward higher demands for path planning algorithms of UAVs, thus the research in autonomous obstacle avoidance path planning algorithms for UAVs is necessary.</p>", "<p id=\"Par5\">It has to find the optimal flight path from the initial location to the target location under the constraints of environmental factors such as terrain, weather, threats, and flight performance of autonomous path planning for UAVs. Significantly, the optimal path does not always mean the shortest path or a straight line between two locations; instead, the UAV aims to find a safe path under limited power and flight task. There are a lot of UAV path planning algorithms, such as the Voronoi diagram algorithm, Rapidly-exploring Random Tree (RRT) algorithm, A* algorithm, etc. However, these algorithms cannot deal with dynamic environments effectively because they require global environmental information to calculate the optimal result. Once the environment changes, the original results will fail. Furthermore, the process of recalculating the optimal results is too slow for real-time operations because of the large number of calculations required. The above algorithms may still be effective if the obstacle is moving slowly. But when moving faster, the movement of the surrounding vehicles may cannot be predicted thus result in a collision. These shortcomings limit the application of the above algorithms to UAVs in real, dynamic environments.</p>", "<p id=\"Par6\">To address these shortcomings, reinforcement learning algorithms are applied to the path planning process. Reinforcement learning (RL) is a branch of machine learning. UAVs can learn through continuous interaction with the environment, using training and learning to master the environment gradually, and optimize the state-behavior continuously to obtain the optimal strategy through the feedback (rewards) given by the environment, which is closer to the human learning process.</p>", "<p id=\"Par7\">Compared with traditional algorithms, RL performs better when the environment is unknown and dynamic. Moreover, the inference speed and generalization of RL have advantages in real-time decision-making tasks. Therefore, the path planning algorithm based on RL has certain advantages in solving the UAV path planning problem in unknown and dynamic environments.</p>", "<p id=\"Par8\">This paper considers the real-time and location limitation characteristics of path planning and refers to the existing research on UAV path planning problems and collision avoidance strategies for various stationary/motion threats. An autonomous collision-free path planning algorithm for UAVs in unknown complex 3D environments (APPA-3D) is proposed. Thus, UAVs can perform tasks with APPA-3D more safely and efficiently in complex flight environments. Firstly, the UAV spherical safety envelope is designed to research the anti-collision avoidance strategy, which will be used as an action plan for UAVs to realize dynamic obstacle avoidance. Secondly, we assume that the environment model when path planning is unknown, so the UAV needs to have the ability to learn and adjust flight state intelligently according to its surroundings. In this paper, the traditional model-free RL algorithm is improved to reduce the complexity of the algorithm and adapt to the demands of UAV path planning in an unknown complex 3D environment. It takes into account the search efficiency while guaranteeing the optimal search path.</p>", "<p id=\"Par9\">Compared with the existing research, the innovative work of this paper mainly manifests in the following several aspects:</p>", "<p id=\"Par10\">Based on the UAV environment sensing capability, a collision safety envelope is designed, and the anti-collision control strategy is studied concerning the Near Mid Air Collision (NMAC) rules for civil airliners and the International Regulations for Preventing Collisions at Sea (COLREGS). It provides a theoretical basis for UAVs to carry out collision detection and avoidance schemes, which can detect and avoid dynamic threats effectively in the flight environment.</p>", "<p id=\"Par11\">To address the difficulty of convergence of traditional algorithms in solving 3D path planning. The artificial potential field method (APF) is used to optimize the mechanism of reward function generation in RL. The optimized algorithm can output the dynamic reward function by combining the actual flight environment information. Thus, the problems of path planning convergence difficulty, unreachable target point and model stop learning in high dimensional space caused by sparse reward function are solved.</p>", "<p id=\"Par12\">Aiming at the \"exploration-exploitation dilemma\" of RL in the path planning process of UAVs, an RL action exploration strategy based on action selection probability is proposed. The strategy dynamically adjusts the action selection strategy by combining the size of the value function in different states, thus solving the RL exploration-exploitation problem and improving the efficiency of path search.</p>", "<p id=\"Par13\">The rest of the paper is organized as follows: Section \"<xref rid=\"Sec2\" ref-type=\"sec\">Related research on UAV path planning</xref>\" introduces the research status of UAV path planning; an anti-collision control strategy for UAVs is designed in Section \"<xref rid=\"Sec3\" ref-type=\"sec\">UAV anti-collision control strategy</xref>\"; an Autonomous collision-free path planning algorithm is proposed in Section \"<xref rid=\"Sec6\" ref-type=\"sec\">Design of autonomous collision-free path planning algorithm for UAVs</xref>\"; simulation experiment design and result analysis are presented in Section \"<xref rid=\"Sec10\" ref-type=\"sec\">Experiment and results</xref>\"; the paper is summarized in Section \"<xref rid=\"Sec14\" ref-type=\"sec\">Conclusion</xref>\".</p>" ]

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[ "<title>Experiment and results</title>", "<p id=\"Par75\">To verify the feasibility of an autonomous path planning algorithm in complex 3D environments (APPA-3D) for UAVs, this paper selects real environment maps to conduct simulation experiments. The UAV's range of action is limited to the map, and if the UAV moves outside the range of the map or above the low altitude limit altitude, it is determined that a collision has occurred. The starting point for UAV path planning is represented by a black dot, and the target point is represented by a red dot. The maximum flight altitude is 1 km above the peak line, and the no-fly zone is indicated by a green cylinder. The UAV needs to avoid mountains and no-fly zones to fly from the starting point to the target point.</p>", "<title>UAV anti-collision avoidance strategies experiments</title>", "<p id=\"Par76\">The anti-collision avoidance strategies experiments were designed to verify whether APPA-3D can achieve anti-collision avoidance strategies while implementing path planning. Figures ##FIG##7##7##, ##FIG##8##8## and ##FIG##9##9## are simulation experimental diagrams of anti-collision avoidance strategies for UAVs.</p>", "<p id=\"Par77\">As shown in Fig. ##FIG##7##7##, in the opposing conflict avoidance simulation, the intrusion direction of the dynamic obstacle is set to be directly opposite the movement direction of the UAV. When a dynamic obstacle is detected, the UAV chooses to turn right to avoid the dynamic obstacle according to the anti-collision avoidance strategy. The reward function is recalculated after finishing the anti-collision avoidance strategy and guiding the UAV to continue flying toward the target point.</p>", "<p id=\"Par78\">As shown in Fig. ##FIG##8##8##, in the cross-conflict avoidance simulation, dynamic obstacles invade from the left and right sides of the UAV's flight direction. According to the anti-collision avoidance strategy, when the UAV detects a dynamic obstacle and chooses to pass behind the moving direction of the dynamic obstacle, it can ensure that the UAV and the dynamic obstacle are avoided successfully and the avoidance path is the shortest. The reward function is recalculated after finishing the anti-collision avoidance strategy and guiding the UAV to continue flying toward the target point.</p>", "<p id=\"Par79\">As shown in Fig. ##FIG##9##9##, in the pursuit conflict avoidance simulation, the flight direction of the dynamic obstacle is the same as the UAV flight direction. Referring to the anti-collision avoidance strategy, when the UAV detects a dynamic obstacle, the UAV chooses to complete the overtake from the right side of the dynamic obstacle's direction of motion, which ensures that the UAV can successfully overtake the dynamic obstacle with the shortest overtake avoidance path; The reward function is recalculated after finishing anti-collision avoidance strategy and guiding the UAV to continue flying towards the target point.</p>", "<title>Multi-obstacle path planning and collision avoidance verification</title>", "<p id=\"Par80\">To verify the performance of the APPA-3D, this paper randomly generates 3, 6, and 10 different moving and static obstacles in the same simulation environment and conducts three sets of randomized experiments each. The 3D view of APPA-3D is exhibited in this paper, as shown in Fig. ##FIG##10##10##.</p>", "<p id=\"Par81\">The 3D view of the paths planned by APPA-3D shows that the flight paths of the UAVs are feasible in nine different scenarios. The distance between the UAV and the obstacle is well-maintained in complex terrain. This further demonstrates that APPA-3D can help the UAV to plan a path that is both short and safe at the same time.</p>", "<p id=\"Par82\">This paper calculates four parameters: UAV path planning time, planned path length, number of planned path points, and planned path ground projection length in 9 scenarios, the average values of the four parameters are shown in Table ##TAB##0##1##.</p>", "<title>Comparative experiments</title>", "<p id=\"Par83\">To verify the enhancement effect of the adaptive reward function and the new action selection strategy proposed in this paper, two sets of ablation experiments were conducted firstly before conducting the comparison experiments.</p>", "<p id=\"Par84\">The first set of ablation experiments is to verify the enhancement effect of the new adaptive reward function proposed in this paper, and the experimental results are shown in Fig. ##FIG##11##11##:</p>", "<p id=\"Par85\">The yellow path in Fig. ##FIG##11##11## represents the UAV flight path under the sparse reward function, and the blue path represents the flight path under the adaptive reward function proposed in this paper. Figure ##FIG##11##11## clearly shows that the performance of UAV path planning based on sparse reward function is poor in complex 3D environments. This is because under sparse reward function, it can only obtain positive and negative reward when reaching the target point or colliding with obstacles, and other actions will not get any positive or negative feedback. So the UAV is random flight blindly, unable to find the correct flight direction in this way. Compared with the sparse reward function, the adaptive reward function we proposed combines the good performance of APF to make the reward accumulation process smoother and can also reflect the relationship between the current state and the target state of the UAV.</p>", "<p id=\"Par86\">To verify the improvement effect of the new action selection strategy proposed in this paper, the second set of ablation experiments was set up. The experiments were analyzed using the strategy, Softmax distribution strategy, and the new action selection strategy. All RL algorithms adopt Q-learning algorithm, which excludes the influence of learning algorithm on different exploration strategies.</p>", "<p id=\"Par87\">Tables ##TAB##1##2## and ##TAB##2##3## show the results of three exploration strategies. To prevent the impact of single data on the experiment, the data in Tables ##TAB##1##2## and ##TAB##2##3## is the average value obtained after 5 experiments.</p>", "<p id=\"Par88\">The experimental results show that after a period of exploration, three different exploration strategies are able to guide the UAV to the target point. Compared with the other two exploration strategies, the action selection probability we proposed is more advantageous in terms of path planning time and number of path planning points.</p>", "<p id=\"Par89\">To evaluate whether the APPA-3D proposed in this paper has significant advantages over other classical or RL based algorithms, two sets of experiments were utilized to test the ability of the six methods to solve path planning problems under the same conditions. According to the characteristics of algorithms, they can be divided into two categories: classic algorithms (APF, RRT, and A*) and QL-based algorithms (DFQL, IQL, and MEAEO-RL). It should be noted that, to prevent the impact of single data on the experiment, the data in Table ##TAB##3##4##, ##TAB##4##5##, ##TAB##5##6## and ##TAB##6##7## is the average value obtained after 5 experiments.</p>", "<p id=\"Par90\">The experimental results of the first group are displayed in Fig. ##FIG##12##12## and Tables ##TAB##3##4## and ##TAB##4##5##:</p>", "<p id=\"Par91\">It can be seen from Fig. ##FIG##12##12## that the three classic algorithms perform better than APPA-3D algorithm in the front part of the path. However, the performance of classic algorithms is poor in the latter part of the path, which is caused by their algorithm characteristics. Because sampling-based and search-based characteristics of algorithms respectively, it is hard to generate smooth and optimal paths with RRT and A*. Although the path planning time of A* is short, the UAV collided with obstacles unfortunately. The reason for the poor effect of APF is that the obstacle surrounds the destination, and the repulsive force field of the obstacle directly acts on the agent, making it unable to approach the obstacle. The agent can only move in the direction where the gravitational force is greater than the repulsive force.</p>", "<p id=\"Par92\">The results of the second group of experiments are displayed in Fig. ##FIG##13##13##. It is worth mentioning that DFQL, IQL, MEAEO-R, and APPA-3D are all optimized based on traditional RL algorithms. The simulation results are shown in Fig. ##FIG##13##13##, Table ##TAB##5##6## and Table ##TAB##6##7##.</p>", "<p id=\"Par93\">Experimental results clearly show that APPA-3D can reach the destination with the shortest distance and time. In the initial phase of path planning, APPA-3D is not very different from other algorithms, and all four algorithms can help the UAV plan a relatively high-quality flight path quickly. While in the middle and later stages of path planning, the differences between APPA-3D and the other three compared algorithms can be seen clearly, especially when facing multi-dynamic obstacles. Because RL algorithm assigns a probability to each possible action and selects the action based on these probabilities, path planning algorithms based on RL often fall into the dilemma of exploration–exploitation when facing complex environments.</p>", "<p id=\"Par94\">To solve this problem, the APPA-3D algorithm proposes a new action selection strategy. This strategy solves the balance problem between exploration and exploitation by introducing the concept of <italic>action selection probability</italic> and making action preference selection accordingly.</p>", "<p id=\"Par95\">The Fig. ##FIG##14##14## presents the loss function used to observe the convergence behavior over iterations of all algorithms. It can be seen that after about 130 iterations, the loss function begins to stabilize. The rapid convergence of value loss also shows that the APPA-3D is more accurate, which is a good performance and means that the agents won’t fall into a local optimum. The algorithms compared requires more iteration to complete convergence. This is because they use strategy or Softmax distribution strategy as an action exploration strategy of reinforcement learning. And their performance is consistent with the results of the second set of ablation experiments.</p>", "<p id=\"Par96\">In conclusion, APPA-3D is far better than the compared algorithms in the 3D UAV path planning optimization problem. This is because APPA-3D dynamically adjusts the action selection strategy by combining the size of the value function in different states, thus solving the problem of exploration-utilization of RL and improving the efficiency of path search.</p>" ]

[]

[ "<title>Conclusion</title>", "<p id=\"Par97\">The path planning problem in unknown environments is the focus of UAV task planning research and the key to achieving autonomous flight. Therefore, UAVs need to have the ability to autonomous path planning and avoid potential obstacles. In this paper, an autonomous collision-free path planning algorithm for unknown complex 3D environments is proposed. Firstly, based on the environment sensing capability, a UAV collision safety envelope is designed, and the anti-collision control strategy is investigated, which can effectively deal with the collision problem triggered by dynamic obstacles in the flight environment. Secondly, this paper optimizes the traditional RL algorithm. On the one hand, the reward function for RL is optimized by transforming the relationship between the current state of the UAV and the task into a suitable dynamic reward function. The presence of a dynamic reward function allows the UAV to fly toward the target point without getting too close to the obstacles. On the other hand, an RL action exploration strategy based on action selection probability is proposed. The strategy dynamically adjusts the action selection strategy by combining the size of the value function in different states, thus solving the RL exploration-utilization problem and improving the efficiency of path search. To verify the effectiveness of the designed APPA-3D algorithm in the dynamic collision avoidance model, three typical collision experiments were set up, including flight path opposing collision, pursuit collision, and cross collision. The experimental results verify that the APPA-3D can effectively avoid safety threats that may be caused by dynamic obstacles in complex environments according to the designed anti-collision control strategy. Meanwhile, the results of the algorithm testing experiments in nine different scenarios verified that the algorithm still performs well in the face of random and complex flight environments.</p>", "<p id=\"Par98\">APPA-3D demonstrates better performance in path planning performance comparison tests with other classical and novel optimized RL algorithms. The advantages in path planning length and convergence curves again show that APPA-3D can effectively help UAVs solve the path planning problem.</p>" ]

[ "<p id=\"Par1\">Due to their high flexibility, low cost, and ease of handling, Unmanned Aerial Vehicles (UAVs) are often used to perform difficult tasks in complex environments. Stable and reliable path planning capability is the fundamental demand for UAVs to accomplish their flight tasks. Most researches on UAV path planning are carried out under the premise of known environmental information, and it is difficult to safely reach the target position in the face of unknown environment. Thus, an autonomous collision-free path planning algorithm for UAVs in unknown complex environments (APPA-3D) is proposed. An anti-collision control strategy is designed using the UAV collision safety envelope, which relies on the UAV's environmental awareness capability to continuously interact with external environmental information. A dynamic reward function of reinforcement learning combined with the actual flight environment is designed and an optimized reinforcement learning action exploration strategy based on the action selection probability is proposed. Then, an improved RL algorithm is used to simulate the UAV flight process in unknown environment, and the algorithm is trained by interacting with the environment, which finally realizes autonomous collision-free path planning for UAVs. The comparative experimental results in the same environment show that APPA-3D can effectively guide the UAV to plan a safe and collision-free path from the starting point to the target point in an unknown complex 3D environment.</p>", "<title>Subject terms</title>" ]

[ "<title>Related research on UAV path planning</title>", "<p id=\"Par14\">Autonomous mobile robots (AMRs) has attracted more and more attention due to their practicality and potential uses in the modern world^{##UREF##3##4##}. AMRs is widely used in different fields, such as agricultural production^{##UREF##4##5##,##UREF##5##6##}, unmanned underwater vehicles (AUVs)^{##UREF##6##7##,##UREF##7##8##}, automated guided vehicles (AGVs)^{##UREF##8##9##}, autonomous cleaning robots^{##UREF##9##10##}, industrial robots^{##UREF##10##11##,##UREF##11##12##}, etc. The similarity of the above studies is that they are all need 3D path planning algorithms. Path planning is one of the most important tasks in AMR navigation since it demands the robot to identify the best route based on desired performance criteria such as safety margin, shortest time, and energy consumption. As an important part of AMRs, with the popularization of consumer-grade UAVs, the research on path planning of UAVs has become a hot topic.</p>", "<p id=\"Par15\">UAV path planning refers to the formulation of the optimal flight path from the initial location to the target location, considering environmental factors such as terrain, meteorology, threats, and their flight performance constraints The aim is to improve the reliability and safety of UAVs while ensuring the efficiency of their task execution.</p>", "<p id=\"Par16\">A lot of research has been done on the UAV path planning problem. Sampling-based path planning algorithms are widely used in UAV path planning due to their simplicity, intuitiveness, and ease of implementation. A simple sampling-based path planning algorithm is the Voronoi diagram algorithm^{##UREF##12##13##}. The Voronoi diagram algorithm transforms the complex problem of searching for a trajectory in a spatial region into a simple search problem with a weighted diagram. However, the Voronoi diagram algorithm is only suitable for solving 2D path planning problems. 2D path planning divides the flight environment into passable and impassable areas through \"rasterization\" processing, and then route planning is performed on the processed map. The algorithm is easy to implement and is more intuitive and feasible, but it is difficult to consider terrain following, terrain avoidance, and threat avoidance simultaneously. Therefore, it is necessary to consider the real sense of 3D route planning with real-time and effective requirements to solve the UAV path planning problem in real scenarios. Another intuitive algorithm is the Rapidly exploring Random Tree (RRT)^{##UREF##13##14##}. RRT can quickly and efficiently search in the smallest possible space, avoiding the need to model the space, and can effectively solve motion planning problems with high-dimensional spaces and complex constraints. However, it is less repeatable and the planned paths are often far from the shortest path.</p>", "<p id=\"Par17\">In node-based path planning algorithms, Dijkstra's algorithm searches for the shortest path by cyclic traversal^{##UREF##14##15##}, However, as the complexity of the flight map increases and the number of nodes increases, Dijkstra's algorithm suffers from too low execution efficiency. Reference^{##UREF##15##16##} designed the solution model of the \"Dijkstra -based route planning method\", which simplifies the search path, reduces the calculation amount, and improves the execution efficiency through the optimization of correction strategies, correction schemes, and O-D Adjacency matrix processing methods, thereby improving the traditional Dijkstra algorithm. The A* algorithm is a classical and commonly used heuristic search algorithm^{##UREF##16##17##}. The A* algorithm guides the search through heuristic information to achieve the purpose of reducing the search range and improving the computational speed and can obtain real-time feasible paths. The A* algorithm is well-established in the field of path search in 2D environments^{##UREF##17##18##}. If it is directly applied to a 3D environment, the problem of exponential rise in computing data and increase in computing time, which leads to slow search efficiency, needs to be improved. Reference^{##UREF##18##19##} proposes a model-constrained A * -based three-dimensional trajectory planning for unmanned aerial vehicles. By optimizing the cost function of the traditional A * and selecting extension nodes by controlling the value of the coefficient, the search efficiency of the algorithm is improved. Reference^{##UREF##19##20##} proposes a model-constrained A * -based three-dimensional trajectory planning for unmanned aerial vehicles. By optimizing the cost function of the traditional A * and selecting extension nodes by controlling the value of the coefficient, the search efficiency of the is improved.</p>", "<p id=\"Par18\">Computational intelligence (CI) algorithms can provide solutions to NP-hard problems with many variables. CI algorithms are a group of nature-inspired methods, which have been raised as a solution for these problems. They can address complex real-world scenarios that algorithms. Genetic Algorithm (GA)^{##UREF##20##21##} is an adaptive global optimization probabilistic search algorithm developed by simulating the genetic and evolutionary processes of organisms in the natural environment. However, the GA algorithm is time-consuming and generally not suitable for real-time planning. Reference^{##UREF##21##22##} proposes an improved adaptive GA that adaptively adjusts the probabilities of crossover and genetic operators in a nonlinear manner, enabling the generation of more optimal individuals during the evolution process and obtaining the global optimal solution. Simulation results show that the improved adaptive GA enhances the local search capability of the genetic algorithm, improves the planning efficiency, and can accomplish the UAV path planning task. Particle Swarm Optimization (PSO)^{##UREF##22##23##} is an evolutionary computational method based on group intelligence. The biggest advantage of PSO is its simplicity, fast operation speed, and short convergence time. However, in the face of high-dimensional complex problems, PSOs often encounter the drawbacks of premature convergence and poor convergence performance, which cannot guarantee convergence to the optimal point. In recent years, the grey wolf optimization (GWO) algorithm has been widely used in various fields^{##UREF##23##24##}. The while optimizer (WOA)^{##UREF##24##25##} is a GWO-based method because of the success of GWO. Reference^{##REF##37123920##26##} proposes a parallel PSO and enhanced sparrow search algorithm (ESSA) for unmanned aerial vehicle path planning. In the ESSA, the random jump of the producer’s position is strengthened to guarantee the global search ability. Ni and Wu et al.^{##REF##28255297##27##} proposes an improved dynamic bioinspired neural network (BINN) to solve the AUV real-time path planning problem. A virtual target is proposed in the path planning method to ensure that the AUV can move to the real target effectively and avoid big-size obstacles automatically. Furthermore, a target attractor concept is introduced to improve the computing efficiency of neural activities. Ni and Yang^{##UREF##25##28##} studied the heterogeneous AUV cooperative hunting problem and proposed a novel spinal neural system-based approach. The presented algorithms not only accomplishes the search task but also maintains a stable formation without obstacle collisions. These methods provide some new ideas for the study of UAV path planning in this paper.</p>", "<p id=\"Par19\">Real-time and autonomy in complex flight environments are important indicators for measuring different path-planning algorithms. In the above algorithms, the sampling-based path planning algorithms reduce the traversal search space by sampling, sacrificing the optimality of paths in exchange for a shorter computation time. As the size of the environment increases, the number of operation iterations increases dramatically, making it difficult to achieve simultaneous optimization accuracy and optimal paths in 3D complex environments. Node-based path planning algorithms can obtain the optimal path between the start and endpoints. However, as the environment expands, the dimensionality increases and the number of search nodes increases, the computational size of these algorithms will increase dramatically. Intelligent biomimetic algorithms optimize paths in a mutation-like manner, which can better handle unstructured constraints in complex scenarios. However, its variational solving process requires a long iteration period and cannot be adapted to path planning in dynamic environments^{##UREF##26##29##}.</p>", "<p id=\"Par20\">In response to the limitations of the traditional algorithms mentioned above, a new feasible solution is to update the distance information between the UAVs and the obstacles and target points in real-time and feed it back to the UAV, as well as to make real-time adjustments to its flight status and maneuvers^{##UREF##27##30##}. Reinforcement learning (RL)is a branch of machine learning. The UAVs and the flight environment are modeled using Markov Decision Process (MDP), then the UAV chooses the optimal action to maximize the cumulative reward^{##UREF##28##31##}. UAVs can learn through continuous interaction with the environment, using training and learning to help UAVs gradually master the environment, and continuously optimize the state-behavior to obtain the optimal strategy through the feedback (rewards) given by the environment, which is closer to the human learning process.</p>", "<p id=\"Par21\">In the face of the problem that the environment model is unknown and the transfer probability and value function are difficult to determine, the RL algorithm of interactive learning with the environment to obtain the optimal strategy needs to be a model-free RL algorithm. The Q-Learning (QL) algorithm is one of the most commonly used model-free RL algorithms and has been widely applied to solve path-planning problems. Reference^{##UREF##29##32##} proposes a Dynamic Fast Q-Learning (DFQL) algorithm to solve the path planning problem of USV in partially known marine environments, DFQL algorithm combines Q-Learning with an Artificial Potential Field (APF) to initialize the Q-table and provides USV with a priori knowledge from the environment. Reference^{##UREF##30##33##} introduces an Improved Q-Learning (IQL) with three modifications. First, add a distance metric to QL to guide the agent toward the target. Second, modify the Q function of QL to overcome dead ends more effectively. Finally, introduce the concept of virtual goal in QL to bypass the dead end. Reference^{##UREF##31##34##} proposed a multi-strategy Cuckoo search based on RL. Reference^{##UREF##32##35##} uses potential field information to simply initialize the Q-value table, giving it certain basic guidance for the target point. Reference^{##UREF##33##36##} proposes a QL algorithm based on neural networks, which uses Radial Basis Function (RBF) networks to approximate the action value function of the QL algorithm.</p>", "<p id=\"Par22\">All in all, RL takes rewards from exploring the environment as training data by imitating the learning process of human beings and trains itself without requiring preset training data. The path planning algorithm of UAV based on RL senses the state information of obstacles in the environment continuously and inputs the information into the algorithm, The optimal collision-free path can be obtained by adjusting the flight state of the UAV through RL, which can solve the problems of poor real-time and long planning time of traditional trajectory planning.</p>", "<p id=\"Par23\">However, in practice, due to the complexity of the flight environment, the traditional RL algorithms do not run well in complex scenarios. More concretely, the memory size of a Q-table increases exponentially as the dimensionality of the state space or action space associated with the environment increases^{##UREF##34##37##}; The slow convergence caused by dimension explosion will lead to disastrous consequences in path planning, thus limiting the performance of RL in practice; The sparse reward function of the traditional RL algorithm will lead to algorithm convergence difficulties, resulting in the model stops learning and cannot improve; The algorithm faces the \"exploration–exploitation dilemma\" because it needs to consider both exploration and exploitation in action selection^{##UREF##35##38##}. Therefore, the RL algorithm needs to be improved and optimized before it is used to solve the UAV path planning problem.</p>", "<title>UAV anti-collision control strategy</title>", "<title>UAV spherical safety envelope</title>", "<p id=\"Par24\">UAVs are unable to obtain complete priori information about the environment during the flight, and can only obtain the information within a certain range centered on themselves through various onboard sensors such as Light Detection And Ranging (LiDAR), and vision sensors. The maximum distance that the sensors of a UAV can detect is defined as . This paper constructs a spherical safety envelope for UAVs The spherical security envelope is centered at the centroid position of the UAV, which is the demarcation of the threat that the UAV can avoid. It can be used to calculate the action reward of the UAV during RL, and act as an event-triggered mechanism for mandatory UAV anti-collision avoidance strategies. As is shown in Fig. ##FIG##1##2##, the thresholds of the safety zone named SZ) is ; the thresholds of the collision avoidance zone (named CZ) and the mandatory collision avoidance zone (named MZ) are represented by and , respectively. When the obstacle is in SZ, there is no collision risk between the UAV and the obstacles; when the obstacle is in CZ, the UAV needs to conduct a collision warning and be aware that the obstacle may enter the MZ; when the obstacle is in MZ, the anti-collision avoidance strategy will be triggered to ensure safety.</p>", "<title>UAV anti-collision avoidance strategies</title>", "<p id=\"Par25\">Before applying APPA-3D to solve the UAV path planning problem, an anti-collision avoidance strategy should be designed. The purpose is to adjust the UAV's flight status such as direction or speed in response to dynamic obstacles (such as other vehicles in the airspace, birds, etc.) to achieve obstacle avoidance. The design of the anti-collision avoidance strategy refers to the method of setting up collision zones in (NMAC) and (COLREGS).</p>", "<p id=\"Par26\">When a dynamic obstacle enters a UAV's MZ, a collision avoidance strategy will be triggered to reduce the risk of collision until the distance between the UAV and the obstacle is greater than . According to the rules of NMAC, we divide the possible conflict scenarios into flight path opposing conflict、pursuit conflict, and cross conflict. The relative position of the UAV to the dynamic obstacle is shown in Fig. ##FIG##2##3##.</p>", "<p id=\"Par27\">In Fig. ##FIG##2##3##, when the flight path of the dynamic obstacle is in the same straight line as the UAV, the two are about to have an opposing conflict or pursuit conflict, and their relative positions are schematically shown in Fig. ##FIG##2##3##A,B. The vertical direction vector is added to the direction vector of the connection between the UAV and the obstacle. The UAV flies along the direction of merging vector of vectors and until it avoids or overtakes an obstacle.</p>", "<p id=\"Par28\">When the flight path of the dynamic obstacle is in the same straight line as the UAV, the two flight paths cross and conflict, and their relative positions are shown in Fig. ##FIG##2##3##C. Vector is the combined vector direction of vector and vector . Vector is opposite to the direction of obstacle movement . The UAV flies along the merging vector to avoid the obstacle.</p>", "<p id=\"Par29\">Based on the different collision scenarios generated by the relative positions of the UAV and dynamic obstacles, four corresponding anti-collision avoidance strategies are designed, as shown in Fig. ##FIG##3##4##.</p>", "<p id=\"Par30\">In Fig. ##FIG##3##4##A, there is a risk of opposing conflict between the dynamic obstacle and the UAV. Similar to the method shown in Fig. ##FIG##2##3##A, the UAV will fly along the merging vector , to avoid obstacles. The flight paths of the UAV and the dynamic obstacle are shown in Fig. ##FIG##3##4##A.</p>", "<p id=\"Par31\">In Fig. ##FIG##3##4##B,C, there is a risk of cross-conflict between dynamic obstacles and UAVs. Similar to the method shown in Fig. ##FIG##2##3##C, the UAV will fly along the merging vector direction and pass behind the moving direction of the dynamic obstacle, thus the UAV can avoid the dynamic obstacle successfully with the shortest avoidance path. The flight paths of the UAV and the dynamic obstacle are shown in Fig. ##FIG##3##4##B,C.</p>", "<p id=\"Par32\">In Fig. ##FIG##3##4##D, dynamic obstacles are in the UAV's path of travel and moving at a speed less than the UAV. There is a risk of pursuit and conflict between the dynamic obstacles and the UAV. Similar to the method shown in Fig. ##FIG##2##3##B, the UAV will fly along the merging vector direction to complete the overtaking of the dynamic obstacle. The flight paths of the UAV and the dynamic obstacle are shown in Fig. ##FIG##3##4##D.</p>", "<title>Design of autonomous collision-free path planning algorithm for UAVs</title>", "<p id=\"Par33\">The basic framework of RL is shown in Fig. ##FIG##4##5##.</p>", "<p id=\"Par34\">Essentially, RL is the use of the Agent to interact with the environment constantly, and obtain the optimal value function for state , through the feedback (reward) given by the environment to continuously optimize the state-action to obtain the optimal strategy . The mathematical formula is expressed as Eq. (##FORMU##22##1##) and Eq. (##FORMU##23##2##):</p>", "<p id=\"Par35\">Thus, the problem of finding the optimal strategy translates into finding the largest of the action state value functions produced under all strategies.</p>", "<p id=\"Par36\">RL-based path planning algorithm allows UAVs to learn and gain rewards through constant interaction with the surroundings through trial and error with little knowledge of the environment and is, therefore, suitable for UAV ‘s path planning under complex conditions. The advantage of an RL-based path planning algorithm is that it can realize path planning in the absence of a priori information about the environment and is highly searchable, but it suffers from the problem of reward sparsity^{##UREF##36##39##}, which can cause convergence difficulties in high-dimensional spaces.</p>", "<p id=\"Par37\">APPA-3D first combines the principle of the APF method and designs an adaptive reward function. Dynamic rewards are generated in real time by judging the effectiveness of UAV movements with environmental information. Secondly, to address the \"exploration-utilization dilemma\" of RL in the UAV path planning process, an RL action exploration strategy based on action selection probability is proposed. The strategy dynamically adjusts the action selection strategy by combining the size of the value function in different states, to solve the exploration-utilization problem of RL and improve the efficiency of path search.</p>", "<title>Virtual force generation for UAV based on APF</title>", "<p id=\"Par38\">The basic idea of path planning with the APF^{##UREF##37##40##} is to design the motion of an object in its surroundings as the motion of an abstract artificial gravitational field. The target point has \"gravitational force\" on the object, while the obstacle has \"repulsive force\" on the object, and the motion of the object is controlled by the net force.</p>", "<p id=\"Par39\">The current position of the UAV is denoted as ; the position of the target point is denoted as ; and the position of the start point is denoted as . The gravitational potential field function is defined as Eq. (##FORMU##27##3##):</p>", "<p id=\"Par40\">In Eq. (##FORMU##27##3##), &gt; 0 is the gravitational potential field function coefficient constant. The distance from the UAV to the target point is , and the gravitational force is the negative gradient of the gravitational potential field function, defined as Eq. (##FORMU##30##4##):</p>", "<p id=\"Par41\">Define the repulsive potential field function as Eq. (##FORMU##31##5##):</p>", "<p id=\"Par42\">In Eq. (##FORMU##31##5##), &gt; 0 is a repulsive potential field coefficient constant. The position of the obstacle is . The distance from the UAV to the obstacle is . is the maximum range of influence of the obstacle. Define the repulsive force as Eq. (##FORMU##36##6##) and Eq. (##FORMU##37##7##):</p>", "<p id=\"Par43\">Thus the net force on the UAV is shown in Eq. (##FORMU##39##8##)</p>", "<title>Design of adaptive reward function</title>", "<p id=\"Par44\">The reward function is used to evaluate the actions of the Agent. In traditional RL algorithms, the Agent can only obtain the positive and negative sparse reward function by reaching the target point or colliding with an obstacle. The model does not receive any feedback until it receives the first reward, which may cause the model to stop learning and fail to improve. This reward function will make the algorithm convergence difficult, and in most states cannot reflect the good or bad of its action choice. he sparse reward function is shown in Eq. (##FORMU##41##9##):</p>", "<p id=\"Par45\">In Eq. (##FORMU##41##9##), means that the UAV collides with an obstacle in state t and receives a negative reward − 1, while means that the UAV reaches the target point in state t and receives a positive reward + 1. Other states have no reward.</p>", "<p id=\"Par46\">To solve the difficult problem of sparse rewards, in this paper, combined with the artificial potential field algorithm, the gravitational force generated by the target point and the repulsive force generated by the obstacle on the agent are converted into the reward or punishment obtained by the agent after performing the action in the state . The optimized reward function is shown in Eq. (##FORMU##46##10##):</p>", "<p id=\"Par47\">In Eq. (##FORMU##46##10##), represents the reward function when the obstacle is within the SZ or when no obstacle is detected. the collision avoidance action reward function is , and the mandatory collision avoidance action reward function is .</p>", "<p id=\"Par48\">The Euclidean distance between the starting point of the agent and the target is denoted by , and the Euclidean distance between the current position of the agent and the target is denoted by . The formula as Eq. (##FORMU##52##11##) and Eq. (##FORMU##53##12##):</p>", "<p id=\"Par49\">The hyperbolic tangent function can map all will any real number to (− 1, 1). The hyperbolic tangent function can be written as Eq. (##FORMU##54##13##):</p>", "<p id=\"Par50\">As shown in Fig. ##FIG##5##6##A, when the obstacle is in the SZ, or no obstacle is detected, the UAV is only affected by the gravitational force generated by the target point, reward function is as shown in Eq. (##FORMU##57##14##)</p>", "<p id=\"Par51\">In Eq. (##FORMU##57##14##): denotes the Euclidean distance between the agent position and the target point position at moment .</p>", "<p id=\"Par52\">From Eq. (##FORMU##57##14##), it can be seen that after each state change of the agent, if the distance between the agent and the target point under decreases compared to moments, then , the agent gets a positive reward at this time, and vice versa, it gets a negative reward, which is consistent with the principle of RL.</p>", "<p id=\"Par53\">As shown in Fig. ##FIG##5##6##B, when the obstacle is in the CZ, the UAV is affected by the repulsive force of the obstacle and the attractive force of the target point. At this time, the reward function decreases with the increase of the distance between the agent and the obstacle. The reward function can be written as Eq. (##FORMU##66##15##):where: denotes the Euclidean distance between the agent position and the obstacle position at moment .</p>", "<p id=\"Par54\">From Eq. (##FORMU##66##15##), it can be seen that the reward function when the obstacle is in the CZ consists of two parts, one is the reward generated by the obstacle to the UAV, if the distance between the UAV and the obstacle under the moment is reduced compared to the moment, then the reward generated by the obstacle to the agent is negative, and vice versa is positive. The other is the reward generated by the target point to the UAV, and the principle is the same as Eq. (##FORMU##31##5##). When the obstacle is in the CZ, the agent accepts the reward function of the obstacle and the target point at the same time, which can solve the defects that the traditional APF method is easy to fall into the local minima and oscillate in the narrow passage, to guide the UAV out of the trap area and move toward the target point smoothly.</p>", "<p id=\"Par55\">As shown in Fig. ##FIG##5##6##C, when the obstacle is within the MZ, the risk of UAV collision with the obstacle is high. To prevent conflicts, A collision avoidance strategy is mandatory for the UAV, The reward function can be written as Eq. (##FORMU##74##16##):</p>", "<p id=\"Par56\">The adaptive reward function is consistent with RL. By converting the reward values of each action-state into continuous value between (− 1, 1), the problem of sparse reward functions is solved. The adaptive reward function solves the problem that traditional reward functions can only earn positive or negative rewards by reaching a target point or colliding with an obstacle, and other actions do not receive any positive or negative feedback. The adaptive reward functions are generated by determining the validity of the executed action and environmental information. Compared to the traditional sparse reward function, the adaptive reward function proposed in this paper combines the good performance of APF to make the reward accumulation process smoother, and can also reflect the relationship between the current state of the UAV and the target state.</p>", "<title>Action exploration strategy optimization of reinforcement learning</title>", "<p id=\"Par57\">In the process of constant interaction with the environment, the Agent keeps exploring different states and obtains feedback on different actions. Exploration helps the Agent to obtain feedback through continuous experimentation, and Exploitation is where the Agent refers to the use of existing feedback to choose the best action.</p>", "<p id=\"Par58\">On the one hand, RL obtains more information by exploring more of the unknown action space to search for the global optimal solution, but a large amount of exploration reduces the performance of the algorithm and leads to the phenomenon of non-convergence of the algorithm. On the other hand, too much exploitation will fail to choose the optimal behavior because of the unknown knowledge of the environment. Therefore how to balance exploration and utilization is an important issue for the Agent to continuously learn in interaction.</p>", "<p id=\"Par59\">There is a contradiction between \"exploration\" and \"exploitation \", as the number of attempts is limited, and strengthening one naturally weakens the other. Excessive exploration of the unknown action space can degrade the performance of the algorithm and lead to non-convergence of the algorithm while obtaining more information to search for a globally optimal solution. In contrast, too much exploitation prevents the selection of optimal behavior because of the unknown knowledge of the environment. This is the Exploration—Exploitation dilemma faced by RL. To maximize the accumulation of rewards, a better compromise between exploration and exploitation must be reached.</p>", "<p id=\"Par60\">Action exploration strategies can be categorized into directed and undirected exploration methods. The directed exploration approach reduces the blindness in the pre-exploration phase of action exploration and thus improves the exploration efficiency by introducing a priori knowledge into the action exploration strategy. directed exploration methods, on the other hand, make a compromise between exploration and exploitation by setting parameters, and the usual approaches are the strategy and the Softmax distribution strategy.</p>", "<p id=\"Par61\">The strategy usually sets a parameter to select the current optimal action with a probability of , and randomly selects among all the actions with a probability of , which is represented by Eq. (##FORMU##80##17##):</p>", "<p id=\"Par62\">In Eq. (##FORMU##80##17##), When is 0, the strategy is transformed into a greedy strategy, and the degree of exploration gradually increases as is gradually increased from 0 to 1; when is 1, the strategy is transformed into a randomized choice action. Although the strategy solves the problem between exploration and exploitation to a certain extent, the problem of exploration and exploitation still exists because the parameter is fixed and there are problems such as the difficulty of setting the parameter , and the lack of differentiation between non-optimal actions.</p>", "<p id=\"Par63\">The Softmax distribution strategy makes a tradeoff between exploration and exploitation based on the average reward of currently known actions. If the average rewards of the maneuvers are comparable, the probability of selecting each maneuver is also comparable; if the average reward of some maneuvers is significantly higher than that of other maneuvers, the probability of their selection is also significantly higher.</p>", "<p id=\"Par64\">The action assignment for the Softmax distribution strategy is based on the Boltzmann distribution, which is represented by Eq. (##FORMU##89##18##):</p>", "<p id=\"Par65\">In Eq. (##FORMU##89##18##), records the average reward of the current action; is called “temperature”, The smaller of , the higher the probability of selecting actions with higher average rewards. When τ tends to 0, Softmax tends to \" exploitation only\", when τ tends to infinity. Softmax tends to \"exploration only\".</p>", "<p id=\"Par66\">Both strategy and the Softmax distribution strategy are iterated in such a way that the action with the largest action-value function has the largest probability of selection. Based on this, this paper proposes a new action selection strategy, the new strategy solves the balance problem between exploration and exploitation by introducing the concept of \"action selection probability \" and making action preference selection accordingly.</p>", "<p id=\"Par67\">Action selection probability represents the probability value that an Agent chooses to perform an action in a given state. As shown in Eq. (##FORMU##94##19##), the initial value of the action selection probability for a state-action is the inverse of the size of the action set for that state:</p>", "<p id=\"Par68\">In Eq. (##FORMU##94##19##), denotes the number of actions in the action set in state .</p>", "<p id=\"Par69\">The action selection probability is dynamically adjusted as the size of the value function of the action changes. During the RL process, Agent in state , selects action based on the size of the action selection probability value, and after executing the action, Agent obtains the reward and enters state and selects the action with the largest value function to update the value function. Subsequently, the value function for each action in state is is divided into two parts according to the size of the value: The largest value function is the first part; the rest is the second part. Reduce the probability values of each action in the second part by half and add them evenly to the first part.</p>", "<p id=\"Par70\">The Agent updates the action selection probability after completing an action, according to the size of the state action value function. The update rule is as Eq. (##FORMU##104##20##):</p>", "<p id=\"Par71\">In Eq. (##FORMU##104##20##): is the rate of change, which represents the rate of change of the action probability; is the set of actions with the largest value function, is the action of the set , and is the action with non-maximum value function.</p>", "<p id=\"Par72\">In the initial phase of the algorithm, each action has the same probability of being selected by the Agent, i.e., the action selection probabilities are equal, at which point the Agent will randomly select the action.</p>", "<p id=\"Par73\">After an Agent completes the exploration of an action, if this exploration results in , the action selection probability for that action is halved, at which point the probability of other actions being selected increases, so that in the early stages of the exploration the Agent will be more inclined to select actions that have not been performed. If for this exploration, it indicates that this exploration is a beneficial exploration, which will increase the action selection probability of this action, when the probability of other actions being selected decreases, and therefore the Agent tends to select this action more often; However, there is still a probability of exploration for other actions, thus reducing the risk of action exploration falling into a local optimum.</p>", "<p id=\"Par74\">The pseudo-code for APPA-3D is shown in Algorithm 1:</p>" ]

[ "<title>Author contributions</title>", "<p>J.W. designed the study and wrote the main manuscript text. Z.Z. experimented and analyzed the results and J.Q. collected the data and analyzed the results. X.C. prepared figures and tables, and all authors reviewed the manuscript.</p>", "<title>Data availability</title>", "<p>The datasets used and analysed during the current study will be available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par99\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Schematic diagram of UAV perception and avoidance.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>UAV spherical safety envelope profile.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>The relative position of the UAV and the dynamic obstacle.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Schematic of UAV anti-collision avoidance strategies.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Framework of RL.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Direction of UAV movement when the obstacle in different zones.</p></caption></fig>", "<fig id=\"Figa\"><label>Algorithm 1</label><caption><p>APPA-3D.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Opposing Conflict Avoidance Simulation.</p></caption></fig>", "<fig id=\"Fig8\"><label>Figure 8</label><caption><p>Cross-conflict avoidance simulation.</p></caption></fig>", "<fig id=\"Fig9\"><label>Figure 9</label><caption><p>Pursuit conflict avoidance simulation.</p></caption></fig>", "<fig id=\"Fig10\"><label>Figure 10</label><caption><p>3D view of APPA-3D flight path.</p></caption></fig>", "<fig id=\"Fig11\"><label>Figure11</label><caption><p>UAV path planning results under sparse reward function and adaptive reward function.</p></caption></fig>", "<fig id=\"Fig12\"><label>Figure12</label><caption><p>Path planning comparison of A*, RRT, APF and APPA-3D.</p></caption></fig>", "<fig id=\"Fig13\"><label>Figure13</label><caption><p>Path planning comparison of DFQL, IQL, MEAEO-RL and APPA-3D.</p></caption></fig>", "<fig id=\"Fig14\"><label>Figure14</label><caption><p>The loss function of DFQL, IQL, MEAEO-RL and APPA-3D.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Simulation results in different scenarios.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Number of random obstacles</th><th align=\"left\">Path planning time</th><th align=\"left\">Planning path length</th><th align=\"left\">Number of planning path points</th><th align=\"left\">Planning path ground projection length</th></tr></thead><tbody><tr><td align=\"left\">3</td><td align=\"left\">32.30 s</td><td align=\"left\">14.31083 km</td><td align=\"left\">94</td><td align=\"left\">11.51960 km</td></tr><tr><td align=\"left\">6</td><td align=\"left\">45.05 s</td><td align=\"left\">14.28151 km</td><td align=\"left\">118</td><td align=\"left\">13.87523 km</td></tr><tr><td align=\"left\">10</td><td align=\"left\">51.12 s</td><td align=\"left\">13.74009 km</td><td align=\"left\">85</td><td align=\"left\">10.29533 km</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Number of planning path points for different strategies.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"></th><th align=\"left\">Softmax</th><th align=\"left\">Action selection strategy</th></tr></thead><tbody><tr><td align=\"left\">Number of planning path points</td><td align=\"left\">112</td><td align=\"left\">96</td><td align=\"left\">85</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Planning path time for different strategies.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"></th><th align=\"left\">Softmax</th><th align=\"left\">Action selection strategy</th></tr></thead><tbody><tr><td align=\"left\">Planning path time</td><td align=\"left\">68.33 s</td><td align=\"left\">60.15 s</td><td align=\"left\">53.37 s</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Path length of different algorithms.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">A*</th><th align=\"left\">RRT</th><th align=\"left\">APF</th><th align=\"left\">APPA-3D</th></tr></thead><tbody><tr><td align=\"left\">Planning path length</td><td align=\"left\">15.3205 km</td><td align=\"left\">16.5351 km</td><td align=\"left\">14.9667 km</td><td align=\"left\">13.9533 km</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Path planning time of different algorithms.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">A*</th><th align=\"left\">RRT</th><th align=\"left\">APF</th><th align=\"left\">APPA-3D</th></tr></thead><tbody><tr><td align=\"left\">Planning path time</td><td align=\"left\">49.12 s</td><td align=\"left\">59.67 s</td><td align=\"left\">51.34 s</td><td align=\"left\">52.45 s</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab6\"><label>Table 6</label><caption><p>Path lengths of four algorithms.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">DFQL</th><th align=\"left\">IQL</th><th align=\"left\">MEAEO-RL</th><th align=\"left\">APPA-3D</th></tr></thead><tbody><tr><td align=\"left\">Planning path length</td><td align=\"left\">15.0154 km</td><td align=\"left\">14.8301 km</td><td align=\"left\">14.6506 km</td><td align=\"left\">13.9533 km</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab7\"><label>Table 7</label><caption><p>Path planning time of four algorithms.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">DFQL</th><th align=\"left\">IQL</th><th align=\"left\">MEAEO-RL</th><th align=\"left\">APPA-3D</th></tr></thead><tbody><tr><td align=\"left\">Planning path time</td><td align=\"left\">54.46 s</td><td align=\"left\">57.34 s</td><td align=\"left\">54.76 s</td><td align=\"left\">52.12 s</td></tr></tbody></table></table-wrap>" ]

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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mi>f</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${f}_{1}$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:msub><mml:mi>f</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${f}_{1}$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:msub><mml:mi>f</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$v$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:mi>v</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:mi>F</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\overrightarrow{F}$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:mover accent=\"true\"><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">→</mml:mo></mml:mover></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq18\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\overrightarrow{F}$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:mover accent=\"true\"><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">→</mml:mo></mml:mover></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq19\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\overrightarrow{F}$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:mover accent=\"true\"><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">→</mml:mo></mml:mover></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq20\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}^{*}$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq21\"><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$S$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mi>S</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq22\"><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\pi }^{*}$$\\end{document}</tex-math><mml:math id=\"M44\"><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$q^{*} \\left( {s,\\;a} \\right) = \\mathop {\\max }\\limits_{\\pi } q_{\\pi } \\left( {s,\\;a} \\right)$$\\end{document}</tex-math><mml:math id=\"M46\" display=\"block\"><mml:mrow><mml:msup><mml:mi>q</mml:mi><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mi>a</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits=\"false\">max</mml:mo><mml:mi>π</mml:mi></mml:munder><mml:msub><mml:mi>q</mml:mi><mml:mi>π</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mi>a</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\pi^{*} \\left( {a|s} \\right) = \\left\\{ {\\begin{array}{*{20}c} {1, \\;\\;\\;\\;\\;\\;\\;\\; a = argmax_{a \\in A} q^{*} \\left( {s,a} \\right)}\\\\ {0, \\;\\;\\;\\;\\;\\;\\;\\;\\;\\; other} \\\\ \\end{array} } \\right.$$\\end{document}</tex-math><mml:math id=\"M48\" display=\"block\"><mml:mrow><mml:msup><mml:mi>π</mml:mi><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>a</mml:mi><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mfenced open=\"{\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mo>∈</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>q</mml:mi><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>a</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mspace width=\"0.277778em\"/><mml:mi>o</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq23\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$X=\\left(x,y,z\\right)$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq24\"><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${X}_{g}=\\left({x}_{g},{y}_{g},{z}_{g}\\right)$$\\end{document}</tex-math><mml:math id=\"M52\"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>x</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq25\"><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${X}_{0}=\\left({x}_{0},{y}_{0},{z}_{0}\\right)$$\\end{document}</tex-math><mml:math id=\"M54\"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>x</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{att} = \\frac{1}{2}kD_{goal}^{2}$$\\end{document}</tex-math><mml:math id=\"M56\" display=\"block\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">att</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mi>k</mml:mi><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq26\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$k$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:mi>k</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq27\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${D}_{goal}=\\Vert X-{X}_{g}\\Vert$$\\end{document}</tex-math><mml:math id=\"M60\"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">‖</mml:mo><mml:mi>X</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo stretchy=\"false\">‖</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_{att} \\left( X \\right) = - {\\triangledown }\\left( {U_{att} \\left( X \\right)} \\right) = k\\left( {X_{g} - X} \\right)$$\\end{document}</tex-math><mml:math id=\"M62\" display=\"block\"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">att</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mo>▿</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">att</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{rep} \\left( X \\right) = \\left\\{ {\\begin{array}{*{20}c} {\\frac{1}{2}m\\left( {\\frac{1}{{D_{barrier} }} - \\frac{1}{{\\rho_{0} }}} \\right)^{2} } &amp; {D_{goal} \\le \\rho_{0} } \\\\ 0 &amp; {D_{goal} &gt; \\rho_{0} } \\\\ \\end{array} } \\right.$$\\end{document}</tex-math><mml:math id=\"M64\" display=\"block\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">rep</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mfenced open=\"{\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mi>m</mml:mi><mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfrac></mml:mrow></mml:mfenced><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mn>0</mml:mn></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq28\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:mi>m</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq29\"><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${X}_{b}=\\left({x}_{b},{y}_{b},{z}_{b}\\right)$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>x</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq30\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${D}_{barrier}=\\Vert X-{X}_{b}\\Vert$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">‖</mml:mo><mml:mi>X</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy=\"false\">‖</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq31\"><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\rho }_{0}$$\\end{document}</tex-math><mml:math id=\"M72\"><mml:msub><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_{rep} \\left( X \\right) = - {\\triangledown }\\left( {U_{rep} \\left( X \\right)} \\right) = \\left\\{ {\\begin{array}{*{20}c} {m\\left( {\\frac{1}{{D_{barrier} }} - \\frac{1}{{\\rho_{0} }}} \\right)\\frac{1}{{D_{battier}^{2} }}\\frac{{\\partial D_{barrier} }}{\\partial X}} &amp; {D_{goal} \\le \\rho_{0} } \\\\ 0 &amp; {D_{goal} &gt; \\rho_{0} } \\\\ \\end{array} } \\right.$$\\end{document}</tex-math><mml:math id=\"M74\" display=\"block\"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">rep</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mo>▿</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">rep</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mfenced open=\"{\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mi>m</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfrac></mml:mrow></mml:mfenced><mml:mfrac><mml:mn>1</mml:mn><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">battier</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mfrac><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mn>0</mml:mn></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M75\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{\\partial D_{barrier} }}{\\partial X} = \\left( {\\frac{{\\partial D_{barrier} }}{\\partial x},\\;\\frac{{\\partial D_{barrier} }}{\\partial y},\\;\\frac{{\\partial D_{barrier} }}{\\partial z}} \\right)$$\\end{document}</tex-math><mml:math id=\"M76\" display=\"block\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq32\"><alternatives><tex-math id=\"M77\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F\\left(X\\right)$$\\end{document}</tex-math><mml:math id=\"M78\"><mml:mrow><mml:mi>F</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M79\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F\\left( X \\right) = F_{att} \\left( X \\right) + F_{rep} \\left( X \\right)$$\\end{document}</tex-math><mml:math id=\"M80\" display=\"block\"><mml:mrow><mml:mi>F</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">att</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">rep</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>X</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq33\"><alternatives><tex-math id=\"M81\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R$$\\end{document}</tex-math><mml:math id=\"M82\"><mml:mi>R</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M83\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R = \\left\\{ {\\begin{array}{*{20}c} { - 1,} &amp; {s_{t} = Filure} \\\\ { + 1,} &amp; {s_{t} = Success} \\\\ {0,} &amp; {s_{t} = Other} \\\\ \\end{array} } \\right.$$\\end{document}</tex-math><mml:math id=\"M84\" display=\"block\"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mfenced open=\"{\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>F</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>S</mml:mi><mml:mi>u</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>O</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq34\"><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${s}_{t}=Filure$$\\end{document}</tex-math><mml:math id=\"M86\"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>F</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq35\"><alternatives><tex-math id=\"M87\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${s}_{t}=Success$$\\end{document}</tex-math><mml:math id=\"M88\"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>S</mml:mi><mml:mi>u</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq36\"><alternatives><tex-math id=\"M89\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${a}_{t}$$\\end{document}</tex-math><mml:math id=\"M90\"><mml:msub><mml:mi>a</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq37\"><alternatives><tex-math id=\"M91\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${s}_{t}$$\\end{document}</tex-math><mml:math id=\"M92\"><mml:msub><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ10\"><label>10</label><alternatives><tex-math id=\"M93\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R = \\left\\{ {\\begin{array}{*{20}c} {R_{a} } &amp; {D \\ge D_{cz} { }or{ }D_{cz} \\le D &lt; D_{max} } \\\\ {R_{cz} } &amp; {D_{mz} \\le D &lt; D_{cz} } \\\\ {R_{mz} } &amp; {D &lt; D_{mz} } \\\\ \\end{array} } \\right.$$\\end{document}</tex-math><mml:math id=\"M94\" display=\"block\"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mfenced open=\"{\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:msub><mml:mi>R</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:mtd><mml:mtd><mml:mrow><mml:mi>D</mml:mi><mml:mo>≥</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">cz</mml:mi></mml:mrow></mml:msub><mml:mrow/><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mrow/><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">cz</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mi>D</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">max</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">cz</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">mz</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mi>D</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">cz</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">mz</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>D</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">mz</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq38\"><alternatives><tex-math id=\"M95\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{a}$$\\end{document}</tex-math><mml:math id=\"M96\"><mml:msub><mml:mi>R</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq39\"><alternatives><tex-math id=\"M97\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{ca}$$\\end{document}</tex-math><mml:math id=\"M98\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ca</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M99\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{mz}$$\\end{document}</tex-math><mml:math id=\"M100\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">mz</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M101\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${d}_{max}$$\\end{document}</tex-math><mml:math id=\"M102\"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">max</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq42\"><alternatives><tex-math id=\"M103\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${d}_{goal}$$\\end{document}</tex-math><mml:math id=\"M104\"><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ11\"><label>11</label><alternatives><tex-math id=\"M105\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{max} = \\parallel X_{0} - X_{g}\\parallel$$\\end{document}</tex-math><mml:math id=\"M106\" display=\"block\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">max</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">‖</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo stretchy=\"false\">‖</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ12\"><label>12</label><alternatives><tex-math id=\"M107\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{goal} = \\parallel X - X_{g} \\parallel$$\\end{document}</tex-math><mml:math id=\"M108\" display=\"block\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">‖</mml:mo><mml:mi>X</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo stretchy=\"false\">‖</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ13\"><label>13</label><alternatives><tex-math id=\"M109\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\tanh x = \\frac{\\sinh x}{{\\cosh x}} = \\frac{{e^{x} - e^{ - x} }}{{e^{x} + e^{ - x} }}$$\\end{document}</tex-math><mml:math id=\"M110\" display=\"block\"><mml:mrow><mml:mo>tanh</mml:mo><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>sinh</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mo>cosh</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mi>x</mml:mi></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mi>x</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq43\"><alternatives><tex-math id=\"M111\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${F}_{att}$$\\end{document}</tex-math><mml:math id=\"M112\"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">att</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq44\"><alternatives><tex-math id=\"M113\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{a}$$\\end{document}</tex-math><mml:math id=\"M114\"><mml:msub><mml:mi>R</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ14\"><label>14</label><alternatives><tex-math id=\"M115\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{a} = \\left| {\\tanh \\left( {d_{max} - d_{goal}^{t} } \\right)} \\right|\\frac{{d_{goal}^{t} - d_{goal}^{t + 1} }}{{\\left| {d_{goal}^{t} - d_{goal}^{t + 1} } \\right|}}$$\\end{document}</tex-math><mml:math id=\"M116\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:mo>tanh</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">max</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfenced></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq45\"><alternatives><tex-math id=\"M117\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${d}_{goal}^{t}$$\\end{document}</tex-math><mml:math id=\"M118\"><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq46\"><alternatives><tex-math id=\"M119\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$t$$\\end{document}</tex-math><mml:math id=\"M120\"><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq47\"><alternatives><tex-math id=\"M121\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$t+1$$\\end{document}</tex-math><mml:math id=\"M122\"><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq48\"><alternatives><tex-math id=\"M123\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$t$$\\end{document}</tex-math><mml:math id=\"M124\"><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq49\"><alternatives><tex-math id=\"M125\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{a}&gt;0$$\\end{document}</tex-math><mml:math id=\"M126\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq50\"><alternatives><tex-math id=\"M127\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${F}_{rep}$$\\end{document}</tex-math><mml:math id=\"M128\"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">rep</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq51\"><alternatives><tex-math id=\"M129\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${F}_{att}$$\\end{document}</tex-math><mml:math id=\"M130\"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">att</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq52\"><alternatives><tex-math id=\"M131\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{ca}$$\\end{document}</tex-math><mml:math id=\"M132\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ca</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ15\"><label>15</label><alternatives><tex-math id=\"M133\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{cz} = \\left| {\\tanh \\left( {D_{cz} - d_{barrier}^{t} } \\right)} \\right|\\frac{{d_{barrier}^{t + 1} - d_{barrier}^{t} }}{{\\left| {d_{barrier}^{t + 1} - d_{barrier}^{t} } \\right|}} + \\left| {\\tanh \\left( {d_{max} - d_{goal}^{t} } \\right)} \\right|\\frac{{d_{goal}^{t} - d_{goal}^{t + 1} }}{{\\left| {d_{goal}^{t} - d_{goal}^{t + 1} } \\right|}}$$\\end{document}</tex-math><mml:math id=\"M134\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">cz</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:mo>tanh</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">cz</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfenced></mml:mfrac><mml:mo>+</mml:mo><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:mo>tanh</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">max</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">goal</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfenced></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq53\"><alternatives><tex-math id=\"M135\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${d}_{barrier}^{t}$$\\end{document}</tex-math><mml:math id=\"M136\"><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq54\"><alternatives><tex-math id=\"M137\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$t$$\\end{document}</tex-math><mml:math id=\"M138\"><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq55\"><alternatives><tex-math id=\"M139\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{ca}$$\\end{document}</tex-math><mml:math id=\"M140\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ca</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq56\"><alternatives><tex-math id=\"M141\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$t+1$$\\end{document}</tex-math><mml:math id=\"M142\"><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq57\"><alternatives><tex-math id=\"M143\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$t$$\\end{document}</tex-math><mml:math id=\"M144\"><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq58\"><alternatives><tex-math id=\"M145\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${A}_{C}$$\\end{document}</tex-math><mml:math id=\"M146\"><mml:msub><mml:mi>A</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq59\"><alternatives><tex-math id=\"M147\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{ca}$$\\end{document}</tex-math><mml:math id=\"M148\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ca</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ16\"><label>16</label><alternatives><tex-math id=\"M149\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{mz} = \\left| {\\tanh \\left( {D_{cz} - d_{barrier}^{t} } \\right)} \\right|\\frac{{d_{barrier}^{t + 1} - d_{barrier}^{t} }}{{\\left| {d_{barrier}^{t + 1} - d_{barrier}^{t} } \\right|}}$$\\end{document}</tex-math><mml:math id=\"M150\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">mz</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:mo>tanh</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">cz</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow><mml:mfenced close=\"|\" open=\"|\"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">barrier</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msubsup></mml:mrow></mml:mfenced></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq60\"><alternatives><tex-math id=\"M151\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M152\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq61\"><alternatives><tex-math id=\"M153\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M154\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq62\"><alternatives><tex-math id=\"M155\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon$$\\end{document}</tex-math><mml:math id=\"M156\"><mml:mi>ϵ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq63\"><alternatives><tex-math id=\"M157\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left(1-\\epsilon \\right)$$\\end{document}</tex-math><mml:math id=\"M158\"><mml:mfenced close=\")\" open=\"(\"><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>ϵ</mml:mi></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq64\"><alternatives><tex-math id=\"M159\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon$$\\end{document}</tex-math><mml:math id=\"M160\"><mml:mi>ϵ</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ17\"><label>17</label><alternatives><tex-math id=\"M161\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$a = \\left\\{ {\\begin{array}{*{20}l} {Actions \\;selected \\;with \\;uniform \\;probability\\; in\\; A} \\hfill &amp; {P = \\varepsilon } \\hfill \\\\ {a = argmax_{a \\in A} Q\\left( {s,\\;a} \\right)} \\hfill &amp; {P = 1 - \\varepsilon } \\hfill \\\\ \\end{array} } \\right.$$\\end{document}</tex-math><mml:math id=\"M162\" display=\"block\"><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mfenced open=\"{\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"left\"><mml:mrow><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>w</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>u</mml:mi><mml:mi>n</mml:mi><mml:mi>i</mml:mi><mml:mi>f</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>y</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>A</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mi>ε</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"left\"><mml:mrow><mml:mrow/><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>g</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mo>∈</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mi>Q</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mi>a</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>ε</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq65\"><alternatives><tex-math id=\"M163\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\varepsilon$$\\end{document}</tex-math><mml:math id=\"M164\"><mml:mi>ε</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq66\"><alternatives><tex-math id=\"M165\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M166\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq67\"><alternatives><tex-math id=\"M167\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\varepsilon$$\\end{document}</tex-math><mml:math id=\"M168\"><mml:mi>ε</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq68\"><alternatives><tex-math id=\"M169\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\varepsilon$$\\end{document}</tex-math><mml:math id=\"M170\"><mml:mi>ε</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq69\"><alternatives><tex-math id=\"M171\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M172\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq70\"><alternatives><tex-math id=\"M173\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M174\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq71\"><alternatives><tex-math id=\"M175\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon$$\\end{document}</tex-math><mml:math id=\"M176\"><mml:mi>ϵ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq72\"><alternatives><tex-math id=\"M177\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon$$\\end{document}</tex-math><mml:math id=\"M178\"><mml:mi>ϵ</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ18\"><label>18</label><alternatives><tex-math id=\"M179\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P\\left( {a_{i} |s} \\right) = \\frac{{e^{{\\frac{{Q\\left( {s,\\;a_{i} } \\right)}}{\\tau }}} }}{{\\mathop \\sum \\nolimits_{j = 1}^{m} e^{{\\frac{{Q\\left( {s,\\;a_{j} } \\right)}}{\\tau }}} }}$$\\end{document}</tex-math><mml:math id=\"M180\" display=\"block\"><mml:mrow><mml:mi>P</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mfrac><mml:msup><mml:mi>e</mml:mi><mml:mfrac><mml:mrow><mml:mi>Q</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mi>τ</mml:mi></mml:mfrac></mml:msup><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:msup><mml:mi>e</mml:mi><mml:mfrac><mml:mrow><mml:mi>Q</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mi>τ</mml:mi></mml:mfrac></mml:msup></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq73\"><alternatives><tex-math id=\"M181\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Q\\left(s,{a}_{j}\\right)$$\\end{document}</tex-math><mml:math id=\"M182\"><mml:mrow><mml:mi>Q</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq74\"><alternatives><tex-math id=\"M183\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\tau &gt;0$$\\end{document}</tex-math><mml:math id=\"M184\"><mml:mrow><mml:mi>τ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq75\"><alternatives><tex-math id=\"M185\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\tau$$\\end{document}</tex-math><mml:math id=\"M186\"><mml:mi>τ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq76\"><alternatives><tex-math id=\"M187\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M188\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ19\"><label>19</label><alternatives><tex-math id=\"M189\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P\\left( {a|s} \\right) = \\frac{1}{{card\\left( {A_{s} } \\right)}}$$\\end{document}</tex-math><mml:math id=\"M190\" display=\"block\"><mml:mrow><mml:mi>P</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>a</mml:mi><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>d</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>A</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq77\"><alternatives><tex-math id=\"M191\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$card\\left({A}_{s}\\right)$$\\end{document}</tex-math><mml:math id=\"M192\"><mml:mrow><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>d</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>A</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq78\"><alternatives><tex-math id=\"M193\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${A}_{s}$$\\end{document}</tex-math><mml:math id=\"M194\"><mml:msub><mml:mi>A</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq79\"><alternatives><tex-math id=\"M195\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$s$$\\end{document}</tex-math><mml:math id=\"M196\"><mml:mi>s</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq80\"><alternatives><tex-math id=\"M197\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$s$$\\end{document}</tex-math><mml:math id=\"M198\"><mml:mi>s</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq81\"><alternatives><tex-math id=\"M199\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$A$$\\end{document}</tex-math><mml:math id=\"M200\"><mml:mi>A</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq82\"><alternatives><tex-math id=\"M201\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R$$\\end{document}</tex-math><mml:math id=\"M202\"><mml:mi>R</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq83\"><alternatives><tex-math id=\"M203\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${S}^{\\mathrm{^{\\prime}}}$$\\end{document}</tex-math><mml:math id=\"M204\"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq84\"><alternatives><tex-math id=\"M205\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${A}^{\\mathrm{^{\\prime}}}$$\\end{document}</tex-math><mml:math id=\"M206\"><mml:msup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq85\"><alternatives><tex-math id=\"M207\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$s$$\\end{document}</tex-math><mml:math id=\"M208\"><mml:mi>s</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ20\"><label>20</label><alternatives><tex-math id=\"M209\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left\\{ {\\begin{array}{*{20}l} {P\\left( {a_{i} |s} \\right) + \\mathop \\sum \\limits_{{j = 1{}a_{j} \\notin A^{*} \\left( s \\right)}}^{n} \\frac{{P\\left( {a_{j} |s} \\right)}}{m}} \\hfill &amp; {a_{i} \\in A^{*} \\left( s \\right) = \\arg \\max_{a \\in A} Q^{*} \\left( {s,\\;a} \\right)} \\hfill \\\\ {P\\left( {a_{j} |s} \\right)\\left( {1 - \\frac{1}{m}} \\right)} \\hfill &amp; {other} \\hfill \\\\ \\end{array} } \\right.$$\\end{document}</tex-math><mml:math id=\"M210\" display=\"block\"><mml:mfenced open=\"{\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"left\"><mml:mrow><mml:mi>P</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:munderover><mml:mo movablelimits=\"false\">∑</mml:mo><mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mrow/><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>∉</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>s</mml:mi></mml:mfenced></mml:mrow></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:mfenced></mml:mrow><mml:mi>m</mml:mi></mml:mfrac></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>∈</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>s</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mo>arg</mml:mo><mml:msub><mml:mo movablelimits=\"true\">max</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>∈</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>Q</mml:mi><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.277778em\"/><mml:mi>a</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"left\"><mml:mrow><mml:mrow/><mml:mrow><mml:mi>P</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mrow></mml:mfenced><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>m</mml:mi></mml:mfrac></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mi mathvariant=\"italic\">other</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq86\"><alternatives><tex-math id=\"M211\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m$$\\end{document}</tex-math><mml:math id=\"M212\"><mml:mi>m</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq87\"><alternatives><tex-math id=\"M213\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${A}^{*}\\left(s\\right)$$\\end{document}</tex-math><mml:math id=\"M214\"><mml:mrow><mml:msup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>s</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq88\"><alternatives><tex-math id=\"M215\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${a}_{i}$$\\end{document}</tex-math><mml:math id=\"M216\"><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq89\"><alternatives><tex-math id=\"M217\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${A}^{*}\\left(s\\right)$$\\end{document}</tex-math><mml:math id=\"M218\"><mml:mrow><mml:msup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>s</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq90\"><alternatives><tex-math id=\"M219\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${a}_{j}$$\\end{document}</tex-math><mml:math id=\"M220\"><mml:msub><mml:mi>a</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq91\"><alternatives><tex-math id=\"M221\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P\\left(a|s\\right)$$\\end{document}</tex-math><mml:math id=\"M222\"><mml:mrow><mml:mi>P</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>a</mml:mi><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>s</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq92\"><alternatives><tex-math id=\"M223\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R&lt;0$$\\end{document}</tex-math><mml:math id=\"M224\"><mml:mrow><mml:mi>R</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq93\"><alternatives><tex-math id=\"M225\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R&gt;0$$\\end{document}</tex-math><mml:math id=\"M226\"><mml:mrow><mml:mi>R</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq94\"><alternatives><tex-math id=\"M227\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M228\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq96\"><alternatives><tex-math id=\"M229\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M230\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq97\"><alternatives><tex-math id=\"M231\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M232\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq95\"><alternatives><tex-math id=\"M233\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon -greedy$$\\end{document}</tex-math><mml:math id=\"M234\"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>" ]

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[ "<title>Introduction</title>", "<p id=\"Par3\">Strong-field ionization serves as a cornerstone for various ultrafast phenomena such as high harmonic generation^{##UREF##0##1##,##REF##11387467##2##}, laser-induced electron diffraction^{##REF##18556555##3##,##REF##22398558##4##}, nonsequential double ionization^{##UREF##1##5##,##REF##18764387##6##} and photoelectron holography^{##REF##21163963##7##–##REF##29694204##9##} that underpin strong-field physics and attosecond science^{##UREF##2##10##–##REF##22404594##12##}. The liberated photoelectrons carry dynamical information about the ionization process^{##REF##20576884##13##–##REF##30387676##15##} and encode structural details of atoms and molecules^{##REF##10035089##16##–##UREF##4##20##}. To reveal the underlying ionization dynamics, it is essential to track and probe the electron dynamics on its natural timescale (1as = 10⁻¹⁸s), which is the primary goal of attosecond science. Recent progress in attosecond metrology has opened up the possibilities both for the characterization of electron wave function and for its laser-driven shaping in real time^{##REF##15333834##21##–##REF##31951453##32##}. Notable techniques include attosecond streak camera^{##REF##15333834##21##,##REF##14985755##22##}, attosecond transient absorption spectroscopy^{##REF##20686571##23##,##REF##27846603##24##}, high harmonic spectroscopy^{##REF##19626004##25##,##UREF##5##26##}, and attoclock^{##UREF##6##27##}. Among these techniques, attoclock serves as a powerful tool in time-resolving electron dynamics in strong-field regime. It achieves attosecond precision based on the fact that in strong-field ionization by circularly polarized laser pulses, the ionization time of photoelectron is mapped to the emission angle. Since the pioneering implement^{##UREF##6##27##}, attoclock has been widely used to probe the tunneling time delay^{##REF##19056981##28##,##UREF##7##29##}, reveal the tunneling geometry^{##UREF##8##30##}, time the release of electrons^{##UREF##9##31##}, and image the ultrafast electronic and nuclear motion inside molecules^{##REF##31951453##32##}, providing insight into the fundamental aspects of intense light-matter interactions.</p>", "<p id=\"Par4\">However, in conventional attoclock experiments, owing to the adoption of few-cycle laser pulses, the photoelectron interference effect has been largely suppressed. As a result, the phase information of ionized electrons is lost. This hinders the complete characterization of electron wave function, especially for the unraveling of the quantum properties embedded in strong-field ionization. Generally, the electron dynamics in strong-field ionization involves passing through the potential barrier suppressed by strong laser fields and propagating in the continuum states. While the latter can be well understood within the classical mechanics, the former dynamics in the classically forbidden region, which dictates the main quantum nature of strong-field interaction and influences the following dynamics, remains obscure. Although recent advances in experimental techniques have offered a glimpse of the under-barrier dynamics^{##UREF##5##26##,##UREF##10##33##–##REF##29542985##36##}, comprehensively understanding it is still far off. This calls for a detailed look into the barrier. In particular, two fundamental questions, i.e., how does the field-modulated potential barrier influence the ionization dynamics and can we resolve the fingerprint of modulated potential barrier from the ionized electron wave function, need to be addressed. Answering these questions requires not only an accurate modulation of the barrier but also the measurement and shaping on the amplitude and phase of electron wave function.</p>", "<p id=\"Par5\">In this work, we demonstrate a novel two-color attoclock technique that integrates with a temporal interferometry to shape and image electron wave function during strong-field ionization and thereby to uncover the under-barrier dynamics. We achieve this by using a combination of a strong second harmonic field with circular polarization at 400 nm and a weak linearly polarized fundamental field at 800 nm. Here, the fundamental field introduces a spatiotemporal perturbation to the potential barrier bended by the intense second harmonic that depends on the two-color relative phase and the spatial orientation of the potential barrier. This perturbation shapes the amplitude and phase of the ionized electron wave function and is finally mapped into the temporal interferometry. Through the analysis of the two-color phase-resolved photoelectron interference at specific emission angles, we fully reconstruct the temporal shaping of electron wave function, thereby visualizing how the ionization dynamics evolves with respect to a fast-oscillating potential barrier under different interaction configurations. Furthermore, based on the analysis of angle-resolved photoelectron interference at fixed two-color relative phases, we are able to take snapshots of the shaped electron wave function in the full momentum space and thus reveal the effect of the spatial property of potential barrier on electron dynamics. This innovative two-color attoclock interferometry provides valuable insights into the quantum dynamics in strong-field ionization dictated by the field-modulated potential barrier. It has promising implications for visualizing ultrafast electronic dynamics inside molecules, solids, and liquids in time and space.</p>" ]

[ "<title>Methods</title>", "<title>Experimental setup</title>", "<p id=\"Par25\">The second harmonic pulse at 400 nm is obtained by frequency doubling the fundamental pulses (800 nm, 25 fs, 3k Hz) derived from the Ti: sapphire laser system with a 200-μm-thick beta barium borate (BBO) crystal. The fundamental pulse and second harmonic pulse aresynchronized in a Mach-Zehnder interferometer geometry. In each arm, the laser field intensity is controlled using a combination of a half-wave plate and a wire grid polarizer that are successively inserted in light path. The polarization of the fundamental pulse is turned to <italic>z</italic> axis by rotating the wire grid polarizer, while the circular polarization of the second harmonic is guaranteed by rotating a quarter-wave plate placed after a wire grid polarizer in the path. The relative phase between the two colors is finely controlled by a pair of fused silica wedges mounted on a motorized stage. The pulses are then focused into a supersonic gas jet of Ar atoms in an ultrahigh vacuum chamber of COLTRIMS. A homogenous electric field of 3.2 V/cm and a magnetic field of 5.4 Gauss are exerted along <italic>z</italic> axis (time-of-flight direction) in order to guide the charged fragments to the time- and position-sensitive detectors, from which the three-dimensional momentum distributions of electrons and ions can be reconstructed. Only the single ionization events, i.e., the electrons are coincident with Ar⁺ ions, are presented. The intensity of 400 nm circular field is calibrated to be 1.42 × 10¹⁴W/cm² according to the location of ATI peaks as shown in Fig. ##FIG##0##1b##. The intensity of the weak 800 nm field is estimated by comparing the measured photoelectron energy spectrum in two-color fields with the solution of the time-dependent Schrödinger equation^{##UREF##20##48##}. Atomic units (a.u.) are used throughout unless specified otherwise.</p>", "<title>Analytical derivation of the complex phase σ using saddle-point approach</title>", "<p id=\"Par26\">The synthesized two-color light field can be expressed as <bold>E</bold>(<italic>t</italic>) = <italic>E</italic>_{2<italic>ω</italic>}[cos(2<italic>ωt</italic>)<bold>z</bold> + sin(2<italic>ωt</italic>)<bold>x</bold>] + <italic>E</italic>_{<italic>ω</italic>}cos(<italic>ωt</italic> + <italic>φ</italic>)<bold>z</bold>, with <italic>E</italic>_{2<italic>ω</italic>} and <italic>E</italic>_{<italic>ω</italic>} representing the electric field strengths of the two colors, and <italic>ω</italic> the laser frequency of the fundamental pulse. Using the expression of the electric field, we can derive the analytical formula for the complex phase <italic>σ</italic>, with its real part Re[<italic>σ</italic>] and imaginary part Im[<italic>σ</italic>] following</p>", "<p id=\"Par27\">Here, <italic>t</italic>_{<italic>r</italic>} and <italic>t</italic>_{<italic>i</italic>} correspond to the real part and imaginary part of the saddle-point <italic>t</italic>_{<italic>s</italic>}. In Supplementary Fig. ##SUPPL##0##1##, we present the derived <italic>t</italic>_{<italic>s</italic>} for electrons emitted within [0, <italic>T</italic>₄₀₀] in the momentum space. Clearly, <italic>t</italic>_{<italic>r</italic>} is mapped to the emission angle. <italic>t</italic>_{<italic>i</italic>} reveals an isotropic property and it shows a pronounced dependence on the radial momentum <italic>p</italic>_{<italic>r</italic>}, i.e., with the increase of <italic>p</italic>_{<italic>r</italic>}, <italic>t</italic>_{<italic>i</italic>} decreases. Based on the analytical formulas, we can directly calculate the amplitude and phase modulations of the ionized electron wave function for the parallel (<italic>θ</italic> = 90°) and perpendicular (<italic>θ</italic> = 0°) interaction configurations. The corresponding results are shown in Supplementary Fig. ##SUPPL##0##4##, which agree well with the retrieved results from the SFA calculations (as displayed in Figs. ##FIG##2##3a, b## and  ##FIG##3##4a, b##). Therefore, the validity of the Fourier transform analysis is confirmed.</p>" ]

[ "<title>Results and discussion</title>", "<title>Two-color attoclock interferometry</title>", "<p id=\"Par6\">In our experiment, a strong circularly polarized field at 400 nm (3k Hz, 40 fs) with an intensity of 1.42 × 10¹⁴W/cm² is employed to ionize Ar atoms. Here, the polarization plane of 400 nm field is in <italic>x–z</italic> plane. As illustrated in Fig. ##FIG##0##1a##, the rotating electric field vector of 400 nm bends the atomic potential and forms a rotating Coulomb barrier, through which the bound electron is released. Depending on their ionization times, the emitted electrons would be deflected to different emission angles. Here, the emission angle <italic>θ</italic> is defined as the angle between the direction of the electron final momentum <bold>p</bold> and +<italic>z</italic> axis. This time-to-angle mapping is the principle of attoclock. Since multicycle pulses have been used, the electrons that release at times separated by laser cycles would interfere with each other at a specific angle, giving rise to the intercycle interference^{##UREF##13##37##}, which manifests as the well-known above-threshold ionization (ATI)^{##UREF##14##38##} peaks in photoelectron momentum (energy) spectrum. This defines the angle-resolved temporal interferometry in attoclock geometry. Experimentally, the three-dimensional momentum distributions (PMDs) of photoelectrons are measured by cold-target recoil-ion reaction momentum spectroscopy (COLTRIMS)^{##UREF##15##39##}. (Details of the experimental setup can be found in “Methods”). Since the circular field vector is angularly uniform, the measured PMD on the <italic>x–z</italic> polarization plane, as shown in Fig. ##FIG##0##1b##, reveals a series of isotropic ATI rings.</p>", "<p id=\"Par7\">We then add a weak linearly polarized field at 800 nm with the intensity of 8.8 × 10¹¹W/cm² and its polarization along <italic>z</italic> direction to manipulate the spatiotemporal shape of the potential barrier and introduce changes in the attoclock interferometry constructed by 400 nm circular fields. As depicted in Fig. ##FIG##0##1c##, in two-field fields with a fixed relative phase <italic>φ</italic>, both the polarization configuration (indicated by the blue and red arrows) and the perturbative field strength are changing over time. The spatially rotating potential barrier undergoes spatial modulations imposed by the perturbative field that depends on the ionization time. Consequently, the electrons that release at different times would experience distinct modulations. In particular, for the two electron wave packets that are released at times separated by one 400 nm cycle, they experience opposite modulations as the potential barrier is perturbed by opposite 800 nm electric field vector (the modified potential barriers along <italic>z</italic> direction are depicted by the red and blue dashed lines in the lower panel of Fig. ##FIG##0##1c##). Such modulation would be finally imprinted into the angle-resolved photoelectron interference pattern. And for each emission angle <italic>θ</italic>, it represents a distinct interaction configuration. Therefore, by analyzing the angle-resolved photoelectron interference pattern and retrieving the amplitude and phase of electron wave function for each emission angle, one can realize the spatial imaging of the ionization dynamics under various interaction configurations in the full momentum space. Besides, scanning the two-color relative phase also provides an additional knob to manipulate the potential barrier in time domain. As shown in Fig. ##FIG##0##1c##, varying the two-color relative phase, the perturbative field strength is modified for ionization at different times (angles). By inspecting the two-color phase-dependent photoelectron interference at a specific emission angle, one is allowed to monitor how the ionized electron wave function evolves with respect to the fast-oscillating potential barrier, thus achieving the temporal imaging of the ionization dynamics.</p>", "<p id=\"Par8\">Figure ##FIG##0##1d## displays the measured two-color phase-integrated PMD on the <italic>x–z</italic> polarization plane. One can see that adding a weak fundamental field gives rise to the formation of sideband structures between adjacent ATI rings on PMD. Moreover, due to the utilization of linearly polarized perturbative fields, the two-color phase-integrated interference pattern becomes no longer isotropic. Instead, it shows a slight angle-dependence. To visualize the spatiotemporal modulations induced by the perturbative field in the attoclock interferometry, we inspect the measured two-color phase-resolved photoelectron energy spectra at different emission angles. The corresponding spectra for <italic>θ</italic> = 0°, 45°, 90°, and 135° are displayed in Fig. ##FIG##1##2a–d##, respectively. Apparently, the spectra are dominated by equidistant interference peaks spaced by the 800 nm photon energy, which correspond to the alternating ATI peaks and sidebands. This is analogous to the traditional optical interference fringes in real space. More importantly, the photoelectron interference pattern undergoes very different evolution with respect to the relative phase for different emission angles, implying the time- and space-dependent features of the ionization dynamics in two-color attoclock geometry.</p>", "<title>SFA analysis of photoelectron interference</title>", "<p id=\"Par9\">To understand the two-color phase- and angle-dependent photoelectron interference in the geometry, we resort to the strong-field approximation (SFA)^{##UREF##16##40##}. This model has been verified to work well in describing strong-field ionization by sculptured circular fields^{##REF##29542985##36##,##REF##31012680##41##,##UREF##17##42##}. Within saddle-point approach^{##UREF##18##43##}, the transition amplitude of the photoelectron, from the initial ground state to the final Volkov state with the final momentum <bold>p</bold>, can be regarded as the coherent supposition of all quantum orbits, i.e., . Here, is the pre-exponential factor with <bold>A</bold>(<italic>t</italic>) and <bold>E</bold>(<italic>t</italic>) denoting the vector potential and electric field of laser pulses, respectively. The saddle-point <italic>t</italic>_{<italic>s</italic>}, which can be derived from the equation of [<bold>p</bold> + <bold>A</bold>(<italic>t</italic>_{<italic>s</italic>})]²/2 + <italic>I</italic>_{<italic>p</italic>} = 0 with <italic>I</italic>_{<italic>p</italic>} being the ionization potential, represents the complex ionization instant of the quantum orbit. is the classical action (or complex phase) of the quantum orbit. In single 400 nm circular fields, the photoelectron interference at the final momentum <bold>p</bold> along <italic>θ</italic> originates from the intercycle interference among quantum orbits whose ionization instants are separated by 400 nm cycles. When adding a weak linearly polarized 800 nm field, as illustrated in Fig. ##FIG##0##1c##, the quantum orbits that release in adjacent 400 nm cycles with their ionization instants satisfying <italic>t</italic>_{<italic>s</italic>}⁽²⁾= <italic>t</italic>_{<italic>s</italic>}⁽¹⁾ + <italic>T</italic>₄₀₀ would experience opposite modulations by the perturbative fundamental field. Here, <italic>T</italic>₄₀₀ denotes the optical period of 400 nm laser pulses. In the next 800 nm cycle, there arises a similar pair of quantum orbits with their ionization instants satisfying <italic>t</italic>_{<italic>s</italic>}⁽³⁾= <italic>t</italic>_{<italic>s</italic>}⁽¹⁾ + <italic>T</italic>₈₀₀ and <italic>t</italic>_{<italic>s</italic>}⁽⁴⁾= <italic>t</italic>_{<italic>s</italic>}⁽²⁾ + <italic>T</italic>₈₀₀ (<italic>T</italic>₈₀₀ represents the optical period of 800 nm pulses). Considering the periodicity of the light field, four quantum orbits releasing in two 800 nm cycles can well account for the photoelectron interference in two-color synthesized fields. In this case, the photoelectron interference in two-color fields at the emission angle <italic>θ</italic> can be written aswhere <italic>ψ</italic> = <italic>ρ</italic>(<bold>p</bold>)<italic>e</italic>^{<italic>iS</italic>} represents the ionized electron wave packet, <italic>b</italic> = (<italic>U</italic>_{<italic>p</italic>}⁽⁴⁰⁰⁾+<italic>U</italic>_{<italic>p</italic>}⁽⁸⁰⁰⁾+<italic>E</italic>_{<italic>k</italic>} + <italic>I</italic>_{<italic>p</italic>})<italic>T</italic>₈₀₀ is the action difference due to the time difference of traveling in the continuum. <italic>U</italic>_{<italic>p</italic>} is the pondermotive energy and <italic>E</italic>_{<italic>k</italic>} = <italic>p</italic>²/2 denotes the photoelectron energy. And <italic>ψ</italic>₃= <italic>ψ</italic>₁e^{<italic>ib</italic>}, <italic>ψ</italic>₄= <italic>ψ</italic>₂e^{<italic>ib</italic>}, respectively.</p>", "<p id=\"Par10\">Figure ##FIG##1##2e–h## displays the calculated photoelectron energy spectra as a function of the two-color relative phase based on Eq. (##FORMU##5##1##) for the selected angles. They show good agreement with the measured results. As for the slight discrepancies in low-energy region, this can be attributed to the neglect of Coulomb effect in SFA model (Comparison among the experimental results, SFA and Coulomb-corrected SFA (CCSFA) calculations can be seen in Supplementary Fig. ##SUPPL##0##2##). According to the time-to-angle mapping governed by SFA, i.e., <bold>p</bold> = −<bold>A</bold>(<italic>t</italic>₀), we can determine the direction of the 400 nm electric field vector at the ionization instant <italic>t</italic>₀ for these emission angles, and thus obtain the corresponding polarization configurations, as labeled by the blue and red arrows in Fig. ##FIG##1##2a–d##. Note that since the 800 nm field is perturbative weak, we have neglected its influence on the time-to-angle mapping.</p>", "<p id=\"Par11\">Having demonstrated good agreement between the experiment and SFA calculations, we continue analyzing the photoelectron interference using the SFA model. In two-color synthesized fields, the complex phase of the electron wave packet can be expressed as , where represents the action induced solely by the 400 nm circular field, is the additional action induced by the weak linearly polarized 800 nm field and is the high-order quantity and can be reduced to a linear phase shift <italic>U</italic>_{<italic>p</italic>}⁽⁸⁰⁰⁾<italic>t</italic>_{<italic>s</italic>}. Consequently, the photoelectron interference in two-color fields at the emission angle <italic>θ</italic> in the energy space can be rearranged as</p>", "<p id=\"Par12\">Here, represents the amplitude of ionized electron wave packet in 400 nm circular field. Re[<italic>σ</italic>] and Im[<italic>σ</italic>], which refer to the real part and imaginary part of the additional phase <italic>σ</italic>, respectively, quantify the phase and amplitude modulations of the electron wave function induced by 800 nm perturbative field. Note that the amplitude modulation induced by the change of <italic>ρ</italic>(<bold>p</bold>) when adding a weak 800 nm field has been neglected since it is much smaller as compared with that induced by the change of imaginary part of the complex phase (Supplementary Fig. ##SUPPL##0##3##). The <italic>a</italic> = (<italic>I</italic>_{<italic>p</italic>} + <italic>U</italic>_{<italic>p</italic>}⁽⁸⁰⁰⁾<italic>+U</italic>_{<italic>p</italic>}⁽⁴⁰⁰⁾)<italic>T</italic>₄₀₀ denotes a constant phase. Detailed derivation of Eq. (##FORMU##10##2##) can be found in Supplementary Information. When the perturbative field is absent, the two-color interference will be reduced to the single-color case with the formula governed by</p>", "<p id=\"Par13\">From the expressions in Eqs. (##FORMU##10##2##) and (##FORMU##12##3##), one can see that the photoelectron interference among four electron wave packets emitting within two 800 nm cycles contains multiple frequencies along <italic>E</italic>_{<italic>k</italic>}, i.e., the zero-frequency component, 1<italic>f</italic>_{<italic>x</italic>}, 2<italic>f</italic>_{<italic>x</italic>}, and 3<italic>f</italic>_{<italic>x</italic>} frequency components with <italic>f</italic>_{<italic>x</italic>} = <italic>T</italic>₄₀₀/2<italic>π</italic>. This indicates that we can apply the Fourier transform analysis^{##UREF##19##44##}, which has been frequently used in analyzing the traditional optical interferogram, to the photoelectron interference in order to extract the amplitude and phase modulations of the electron wave function induced by the spatiotemporal manipulation of potential barrier.</p>", "<title>Fourier transform analysis for fully retrieving the electron wave function</title>", "<p id=\"Par14\">As presented in Eq. (##FORMU##10##2##), the amplitude modulation Im[<italic>σ</italic>] caused by the perturbative field is encoded in the amplitudes of the zero-frequency term and 2<italic>f</italic>_{<italic>x</italic>} frequency term of the photoelectron interference. Here, we utilize the zero-frequency term of the photoelectron interference to extract Im[<italic>σ</italic>]. By performing Fourier transform on the photoelectron interference along <italic>E</italic>_{<italic>k</italic>} at a specific angle <italic>θ</italic>, we obtain the frequency spectra in single- and two-color cases. Then, we filter out the zero-frequency components and perform the inverse Fourier transform. Accordingly, we obtain the amplitudes of zero-frequency terms in single- and two-color fields, which correspond to 4<italic>W</italic>₀² and 2<italic>W</italic>₀²(e^2Im[σ]+e^{−2Im[<italic>σ</italic>]}), respectively. Dividing 2<italic>W</italic>₀²(e^2Im[σ]+ e^{−2Im[<italic>σ</italic>]}) by 4<italic>W</italic>₀², we obtain the ratio <italic>k</italic> = (e^2Im[σ]+ e^{−2Im[<italic>σ</italic>]})/2, from which Im[<italic>σ</italic>] can be analytically derived with the formula of Im[<italic>σ</italic>] =  (The other root equaling is unphysical and should be discarded). While to retrieve the phase modulation Re[<italic>σ</italic>], we focus on the 3<italic>f</italic>_{<italic>x</italic>} frequency term, i.e., 2<italic>W</italic>₀²cos(3<italic>E</italic>_{<italic>k</italic>}<italic>T</italic>₄₀₀ + 2Re[<italic>σ</italic>] + 3<italic>a</italic>), as Re[<italic>σ</italic>] is directly imprinted into its phase. By applying the Fourier transform to the two-color phase-dependent photoelectron interference along <italic>E</italic>_{<italic>k</italic>}, we obtain the two-color phase-resolved frequency spectrum, from which we filter out the 3<italic>f</italic>_{<italic>x</italic>} frequency term and shift it to the zero-frequency position. We then perform the inverse Fourier transform and obtain a complex value of 2<italic>W</italic>₀²<italic>e</italic>^{<italic>i</italic>(2Re[<italic>σ</italic>]+3<italic>a</italic>)} whose phase corresponds to 2Re[<italic>σ</italic>]+3<italic>a</italic>. Afterward, we subtract the constant phase 3<italic>a</italic> from the retrieved phase and finally access the phase modulation Re[<italic>σ</italic>]. In fact, within the saddle-point approach, the amplitude and phase modulations can be analytically derived by substituting the expression of two-color electric field into the definition of <italic>σ</italic>. The analytical formulas for Im[<italic>σ</italic>] and Re[<italic>σ</italic>] are given in Eq. (4) in “Methods”. By comparing the calculated Im[<italic>σ</italic>] and Re[<italic>σ</italic>] (Supplementary Fig. ##SUPPL##0##4##) with the retrieved results, one can validate the Fourier transform analysis.</p>", "<title>Temporal shaping and imaging of electron wave function</title>", "<p id=\"Par15\">In the following, we apply the Fourier transform analysis to the two-color phase-dependent photoelectron interference at specific angles in order to retrieve the temporal evolution of the ionized electron wave function through a fast-oscillating potential barrier. Here, we concentrate on two intriguing strong-field interaction configurations, in which the potential barrier is manipulated by the weak fundamental field along longitudinal (parallel) and transverse (perpendicular) directions, corresponding to the situations at <italic>θ</italic> = 90° and 0°, respectively.</p>", "<p id=\"Par16\">In Fig. ##FIG##2##3##, we present the retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra from the SFA calculations and from the measured results in the parallel configuration (<italic>θ</italic> = 90°). Good agreement has been achieved between the experiment and the SFA calculations. As depicted, in this configuration, the ionizing electric field vector points to the negative <italic>z</italic> axis, parallel with the perturbative field. Varying the two-color relative phase modifies the perturbative field strength at the ionization instant. Interestingly, as the perturbative field increases from zero to its maximum, the amplitude modulation Im[<italic>σ</italic>] on electron wave function increases from zero to maximum, whereas the phase modulation Re[<italic>σ</italic>] decreases from maximum to zero.</p>", "<p id=\"Par17\">In parallel interaction configuration, increasing the perturbative field strength is equivalent to reducing the thickness of the potential barrier along the ionization direction. More photoelectrons would be ionized through a narrower barrier, resulting in the increased ionization amplitude. Since the classical propagation after ionization does not influence the ionization probability^{##UREF##10##33##}, the retrieved Im[<italic>σ</italic>] directly reflects changes in the imaginary phase accumulated during the electrons’ under-barrier motion. On the other side, the photoelectron acquires an additional drift momentum along <italic>z</italic> direction governed by –<bold>A</bold>₈₀₀(<italic>t</italic>,<italic>φ</italic>) from the perturbative field. With the increase of the perturbative electric field, the drift momentum decreases. Such momentum is parallel to the ionizing direction but perpendicular to the final momentum <bold>p</bold> of electron. It would induce an additional real phase during the under-barrier excursion and also a lateral phase shift during the classical propagation (Supplementary Fig. ##SUPPL##0##5a##, ##SUPPL##0##b##). These two phases jointly contribute to the retrieved phase modulation Re[<italic>σ</italic>] as shown in Fig. ##FIG##2##3b, d##. Besides, one could see that the retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra exhibit prominent energy-dependences, i.e., the photoelectrons with lower energies (or lower radial momenta <italic>p</italic>_{<italic>r</italic>}) experience larger modulations than those of higher energies. This phenomenon can be ascribed to the energy-dependent imaginary part <italic>t</italic>_{<italic>i</italic>} of the ionization time <italic>t</italic>_{<italic>s</italic>} in circular fields, as shown in Supplementary Fig. ##SUPPL##0##1##, which quantifies the excursion time under the barrier and determines the real and imaginary phase of electron accumulated during under-barrier motion [see Eq. (4) in “Methods”].</p>", "<p id=\"Par18\">Another intriguing scenario is that the potential barrier is manipulated transversely, corresponding to the case of <italic>θ</italic> = 0°. Based on the results shown in Fig. ##FIG##1##2##a, ##FIG##1##e##, we extract the phase-dependent amplitude and phase modulations of the electron wave function in the perpendicular configuration. The corresponding results are displayed in Fig. ##FIG##3##4##. Discrepancies in the high-energy part of the retrieved Im[<italic>σ</italic>] spectra between SFA calculation and experiment can be attributed to the imperfect filter of zero-frequency component from the Fourier frequency spectrum of the experimental result that hampers the accurate retrieval of Im[<italic>σ</italic>]. In this configuration, the ionizing 400 nm electric field vector points to +<italic>x</italic> direction and the potential barrier is perturbed transversely by the weak fundamental field. The retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra reveal distinct phase- and energy-dependences in comparison to the case of parallel configuration. Specifically, when the perturbative field approaches zero, the amplitude modulation maximizes, whereas the phase modulation vanishes. Increasing the perturbative field to its maximum, the amplitude modulation gradually disappears, while the phase modulation reaches the maximum. Moreover, the two flanks of the electron wave packet, i.e., the lower- and higher-energy parts, seem to suffer a larger amplitude modulation than the central part which has a vanishing transverse momentum at the ionization instant and is finally streaked to <italic>p</italic>_{<italic>r</italic>} ~ 0.4 a.u. by the 400 nm circular field. This implies that under the barrier, the imaginary phase of electrons with larger transverse momenta is more susceptible to be influenced by the perpendicular perturbative field. For the retrieved Re[<italic>σ</italic>] spectra, the electrons with higher energies experience a larger phase modulation than the low-energy electrons.</p>", "<p id=\"Par19\">Note that different from the case in parallel configuration, the potential barrier in perpendicular configuration is deformed in transverse direction and its thickness along the ionization direction remains unchanged. Moreover, the additional momentum acquired by the photoelectron from the perturbative field is perpendicular to the ionization direction but parallel to the final momentum. When the perturbative electric field is vanishing (<italic>φ</italic> = 0.25π), the additional momentum maximizes. This causes the largest modulation on the imaginary phase of electrons. However, since the shape of potential barrier remains unchanged in this case, the real phase of the electrons accumulated during the under-barrier motion and the following propagation keeps unchanged (Supplementary Fig. ##SUPPL##0##5##c, d). Increasing the perturbative field to its maximum (<italic>φ</italic> = 0.75π), the momentum acquired by electrons along <italic>z</italic> axis vanishes, and, as a result, the modulation on the imaginary phase of electrons disappears. Nevertheless, it should be noted that the potential barrier in this case experiences the largest lateral perturbation. This results in the largest modulation on the real phase of the electron during its entire motion.</p>", "<p id=\"Par20\">From the retrieved temporal evolutions of shaped electron wave functions in parallel and perpendicular configurations, we find that the employed field geometry also allows for selective manipulation of the amplitude and phase of electron wave function in strong-field ionization, simply by modifying the two-color relative phase. For example, in the parallel configuration, by adjusting the two-color relative phase to <italic>φ</italic> = 0.5π, one can solely manipulate the amplitude of electron wave function while keep its phase unchanged. When modifying <italic>φ</italic> to 0, the selective shaping of the phase of electron wave function is enabled with its amplitude remaining unchanged. In principle, if performing Fourier transform analysis on the measured two-color phase-dependent photoelectron interference for each emission angle, one could access the complete information about electron wave function in time and space under this geometry, thereby shedding light into the underlying quantum dynamics of intense light-matter interactions.</p>", "<title>Spatial shaping and imaging of electron wave function</title>", "<p id=\"Par21\">Apart from temporal shaping and imaging of electrons, spatial shaping and imaging also arouses great interest of scientists, since the spatial property of emitted electrons is closely tied to electronic structures and it dictates the subsequent electron and nuclear dynamics inside molecules such as electron localization^{##REF##16614216##45##} and charge migration^{##REF##26494175##46##}. As illustrated by Fig. ##FIG##0##1c##, in the two-color attoclock geometry, the photoelectron interference along different emission angles encodes ionization dynamics under different strong-field interaction configurations. This reflects the spatial property of the attoclock geometry. By analyzing the angle-resolved photoelectron interference at a fixed two-color relative phase, one is allowed to capture the snapshots of the shaped electron wave function in the full momentum space for diverse configurations.</p>", "<p id=\"Par22\">Figure ##FIG##4##5##a and d display the calculated and measured PMDs in two-color fields with <italic>φ</italic> = 0, respectively. The SFA calculation basically reproduces the main features of the measured PMD, except for the low-energy part which suffers from the Coulomb effect. To facilitate analysis on photoelectron interference, we have transformed the PMD into the angle-resolved photoelectron energy spectrum. The spectrum is rotated by a specific angle in order to eliminate the Coulomb effect. Here, the rotating angle can be read from the comparison between the calculated angle-resolved spectra using the SFA and CCSFA models (Supplementary Fig. ##SUPPL##0##6##). Then, we apply the Fourier transform analysis to the angle-resolved photoelectron energy spectrum and retrieve the angle-resolved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra in energy space. These spectra are later transformed back to the momentum space.</p>", "<p id=\"Par23\">As shown in Fig. ##FIG##4##5b, e## and Fig. ##FIG##4##5c, f##, the retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra reveal obvious angle- and energy-dependent features. And they are symmetric about <italic>p</italic>_{<italic>x</italic>} axis. Actually, such symmetry reflects the field geometry of the two-color synthesized fields, as depicted by the black line in Fig. ##FIG##4##5b##. Particularly, as the ionization amplitude critically depends on the electric field strength, the retrieved angle-dependent amplitude modulation directly maps the evolution of sculptured two-color laser fields. Scanning the emission angle, the spatially rotating potential barrier is manipulated along the <italic>z</italic> direction by the fundamental field of different strength (see the labeled two-color field configurations in Fig. ##FIG##4##5b##). The emission angle indeed encodes the spatial property of the field-modulated potential barrier. Hence, the retrieved angle-resolved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra in the full momentum space reveals the impact of spatial property of potential barrier on the electron dynamics, demonstrating the spatial imaging capability of the two-color attoclock geometry. This capability provides unique possibilities to probe the electronic environment of molecules, solids, and liquids.</p>", "<p id=\"Par24\">In summary, we have demonstrated a novel two-color attoclock interferometry that enables the spatiotemporal shaping and imaging of the electron wave function in strong-field ionization. This interferometry encompasses a wide range of strong-field interaction configurations, thereby allowing the scrutiny of the underlying ionization dynamics in diverse scenarios. Through the analysis of the two-color phase-dependent photoelectron interferences at specific angles, we have gained insights into the temporal evolution of the ionization dynamics with respect to a fast-oscillating potential barrier under different interaction configurations, especially for the quantum dynamics under the barrier. This field geometry, as demonstrated in our experiment, can also be exploited for selectively manipulating the amplitude and phase of the electron wave function. Besides that, the analysis of the angle-resolved photoelectron interference at a specific two-color relative phase permits the spatial imaging of the electron dynamics in the full momentum space. Our study illuminates puzzles in understanding how the spatiotemporal properties of Coulomb barrier influence the ionization process and shape the electron wave function. Looking forward, this novel attoclock interferometry has important implications for spatiotemporally resolving ultrafast electronic dynamics inside molecules following photoionization such as charge migration^{##REF##26494175##46##} and charge transfer processes^{##REF##29333473##47##}, paving the way to real-time measurement and control of chemical transformations.</p>" ]

[ "<title>Results and discussion</title>", "<title>Two-color attoclock interferometry</title>", "<p id=\"Par6\">In our experiment, a strong circularly polarized field at 400 nm (3k Hz, 40 fs) with an intensity of 1.42 × 10¹⁴W/cm² is employed to ionize Ar atoms. Here, the polarization plane of 400 nm field is in <italic>x–z</italic> plane. As illustrated in Fig. ##FIG##0##1a##, the rotating electric field vector of 400 nm bends the atomic potential and forms a rotating Coulomb barrier, through which the bound electron is released. Depending on their ionization times, the emitted electrons would be deflected to different emission angles. Here, the emission angle <italic>θ</italic> is defined as the angle between the direction of the electron final momentum <bold>p</bold> and +<italic>z</italic> axis. This time-to-angle mapping is the principle of attoclock. Since multicycle pulses have been used, the electrons that release at times separated by laser cycles would interfere with each other at a specific angle, giving rise to the intercycle interference^{##UREF##13##37##}, which manifests as the well-known above-threshold ionization (ATI)^{##UREF##14##38##} peaks in photoelectron momentum (energy) spectrum. This defines the angle-resolved temporal interferometry in attoclock geometry. Experimentally, the three-dimensional momentum distributions (PMDs) of photoelectrons are measured by cold-target recoil-ion reaction momentum spectroscopy (COLTRIMS)^{##UREF##15##39##}. (Details of the experimental setup can be found in “Methods”). Since the circular field vector is angularly uniform, the measured PMD on the <italic>x–z</italic> polarization plane, as shown in Fig. ##FIG##0##1b##, reveals a series of isotropic ATI rings.</p>", "<p id=\"Par7\">We then add a weak linearly polarized field at 800 nm with the intensity of 8.8 × 10¹¹W/cm² and its polarization along <italic>z</italic> direction to manipulate the spatiotemporal shape of the potential barrier and introduce changes in the attoclock interferometry constructed by 400 nm circular fields. As depicted in Fig. ##FIG##0##1c##, in two-field fields with a fixed relative phase <italic>φ</italic>, both the polarization configuration (indicated by the blue and red arrows) and the perturbative field strength are changing over time. The spatially rotating potential barrier undergoes spatial modulations imposed by the perturbative field that depends on the ionization time. Consequently, the electrons that release at different times would experience distinct modulations. In particular, for the two electron wave packets that are released at times separated by one 400 nm cycle, they experience opposite modulations as the potential barrier is perturbed by opposite 800 nm electric field vector (the modified potential barriers along <italic>z</italic> direction are depicted by the red and blue dashed lines in the lower panel of Fig. ##FIG##0##1c##). Such modulation would be finally imprinted into the angle-resolved photoelectron interference pattern. And for each emission angle <italic>θ</italic>, it represents a distinct interaction configuration. Therefore, by analyzing the angle-resolved photoelectron interference pattern and retrieving the amplitude and phase of electron wave function for each emission angle, one can realize the spatial imaging of the ionization dynamics under various interaction configurations in the full momentum space. Besides, scanning the two-color relative phase also provides an additional knob to manipulate the potential barrier in time domain. As shown in Fig. ##FIG##0##1c##, varying the two-color relative phase, the perturbative field strength is modified for ionization at different times (angles). By inspecting the two-color phase-dependent photoelectron interference at a specific emission angle, one is allowed to monitor how the ionized electron wave function evolves with respect to the fast-oscillating potential barrier, thus achieving the temporal imaging of the ionization dynamics.</p>", "<p id=\"Par8\">Figure ##FIG##0##1d## displays the measured two-color phase-integrated PMD on the <italic>x–z</italic> polarization plane. One can see that adding a weak fundamental field gives rise to the formation of sideband structures between adjacent ATI rings on PMD. Moreover, due to the utilization of linearly polarized perturbative fields, the two-color phase-integrated interference pattern becomes no longer isotropic. Instead, it shows a slight angle-dependence. To visualize the spatiotemporal modulations induced by the perturbative field in the attoclock interferometry, we inspect the measured two-color phase-resolved photoelectron energy spectra at different emission angles. The corresponding spectra for <italic>θ</italic> = 0°, 45°, 90°, and 135° are displayed in Fig. ##FIG##1##2a–d##, respectively. Apparently, the spectra are dominated by equidistant interference peaks spaced by the 800 nm photon energy, which correspond to the alternating ATI peaks and sidebands. This is analogous to the traditional optical interference fringes in real space. More importantly, the photoelectron interference pattern undergoes very different evolution with respect to the relative phase for different emission angles, implying the time- and space-dependent features of the ionization dynamics in two-color attoclock geometry.</p>", "<title>SFA analysis of photoelectron interference</title>", "<p id=\"Par9\">To understand the two-color phase- and angle-dependent photoelectron interference in the geometry, we resort to the strong-field approximation (SFA)^{##UREF##16##40##}. This model has been verified to work well in describing strong-field ionization by sculptured circular fields^{##REF##29542985##36##,##REF##31012680##41##,##UREF##17##42##}. Within saddle-point approach^{##UREF##18##43##}, the transition amplitude of the photoelectron, from the initial ground state to the final Volkov state with the final momentum <bold>p</bold>, can be regarded as the coherent supposition of all quantum orbits, i.e., . Here, is the pre-exponential factor with <bold>A</bold>(<italic>t</italic>) and <bold>E</bold>(<italic>t</italic>) denoting the vector potential and electric field of laser pulses, respectively. The saddle-point <italic>t</italic>_{<italic>s</italic>}, which can be derived from the equation of [<bold>p</bold> + <bold>A</bold>(<italic>t</italic>_{<italic>s</italic>})]²/2 + <italic>I</italic>_{<italic>p</italic>} = 0 with <italic>I</italic>_{<italic>p</italic>} being the ionization potential, represents the complex ionization instant of the quantum orbit. is the classical action (or complex phase) of the quantum orbit. In single 400 nm circular fields, the photoelectron interference at the final momentum <bold>p</bold> along <italic>θ</italic> originates from the intercycle interference among quantum orbits whose ionization instants are separated by 400 nm cycles. When adding a weak linearly polarized 800 nm field, as illustrated in Fig. ##FIG##0##1c##, the quantum orbits that release in adjacent 400 nm cycles with their ionization instants satisfying <italic>t</italic>_{<italic>s</italic>}⁽²⁾= <italic>t</italic>_{<italic>s</italic>}⁽¹⁾ + <italic>T</italic>₄₀₀ would experience opposite modulations by the perturbative fundamental field. Here, <italic>T</italic>₄₀₀ denotes the optical period of 400 nm laser pulses. In the next 800 nm cycle, there arises a similar pair of quantum orbits with their ionization instants satisfying <italic>t</italic>_{<italic>s</italic>}⁽³⁾= <italic>t</italic>_{<italic>s</italic>}⁽¹⁾ + <italic>T</italic>₈₀₀ and <italic>t</italic>_{<italic>s</italic>}⁽⁴⁾= <italic>t</italic>_{<italic>s</italic>}⁽²⁾ + <italic>T</italic>₈₀₀ (<italic>T</italic>₈₀₀ represents the optical period of 800 nm pulses). Considering the periodicity of the light field, four quantum orbits releasing in two 800 nm cycles can well account for the photoelectron interference in two-color synthesized fields. In this case, the photoelectron interference in two-color fields at the emission angle <italic>θ</italic> can be written aswhere <italic>ψ</italic> = <italic>ρ</italic>(<bold>p</bold>)<italic>e</italic>^{<italic>iS</italic>} represents the ionized electron wave packet, <italic>b</italic> = (<italic>U</italic>_{<italic>p</italic>}⁽⁴⁰⁰⁾+<italic>U</italic>_{<italic>p</italic>}⁽⁸⁰⁰⁾+<italic>E</italic>_{<italic>k</italic>} + <italic>I</italic>_{<italic>p</italic>})<italic>T</italic>₈₀₀ is the action difference due to the time difference of traveling in the continuum. <italic>U</italic>_{<italic>p</italic>} is the pondermotive energy and <italic>E</italic>_{<italic>k</italic>} = <italic>p</italic>²/2 denotes the photoelectron energy. And <italic>ψ</italic>₃= <italic>ψ</italic>₁e^{<italic>ib</italic>}, <italic>ψ</italic>₄= <italic>ψ</italic>₂e^{<italic>ib</italic>}, respectively.</p>", "<p id=\"Par10\">Figure ##FIG##1##2e–h## displays the calculated photoelectron energy spectra as a function of the two-color relative phase based on Eq. (##FORMU##5##1##) for the selected angles. They show good agreement with the measured results. As for the slight discrepancies in low-energy region, this can be attributed to the neglect of Coulomb effect in SFA model (Comparison among the experimental results, SFA and Coulomb-corrected SFA (CCSFA) calculations can be seen in Supplementary Fig. ##SUPPL##0##2##). According to the time-to-angle mapping governed by SFA, i.e., <bold>p</bold> = −<bold>A</bold>(<italic>t</italic>₀), we can determine the direction of the 400 nm electric field vector at the ionization instant <italic>t</italic>₀ for these emission angles, and thus obtain the corresponding polarization configurations, as labeled by the blue and red arrows in Fig. ##FIG##1##2a–d##. Note that since the 800 nm field is perturbative weak, we have neglected its influence on the time-to-angle mapping.</p>", "<p id=\"Par11\">Having demonstrated good agreement between the experiment and SFA calculations, we continue analyzing the photoelectron interference using the SFA model. In two-color synthesized fields, the complex phase of the electron wave packet can be expressed as , where represents the action induced solely by the 400 nm circular field, is the additional action induced by the weak linearly polarized 800 nm field and is the high-order quantity and can be reduced to a linear phase shift <italic>U</italic>_{<italic>p</italic>}⁽⁸⁰⁰⁾<italic>t</italic>_{<italic>s</italic>}. Consequently, the photoelectron interference in two-color fields at the emission angle <italic>θ</italic> in the energy space can be rearranged as</p>", "<p id=\"Par12\">Here, represents the amplitude of ionized electron wave packet in 400 nm circular field. Re[<italic>σ</italic>] and Im[<italic>σ</italic>], which refer to the real part and imaginary part of the additional phase <italic>σ</italic>, respectively, quantify the phase and amplitude modulations of the electron wave function induced by 800 nm perturbative field. Note that the amplitude modulation induced by the change of <italic>ρ</italic>(<bold>p</bold>) when adding a weak 800 nm field has been neglected since it is much smaller as compared with that induced by the change of imaginary part of the complex phase (Supplementary Fig. ##SUPPL##0##3##). The <italic>a</italic> = (<italic>I</italic>_{<italic>p</italic>} + <italic>U</italic>_{<italic>p</italic>}⁽⁸⁰⁰⁾<italic>+U</italic>_{<italic>p</italic>}⁽⁴⁰⁰⁾)<italic>T</italic>₄₀₀ denotes a constant phase. Detailed derivation of Eq. (##FORMU##10##2##) can be found in Supplementary Information. When the perturbative field is absent, the two-color interference will be reduced to the single-color case with the formula governed by</p>", "<p id=\"Par13\">From the expressions in Eqs. (##FORMU##10##2##) and (##FORMU##12##3##), one can see that the photoelectron interference among four electron wave packets emitting within two 800 nm cycles contains multiple frequencies along <italic>E</italic>_{<italic>k</italic>}, i.e., the zero-frequency component, 1<italic>f</italic>_{<italic>x</italic>}, 2<italic>f</italic>_{<italic>x</italic>}, and 3<italic>f</italic>_{<italic>x</italic>} frequency components with <italic>f</italic>_{<italic>x</italic>} = <italic>T</italic>₄₀₀/2<italic>π</italic>. This indicates that we can apply the Fourier transform analysis^{##UREF##19##44##}, which has been frequently used in analyzing the traditional optical interferogram, to the photoelectron interference in order to extract the amplitude and phase modulations of the electron wave function induced by the spatiotemporal manipulation of potential barrier.</p>", "<title>Fourier transform analysis for fully retrieving the electron wave function</title>", "<p id=\"Par14\">As presented in Eq. (##FORMU##10##2##), the amplitude modulation Im[<italic>σ</italic>] caused by the perturbative field is encoded in the amplitudes of the zero-frequency term and 2<italic>f</italic>_{<italic>x</italic>} frequency term of the photoelectron interference. Here, we utilize the zero-frequency term of the photoelectron interference to extract Im[<italic>σ</italic>]. By performing Fourier transform on the photoelectron interference along <italic>E</italic>_{<italic>k</italic>} at a specific angle <italic>θ</italic>, we obtain the frequency spectra in single- and two-color cases. Then, we filter out the zero-frequency components and perform the inverse Fourier transform. Accordingly, we obtain the amplitudes of zero-frequency terms in single- and two-color fields, which correspond to 4<italic>W</italic>₀² and 2<italic>W</italic>₀²(e^2Im[σ]+e^{−2Im[<italic>σ</italic>]}), respectively. Dividing 2<italic>W</italic>₀²(e^2Im[σ]+ e^{−2Im[<italic>σ</italic>]}) by 4<italic>W</italic>₀², we obtain the ratio <italic>k</italic> = (e^2Im[σ]+ e^{−2Im[<italic>σ</italic>]})/2, from which Im[<italic>σ</italic>] can be analytically derived with the formula of Im[<italic>σ</italic>] =  (The other root equaling is unphysical and should be discarded). While to retrieve the phase modulation Re[<italic>σ</italic>], we focus on the 3<italic>f</italic>_{<italic>x</italic>} frequency term, i.e., 2<italic>W</italic>₀²cos(3<italic>E</italic>_{<italic>k</italic>}<italic>T</italic>₄₀₀ + 2Re[<italic>σ</italic>] + 3<italic>a</italic>), as Re[<italic>σ</italic>] is directly imprinted into its phase. By applying the Fourier transform to the two-color phase-dependent photoelectron interference along <italic>E</italic>_{<italic>k</italic>}, we obtain the two-color phase-resolved frequency spectrum, from which we filter out the 3<italic>f</italic>_{<italic>x</italic>} frequency term and shift it to the zero-frequency position. We then perform the inverse Fourier transform and obtain a complex value of 2<italic>W</italic>₀²<italic>e</italic>^{<italic>i</italic>(2Re[<italic>σ</italic>]+3<italic>a</italic>)} whose phase corresponds to 2Re[<italic>σ</italic>]+3<italic>a</italic>. Afterward, we subtract the constant phase 3<italic>a</italic> from the retrieved phase and finally access the phase modulation Re[<italic>σ</italic>]. In fact, within the saddle-point approach, the amplitude and phase modulations can be analytically derived by substituting the expression of two-color electric field into the definition of <italic>σ</italic>. The analytical formulas for Im[<italic>σ</italic>] and Re[<italic>σ</italic>] are given in Eq. (4) in “Methods”. By comparing the calculated Im[<italic>σ</italic>] and Re[<italic>σ</italic>] (Supplementary Fig. ##SUPPL##0##4##) with the retrieved results, one can validate the Fourier transform analysis.</p>", "<title>Temporal shaping and imaging of electron wave function</title>", "<p id=\"Par15\">In the following, we apply the Fourier transform analysis to the two-color phase-dependent photoelectron interference at specific angles in order to retrieve the temporal evolution of the ionized electron wave function through a fast-oscillating potential barrier. Here, we concentrate on two intriguing strong-field interaction configurations, in which the potential barrier is manipulated by the weak fundamental field along longitudinal (parallel) and transverse (perpendicular) directions, corresponding to the situations at <italic>θ</italic> = 90° and 0°, respectively.</p>", "<p id=\"Par16\">In Fig. ##FIG##2##3##, we present the retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra from the SFA calculations and from the measured results in the parallel configuration (<italic>θ</italic> = 90°). Good agreement has been achieved between the experiment and the SFA calculations. As depicted, in this configuration, the ionizing electric field vector points to the negative <italic>z</italic> axis, parallel with the perturbative field. Varying the two-color relative phase modifies the perturbative field strength at the ionization instant. Interestingly, as the perturbative field increases from zero to its maximum, the amplitude modulation Im[<italic>σ</italic>] on electron wave function increases from zero to maximum, whereas the phase modulation Re[<italic>σ</italic>] decreases from maximum to zero.</p>", "<p id=\"Par17\">In parallel interaction configuration, increasing the perturbative field strength is equivalent to reducing the thickness of the potential barrier along the ionization direction. More photoelectrons would be ionized through a narrower barrier, resulting in the increased ionization amplitude. Since the classical propagation after ionization does not influence the ionization probability^{##UREF##10##33##}, the retrieved Im[<italic>σ</italic>] directly reflects changes in the imaginary phase accumulated during the electrons’ under-barrier motion. On the other side, the photoelectron acquires an additional drift momentum along <italic>z</italic> direction governed by –<bold>A</bold>₈₀₀(<italic>t</italic>,<italic>φ</italic>) from the perturbative field. With the increase of the perturbative electric field, the drift momentum decreases. Such momentum is parallel to the ionizing direction but perpendicular to the final momentum <bold>p</bold> of electron. It would induce an additional real phase during the under-barrier excursion and also a lateral phase shift during the classical propagation (Supplementary Fig. ##SUPPL##0##5a##, ##SUPPL##0##b##). These two phases jointly contribute to the retrieved phase modulation Re[<italic>σ</italic>] as shown in Fig. ##FIG##2##3b, d##. Besides, one could see that the retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra exhibit prominent energy-dependences, i.e., the photoelectrons with lower energies (or lower radial momenta <italic>p</italic>_{<italic>r</italic>}) experience larger modulations than those of higher energies. This phenomenon can be ascribed to the energy-dependent imaginary part <italic>t</italic>_{<italic>i</italic>} of the ionization time <italic>t</italic>_{<italic>s</italic>} in circular fields, as shown in Supplementary Fig. ##SUPPL##0##1##, which quantifies the excursion time under the barrier and determines the real and imaginary phase of electron accumulated during under-barrier motion [see Eq. (4) in “Methods”].</p>", "<p id=\"Par18\">Another intriguing scenario is that the potential barrier is manipulated transversely, corresponding to the case of <italic>θ</italic> = 0°. Based on the results shown in Fig. ##FIG##1##2##a, ##FIG##1##e##, we extract the phase-dependent amplitude and phase modulations of the electron wave function in the perpendicular configuration. The corresponding results are displayed in Fig. ##FIG##3##4##. Discrepancies in the high-energy part of the retrieved Im[<italic>σ</italic>] spectra between SFA calculation and experiment can be attributed to the imperfect filter of zero-frequency component from the Fourier frequency spectrum of the experimental result that hampers the accurate retrieval of Im[<italic>σ</italic>]. In this configuration, the ionizing 400 nm electric field vector points to +<italic>x</italic> direction and the potential barrier is perturbed transversely by the weak fundamental field. The retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra reveal distinct phase- and energy-dependences in comparison to the case of parallel configuration. Specifically, when the perturbative field approaches zero, the amplitude modulation maximizes, whereas the phase modulation vanishes. Increasing the perturbative field to its maximum, the amplitude modulation gradually disappears, while the phase modulation reaches the maximum. Moreover, the two flanks of the electron wave packet, i.e., the lower- and higher-energy parts, seem to suffer a larger amplitude modulation than the central part which has a vanishing transverse momentum at the ionization instant and is finally streaked to <italic>p</italic>_{<italic>r</italic>} ~ 0.4 a.u. by the 400 nm circular field. This implies that under the barrier, the imaginary phase of electrons with larger transverse momenta is more susceptible to be influenced by the perpendicular perturbative field. For the retrieved Re[<italic>σ</italic>] spectra, the electrons with higher energies experience a larger phase modulation than the low-energy electrons.</p>", "<p id=\"Par19\">Note that different from the case in parallel configuration, the potential barrier in perpendicular configuration is deformed in transverse direction and its thickness along the ionization direction remains unchanged. Moreover, the additional momentum acquired by the photoelectron from the perturbative field is perpendicular to the ionization direction but parallel to the final momentum. When the perturbative electric field is vanishing (<italic>φ</italic> = 0.25π), the additional momentum maximizes. This causes the largest modulation on the imaginary phase of electrons. However, since the shape of potential barrier remains unchanged in this case, the real phase of the electrons accumulated during the under-barrier motion and the following propagation keeps unchanged (Supplementary Fig. ##SUPPL##0##5##c, d). Increasing the perturbative field to its maximum (<italic>φ</italic> = 0.75π), the momentum acquired by electrons along <italic>z</italic> axis vanishes, and, as a result, the modulation on the imaginary phase of electrons disappears. Nevertheless, it should be noted that the potential barrier in this case experiences the largest lateral perturbation. This results in the largest modulation on the real phase of the electron during its entire motion.</p>", "<p id=\"Par20\">From the retrieved temporal evolutions of shaped electron wave functions in parallel and perpendicular configurations, we find that the employed field geometry also allows for selective manipulation of the amplitude and phase of electron wave function in strong-field ionization, simply by modifying the two-color relative phase. For example, in the parallel configuration, by adjusting the two-color relative phase to <italic>φ</italic> = 0.5π, one can solely manipulate the amplitude of electron wave function while keep its phase unchanged. When modifying <italic>φ</italic> to 0, the selective shaping of the phase of electron wave function is enabled with its amplitude remaining unchanged. In principle, if performing Fourier transform analysis on the measured two-color phase-dependent photoelectron interference for each emission angle, one could access the complete information about electron wave function in time and space under this geometry, thereby shedding light into the underlying quantum dynamics of intense light-matter interactions.</p>", "<title>Spatial shaping and imaging of electron wave function</title>", "<p id=\"Par21\">Apart from temporal shaping and imaging of electrons, spatial shaping and imaging also arouses great interest of scientists, since the spatial property of emitted electrons is closely tied to electronic structures and it dictates the subsequent electron and nuclear dynamics inside molecules such as electron localization^{##REF##16614216##45##} and charge migration^{##REF##26494175##46##}. As illustrated by Fig. ##FIG##0##1c##, in the two-color attoclock geometry, the photoelectron interference along different emission angles encodes ionization dynamics under different strong-field interaction configurations. This reflects the spatial property of the attoclock geometry. By analyzing the angle-resolved photoelectron interference at a fixed two-color relative phase, one is allowed to capture the snapshots of the shaped electron wave function in the full momentum space for diverse configurations.</p>", "<p id=\"Par22\">Figure ##FIG##4##5##a and d display the calculated and measured PMDs in two-color fields with <italic>φ</italic> = 0, respectively. The SFA calculation basically reproduces the main features of the measured PMD, except for the low-energy part which suffers from the Coulomb effect. To facilitate analysis on photoelectron interference, we have transformed the PMD into the angle-resolved photoelectron energy spectrum. The spectrum is rotated by a specific angle in order to eliminate the Coulomb effect. Here, the rotating angle can be read from the comparison between the calculated angle-resolved spectra using the SFA and CCSFA models (Supplementary Fig. ##SUPPL##0##6##). Then, we apply the Fourier transform analysis to the angle-resolved photoelectron energy spectrum and retrieve the angle-resolved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra in energy space. These spectra are later transformed back to the momentum space.</p>", "<p id=\"Par23\">As shown in Fig. ##FIG##4##5b, e## and Fig. ##FIG##4##5c, f##, the retrieved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra reveal obvious angle- and energy-dependent features. And they are symmetric about <italic>p</italic>_{<italic>x</italic>} axis. Actually, such symmetry reflects the field geometry of the two-color synthesized fields, as depicted by the black line in Fig. ##FIG##4##5b##. Particularly, as the ionization amplitude critically depends on the electric field strength, the retrieved angle-dependent amplitude modulation directly maps the evolution of sculptured two-color laser fields. Scanning the emission angle, the spatially rotating potential barrier is manipulated along the <italic>z</italic> direction by the fundamental field of different strength (see the labeled two-color field configurations in Fig. ##FIG##4##5b##). The emission angle indeed encodes the spatial property of the field-modulated potential barrier. Hence, the retrieved angle-resolved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra in the full momentum space reveals the impact of spatial property of potential barrier on the electron dynamics, demonstrating the spatial imaging capability of the two-color attoclock geometry. This capability provides unique possibilities to probe the electronic environment of molecules, solids, and liquids.</p>", "<p id=\"Par24\">In summary, we have demonstrated a novel two-color attoclock interferometry that enables the spatiotemporal shaping and imaging of the electron wave function in strong-field ionization. This interferometry encompasses a wide range of strong-field interaction configurations, thereby allowing the scrutiny of the underlying ionization dynamics in diverse scenarios. Through the analysis of the two-color phase-dependent photoelectron interferences at specific angles, we have gained insights into the temporal evolution of the ionization dynamics with respect to a fast-oscillating potential barrier under different interaction configurations, especially for the quantum dynamics under the barrier. This field geometry, as demonstrated in our experiment, can also be exploited for selectively manipulating the amplitude and phase of the electron wave function. Besides that, the analysis of the angle-resolved photoelectron interference at a specific two-color relative phase permits the spatial imaging of the electron dynamics in the full momentum space. Our study illuminates puzzles in understanding how the spatiotemporal properties of Coulomb barrier influence the ionization process and shape the electron wave function. Looking forward, this novel attoclock interferometry has important implications for spatiotemporally resolving ultrafast electronic dynamics inside molecules following photoionization such as charge migration^{##REF##26494175##46##} and charge transfer processes^{##REF##29333473##47##}, paving the way to real-time measurement and control of chemical transformations.</p>" ]

[]

[ "<p id=\"Par1\">Electrons detached from atoms by photoionization carry valuable information about light-atom interactions. Characterizing and shaping the electron wave function on its natural timescale is of paramount importance for understanding and controlling ultrafast electron dynamics in atoms, molecules and condensed matter. Here we propose a novel attoclock interferometry to shape and image the electron wave function in atomic photoionization. Using a combination of a strong circularly polarized second harmonic and a weak linearly polarized fundamental field, we spatiotemporally modulate the atomic potential barrier and shape the electron wave functions, which are mapped into a temporal interferometry. By analyzing the two-color phase-resolved and angle-resolved photoelectron interference, we are able to reconstruct the spatiotemporal evolution of the shaping on the amplitude and phase of electron wave function in momentum space within the optical cycle, from which we identify the quantum nature of strong-field ionization and reveal the effect of the spatiotemporal properties of atomic potential on the departing electron. This study provides a new approach for spatiotemporal shaping and imaging of electron wave function in intense light-matter interactions and holds great potential for resolving ultrafast electronic dynamics in molecules, solids, and liquids.</p>", "<p id=\"Par2\">Electrons detached from atoms by photoionization carry valuable information about light-atom interactions. Here, authors propose a novel attoclock interferometry to spatiotemporally shape and image the electron wave function, from which the quantum nature of strong-field ionization is identified.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n</p>", "<title>Source data</title>", "<p>\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41467-024-44775-5.</p>", "<title>Acknowledgements</title>", "<p>We thank the support of the National Key Research and Development Program of China (Grant Nos. 2022YFA1604301, Y.L. and 2023YFA1406800, P.G.) and National Science Foundation of China (Grant Nos. 12334013,92050201, 92250306, Y.L. and 8200906472, P.G.) and China Postdoctoral Science Foundation (No. 8206300495, P.G.).</p>", "<title>Author contributions</title>", "<p>P.G. conceived the idea. P.G. and Y. Dou performed the experiment. P.G., M.H., and Y.L. analyzed the experimental data. P.G. and Y.F. performed the theoretical simulation. Y. Deng supported the operation of laser system. C.W. and Q.G. assisted the data analysis. This project was supervised by Y.L. All authors discussed the results and contributed to the final manuscript.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par28\"><italic>Nature Communications</italic> thanks Ihar Babushkin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.</p>", "<title>Data availability</title>", "<p>The data supporting the findings of this study are available within the paper and its Supplementary Information files. The data generated in this study are provided in Supplementary Information/Source data file. <xref ref-type=\"sec\" rid=\"Sec12\">Source data</xref> are provided with this paper.</p>", "<title>Competing interests</title>", "<p id=\"Par29\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Schematic illustration of two-color attoclock interferometry.</title><p><bold>a</bold> Common attoclock geometry constructed by multicycle 400 nm circular fields. The time-dependent rotating barriers formed by 400 nm circular fields are depicted. The time-to-angle mapping is given. <bold>b</bold> Measured PMD of strong-field ionization of Ar atoms on <italic>x–z</italic> polarization plane in 400 nm attoclock geometry. The emission angle <italic>θ</italic> is defined as the angle between the direction of the final momentum <bold>p</bold> and +<italic>z</italic> axis. <bold>c</bold> Temporal evolution of the two-color field configuration in the novel attoclock geometry, where a weak linearly polarized field at 800 nm along <italic>z</italic> direction is added to perturb the attoclock established by 400 nm circular fields. For times separated by one 400 nm optical cycle <italic>T</italic>₄₀₀, the perturbative 800 nm field points to opposite direction, thus leading to opposite modulation on the barrier, as depicted in the lower panel. Here, the barriers at times of <italic>t</italic> = 0 (<italic>T</italic>₄₀₀) and <italic>t</italic> = 0.25<italic>T</italic>₄₀₀ (1.25<italic>T</italic>₄₀₀) which correspond to the situations of <italic>θ</italic> = 270° and <italic>θ</italic> = 0°, respectively, are exemplified. They are manipulated by the fundamental field in parallel and perpendicular directions, respectively. The black lines show the unperturbed potential curves along <italic>z</italic> direction, while the red and blue dashed lines represent the oppositely modulated potential curves by the fundamental field at times separated by one 400 nm cycle. Varying the relative phase between two colors, the polarization configuration remains unchanged, whereas the perturbative field strength at the ionization time changes. <bold>d</bold> Measured two-color phase-integrated PMD on <italic>x–z</italic> polarization plane in two-color attoclock geometry.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Two-color phase-resolved photoelectron energy spectra.</title><p><bold>a</bold>–<bold>d</bold> Measured two-color phase-resolved photoelectron energy spectra at the emission angles of <italic>θ</italic> = 0°, 45°, 90° and 135°, respectively. <bold>e</bold>–<bold>h</bold> Calculated two-color phase-resolved energy spectra by SFA model at the emission angles of <italic>θ</italic> = 0°, 45°, 90° and 135°, respectively. The blue arrow on the top denotes the direction of the rotating 400 nm field vector. The red arrow indicates the polarization direction of 800 nm linearly polarized field.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Temporal shaping of ionized electron wave function in parallel interaction configuration.</title><p><bold>a</bold>, <bold>b</bold> Retrieved two-color phase-dependent Im[<italic>σ</italic>] and Re[<italic>σ</italic>] from the SFA calculated phase-dependent photoelectron energy spectrum (as shown in Fig. ##FIG##1##2g##). The two-color field configurations are shown on the top, with the blue and red arrows indicating the electric field vectors of 400 nm and 800 nm pulses, respectively. The red lines denote the oscillating 800 nm perturbative field. <bold>c</bold>, <bold>d</bold> Same as (<bold>a</bold>), (<bold>b</bold>) but retrieved from the measured result as shown in Fig. ##FIG##1##2c##.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Temporal shaping of ionized electron wave function in perpendicular interaction configuration.</title><p><bold>a</bold>, <bold>b</bold> Retrieved two-color phase-dependent Im[<italic>σ</italic>] and Re[<italic>σ</italic>] from the SFA calculated phase-dependent photoelectron interference (as shown in Fig. ##FIG##1##2e##). The two-color field configurations are shown on the top, with the blue and red arrows indicating the electric field vectors of 400 nm and 800 nm pulses, respectively. The red lines depict the oscillating 800 nm perturbative field. <bold>c</bold>, <bold>d</bold> Same as (<bold>a</bold>), (<bold>b</bold>) but retrieved from the measured result as shown in Fig. ##FIG##1##2a##.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Spatial imaging of the ionized electron wave function in momentum space under two-color synthesized fields.</title><p><bold>a</bold> Calculated PMD in two-color synthesized field with the relative phase <italic>φ</italic> = 0 based on the SFA model. <bold>b</bold>, <bold>c</bold> Retrieved momentum-resolved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra from the SFA calculated PMD (shown in <bold>a</bold>). In (<bold>b</bold>), the two-color synthesized electric field has been plotted. Also, the corresponding field configurations at specific angles are labeled. <bold>d</bold> Measured PMD in the two-color synthesized field with the relative phase <italic>φ</italic> = 0. <bold>e</bold>, <bold>f</bold> Retrieved momentum-resolved Im[<italic>σ</italic>] and Re[<italic>σ</italic>] spectra from the measured PMD (shown in <bold>d</bold>).</p></caption></fig>" ]

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[ "<inline-formula id=\"IEq1\"><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$|{\\psi }_{0}\\rangle$$\\end{document}</tex-math><mml:math id=\"M2\"><mml:mo>∣</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>⟩</mml:mo></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq2\"><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$|{{\\psi }_{{{{{{\\bf{p}}}}}}}}^{V}\\rangle$$\\end{document}</tex-math><mml:math id=\"M4\"><mml:mo>∣</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow></mml:msup><mml:mo>⟩</mml:mo></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq3\"><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${M}_{{{{{{\\bf{p}}}}}}}\\sim {\\sum }_{i}{\\rho }_{s}({{{{{\\bf{p}}}}}}){e}^{iS({{{{{\\bf{p}}}}}},{{t}_{s}}^{(i)})}$$\\end{document}</tex-math><mml:math id=\"M6\"><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi></mml:mrow></mml:msub><mml:mo>~</mml:mo><mml:msub><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq4\"><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\rho }_{s}({{{{{\\bf{p}}}}}}) \\sim \\langle {{{{{\\bf{p}}}}}}+{{{{{\\bf{A}}}}}}({t}_{s})|{{{{{\\bf{r}}}}}}\\cdot {{{{{\\bf{E}}}}}}({t}_{s})|{\\psi }_{0}({{{{{\\bf{r}}}}}})\\rangle$$\\end{document}</tex-math><mml:math id=\"M8\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>~</mml:mo><mml:mo>⟨</mml:mo><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"bold\">A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>∣</mml:mo><mml:mi mathvariant=\"bold\">r</mml:mi><mml:mo>⋅</mml:mo><mml:mi mathvariant=\"bold\">E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>∣</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">r</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>⟩</mml:mo></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq5\"><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$S({{{{{\\bf{p}}}}}},{t}_{s})=-{\\int }_{{t}_{s}}^{\\infty }{[{{{{{\\bf{p}}}}}}+{{{{{\\bf{A}}}}}}(t)]}^{2}/2dt+{I}_{p}{t}_{s}$$\\end{document}</tex-math><mml:math id=\"M10\"><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"bold\">A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mi>d</mml:mi><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I({{{{{\\bf{p}}}}}},\\varphi )={|{\\psi }_{1}+{\\psi }_{2}+{\\psi }_{3}+{\\psi }_{4}|}^{2}={|{\\psi }_{1}+{\\psi }_{2}|}^{2}{|1+{e}^{ib}|}^{2}$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>∣</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>∣</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>∣</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>∣</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mo>∣</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msup><mml:mo>∣</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq6\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$S({{{{{\\bf{p}}}}}},{t}_{s})=-{\\int }_{{t}_{s}}^{\\infty }{[{{{{{\\bf{p}}}}}}+{{{{{{\\bf{A}}}}}}}_{400}(t)+{{{{{{\\bf{A}}}}}}}_{800}(t,\\varphi )]}^{2}/2dt+{I}_{p}{t}_{s}={S}_{0}+\\sigma -{\\int }_{{t}_{s}}^{\\infty }{[{{{{{{\\bf{A}}}}}}}_{800}(t,\\varphi )]}^{2}/2dt$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">A</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">A</mml:mi></mml:mrow><mml:mrow><mml:mn>800</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mi>d</mml:mi><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>σ</mml:mi><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">A</mml:mi></mml:mrow><mml:mrow><mml:mn>800</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq7\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${S}_{0}({{{{{\\bf{p}}}}}},{t}_{s})=-{\\int }_{{t}_{s}}^{\\infty }{[{{{{{\\bf{p}}}}}}+{{{{{{\\boldsymbol{A}}}}}}}_{400}(t)]}^{2}/2dt+{I}_{p}{t}_{s}$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"bold-italic\">A</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mi>d</mml:mi><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq8\"><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma=-{\\int }_{{t}_{s}}^{\\infty }[{{{{{\\bf{p}}}}}}+{{{{{{\\bf{A}}}}}}}_{400}(t)]\\cdot {{{{{{\\bf{A}}}}}}}_{800}(t,\\varphi )dt$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:mi>σ</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">A</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">A</mml:mi></mml:mrow><mml:mrow><mml:mn>800</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq9\"><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-{\\int }_{{t}_{s}}^{\\infty }{[{{{{{{\\bf{A}}}}}}}_{800}(t,\\varphi )]}^{2}/2dt$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∫</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">A</mml:mi></mml:mrow><mml:mrow><mml:mn>800</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I({E}_{k},\\varphi )=\t {|{\\psi }_{1}+{\\psi }_{2}+{\\psi }_{3}+{\\psi }_{4}|}^{2}\\\\=\t 2{W}_{0}^{2}({e}^{2{{\\mbox{Im}}}[\\sigma ]}+{e}^{-2{{\\mbox{Im}}}[\\sigma ]})[1+\\,\\cos (2{E}_{k}{T}_{400}+2a)]\\\\ \t+4{W}_{0}^{2}\\,\\cos ({E}_{k}{T}_{400}+2{{\\mathrm{Re}}}[\\sigma ]+a)\\\\ \t+2{W}_{0}^{2}\\,\\cos ({E}_{k}{T}_{400}-2{{\\mathrm{Re}}}[\\sigma ]+a)\\\\ \t+2{W}_{0}^{2}\\,\\cos (3{E}_{k}{T}_{400}+2{{\\mathrm{Re}}}[\\sigma ]+3a)$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>∣</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>∣</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mstyle><mml:mtext>Im</mml:mtext></mml:mstyle><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mstyle><mml:mtext>Im</mml:mtext></mml:mstyle><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>a</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"normal\">Re</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>a</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"normal\">Re</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>a</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>3</mml:mn><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"normal\">Re</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>3</mml:mn><mml:mi>a</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${W}_{0}=\\rho ({{{{{\\bf{p}}}}}}){e}^{-{{\\mbox{Im}}}[{S}_{0}]}$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">p</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mstyle><mml:mtext>Im</mml:mtext></mml:mstyle><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I({E}_{k},\\varphi )=\t {|{\\psi }_{1}+{\\psi }_{2}+{\\psi }_{3}+{\\psi }_{4}|}^{2}\\\\=\t 4{W}_{0}^{2}[1+\\,\\cos (2{E}_{k}{T}_{400}+2a)]\\\\ \t+6{W}_{0}^{2}\\,\\cos ({E}_{k}{T}_{400}+a)\\\\ \t+2{W}_{0}^{2}\\,\\cos (3{E}_{k}{T}_{400}+3a)$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>φ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>∣</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>∣</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>a</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>6</mml:mn><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>a</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>3</mml:mn><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>3</mml:mn><mml:mi>a</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5ln(k+\\sqrt{{k}^{2}-1})$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:mn>0.5</mml:mn><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:msqrt><mml:mrow><mml:msup><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msqrt></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5ln(k-\\sqrt{{k}^{2}-1})$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:mn>0.5</mml:mn><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:msqrt><mml:mrow><mml:msup><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msqrt></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><label>4a</label><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{\\mathrm{Re}}}[\\sigma ]=\t -\\frac{{p}_{z}{E}_{800}}{{\\omega }^{2}}\\,\\cos (\\omega {t}_{r}+\\varphi )\\cosh (\\omega {t}_{i})+\\frac{{E}_{400}{E}_{800}}{12{\\omega }^{3}}\\,\\sin (3\\omega {t}_{r}+\\phi )\\cosh (3\\omega {t}_{i})\\\\ \t -\\frac{{E}_{400}{E}_{800}}{4{\\omega }^{3}}\\,\\sin (\\omega {t}_{r}-\\phi )\\cosh (\\omega {t}_{i})$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:mi 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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>" ]

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[ "<media xlink:href=\"41467_2024_44775_MOESM1_ESM.pdf\"><caption><p>Supplementary information</p></caption></media>", "<media xlink:href=\"41467_2024_44775_MOESM2_ESM.pdf\"><caption><p>Peer Review File</p></caption></media>", "<media xlink:href=\"41467_2024_44775_MOESM3_ESM.zip\"><caption><p>Source Data</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Scale insects, which are distributed worldwide, are classified into 22 families including Pseudococcidae (mealybugs)^{##UREF##0##1##}. Mealybugs are distinguished by their production of fine, powdery, integumentary wax. The hydrophobic layers of the wax are arranged in long, lateral filaments, hence the common name, “mealybug”, attributed to the Pseudococcidae^{##UREF##1##2##}. The integument is an important protective tissue that prevents inner moisture from excessive evaporation and environmental attacks by inorganic compounds, pathogens, microorganisms, and insecticide sprays^{##UREF##2##3##}. Gullan and Cranston suggested that the wax helps protect the mealybug from predators and insecticides across the different developmental stages of its life cycle^{##UREF##2##3##}. The types and distribution of pores and ducts associated with wax production have been considered by taxonomists as invaluable characters for the identification and classification of mealybugs and other scale insects^{##UREF##3##4##–##UREF##9##10##}. On the basis of the dermal pores producing the wax, Cox and Pearce distinguished three species of mealybugs, <italic>Ferrisia virgate</italic> (Cockerell), <italic>Phenacoccus manihoti</italic> (Matile-Ferrero), and <italic>Planococcus citri</italic> (Risso)^{##UREF##10##11##}.</p>", "<p id=\"Par3\">In Pseudococcidae, the males go through six developmental stages, namely the egg, first instar nymph, second instar nymph, prepupa, pupa, and adult. The male is usually slim in appearance and easily distinguishable from the adult females. Adult males resemble aphids in that they have a non-functional mouth, 9–10 segmented antennae, a pair of tiny mesothoracic wings, metathoracic hamulohalterae, 5-segmented legs, an abdomen that bears 0–3 pairs of caudal filaments associated with tail-forming pore clusters, and an aedeagus, distinguished by a penile sheath, at the end of the abdominal segments^{##UREF##0##1##}.</p>", "<p id=\"Par4\">The cotton mealybug, <italic>Phenacoccus solenopsis</italic> Tinsley, has become established as an invasive pest in the Afrotropical, Australasian, Nearctic, Neotropical, and Oriental regions, and causes direct economic and ecological damage to crops and native flora^{##REF##36517816##12##}. The adult females weigh about 100 to 200 times more than the adult males^{##UREF##11##13##}. Mealybug females are neotenic and have three nymphal instars; in contrast, the males go through two nymphal instars and additional prepupal and pupal stages, which develop inside a waxy cocoon^{##REF##20874596##14##,##UREF##12##15##}. Females live for several months, whereas the tiny, winged male is ephemeral (2–3 days). The adult male remains inside the wax webbing of the pupal cocoon for 4–12 h before emerging. It resembles a fluffy gnat and has two pairs of waxy caudal filaments, whereas most mealybug species have one pair of waxy caudal filaments. The wax tail consists of two pairs of caudal filaments that are secreted by clusters of glandular pouch pleural pores located on the 7th and 8th abdominal segments^{##UREF##13##16##–##UREF##15##18##}. The length of these filaments increases from the time of the emergence of the adult male until maturation occurs. The adult male takes 1–2 days to complete the formation of its wax tail, which assists in flight stabilization^{##UREF##16##19##}.</p>", "<p id=\"Par5\">The mature male is polygynous in that it mates with different females during its lifetime. Seven mealybug species of the genera, <italic>Pseudococcus, Planococcus,</italic> and <italic>Nipaecoccus</italic>, were studied to estimate at which physiological age the males are sexually active and for how long^{##REF##22082650##20##,##UREF##17##21##}. They determined that the adult males take 30–40 h to achieve sexual maturity and being able to fly. The lengths of the caudal filaments ranging from 0.96 to 1.15 mm for seven mealybug species which are the spherical mealybug, <italic>Nipaecoccus viridis</italic> Newstead; the cypress mealybug, <italic>Planococcus vovae</italic> Nasonov; the citrus mealybug, <italic>Pl. citri Risso</italic>; the vine mealybug, <italic>Pl. ficus</italic> Signoret; the citriculus or cryptic mealybug, <italic>Pseudococcus cryptus</italic> Hempel; the long-tailed mealybug, <italic>Ps. longispinus</italic> Targioni Tozzetti; and the obscure mealybug, <italic>Ps. viburni</italic> Signoret^{##REF##22082650##20##}.</p>", "<p id=\"Par6\">Identification of the various species of mealybug is usually based on the morphological features of the specimens^{##UREF##18##22##}. Easy separation of the adult female from the nymphal stages for all species is based on their characteristic genital structure called the vulva, present posteriorly on the ventral side of the female abdomen and absent in the nymphal stages. However, differentiation in such cases takes a long time, approximately 1 month, to enable the adult female to be distinguished. Therefore, rapid and accurate identification is in demand and is a critical step for both the control of the pests and for agricultural quarantine purposes regarding imported and exported crops. Furthermore, identifying the immature stages of mealybugs allows accelerated decision-making for control strategies.</p>", "<p id=\"Par7\">Previous studies have provided important morphological descriptions of the adult male of <italic>P. solenopsis</italic>^{##UREF##10##11##,##UREF##18##22##}, but the genitalia and structures associated with wax production, such as the dermal pores and ducts, have received little attention. Moreover, descriptions of the ultrastructural features of the adult male genitalia, the types and distribution of sensilla, and the dermal pores, are limited.</p>", "<p id=\"Par8\">For the adult male of <italic>P. solenopsis</italic>, few studies have been performed on the pleural pores of the glandular pouch as a form of wax pore different from those of the other immature stages, although, the structure of the pleural pores and ducts of four species from 4 genera of Pseudococcidae, namely <italic>Ferrisia virgate</italic> Cockerell<italic>, P. manihoti</italic> Matile-Ferrero, <italic>Pl. citri</italic> Risso, <italic>Maconellicoccus hirsutus</italic> Green)^{##UREF##4##5##,##UREF##10##11##}, have been described. These articles only contain scanning electron micrographs of the glandular pouch, pleural pores, and ducts.</p>", "<p id=\"Par9\">For this reason, the present study aimed to contribute to the identification of the nymphal and adult stages of the <italic>P. solenopsis</italic> male by describing the ultrastructural morphology of their dermal pores. Moreover, the study explores the morphometry of the genitalia and its sensilla types. The importance of such knowledge is that it would provide an identification key for the rapid diagnosis of the nymphal stages found on crops at pre-export inspections. The present study provides insights into the structures found on the genitalia of the adult male <italic>P. solenopsis</italic> that possibly having an important role in mating events and copulatory behavior.</p>" ]

[ "<title>Materials and methods</title>", "<title>Insects</title>", "<p id=\"Par30\">A colony of the cotton mealybug, <italic>P. solenopsis</italic>, was established in the laboratory of Pests &amp; Plant Protection Department, Agricultural &amp; Biological Research Institute, National Research Centre, Giza, Egypt. The colony was reared on sprouting potato tubers (<italic>Solanum</italic> <italic>tuberosum</italic>). Studies on plants complied with relevant institutional, national, and international guidelines and legislation.</p>", "<p id=\"Par31\">The mealybug colony was established under laboratory conditions (temperature of 26 ± 2 °C, 60–70% relative humidity, and 16 h light: 8 h dark photoperiod), in glass jars (30-cm deep and 15-cm width). Both immature stages and adult males were manually separated from the colony in order to prepare them for scanning electron microscopy (SEM) examination.</p>", "<title>Sample preparation for SEM</title>", "<p id=\"Par32\">Fifteen samples of both immature stages and adult males were collected from the laboratory colony and stored in 70% ethanol, followed by a gradual dehydration using a series of ethanol concentrations (80%, 90%, 95% and 100% [v/v]), without distorting the samples. The waxy layer that affects the investigation process of such fine structures as sensilla was removed by soaking in hexane for 10 min, according to Abd El-Ghany et al.^{##REF##36517816##12##,##UREF##29##35##}. Samples of immature stages and adult males were rinsed in 100% ethanol, oriented and mounted on aluminum stubs with double sticky tape. The mounted samples were coated with gold film using the High Resolution Turbomolecular-pumped coater system (Q150T ES, Quorum Technologies Ltd, United Kingdom). The SEM Model TESCANVEGA3 (thermionic emission SEM system) (TescanTM, Tescan Orsay Holding, Kohoutovice, Czech Republic) was used to capture micrograph of the desired parts at high magnification ranging from 2500 to × 30,000.</p>", "<title>Nomenclature and morphological description of sensilla</title>", "<p id=\"Par33\">The nomenclature used and identification of various sensillum types and wax pores was performed according to earlier literature^{##UREF##10##11##,##UREF##13##16##–##UREF##15##18##}. The mean length and standard deviation were determined from measurements of 5 samples. The measurements were performed using ImageJ software (<ext-link ext-link-type=\"uri\" xlink:href=\"http://imagej.nih.gov/ij/\">http://imagej.nih.gov/ij/</ext-link>).</p>" ]

[ "<title>Results</title>", "<title>Immature stages</title>", "<title>Morphology of the nymphal instars</title>", "<p id=\"Par10\">The first instar nymph (crawler) of <italic>P. solenopsis</italic> is mobile, with well-developed, 5-segmented legs, 6-segmented antennae, 18 pairs of cerari, trilocular wax pores, and tubular ducts. The total length of the first instar nymph is 322.54 ± 13.34 µm and the width is about half the value of its length at 150.05 ± 5.37 µm (Fig. ##FIG##0##1##A). The second instar nymph is more pronounced than the first instar nymph, with a total length ranging from 0.63 to 0.66 mm. The second instar nymph of the male appeared more elliptical than the more ovoid females. Nymphal stage is characterized by 7-segmented antennae (Fig. ##FIG##0##1##E). A thin powdery secretion covers most of the body dorsum. The body margin has 18 pairs of cerarii, with each cerarius consisting of two small conical sensilla (CS, length 2.63 ± 0.05 µm) that are surrounded by groups of trilocular pores throughout the body surface (Fig. ##FIG##0##1##F).</p>", "<title>Types of wax pores and sensilla of the nymphal instars</title>", "<p id=\"Par11\">In the first instar nymph, an aggregation of auxiliary sensilla (two types of sensilla trichodea, TS1 &amp; TS2), sensillum basiconicum (BS1) and lanceolate setae, and 1–2 trilocular pores, are associated with the anal lobe (Fig. ##FIG##0##1##B). TS1 is a hair-like structure that is thicker at the base and tapers towards the tip. The TS2 is a short to medium length hair-like structure, with straight or slightly curved with a slightly sharp tip. The mean lengths of TS1 and TS2 are 69.80 ± 7.08 µm and 32.20 ± 3.43 µm, while their width measures 2.69 ± 0.13 µm and 1.06 ± 0.05 µm, respectively.</p>", "<p id=\"Par12\">Two types of wax pores, trilocular (TP) and quinquelocular (QP), are present on the integument of nymphal instars. Trilocular pores were detected on both sides (dorsal and ventral), being more abundant on the dorsal surface (Fig. ##FIG##0##1##C). The TP consists of a triangular depression along each edge with three elongated, dumbbell-shaped loculi (Fig. ##FIG##0##1##C). In contrast, the quinquelocular pores were located only on the ventral surface of the body (Fig. ##FIG##0##1##D). In addition, tubular ducts (TD) were observed on both the dorsal and ventral surfaces.</p>", "<p id=\"Par13\">For the 2nd instar nymph, the anal ring (39–44 µm in width) has associated with 6 long sensilla chaetica (ChS). ChS is characterized by a slightly grooved wall and sharp tip (35.46 ± 1.78 µm in length; 1.69 ± 0.14 µm in basal diameter), located between the two anal lobe cerari (Fig. ##FIG##0##1##F,G). A cerarius consists of an aggregation of auxiliary sensilla (also called “auxiliary setae”) composed of two subtypes of sensilla trichodea (TS1 &amp; TS2), a pair of sensilla basiconica (BS1), and 4–5 trilocular pores (Fig. ##FIG##0##1##H,I). TS1 and TS2 are characterized by a smooth wall hair-like structures with sharp tips with varied lengths of 57.33 ± 2.50 µm and 29.0 ± 0.82 µm, respectively. The BS1 is a smooth-walled sensillum with a mean length of 10.22 ± 0.39 µm and 1.80 ± 0.08 µm in diameter. Various trilocular pores are distributed throughout both surfaces of the body. They produce curled wax filaments which resemble a railway track in shape, ranging from 1.30 to 1.55 µm (Fig. ##FIG##0##1##G,I). The TPs consisted of a triangular depression with three elongated, dumbbell-shaped loculi (1.70 ± 0.06 µm length of the opening of the loculi) (Fig. ##FIG##0##1##J,K).</p>", "<p id=\"Par14\">Tubular ducts (TD) were observed on both the dorsal and ventral surfaces in the two nymphal instars of the mealybug male. These TDs are more numerous and abundance in the second instar male, which appeared as circular apertures with a slightly elevated rim of 1.46 ± 0.15 µm diameter; uniloculus (Fig. ##FIG##0##1##J,K). Similar to the first instar nymph, QPs were distributed only on the ventral surface of the second instar nymph, in the middle parts of the segments (Fig. ##FIG##0##1##L).</p>", "<title>Prepupal and pupal stages</title>", "<p id=\"Par15\">Pupation of the <italic>P. solenopsis</italic> male includes two instars, the prepupal and pupal stages, each of which occurs inside a fluffy puparium composed of waxy threads. The prepupal stage becomes more elliptical than the second instar nymph and has a total length of 1.05–1.08 mm (Fig. ##FIG##1##2##A). It is characterized by numerous tubular ducts, particularly on the ventral surface of the abdomen. Protruding from the anal ring, a pipe of densely matted, fine wax filaments is supported by long sensilla chaetica with a mean length of 45.05 ± 1.22 µm and 1.60 ± 0.08 µm in diameter (Fig. ##FIG##1##2##B). Trilocular pores and TDs are distributed throughout the integument (Fig. ##FIG##1##2##C). The anal lobe is associated with a single long TS1 (91.04 ± 1.73 µm in length; 1.86 ± 0.05 µm in diameter), and a single thin TS2 (39.67 ± 3.17 µm in length; 0.67 ± 0.06 µm in diameter), and a pair of BS1 (12.36 ± 1.15 µm in length; 1.83 ± 0.13 µm in diameter).</p>", "<p id=\"Par16\">There are also trilocular pores which produce curled, railway track-shaped wax filaments (1.40 to 1.45 µm in width) (Fig. ##FIG##1##2##D). In the pupal stage, the TDs are mainly produced several longitudinal waxed ridges that are sticky and known to be utilized in forming its cocoon (Fig. ##FIG##1##2##E). The full length of pupae ranging from 1.45 to 1.61 mm. Ecdysis of the emerged adult male, seen as the shedding of the pupal cuticle, reveals an elliptical body that has a length of 1.3 mm and a width of 0.3 mm (Fig. ##FIG##1##2##F).</p>", "<title>Adult male</title>", "<p id=\"Par17\">The adult male of <italic>P. solenopsis</italic> is characterized by a slender and narrow body with a pair of well-developed forewings and modified hindwings in a hamulohalterae. It is distinguished by a largely membranous abdomen, becoming gradually narrower posteriorly. The abdomen is composed of 10 segments; the eight pregenital segments are distinct, but the genital segments (9th and 10th) are fused. The adult male is also distinguished by the presence of various glands and ducts, which are usually absent or reduced in the females and immature stages (Fig. ##FIG##2##3##).</p>", "<p id=\"Par18\">Each pregenital segment bears a pair of lateral stellate pores (SP1 and SP2) which secrete wax that covers the male body, SP1 has 4 projections (peripheral loculi) resembling short sensillum basiconicum. Sensilla trichodea subtype 2 and numerous microtrichia were observed on each pregenital segment (Fig. ##FIG##2##3##A). The adult male also displays two pairs of waxy caudal filaments (CF), with mean lengths of 245.73 ± 12.64 µm, which are located on the 7th and 8th abdominal segments (Fig. ##FIG##2##3##B). The ratio of the caudal filament length to the total body length was1:4.64. The caudal filaments arise from the center of the tail-forming pore, which is known as the glandular pouch. The pouch is composed of a cluster of stellate pores on the lateral surfaces of the seventh and eighth abdominal segments (Fig. ##FIG##2##3##B–D). The caudal filament is set in a small, cup-shaped depression surrounded by a cluster of 55–60 stellate pores (SP2 and SP3), which secrete the wax that covers the caudal filaments. Each cluster is associated with a pair of TS1 with lengths ranging from 88.0 to 117.0 µm and 1.33 to 1.68 µm in diameter, and a pair of shorter sensilla trichodea (TS2) with mean lengths of 56.82 ± 3.26 µm and 0.79 ± 0.07 µm in diameter.</p>", "<p id=\"Par19\">Two types of stellate pores are present in the adult male of <italic>P. solenopsis</italic>; type SP2 has 5 projections (peripheral loculi) resembling short sensillum basiconicum (1.40 ± 0.08 µm in length and 0.43 ± 0.02 µm in diameter). The type SP3 has 6 projections (Fig. ##FIG##2##3##E). These stellate pores have an outside diameter of 4.20–5.03 µm and an inside diameter of 3.38–4.00 µm. In addition, the medial part of the last abdominal segment has microtrichia (Mt) which are arranged singly or in pairs; their lengths ranging from1.00 µm to 1.13 µm (Fig. ##FIG##2##3##F).</p>", "<p id=\"Par20\">The dorsal surface of the ninth and tenth abdominal segments has a strongly sclerotized triangular arrangement; however, it appears largely membranous towards the ventral portion around the base of the aedeagus (Figs. ##FIG##2##3##A,B, ##FIG##3##4##A). Ventrally, the genital segments are modified as the incompletely fused ninth and tenth abdominal segments which compose the penile sheath that is characterized by a longitudinal slit along the median ventral part, and its distal part terminates in an evenly rounded tip called the style (Fig. ##FIG##3##4##A,B).</p>", "<p id=\"Par21\">Three subtypes of sensilla basiconica, BS2, BS3, BS4, were distributed on both sides of the penile sheath (Fig. ##FIG##3##4##C,D). Type BS2, which is the most abundant sensillum of the basiconica type, with a mean length of 7.91 ± 0.71 µm and 0.86 ± 0.04 µm basal diameter. BS3 is the longest sensilla, with a mean length of 22.96 ± 1.19 µm and 0.76 ± 0.08 µm in diameter. BS4 is the shortest subtype of the sensilla basiconica with a mean length of 4.37 ± 0.54 µm and 0.79 ± 0.07 µm in diameter. The terminal portion of the style has a group of sensilla campaniformia (CaS1) (Fig. ##FIG##3##4##E,F). The silt (sutural line) of the penile sheath allows the protrusion of the aedeagus during copulation, (Fig. ##FIG##4##5##A). Dorsally, the genital segments are characterized by a small, sclerotized area that represents the fused tergites of the ninth and tenth abdominal segments. The lateral surfaces of each genital segment have numerous BS3 and CaS2 (Fig. ##FIG##4##5##B).</p>", "<p id=\"Par22\">The aedeagus is connected ventrally to the penile sheath wall behind the basal ridge (Fig. ##FIG##4##5##A). The aedeagus appears as a long, strongly cylindrical tube with curved, hook-shaped, trapped apex (Fig. ##FIG##4##5##C). Groups of CaS1 are associated with the tip of the penile sheath (Fig. ##FIG##4##5##D). At the dorso-distal margin of the penile sheath, there are two subtypes of sensillum campaniformium, namely, a group of CaS3 and a unique CaS4 (Fig. ##FIG##4##5##E,F).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par23\">The wax secretions produced by various hemipteran species, especially among mealybugs (Pseudococcidae), whiteflies (Aleyrodidae), aphids (Aphididae), scale insects (Coccidae), and flatid planthoppers (Flatidae), have been reported to cover all or part of their integuments^{##UREF##19##23##}. The wax pores and ducts of the immature and adult stages of mealybug species, seen as trilocular pores and tubular duct glands, can synthesize waxy substances. The components for the waxy secretion are transferred from the haemolymph, stored in reservoirs, then secreted through the wax pore canals onto the surface of the integument^{##UREF##1##2##}. The immature stages that are destined to develop as adult males construct a loosely woven, silky, filamentous cocoon after the second moult and undergo a further two moults as prepupal and pupal stages inside the cocoon before they emerge as winged adults^{##REF##20874596##14##,##UREF##12##15##,##UREF##20##24##,##UREF##21##25##}. The adult males are short-lived and non-feeding^{##UREF##17##21##}.</p>", "<p id=\"Par24\">Taxonomists use the types and distributions of the wax-producing pores and their ducts as an invaluable aid in the identification and classification of different mealybug species. For the family Pseudococcidae, several studies have focused on the female wax pores; however, few studies have been performed on the ultrastructure of the wax pores of the adult male^{##UREF##4##5##,##UREF##10##11##}.</p>", "<p id=\"Par25\">In that context, our study aimed to fill part of the knowledge gap on mealybug males and their nymphal instars. Results of the present study indicate that tubular ducts are more numerous in the second instar male; however, trilocular pores distributed among both nymphal stages. Trilocular pores are characterized by the production of a long, spiral wax filaments. However, the wax produced from the pores differs in the adult from that of the immature male instars^{##UREF##4##5##,##UREF##10##11##}.</p>", "<p id=\"Par26\">For the winged male, our morphological findings are very similar to those for the three species of mealybugs, <italic>F. virgate</italic>, <italic>P. manihoti</italic>, and <italic>Pl. citri</italic>^{##UREF##10##11##}. The wax pores (pleural pores) of <italic>M. hirsutus</italic> are distinctively different in the adult males from those in the instars^{##UREF##4##5##}. The function of the loose, filamentous wax on the body surface of the adult male was difficult to determine^{##UREF##4##5##}. On the other hand, the pleural pores of the <italic>Pl. citri</italic> male which are merely vestiges from the immature stages and only found in adult that largely produces a white, powdery wax which trails behind the body could help with balance during the flight process^{##UREF##10##11##}. Another report has also suggested that the pleural pores of the winged male of <italic>M. hirsutus</italic> are a probably a vestige from the immature stages^{##UREF##4##5##}. Furthermore, the same authors described the morphological structures of the cluster of stellate pores containing four-five loculi which produce long spiral wax filaments^{##UREF##4##5##,##UREF##10##11##}. Our findings regarding stellate pores morphology are very similar to^{##UREF##10##11##}, except for the number of the loculi, which is five-six in the present study for <italic>P. solenopsis</italic> male. Therefore, the number of loculi of the stellate pores of the glandular pouch on the seventh and eighth abdominal segments should be characteristic for the differentiation between mealybug species.</p>", "<p id=\"Par27\">For the nymphal instars of the cotton mealybug<italic>,</italic> the anal ring is associated with 3 pairs of long sensilla chaetica (ChS). Our findings match those reported for the adult females of <italic>Pl. citri, Pl. ficus</italic>, and <italic>P. solenopsis</italic>^{##UREF##22##26##,##UREF##23##27##}. However, neither the ultrastructure description nor details on the sensillum types and their distribution are available for the prepupal stage of <italic>P. solenopsis</italic>, or any mealybug species. This lack of information has been addressed partially but significantly by the present study's findings, which suggest the value of these morphological characters for the discrimination of prepupal stages. Numerous tubular ducts and trilocular pores were distributed on the integument of the <italic>P. solenopsis</italic> nymphs. In addition, the prepupa has 3 pairs of long ChS, such as those found in the nymphal stages.</p>", "<p id=\"Par28\">In adult mealybug males, the sensilla trichodea, basiconica, and campaniformia distributed on the surface of the genitalia may have an important role in mating events and copulatory behavior. Discerning from the morphological characteristics of the mentioned sensillum types, long and slender sensilla trichodea (ST1 and ST2) with a pointed tip are candidates for tactile mechanoreception, while some short sensilla basiconica (SB) with presumed terminal pore or wall pores could have an olfactory function^{##UREF##24##28##}. Furthermore, the presence of numerous sensilla campaniformia on the terminal portion of the style of the penis of the cotton mealybug male is particularly interesting to consider. These sensilla are frequently in great numbers on the male genitalia of certain insects from different taxonomic groups, such as the uncus of the cabbage white butterfly, <italic>Pieris brassicae</italic> Linnaeus (Lepidoptera)^{##UREF##25##29##}; the genital valves, epiproct and paraprocts of the Mediterranean katydid, <italic>Phaneroptera nana</italic> Fieber (Orthoptera)^{##UREF##26##30##}; and the aedeagus of the false firefly beetle, <italic>Drilus mauritanicus</italic> Lucas (Coleoptera)^{##UREF##27##31##}. In a hemipteran, the tip of the aedeagus in the soapberry bug, <italic>Leptocoris augur</italic> Fabricius, only bears numerous, short sensilla trichodea, sometimes misinterpreted as sensilla coeloconica, but do not bear sensilla campaniformia^{##UREF##28##32##}. All the sensilla campaniformia of insects are mechanoreceptors and proprioceptors that respond to the stresses and strains in the exoskeleton of insects^{##REF##1090241##33##,##REF##35255307##34##}, i.e., they monitor mechanical deformation of the cuticle. During the courtship behavior of mealybugs, these receptors may be having important role by strong touch of male genital stimulation, causing a response of the female^{##REF##1090241##33##,##REF##35255307##34##}.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par29\">This study explored the ultrastructure of wax pores of both the adult male and immature stages of the cotton mealybug<italic>, P. solenopsis</italic> Tinsley. In addition, the adult genital structures were imaged for the first time with a SEM. These findings provide useful insights that can help in the identification of the nymphal stages of <italic>P. solenopsis</italic> found on produce at pre-export inspections. Information generated for the adult male hopefully enriches our knowledge to better understand the morphology of the traits that contribute to the biology and behavior, especially mating events and copulatory behavior of <italic>P. solenopsis</italic>.</p>" ]

[ "<p id=\"Par1\">The cotton mealybug, <italic>Phenacoccus solenopsis</italic>, has established itself as an invasive insect pest worldwide. It causes structural and physiological damage to various crops and can cause substantial financial losses in their production. The successful reproduction of this pest under a wide range of conditions is a key to its success. Despite this, the morphology of its genitalia, genital sensilla, and wax-producing dermal pores has received little attention, with little descriptions of their ultrastructure. By investigating those features with SEM, the present study revealed considerable new insights into the identification of the nymphal and adult stages of <italic>P. solenopsis</italic>. In addition, the description of the ultrastructural genital morphology of the immature stages of <italic>P. solenopsis</italic> has revealed characteristics that facilitate their discrimination. Trilocular pores were observed on both sides of the body, while the quinquelocular pores were distributed only on the ventral surface in both the first and second nymphal instars. The adult male is characterized by two pairs of waxy caudal filaments surrounded by clusters of 55 to 60 stellate pores, and each pregenital segment bears a pair of stellate pores composed of 4 or 5 peripheral loculi. Sensilla trichodea and numerous microtrichia are present on the pregenital segments. The penile sheath bears three subtypes of sensilla basiconica and also campaniformia, whereas the style bears three subtypes of sensilla campaniformia. The findings of this study could assist in the identification of the adult and nymphal stages of <italic>P. solenopsis</italic>, and also provide insights into the structures found on the genitalia of the adult male that possibly have an important role in mating events and copulatory behavior. Furthermore, these findings were able to contribute to better understanding the functional morphology of <italic>P. solenopsis</italic>.</p>", "<title>Subject terms</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).</p>" ]

[]

[ "<title>Acknowledgements</title>", "<p>The authors thank Dr. Gregory T. Sullivan of the School of the Environment at The University of Queensland in Brisbane, Australia for his language corrections for this manuscript.</p>", "<title>Author contributions</title>", "<p>N.M.A. contributed to the study conception and design<italic>.</italic> Material preparation and SEM experiments were performed by N.M.A. All authors (N.M.A., S.E.A., M.J.F.) shared in the identification of the sensillum types, interpreted the data, and drafted the manuscript. All authors provided critical editing and reading and approved the final manuscript.</p>", "<title>Funding</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).</p>", "<title>Data availability</title>", "<p>The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par34\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Nymphal instars of <italic>P. solenopsis</italic> male: (<bold>A–D</bold>) Showing different sensillum types distributed on the first instar nymph. (<bold>A</bold>) Dorsal view of the first instar nymph, showing the whole body with 7-segmented antennae (An) and pair of anal lobe (AL) at the distal end. (<bold>B</bold>) Magnified lateral view of the anal lobe cerarius (AL) with sensillum basiconicum (BS1); two types of sensilla trichodea (TS1, TS2), and a part of the anal ring (Ar) associated with sensilla chaetica (ChS). (<bold>C</bold>) Dorsal view of the integument of the first instar nymph with various groups of trilocular pores (TP) and short sensillum conical (CS). (<bold>D</bold>) Ventral view of the 1st instar nymph shows various sensilla trichodea (TS2), quinquelocular pores (QP), and tubular ducts (TD). Magnified view of quinquelocular pore (QP) at the bottom left of the micrograph. (<bold>E–L</bold>) The second instar nymph; (<bold>E</bold>) Ventral view of complete second instar nymph (An: Antenna, Lg: Leg, Ar: Anal ring, Al: Anal lobe, Cr: cerari), (<bold>F</bold>) Magnified view of the last abdominal segments showing various groups of trilocular pores (TP); wax filaments (WF), short sensillum conical (CS) distributed along the integument; anal lobes (AL), and anal ring (Ar) in the medial area. (<bold>G</bold>) Magnified view of the anal ring with associated sensilla chaetica (ChS); group of wax filaments (WF), and sensillum basiconicum (BS1) on the anal lobe. (<bold>H</bold>) Magnified view of the anal lobe cerarius with associated pair of sensilla basiconica (BS1), two types of sensilla trichodea (TS1, TS2), trilocular pores (TP), and short sensillum conical (CS). (<bold>I</bold>) Lateral view of the anal lobe cerarius, showing a pair of sensilla basiconica (BS1); trilocular pores (TP) associated with wax filaments (WF); (<bold>J</bold>) Magnified view of trilocular pores (TP) and tubular ducts (TD) on the dorsal surface of the second instar nymph. (<bold>K</bold>) Magnified view of trilocular pores (TP) and tubular ducts (TD) on the ventral side of the second instar nymph. (<bold>L</bold>) Ventral view of the second instar nymph associated with quinquelocular pores (QP) and short sensilla trichodea (TS2).</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Pupation of <italic>P. solenopsis</italic> male: (<bold>A</bold>) Lateral view of prepupal stage characterized by 7-segmented antenna (An), 3 pairs of legs (Lg), a pair of anal lobes (AL) at the distal end, and excess of secreted wax filaments. (<bold>B</bold>) Magnified view of the last two abdominal segments showing various groups of wax filaments (WF) secreted from trilocular pores (TP), short sensillum conical (CS), Cr: cerari, anal ring (Ar) in the medial area bears 6 sensilla chaetica (ChS), anal lobe with a pair of sensilla basiconica (BS1), sensilla trichodea (TS1, TS2). (<bold>C</bold>) Magnified view of trilocular pore (TP) and tubular duct (TD). (<bold>D</bold>) Magnified view of the anal lobe cerarius of the prepupa with a pair of sensilla basiconica (BS1), sensillum trichodeum (TS1), sensillum trichodeum (TS2), and folded wax filaments (WF) secreted from trilocular pore. (<bold>E</bold>) Pupal stage covered by layers of wax filaments. (<bold>F</bold>) The molted skin after male adult emergence.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Wax pores associated with adult male of <italic>P. solenopsis</italic>: (<bold>A</bold>) The 5th and 6th abdominal segments bear sensilla trichodea (TS2), each segment laterally bears a pair of stellate pores (SP1) or (SP2), rows of microtrichia (Mt) are distributed on the integument; at the top-right of the micrograph, magnified view of stellate pore (SP1) with 4 peripheral loculi resembling short sensillum basiconicum. (<bold>B</bold>) Ventral view of the 7th–10th abdominal segments, with the genital segments (9th and 10th) fused and forming the penile sheath (PSh) and two pairs of caudal filaments (CF) surrounded by various groups of stellate pores (SP) on the lateral surface of the 7th and 8th abdominal segments. (<bold>C</bold>) Magnified view of the last three abdominal segments showing two types of stellate pores (SP2, SP3), a chaplet of 3 spores (Cp), two types of sensilla trichodea (TS1, TS2), a pair of sensilla basiconica (BS2), and microtrichia (Mt) on the medial part of 9th abdominal segment. (<bold>D</bold>) Magnified view of the stellate pores (SP2, SP3) with central opening (SPo) surrounding a pair of caudal filaments (CF) at the center and two types of sensilla trichodea (TS1, TS2). (<bold>E</bold>) Magnified view of stellate pores; SP2 associated with 5 peripheral loculi resembling short sensillum basiconicum: SP3 associated with 6 peripheral loculi. (<bold>F</bold>) Magnified view of the sensillum basiconicum (BS2) and microtrichia (Mt) distributed on the penile sheath.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Genitalia of adult male of <italic>P. solenopsis</italic>: (<bold>A</bold>) Ventral view of the genital segments and a part of 8th abdominal segment with two pairs of caudal filaments (CF) surrounded by various groups of stellate pores (SP) and sensillum trichodeum (TS1). The style (St) illustrated at the distal end of the penile sheath (PSh) with various sensilla basiconica (BS2, BS3) and microtrichia (Mt). (<bold>B</bold>) Magnified ventral view of the terminal part of the last abdominal segment showing parts of caudal filaments (CF), the penile sheath (PSh) bearing various types of sensilla basiconica (BS2, BS3, BS4), and sensilla campaniformia (CaS1) at the tip of the style (St). (<bold>C</bold>) Magnified ventral view of the middle part of the penile sheath (PSh) showing sensilla basiconica (BS2), short sensillum basiconicum subtype 4 (BS4), and longitudinal slit (Ls) of the penile sheath. (<bold>D</bold>) Part of the penile sheath with longitudinal slit (Ls) showing magnified view of sensilla basiconica (BS2, BS3), broken basiconic sensillum subtype 2 (black arrow). (<bold>E &amp; F</bold>) Magnified dorsal and ventral views of sensilla campaniformia (CaS1) on the terminal part of the style, respectively.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Genitalia of adult male of <italic>P. solenopsis</italic>: (<bold>A</bold>) Ventral view of the genital segments, showing extended aedeagus (Aed) and rows of microtrichia (Mt) located on the last abdominal segments. (<bold>B</bold>) Magnified lateral view of the middle abdominal segment with sensilla campaniformia subtype 2 (CaS2) and group of sensilla basiconica (BS3). (<bold>C</bold>) Magnified view of the terminal part of the genital segment showing the tip of aedeagus (Aed), style (St) associated with sensilla campaniformia subtype 1 (CaS1), and various sensillum types (BS2, BS4) on the penile sheath. (<bold>D</bold>) Magnified view of sensilla campaniformia subtype 1 (CaS1) on the distal part of the style. (<bold>E</bold>) Lateral view of the last abdominal segments shows sensilla campaniformia subtype 3 (CaS3) and sensilla basiconica (BS2). (<bold>F</bold>) Magnified view of sensilla campaniformia subtypes 3 and 4 (CaS3, CaS4).</p></caption></fig>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">The human brain’s structural topology is estimated from diffusion tensor images (DTI) to derive the structural connectivity (SC) matrix that summarizes the fiber connectivity density among the brain regions. On the other hand, static or steady-state functional connectivity (FC) among these regions is estimated by computing the correlation coefficient (usually Pearson) of the respective time-varying resting-state functional magnetic resonance imaging (rsfMRI) signals. The correlation captures the spontaneous brain activity when participants are not engaged in any specified task. Furthermore, the brain activity observed in the rsfMRI signals is constrained and influenced by the connectome^{##REF##18771736##1##,##REF##23528922##2##}. Characterizing the SC-FC mapping is an open and challenging research problem in cognitive neuroscience^{##REF##24384152##3##}. Such models can be used to identify the biomarkers that underlie any deviation from the expected FC based on the SC in various diseases such as Autism Spectrum Disorder (ASD), Dementia, and many more^{##REF##30626917##4##,##REF##34025376##5##}. These models will also be helpful in characterizing the functional recovery patterns resulting from therapy by comparing the FC observed with the predicted FC based on healthy structural topology^{##REF##30626917##4##,##REF##34025376##5##}.</p>", "<p id=\"Par3\">Traditionally, graph-based modeling has been popular for solving SC-FC mapping. One of the seminal works in this direction by Abdelnour et al.^{##REF##24384152##3##} formulated a linear model that considers the diffusion of regional brain activity over the graph topology by choosing a single optimal diffusion kernel. Later^{##UREF##0##6##,##REF##29311619##7##}, utilized multiple diffusion kernels for learning the SC-FC mapping and demonstrated the superiority of using multiple diffusion kernels. The idea of multiple diffusion kernels formulation is specifically interesting and demonstrates the integration of multiple kernels within the same machine learning model. Becker et al.^{##REF##29311619##8##} proposed a versatile nonlinear mapping approach to obtain the functional connectivity from the structural connectivity random walks using spectral graph theory. In another relevant work on functional brain connectivity, [5] derived a relation between SC and FC via Laplacian spectra, where FC and SC share eigenvectors and their eigenvalues are exponentially related. However, most of these methods suffer from the computational overhead related to scalability or exhibit sub-optimal performance on SC-FC mapping over brain graphs.</p>", "<p id=\"Par4\">A novel deep learning method called graph convolution network(GCN)^{##UREF##1##9##} has recently been proposed to generalize convolutional neural network models for graph data. GCNs achieve state-of-the-art results in various application domains such as, computer vision^{##UREF##2##10##}, applied chemistry^{##UREF##3##11##}, natural language processing^{##UREF##4##12##}, and neuroscience^{##UREF##5##13##}. The GCN-based Encoder-Decoder network was proposed for SC-FC mapping where the normalized Laplacian of SC was provided as input to GCN, and training was accomplished using the ground truth FC with an MSE loss function^{##UREF##6##14##,##UREF##7##15##}. The primary limitation of the GCN-based Encoder-Decoder method is the absence of diffusion over multiple scales that is useful for the integration of information from the node attributes and the network topology. A recent variant of GCN, <italic>GraphHeat Network</italic> (GHN), attempts semi-supervised classification^{##UREF##8##16##} and enables control over heat diffusion scales while filtering out the influence of high-frequency spectral components of the graph Laplacian. Another recent work proposed by^{##UREF##9##17##} learned the graph kernels based on the intuition of the specific application domain instead of choosing standard kernels such as heat kernels and normalized heat kernels. However, the reported performance is poor on the SC-FC mapping experiments. Deep learning models such as CNNs and LSTMs, including GCNs, require large datasets for training and evaluation. Hence, in this paper, we evaluated our A-GHN model on the HCP dataset (i.e. 1058 SC-FC pairs) to learn the complex FC structure.</p>", "<p id=\"Par5\">Recently, attention mechanisms have become popular and standard to enable working with variable size inputs and for focusing on the most relevant parts of the input to make decisions^{##UREF##10##18##,##UREF##11##19##}. In the proposed model, A-GHN incorporates the propagation and aggregation of node representations by heat diffusion mechanism at multiple scales over the SC matrices. It is expected that the multiple scales contribute differently to the predicted FC. Thus, we introduce the attention mechanism to capture the contribution of each scale-specific A-GHN sub-models for learning the SC-FC mapping.</p>", "<p id=\"Par6\">In summary, these methods together establish the usefulness of single or multi-scale diffusion^{##REF##24384152##3##,##REF##29311619##7##} and the feasibility of graph neural networks for solving the SC-FC mapping problem^{##UREF##6##14##}. Inspired by these and the attention mechanism over multiple scale-specific GHNs, we propose an attention-based fusion of multiple GraphHeat networks (A-GHN) that efficiently employs multi-scale diffusion to promote computational tractability and scalability. Figure ##FIG##0##1## display the pipeline of A-GHN model. The A-GHN model utilizes multiple GHNs, each with an independent channel of input based on heat kernels. Predicted FC is then computed based on the weighted combination of these outputs and is compared with the empirical FC. Here, the attention scores are computed by taking the softmax over weight coefficients, where each attention score corresponds to the A-GHN sub-models output. As a result, the proposed model approximates the empirical FC well, and the FCs recovered with the A-GHN approach seem to have better correspondence with the ground truth than related models that incorporate either multi-scale diffusion or GHN. The key contributions of this paper are the following:<list list-type=\"bullet\"><list-item><p id=\"Par7\">We propose a novel, end-to-end learnable A-GHN architecture for learning the SC-FC mapping on brain graphs.</p></list-item><list-item><p id=\"Par8\">Our method is grounded in the theory of the reaction-diffusion process in the cognitive domain while retaining the key properties of generalizability, scalability, and tractability in the deep learning framework.</p></list-item><list-item><p id=\"Par9\">We present a comprehensive empirical analysis, including perturbation experiments and a detailed ablation study, to demonstrate the proposed model’s robustness and validity on a large publicly available dataset.</p></list-item></list></p>" ]

[ "<title>Baseline methods</title>", "<p id=\"Par31\">Since the proposed model combines graph convolutional network with multiple heat kernel diffusion, we chose two related baseline methods for comparative analysis. The first method, multiple kernel learning (MKL) model proposed in^{##REF##29311619##7##}, utilizes multi-scale diffusion over brain graphs to learn the subject’s SC-FC mapping but does not incorporate deep networks. On the other hand, the second method uses GCN-based Encoder-Decoder architecture^{##UREF##6##14##} is a deep learning-based model. However, this does not incorporate multi-scale diffusion. Thus, the two baselines together allow us to evaluate the impact of deep networks and that of the multi-scale diffusion independently against our proposed A-GHN model. We replicated both the MKL and GCN Encoder-Decoder models with the same choice of parameters as indicated in the original papers on the data from 1058 participants from HCP for training and testing experiments. We further compared our A-GHN results with several previous state-of-the-art methods such as Autoencoder^{##REF##33271268##27##}, Macroscale mapping of SC-FC^{##REF##32160567##38##}, and Graph Neural Networks which uses both Graph Convolutional Network (GCN) and Graph Transformer Network (GTN)^{##UREF##7##15##}.</p>" ]

[ "<title>Experimental setup and results</title>", "<p id=\"Par29\">This section provides details of the experimental setup, dataset, model design, and comprehensive evaluation of the proposed model. Further, we performed detailed ablation studies where we induced perturbations in the input and conducted studies by removing the attention module to see the impact on the performance in all the cases and justify the proposed architecture.</p>", "<title>Dataset analysis</title>", "<p id=\"Par30\">Deep learning models typically require a large amount of data for training as they involve learning a huge number of parameters. Further, MRI data acquisition comprising different modalities such as T1, DTI, and rsfMRI is a costly and time-consuming process. In light of these issues and in order to obtain a meaningful comparison against the existing results, we considered a popular and widely used dataset from the human connectome project (HCP) [ <ext-link ext-link-type=\"uri\" xlink:href=\"http://www.humanconnectomeproject.org/data/\">http://www.humanconnectomeproject.org/data/</ext-link>]. We have considered the structural connectivity - functional connectivity (SC-FC) pairs of a total of 1058 subjects from the HCP repository (see^{##REF##23702415##33##} for data pre-processing methodology). All these participants underwent resting-state functional imaging (no task condition) with their eyes closed. The structural connectivity (SC) matrix, derived from diffusion tensor imaging (DTI), reveals the white-matter fiber connections between regions of interest (ROIs). The elements of the SC matrix correspond to the normalized count of streamlines connecting pairs of regions. On the other hand, the FC matrix is characterized by Pearson’s correlation of time series from resting state fMRI for different brain regions. The blood oxygen level-dependent (BOLD) time-series signal available for each participant has 1200 time points aggregated across 87 regions of interest (ROIs) as per the Desikan-Killiany brain atlas^{##REF##16530430##34##}. Therefore, 87 brain regions with 1200 time points result in FC matrix. The HCP 1058 subjects dataset with Desikan-Killiany parcellation has been made available by <italic>Zhang et al.</italic>^{##REF##29355769##35##} [<ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/maxwass/brain_data_processing\">https://github.com/maxwass/brain_data_processing</ext-link>]. We also evaluated our model on 100 subjects from the HCP repository as per the AAL brain atlas across 86 brain ROIs^{##REF##21769991##36##}. The HCP 100 subjects dataset with AAL parcellation is obtained from <italic>Surampudi et al.</italic>^{##REF##30267857##37##}.</p>", "<title>Baseline methods</title>", "<p id=\"Par31\">Since the proposed model combines graph convolutional network with multiple heat kernel diffusion, we chose two related baseline methods for comparative analysis. The first method, multiple kernel learning (MKL) model proposed in^{##REF##29311619##7##}, utilizes multi-scale diffusion over brain graphs to learn the subject’s SC-FC mapping but does not incorporate deep networks. On the other hand, the second method uses GCN-based Encoder-Decoder architecture^{##UREF##6##14##} is a deep learning-based model. However, this does not incorporate multi-scale diffusion. Thus, the two baselines together allow us to evaluate the impact of deep networks and that of the multi-scale diffusion independently against our proposed A-GHN model. We replicated both the MKL and GCN Encoder-Decoder models with the same choice of parameters as indicated in the original papers on the data from 1058 participants from HCP for training and testing experiments. We further compared our A-GHN results with several previous state-of-the-art methods such as Autoencoder^{##REF##33271268##27##}, Macroscale mapping of SC-FC^{##REF##32160567##38##}, and Graph Neural Networks which uses both Graph Convolutional Network (GCN) and Graph Transformer Network (GTN)^{##UREF##7##15##}.</p>", "<title>Model setup</title>", "<p id=\"Par32\">Here, we describe the model setup, training and testing phases for the proposed A-GHN model.</p>", "<title>Training phase</title>", "<p id=\"Par33\">We trained the A-GHN model on HCP rsfMRI data where a randomly chosen set of 550 subjects of which 500 subjects used for training (500 SC-FC pairs), 50 subjects (50 SC-FC pairs) for validation and the remaining 508 subjects (508 SC-FC pairs) for testing. The 87 87 heat kernel matrix obtained from the Laplacian of structural connectivity (SC) matrix was given as input to the graph convolution networks (GCN) and the 87 87 empirical functional connectivity (FC) matrix as the target output to train the model. Here, the number of vertices corresponds to the 87 brain regions, and the edges represent the structural fibers connecting the brain regions over which heat diffusion takes place. As shown in Fig. ##FIG##1##2##, outputs of the one-layer A-GHN models were combined in a weighted manner using the corresponding attention scores obtained from the Softmax layer. The number of coefficients obtained is equal to the number of scales (), and the final output is an () predicted FC. We used mean squared error (MSE) between empirical and predicted FC matrices as the loss function for learning.</p>", "<title>A-GHN hyper-parameters</title>", "<p id=\"Par34\">To perform SC-FC mapping using A-GHN, we set the convolution layer’s embedding size as 87 and the input node feature vector <italic>X</italic> as the identity matrix (. We used Adam optimizer^{##UREF##13##39##} with an initial learning rate of 0.001, <italic>tanh</italic> as the activation function, and the weight decay was set to . We applied dropout with a keep-probability of 0.5 and trained the A-GHN model for a maximum of 100 epochs. To overcome the over-fitting problem, we stopped training if the validation loss did not decrease for 10 consecutive epochs (See supplementary material for the profiles of learning curves in Fig. ##SUPPL##0##SF1##).</p>", "<title>Testing phase</title>", "<p id=\"Par35\">We used the other half (508 SC-FC pairs) to predict the corresponding FC matrices in model testing. We followed the same parameters used in model training except omitting the drop-out parameter. We use the Pearson correlation coefficient between the empirical (ground truth) and the predicted functional connectivity (FC) matrices to measure the model performance. There were two kinds of validation experiments performed—5-runs (each run with different random initialization), and 5-fold cross-validation (CV). For the 5-runs set-up, we report the average Pearson correlation over the 5-runs on the 508 test subjects. The average results for each test subject are shown in Fig. ##FIG##3##4## (depicting Pearson Correlation values) and Fig. ##SUPPL##0##SF2## (depicting MSE values). For ease of visualization, we also report the results for randomly sampled 100 test subjects from the 508 test cohort in Figs. ##SUPPL##0##SF3## and ##SUPPL##0##SF4## (please refer to Supplementary material). For the 5-fold CV experiments, 4-folds are used for training and one-fold for testing. The results of the 5-fold CV are shown in Fig. ##FIG##4##5##. Thus, the validation results establish the generalizability of the results with different data splits.</p>", "<p id=\"Par36\">Choice of Model Parameters The choice of various model parameters is explained below.</p>", "<title>Choice of <italic>m</italic></title>", "<p id=\"Par37\">Figure ##FIG##2##3## shows the profile of heat kernels for various scales of diffusion () ranging from 0.5-10. The GraphHeat formalism^{##UREF##8##16##} allows for selective focus on low-frequency spectral components at higher scales, whereas high-frequency spectral components are suppressed at lower scales. Hence, in this paper, we chose multiple scales where each scale of diffusion characterise to determine neighboring nodes that reflect the local structure or the relevant information of smoothness manifested in the graph structure. As can be seen in Fig. ##FIG##2##3##, the local diffusion phenomenon is observed for smaller scales (0.5–1) with contribution from many eigenvalues/vectors, including the large eigenvalues. On the other hand, the global diffusion phenomenon is noticed for bigger scales (1-10) that depend predominantly on the contribution from eigenvalues/vectors corresponding to smaller eigenvalues. The number of heat diffusion scales (see Eq. ##FORMU##44##7##) was set to empirically, based on the performance of the proposed model. We used ascending order of scales that correspond to the global diffusion phenomenon in case of lower scale indices ( values of 0.6 and 0.8) and local diffusion phenomenon in case of higher scale indices ( values of 1, 2, 4, 6, and 8) (see Fig. ##FIG##2##3##).</p>", "<title>Choice of activation function</title>", "<p id=\"Par38\">In order to determine the kind of activation function to be used in the output layer, we ran experiments with several choices and found that <italic>tanh</italic> is suitable. We observed that <italic>tanh</italic>, <italic>relu</italic>, and <italic>leaky relu</italic> (with a negative slope of 0.01) activation functions yielded similar performance values while the configuration with <italic>sigmoid</italic> function had a lower performance. Since the FC correlation matrix values are in the range of -1 to 1, we chosen <italic>tanh</italic> as the activation function in the output layer of the A-GHN for further experiments. These results are shown in Fig. ##SUPPL##0##SF7## in the supplementary material.</p>", "<title>Choice of A-GHN layers</title>", "<p id=\"Par39\">To understand the impact of increasing the number of hidden layers of A-GHN, we experimented with a two-layer, and four-layer A-GHN models. The empirical results show that the mean Pearson correlation of test subjects with the two-layer model (0.799) was marginally better than that of the one-layer model (0.788), as shown in Fig. ##SUPPL##0##SF8## (please refer supplementary). However, it appeared that a further increase in the number of layers (four layers) led to over-fitting and a decrease in performance (0.76). In order to estimate the statistical significance of the performance differences, we performed One-way ANOVA on the mean correlation values for the test participants across the A-GHN models with different depths. The main effect of model was significant [F(2,1506)=73.59, <italic>p</italic>=.0000]. Further, the <italic>post hoc</italic> pairwise tests revealed that the mean correlation values of the A-GHN model with one-layer was significantly different from those of the other two models [with two layers: <italic>p</italic>=.0.00004 and with four-layers: <italic>p</italic>=.0000]. Overall, as a trade-off we considered a one-layer A-GHN model for all further experiments based on its smaller training parameter-set.</p>", "<p id=\"Par40\">\n\n\n\n\n</p>", "<title>Results</title>", "<title>Comparison with previous methods</title>", "<p id=\"Par41\">Here, we compare the performance of the A-GHN model with baseline and existing models for the SC-FC mapping, as reported in Table ##TAB##0##1##. The comparison of the proposed A-GHN model is made across four groups of models: (a) general baseline models (Autoencoder, Macroscale SC-FC); (b) non-deep learning model but that uses multiple kernel diffusion (MKL); (c) GCN-based models (GCN Encoder Decoder, GNN); and (d) GraphHeat-based baselines (M-GHN, Random A-GHN). We make the following observations from Table ##TAB##0##1##: (i) On Pearson correlation, A-GHN is better across all the models. (ii) The results of the Random A-GHN model where all the GHN layers are kept frozen and untrained, yields a lower mean Pearson correlation than other GCN-based models. (iii) A-GHN with different layers shows superior performance as compared to multiple GHNs (M-GHN)^{##UREF##14##40##}, Graph Neural Networks (combination of GCNs: Graph Convolutional Networks and GTNs: Graph Transformer Networks) and GCN encoder decoder based models. It is interesting to note that none of these models (except M-GHN) uses multiple scales of diffusion as in the proposed approach.</p>", "<p id=\"Par42\">For further quantitative and qualitative analyses of A-GHN, we proceed with comparison against two of the above approaches: MKL and GCN Encoder Decoder models. While MKL model is a representative of multiple kernel diffusion strategy, GCN Encoder Decoder model signifies a typical graph-based deep learning approach.</p>", "<title>Quantitative evaluation</title>", "<p id=\"Par43\">We compared the performance of our proposed model with two existing approaches: Multiple Kernel Learning (<italic>MKL</italic>) model^{##REF##29311619##7##} and the GCN-based Encoder-Decoder model^{##UREF##6##14##}. The results of the comparative study using the 5-random-run experiments are shown in Fig. ##FIG##3##4## &amp; Table ##TAB##0##1##, where we can see that the proposed A-GHN model performs better with a mean correlation value of 0.788 in the range of [0.60, 0.885] on the test set as compared to GCN-based Encoder-Decoder model (, range in [0.487, 0.892]) and MKL (, range in [0.342, 0.865]). In order to estimate the statistical significance of the performance differences, we performed One-way ANOVA on the mean correlation values for the test participants across the three models. The main effect of model was significant [F(2,1506)=10.26, ]. Further, the <italic>post hoc</italic> pairwise tests revealed that the mean correlation values of the A-GHN model were significantly different from those of the other two models [with GCN Encoder-Decoder: and with MKL: ]. On the other hand, the performance of the two baseline models did not differ significantly [GCN Encoder-Decoder vs. MKL: ].</p>", "<p id=\"Par44\">Similarly, Fig. ##SUPPL##0##SF2## (please see in the Supplementary) displays the mean squared error (MSE) of test subjects using the 5-random-run experiments, where the proposed A-GHN performs a lower MSE value of 0.0265 in the range of [0.013, 0.054] on the test set as compared to GCN-based Encoder-Decoder model (, range in [0.024, 0.067]) and MKL (, range in [0.015, 0.261]). Further, the statistical significance test using the one-way Anova test provides an F-statistic [F(2,1506) = 37.33, ] concludes that the model was significant. Also, the post-hoc Tukey-HSD test reported that the proposed A-GHN model was significantly different with two models [with GCN Encoder-Decoder: and with MKL: ].</p>", "<p id=\"Par45\">Further, Fig. ##FIG##4##5## depicts the results of 5-fold CV experiments, establishing the generalizability of the results with different data splits. From Fig. ##FIG##4##5##, we observe that A-GHN yield an equal performance across all the five folds. The box-plots in Fig. ##FIG##4##5## depicts the range of Pearson correlation values across test subjects in that Fold.</p>", "<title>Qualitative evaluation</title>", "<p id=\"Par46\">We computed the mean of the predicted FC and the mean of the empirical FC matrices of the test subjects. We also computed the mean predicted FC matrices of the baseline models (GCN Encoder-Decoder and MKL). The visualizations of FC matrices are shown in Fig. ##FIG##5##6##. Here, we can observe a better qualitative match between the mean predicted FC of our proposed model and the mean ground truth.</p>", "<p id=\"Par47\">In order to look at the finer details of the goodness of the learned mapping, four FC Networks were derived from the mean FC matrices of the test subjects using the Louvain algorithm available in the brain-connectivity-toolbox^{##REF##19819337##41##}. The edge-connectivity patterns of the predictions of the three models and the ground truth were rendered on a brain surface using BrainNet viewer^{##REF##23861951##42##} to understand the similarity of node and edge distributions between the empirical and the predicted FCs, shown in Fig. ##FIG##6##7##. It can be seen that the proposed A-GHN model has a higher visual similarity to the empirical FC in terms of community assignment and inter-hemispheric connections as compared to the other models.</p>", "<p id=\"Par48\">To empirically evaluate the community assignment across three models, we measure the mutual information based on the entropy (MI)^{##REF##16119262##43##} between communities for ground truth FCs of the three models: A-GHN, GCN Encoder Decoder and MKL. The mutual information MI is computed as follows,where X and Y are the two vectors (community assignments of the nodes as computed by the Louvain algorithm) in consideration, is the Kullback-Leibler divergence. Since mutual information (MI) measures the similarity in the information captured between two communities, it can be seen as a global correspondence measure of the brain community structure^{##REF##33265581##44##}. The higher the MI, the more the similarity with the ground-truth FC. Table ##TAB##1##2## reports the mutual information between different pairs of community assignments for the predicted FCs in the three models with the communities detected in the Ground truth FC. The community detection was done on the average of all the 508 test subjects. It can be observed from Table ##TAB##1##2## that A-GHN model has higher mutual information with ground truth FCs (1.357) across all the test subjects compared to GCN Encoder-Decoder (0.735) and MKL (0.740).</p>", "<title>Ablation studies</title>", "<p id=\"Par49\">We performed various ablation studies to establish the robustness of the proposed model. As an initial step, we estimate the native correlation between the ground truth SC &amp; FC and compare with the SC-FC correlation obtained for the test data using the proposed A-GHN model. Subsequently, an ablation study was carried out to measure the importance of the attention module which is a key element incorporated in the proposed model. The relation between the size of the training data set and the model performance has also been studied. We have also conducted additional perturbation studies to verify whether our model learns the SC-FC relationship correctly and does not simply over-fit the data. One experiment studies the impact of perturbing the test input when the training protocol is intact. The second one verifies the results when the model was trained using perturbed inputs but tested on the original target outputs.</p>", "<title>Comparison with the native SC-FC correlation</title>", "<p id=\"Par50\">As an initial evaluation strategy, we report how the SC-FC correlations between the ground truth compare against those that are predicted from the 508 subjects’ test data using the proposed A-GHN model. From the results shown in Fig. ##SUPPL##0##SF1## (please see in the supplementary), we observe that the mean correlation between SC vs. FC-Actual (-0.0065) is comparable with the SC vs. FC-Predicted (-0.0024) for the proposed A-GHN model.</p>", "<title>Importance of attention</title>", "<p id=\"Par51\">The distinguishing feature of the proposed A-GHN model is the use of attention in order to estimate a weighted combination of the GHN outputs. In order to assess the importance of the attention module, we performed an ablation study. The model was run without attention (called M-GHN^{##UREF##14##40##} in Fig. ##SUPPL##0##SF12## (please see in the Supplementary) weights by simply summing and averaging the outputs of the seven A-GHN sub-models to obtain the predicted FC. It can be observed in Fig. ##SUPPL##0##SF12## that attention makes a difference in that the mean correlation value of A-GHN is 0.788 [range: (0.60, 0.885)] as compared to 0.741 [range: (0.461, 0.873)] of M-GHN. An F-test establishes that these differences are statistically significant [F(1, 1014)=5.3427, <italic>p</italic>=.023]. Similarly, we report the mean squared error (MSE) of test subjects using both A-GHN and M-GHN models in Fig. ##SUPPL##0##SF5##. From Fig. ##SUPPL##0##SF5##, we can observe that the overall MSE value of A-GHN is 0.0254 low as compared to 0.0302 for M-GHN.</p>", "<title>Perturbation experiments with testing dataset</title>", "<p id=\"Par52\">We perturbed the data corresponding to the 508 test subjects from the 5-run experiment reported earlier, where each subject was perturbed times. Here, each test SC matrix was perturbed by randomly generating the values of the elements from a power-law distribution that the elements are known to follow^{##UREF##15##45##}. The A-GHN model was trained on unperturbed data of SC-FC pairs (550 subjects), and the resulting model was tested on each perturbed set of the test SC-FC pair. Figure ##SUPPL##0##SF14## (Please see in the supplementary) depicts the distribution of average Pearson correlation scores for these experiments. It can be observed that the model learned from the 550 unperturbed SCs performs rather poorly in predicting the FCs estimated from the randomly generated SCs. The histogram of mean correlation values ranges in [0.12, 0.45] with a mean correlation around 0.3, thus indicating that the model performance deteriorates when fed with random structural connectivity information during the testing period. Thus, we can empirically conclude that the proposed model indeed learns SC-FC mapping, and the FC predictions are not independent of SC but respect the topology/structure of the input.</p>", "<p id=\"Par53\">We reported other ablation studies experiments such as (i) Random A-GHN (Fig. ##SUPPL##0##SF9##), (ii) Varying the Training Data Size (Fig. ##SUPPL##0##SF10##), (iii) Perturbing the Model Input (Fig. ##SUPPL##0##SF15##), and (iv) Leave-One-Out Results on 100 HCP subjects with AAL Atlas (Fig. ##SUPPL##0##SF16##), in the supplementary.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par54\">The study of the relationship between structural connectivity and functional connectivity and how the functional activity of the brain is generated from the anatomical structure has been a major research topic in the field of cognitive neuroscience. Several methods have been proposed to explore the mapping between SC-FC including, whole brain computational models^{##REF##26317432##21##,##REF##23825427##22##}, simple linear diffusion models^{##REF##24384152##3##} as well as complex non-linear models^{##REF##19003478##24##,##REF##23024632##26##}, and linear multi-scale diffusion models^{##UREF##0##6##,##REF##29311619##7##}. The whole brain computational models have been used as powerful tools to understand the relationship between structural and functional brain connectivity by linking brain function with its physiological underpinnings. On the other hand, non-linear complex drift-diffusion models based on excitatory and inhibitory neuronal populations, though not analytically tractable, give rise to rich dynamics. Abdelnour et al.^{##REF##24384152##3##} introduced a graph-based model with a linear single scale diffusion kernel at an optimal scale over the structural graph topology (SC) to map FC. However, Surampudi et al.^{##UREF##0##6##} showed that single kernel models do not generalize to a larger cohort and demonstrated that FC can be decomposed into multiple diffusion kernels with subject non-specific combination coefficients. Further, the MKL framework, proposed by Surampudi et al.^{##REF##29311619##7##}, revealed that the combination of multiple diffusion kernels was not sufficient to explain the self-organizing resting-state patterns found in FC and hence necessitated the use of additional explanatory parameters.</p>", "<p id=\"Par55\">In this paper, we adopt the representation of the graph signal in terms of graphheat kernel similar to GraphHeat proposed by^{##UREF##8##16##}. The GraphHeat formalism allows for selective focus on low-frequency spectral components at higher scales, whereas high-frequency spectral components are suppressed at lower scales. We consider a bank of such GHN models, each associated with a scale-specific heat kernel over the SC graph as input. The proposed A-GHN model then combines the outputs of the scale-specific GHN models using attention-based fusion. Both the hidden parameters () associated with the scale-specific GHN models as well as the attention scores that combine the A-GHN sub-model outputs are jointly learned to estimate the empirical FC accurately. We have established a correspondence between the initial regional co-activation parameters () in the proposed model and the parameters () from the MKL framework^{##REF##29311619##7##}. It is to be noted that the MKL framework is shown to be a variant of a reaction-diffusion system on the graph topology determined by the underlying structural connectivity (SC) matrix. Thus, the proposed A-GHN method is grounded in the theory of the reaction-diffusion process in the cognitive domain.</p>", "<p id=\"Par56\">The proposed A-GHN model displays superior performance as compared to baseline models such as GCN Encoder-Decoder^{##UREF##6##14##} and MKL model^{##REF##29311619##7##}. The model is able to learn population patterns regarding the SC-FC relationship even with smaller datasets. We validated our proposed model in two different settings: (i) 5-runs with the random initialization, and (ii) 5-Fold cross-validation. The experimental results showed that the correlation structure of the BOLD functional resting-state brain networks is significantly well captured by our model (Fig. ##FIG##3##4##). The predicted mean correlation for 508 test subjects is close to 0.788 (5-Runs experiment), whereas the GCN Encoder-Decoder and MKL yield (0.73), and (0.645), respectively. We conducted several ablation studies and perturbation experiments to establish the robustness of the reported results.</p>", "<p id=\"Par57\">As explained below, the proposed framework enjoys three key properties of generalizability, scalability, and tractability in the deep learning framework.</p>", "<title>Interpretability and generalizability</title>", "<p id=\"Par58\">We formulate the deep learning model, A-GHN, as an end-to-end framework for SC-FC prediction. The challenge in applying deep learning models to neuroimaging research lies in the black-box nature of the process, where it is hard to decipher what the deep network actually learns. In order to address this and to understand the model mechanisms, we devised the following: (i) deciphering the learned parameters , (ii) visualising the outputs of <italic>m</italic> number of A-GHN sub-models (), and (iii) displaying the heatmap of attention probabilities across the test subjects (508 pairs of SC-FC), as shown in Figs. ##SUPPL##0##SF18##, ##SUPPL##0##SF19##, and ##SUPPL##0##SF20##, respectively (Please see in the Supplementary).</p>", "<p id=\"Par59\">From Figs. ##SUPPL##0##SF18## and ##SUPPL##0##SF19##, we observe that lower scales display mean regional activity local to the neighboring nodes by suppressing the high-frequency spectral components. However, as the scale value increases, the large neighborhoods are taken into account with a global structure and captures much more information while discarding some irrelevant low-order neighbors. Thus, the proposed A-GHN model thereby be tuned to produce both local and global connectivity at lower and higher scales, respectively. Similarly, Fig. ##SUPPL##0##SF20## reports that the contribution of attention probabilities is decreasing as the scale value increases. Further, we performed community detection to identify the different networks captured in the FC predicted by the model. The communities were detected using the Louvain algorithm as described in the Brain Connectivity Toolbox (BCT)^{##REF##19819337##41##}. From Fig. ##SUPPL##0##SF21##, it is observed that the communities detected in the predicted FC when compared with empirical FC (ground truth), capture the inter-hemispheric patterns very well.</p>", "<p id=\"Par60\">Similar to the mutual information analysis done for the communities across various models, we perform mutual information between the scales and ground truth based on Eq. (##FORMU##96##15##), where X and Y represent the communities detected in each scale-specific output of the A-GHN model and the ground truth, respectively. Table ##TAB##2##3## shows the comparison of ground-truth similarities captured in the scale outputs. Scale-1 is the most similar to the ground truth in terms of its modularity and detected communities.</p>", "<title>Scalability and computational efficiency</title>", "<p id=\"Par61\">The results reported in the current work use the parcellation based on the Desikan-Killiany Atlas (). We also report our A-GHN model results on 100 HCP subjects with AAL parcellation (), as shown in Fig. ##SUPPL##0##SF17## (please refer Supplementary). Nevertheless, the A-GHN model is easily scalable to any brain parcellation (for example, Gordon Atlas with , or Glasser Atlas with parcellations). Graph-based diffusion models^{##REF##24384152##3##,##REF##29311619##7##,##REF##30267857##37##,##REF##29454104##46##} are not easily scalable for larger parcellations as the matrix operations are difficult to scale for larger matrix sizes. On the other hand, since graph convolutional network (GCN)-based models^{##UREF##6##14##} including the proposed A-GHN model use only node aggregate features that require vector operations; they are easily scalable.</p>", "<p id=\"Par62\">From a computational efficiency perspective, one of the major limitations of the MKL model^{##REF##29311619##7##} is that it uses LASSO optimization that requires computationally expensive matrix inverse operations. Hence the computational complexity is dominated by the cost of LASSO optimization. In contrast, the proposed A-GHN model is more efficient as it uses a stochastic gradient-based backpropagation learning approach. Moreover, the A-GHN model requires learning of 60,552 parameters (7 scales: 7x7569 + Attention Module: 1x7569) that is comparatively lower than learning 118,336 parameters in the MKL framework (16 scales: 16x7569). Further, the proposed framework is inherently scalable to more diffusion scales, more hidden layers in the GHNs, and can potentially be used for transfer learning on other datasets—all these make the proposed A-GHN model very flexible and computationally powerful.</p>", "<title>Limitations and future work</title>", "<p id=\"Par63\">Usually, deep learning models require large datasets to obtain reliable learning and generalization performance results. An interesting point to note of our work is that it is trained and tested on a medium-size dataset of 1058 participants’ data. We demonstrated how A-GHN can be trained to obtain superior results using hyperparameter tuning and various validation experiments even with such a dataset. It would be interesting to demonstrate how A-GHN scales to larger datasets in the future. This research is the first step in applying the A-GHN model to perform automatic resting-state FC prediction from SC. In the near future, we intend to use the A-GHN model as a universal model to predict the FC of different types (both resting-state FC as well as task-based FCs) with the structural graph given as input.</p>", "<p id=\"Par64\">In future work, a biophysical interpretation of the proposed deep learning model (A-GHN) with multi-scale heat kernel diffusion as an instance of a reaction-diffusion system on the structural brain graph needs to be established. Additionally, the proposed model could be used to characterize disease groups as well. It is to be notes that the proposed A-GHN considers average functional connectivity, ignoring the transient functional dynamics over the period of acquisition of the temporally extended rsfMRI signal. The proposed framework could potentially be extended to capture the temporal information in the functional connectivity dynamics (FCD). Finally, the current results utilize the well-known Deskian-Killiany (D-K) atlas that is representative and that has been used in many studies. However, in future we should look at other atlases such as Power2000, Brainnetome, etc.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par65\">This paper proposed a novel A-GHN model that outperforms existing models that use either multiple diffusion kernels (MKL) or that use GCNs (GCN Encoder-Decoder). The current work demonstrates the feasibility of the A-GHN model with experiments on a large-size dataset of 1058 participants. Extensive cross-validation, perturbation, and ablation studies establish the robustness of the proposed architecture for learning the structure-to-function mapping of the brain using the images from DTI and rsfMRI. The model not only captures the SC-FC mapping but the underlying functional connectivity networks as well. The strengths of the deep learning based GHN models over graph diffusion-based linear models such as the MKL model are their computational efficiency and scalability.</p>" ]

[ "<p id=\"Par1\">Over the last decade, there has been growing interest in learning the mapping from structural connectivity (SC) to functional connectivity (FC) of the brain. The spontaneous fluctuations of the brain activity during the resting-state as captured by functional MRI (rsfMRI) contain rich non-stationary dynamics over a relatively fixed structural connectome. Among the modeling approaches, graph diffusion-based methods with single and multiple diffusion kernels approximating static or dynamic functional connectivity have shown promise in predicting the FC given the SC. However, these methods are computationally expensive, not scalable, and fail to capture the complex dynamics underlying the whole process. Recently, deep learning methods such as GraphHeat networks and graph diffusion have been shown to handle complex relational structures while preserving global information. In this paper, we propose a novel attention-based fusion of multiple GraphHeat networks (A-GHN) for mapping SC-FC. A-GHN enables us to model multiple heat kernel diffusion over the brain graph for approximating the complex <italic>Reaction Diffusion</italic> phenomenon. We argue that the proposed deep learning method overcomes the scalability and computational inefficiency issues but can still learn the SC-FC mapping successfully. Training and testing were done using the rsfMRI data of 1058 participants from the human connectome project (HCP), and the results establish the viability of the proposed model. On HCP data, we achieve a high Pearson correlation of 0.788 (Desikan-Killiany atlas with 87 regions) and 0.773 (AAL atlas with 86 regions). Furthermore, experiments demonstrate that A-GHN outperforms the existing methods in learning the complex nature of the structure-function relation of the human brain.</p>", "<title>Subject terms</title>" ]

[ "<title>Related work</title>", "<title>Whole brain modeling of SC-FC</title>", "<p id=\"Par10\">Classical methods proposed non-linear models of cortical activity, which were then extended to model whole-brain behavior via coupling between regions based on structural connectivity^{##REF##19188601##20##}. Also, the whole-brain computational models have been used as powerful tools to understand the relationship between structural and functional brain connectivity by linking brain function with its physiological underpinnings^{##REF##26317432##21##–##REF##26081790##23##}. Several other studies place non-linear oscillators at each cortical location and likewise couple them using anatomic connectivity strength^{##REF##19003478##24##–##REF##23024632##26##}. However, these simulation models are only revealed through large scale, fine-grained stochastic simulations over thousands of time samples, and pose a practical challenge for the task of inferring functional connectivity from structural connectivity.</p>", "<title>Graph-theoretic modeling using linear models</title>", "<p id=\"Par11\">The earlier graph-theoretic modeling experiments studied the mapping of SC-FC relationships by capturing the correlation structure of whole-brain dynamics using linear models^{##REF##24384152##3##}. Specifically^{##REF##24384152##3##}, present a simple, low-dimensional network diffusion linear model producing an accurate description of the SC-FC relationship. However, this model uses one global parameter across all the subjects, and the hypothesis of a single scale best-fitting kernel across subjects is not tenable. Surampudi et al.^{##UREF##0##6##} observed that the combination of multiple diffusion scales exhibits scale-dependent relationships among various regions of interest (ROIs), and these multi-scale diffusion kernels can capture reaction-diffusion systems operating on a fixed underlying connectome (SC). However, multiple diffusion kernels were not sufficient to explain the self-organizing resting-state patterns found in FC. Recently, a new framework, the multiple kernel learning model (MKL), provides plausible mathematical reasoning for the existence of these co-activations along with diffusion kernels by linearizing a variant of the reaction-diffusion model and extending it to generate FC^{##REF##29311619##7##}.</p>", "<title>Deep learning models for SC-FC mapping</title>", "<p id=\"Par12\">The earlier deep learning modeling experiments studied the SC-FC mapping using an autoencoder (multi-layer perceptron as neural network architecture) method^{##REF##33271268##27##}. Recently, the study of GCNs has successfully reconstructed the brain FC from an SC graph by building a graph encoder-decoder system^{##UREF##6##14##}. Moreover, the learned low-dimensional embeddings capture essential information regarding the relationship between functional and structural networks. In another recent work^{##UREF##7##15##}, investigated the SC and FC mapping within a deep learning GNNs-based framework, including graph convolutional networks (GCN) and graph transformer networks (GTN). However, the major limitation of these methods is that they have not utilized either single diffusion kernel at an optimum scale or multiple scales of diffusion. A recent work in these lines^{##UREF##9##17##} proposed a deep graph spectral evaluation network (GSEN) for modeling the graph topology evolution by the composition of a newly generalized kernel. This method efficiently models the global and local evolution patterns between the source (SC) and target (FC) graphs. Global patterns involve features that reflect the general characteristics or relationships present throughout the entire graph structure, whereas local patterns capture the finer details of interactions, considering the influence of nearby nodes or connections within a limited vicinity. Although the method seems interesting, the GSEN model reports a poor performance on SC-FC mapping.</p>", "<title>Proposed solution</title>", "<title>Problem statement and proposed solution</title>", "<p id=\"Par13\">The brain is typically represented as a graph in the computational neuroscience community, where graph nodes are modeled as key brain regions, and edges represent their structural or functional relationships. The aim here is to learn a mapping between the two brain graphs representing a sparse structural connectivity matrix (SC) and a dense static (steady-state) functional connectivity (FC) matrix, as depicted in Fig. ##FIG##1##2##. We propose to employ multi-scale heat diffusion kernels in a novel deep learning framework for this task.</p>", "<title>Mathematical background and notations</title>", "<title>Graph definition</title>", "<p id=\"Par14\">Consider a weighted, undirected graph denoted by ), where is a set of <italic>N</italic> nodes, <italic>A</italic>\n is the symmetric adjacency matrix and <italic>E</italic> is the set of edges connecting the nodes. A graph Laplacian matrix is defined as <italic>L</italic> = <italic>D</italic> – <italic>A</italic>, where <italic>D</italic> is a diagonal matrix with degree of nodes on the diagonal, The spectral decomposition of the Laplacian matrix () yields (i) Eigenvector matrix (<italic>U</italic>) and (ii) Eigenvalue matrix () which is a diagonal matrix with the eigenvalues arranged in increasing order.</p>", "<title>Graph convolutional networks</title>", "<p id=\"Par15\">Graph Convolutional Neural network (GCN) is a multi-layer neural network that convolves neighboring node’s features and propagates a node’s embedding vectors to its nearest neighborhood^{##UREF##1##9##}. For a one-layer GCN with Z hidden units, the latent node feature representation () is computed aswhere <italic>A</italic> is the symmetric adjacency matrix, is the node feature matrix where each row of the matrix represents a M-dimensional content vector for each node in the graph, is weight parameter associated with the layer of GCN, and <italic>f</italic> is activation function. One can incorporate higher-order information of the neighborhoods by stacking multiple GCN layerswhere <italic>i</italic> denotes layer number and </p>", "<title>Graph convolution using heat kernel</title>", "<p id=\"Par16\">The <italic>GraphHeat Network</italic> (GHN) formulation captures the smoothness of labels or features over the neighborhood of the nodes as determined by the graph structure^{##UREF##8##16##}. A heat kernel is defined aswhere is the scale hyper-parameter, and denotes the eigenvalue in . Let denote the kernelized diagonal matrix. Thus, we can define the convolution kernel () aswhere is the weight parameter and here we choose (<italic>i.e.</italic> only considering the first-order polynomial approximation of ChebyNet^{##UREF##12##28##}).</p>", "<p id=\"Par17\">For the given input signal <italic>X</italic>, graph convolution is achieved as follows:Specifically, for our choice of <italic>K</italic> = 2:where is a weight matrix corresponding to scale , represents the heat kernel matrix, and is the scale-specific output of GHN. Please note in the above equation that <italic>X</italic>, the node feature matrix, is taken as an identity matrix in this formulation. To reduce the number of free parameters and to avoid over-fitting, we assume = = , and the equation becomes . Therefore, adding the identity matrix enforces self-connections to the heat kernel matrix (). However, our heat kernel matrix () already has self-connections; hence we ignored the identity matrix . In the A-GHN formulation, multiple graphHeat models are considered for different positive scales; hence has been omitted as it does not affect the overall results.</p>", "<title>Attention based multiple graphheat networks (A-GHN)</title>", "<p id=\"Par18\">Let us consider <italic>m</italic> heat kernel matrices with <italic>m</italic> different scales and corresponding GraphHeat kernels . A-GHN already includes the propagation and aggregation of node representations by heat diffusion mechanism over the SC matrix. Further, the weight matrix parameters associated with the structural graph are learned during the model training process, reflecting the mean regional activities. Hence, the node feature vector <italic>X</italic> was chosen as a one-hot vector (<italic>I</italic>) in our model setting.</p>", "<p id=\"Par19\">Each A-GHN sub-model outputs a matrix and we hypothesize that the linear combination of the softmax probabilities with A-GHN sub-model outputs would give rise to a good estimate of FC. Let denote the weight coefficients in the linear combination corresponding to the <italic>m</italic> GHN branches (A-GHN sub-models). These weight coefficients are learned by feeding the outputs of all <italic>m</italic> GHN branches to a fully connected layer. In our proposed A-GHN model, the attention module is designed such that the differential contribution of multiple scales is weighted appropriately to estimate the predicted FC. In order to obtain the normalized weights (attention scores), we utilize the softmax activation function. Finally, the linear combination of the outputs of <italic>m</italic> GHNs weighted by the corresponding attention scores allows us to jointly train all A-GHN sub-models and the fully connected layer via end-to-end back-propagation learning.where denote the linear coefficients capturing contribution of the individual heat kernel .</p>", "<p id=\"Par20\">Thus, we approximate the empirical FC with weighted combination of output of multiple A-GHN sub-models corresponding to <italic>m</italic> diffusion scales to predict the FC () as follows</p>", "<title>Loss function</title>", "<p id=\"Par21\">The attention parameters and scale-specific parameters are estimated from the training subjects (indexed by <italic>s</italic> that varies from 1 to <italic>S</italic>) and remain fixed during the testing phase. We consider the loss function <italic>J</italic> (Equation of ##FORMU##55##12##) to be the mean squared error between empirical and predicted FCs. Since the target FC matrix is symmetric, we have also made the estimated FC matrix () symmetric by adding its transpose, similar to MKL^{##REF##29311619##7##}. The loss function is then minimized using the stochastic gradient descent procedure.    Here denotes a matrix with subject index (s) and denotes an attention vector. Figure ##FIG##1##2## depicts the proposed architecture that combines attention-based fusion of A-GHN sub-models with multiple heat kernels.</p>", "<title>Relation to reaction diffusion phenomenon</title>", "<p id=\"Par22\">Mutual interaction of the elements of a complex system results in a neural field of activity which in turn leads to the formation of self-organizing patterns. Reaction-Diffusion (RD) model is the mathematical framework that characterizes such a spatio-temporal change in the field. RD systems have been successfully used to model the interaction among neurons belonging to different brain regions and the associated functional connectivity (FC) among the regions of interest (ROIs) of the brain^{##REF##22017986##29##,##REF##20929839##30##}. The reaction part of the RD model corresponds to the interaction of the excitatory and inhibitory neural elements, and the diffusion part corresponds to the spreading of the resultant neural activity over the structural fiber pathways. As the interacting (reacting) neural elements differ in their parameters, the emerging spontaneous activity of the neural ensemble results in non-linear patterns. The growth and the progression of a neural field are mathematically characterized by the Wilson-Cowan model, a variant of the RD framework. The statistical behavior of the mean activity of the neural fields is described by the equations of the Wilson-Cowan model^{##REF##19662434##31##,##REF##4767470##32##}.</p>", "<p id=\"Par23\">Inspired from the multiple kernel learning model (MKL) model^{##REF##29311619##7##} which is based on the RD framework, in this paper, we propose attention-based multiple GraphHeat networks (A-GHN) to map SC-FC. The proposed solution formulation is analogous to MKL and is as follows:</p>", "<title>MKL</title>", "<p id=\"Par24\">The optimization formulation minimizes an objective function <italic>J</italic> comprising the mean squared error between empirical and predicted FCs as in^{##REF##29311619##7##} and is represented as:where are estimated from the training subjects (indexed by <italic>s</italic> that varies from 1 to <italic>S</italic>), and denotes the Heat Kernel matrix of subject <italic>s</italic> associated with scale <italic>i</italic>.</p>", "<p id=\"Par25\">Similarly, in^{##UREF##0##6##}, the mixing coefficients are subsequently learned while solving an optimization formulation as:where is a weight coefficient associated with scale specific heat kernel </p>", "<p id=\"Par26\">From Eqs. (##FORMU##44##7##), (##FORMU##55##12##), and (##FORMU##60##13##), we observe that the learnable parameters () in Eq. (##FORMU##55##12##) in the proposed framework are analogous to the estimated parameters () in Eq. (##FORMU##60##13##) of the MKL framework^{##REF##29311619##7##}. Thus, as hypothesized in^{##REF##29311619##7##}, we can interpret () as corresponding to the initial mean regional activities. Hence, in Eq. (##FORMU##55##12##) of the proposed framework, when viewed along with Eq. (##FORMU##44##7##), would correspond to the diffused output based on the initial mean regional activities.</p>", "<p id=\"Par27\">Additionally, we introduce an attention mechanism in our proposed model (A-GHN) that combines attention scores with the outputs of <italic>m</italic> GHNs. From Eqs. (##FORMU##55##12##) and (##FORMU##63##14##), the learnable mixing coefficients through optimization formulation in Eq. (##FORMU##63##14##) are analogous to the weighted attention scores obtained through gradient descent in Eq. (##FORMU##55##12##).</p>", "<p id=\"Par28\">We present the visualizations of () and the correlation plot between the empirical and predicted FCs without attention in Section “<xref rid=\"Sec30\" ref-type=\"sec\">Ablation studies</xref>”.</p>", "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-50408-6.</p>", "<title>Author contributions</title>", "<p>S.R.O. and A.Y. ran all the experiments S.R.O. and A.D. prepared the figures S.R.O., A.Y., A.D. and B.S.R. wrote the manuscript A.S. and B.S.R. provided their guidance, discussed all the results, and insights.</p>", "<title>Data availability</title>", "<p>All data generated or analysed during this study are included in this published article <italic>Zhang et al.</italic>^{##REF##29355769##35##}. We did not create any new data as part of this work. We used the HCP dataset which is publicly available without any restrictions. HCP dataset can be downloaded from brain_data_processing github repository <ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/maxwass/brain_data_processing\">https://github.com/maxwass/brain_data_processing</ext-link></p>", "<title>Competing interests</title>", "<p id=\"Par66\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Mapping the structural and functional connectivity in brain graphs using the proposed A-GHN network.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Proposed A-GHN architecture for learning SC-FC mapping using multi-scale GraphHeat networks (GHN) along with attention mechanism. A Laplacian matrix is computed from the structural connectivity matrix (SC) input in step 1. Multiple heat kernel matrices are obtained using m different diffusion scales and fed to the individual (A-GHN sub-model) in step 2. In step 3, an attention module is introduced to learn the attention scores corresponding to A-GHN sub-models. A Softmax linear combination of the outputs yields the predicted functional connectivity (), which is compared with the ground truth empirical FC in step 4.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Depicts different diffusion scales () ranging from 0.5-10 (values in the legend), and each exponential curve is a function of the scale () and represents the contribution of every eigenvalue of the Laplacian of the SC matrix (the indices of eigenvalues (in increasing order) are shown on the abscissa).</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Pearson correlation values between empirical and predicted FCs of all the test subjects with the proposed A-GHN model (Green line), averaged over five runs, are compared with the predictions of the other two models. Horizontal lines show the mean correlation values (higher is better) of 0.788, 0.732, and 0.645, respectively, for A-GHN, GCN Encoder-Decoder, and MKL.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Results of performance of A-GHN model in the 5-fold cross-validation setting on 1058 subjects. The box plots depict the Pearson correlation between empirical and predicted FCs in each fold.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Qualitative comparison of the Functional Connectivity matrices (FCs). The mean of the predicted FCs from the proposed A-GHN model is compared with that of the mean FC from ground truth (empirically observed), GCN Encode-Decoder ^{##UREF##6##14##} and MKL ^{##REF##29311619##7##} models.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Qualitative comparison of the Functional Connectivity Networks. Four communities are derived from the mean FC matrices of the test subjects from the ground truth as well as the predicted FCs from the proposed and other models: MKL^{##REF##29311619##7##} and GCN Encoder-Decoder^{##UREF##6##14##}. Color coding of the edges/nodes for different models is done independently, and hence the cross-comparison of community structures is qualitative in nature.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Comparison of A-GHN model with previous state-of-the-art models. Comparison is done by computing the Pearson correlation between the ground-truth FC and predicted FC of test subjects. Overall, the A-GHN model displays a higher correlation value of 0.788, better than previous models. Significant values are in bold.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Model</th><th align=\"left\">Correlation</th></tr></thead><tbody><tr><td align=\"left\">MKL^{##REF##29311619##7##}</td><td align=\"left\">0.645</td></tr><tr><td align=\"left\">GCN Encoder Decoder^{##UREF##6##14##}</td><td align=\"left\">0.732</td></tr><tr><td align=\"left\">Autoencoder^{##REF##33271268##27##}</td><td align=\"left\">0.561</td></tr><tr><td align=\"left\">Macroscale SC-FC^{##REF##32160567##38##}</td><td align=\"left\">0.501</td></tr><tr><td align=\"left\">GNN (GCN + GTN)^{##UREF##7##15##}</td><td align=\"left\">0.715</td></tr><tr><td align=\"left\">M-GHN^{##UREF##14##40##}</td><td align=\"left\">0.741</td></tr><tr><td align=\"left\">Random A-GHN (Freezing GHNs)</td><td align=\"left\">0.557</td></tr><tr><td align=\"left\">A-GHN (one-layer)</td><td align=\"left\"><bold>0.788</bold></td></tr><tr><td align=\"left\">A-GHN (two-layer)</td><td align=\"left\"><bold>0.799</bold></td></tr><tr><td align=\"left\">A-GHN (four-layer)</td><td align=\"left\"><bold>0.760</bold></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Mutual information between the communities detected in various models. Comparison is done by computing the mutual information (MI) between the four communities across different models. Overall, the A-GHN model has higher mutual information with Ground Truth.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Model1 vs. Model2</th><th align=\"left\">Mutual Information</th></tr></thead><tbody><tr><td align=\"left\">Actual vs. Actual</td><td align=\"left\">1.706</td></tr><tr><td align=\"left\">Actual vs. A-GHN</td><td align=\"left\"><bold>1.357</bold></td></tr><tr><td align=\"left\">Actual vs. GCN Encoder Decoder</td><td align=\"left\">0.735</td></tr><tr><td align=\"left\">Actual vs. MKL</td><td align=\"left\">0.740</td></tr><tr><td align=\"left\">A-GHN vs. A-GHN</td><td align=\"left\">2.180</td></tr><tr><td align=\"left\">A-GHN vs. GCN Encoder Decoder</td><td align=\"left\">0.847</td></tr><tr><td align=\"left\">A-GHN vs. MKL</td><td align=\"left\">1.064</td></tr><tr><td align=\"left\">GCN Encoder Decoder vs. MKL</td><td align=\"left\">0.675</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Comparison of A-GHN scale outputs with Ground Truth communities. Mutual information between the communities detected in various scales of A-GHN model. Comparison is done by computing the mutual information (MI) between the four communities across different scales. Overall, A-GHN model has higher mutual information with Ground Truth.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Model1 vs. Model2</th><th align=\"left\">Mutual Information</th></tr></thead><tbody><tr><td align=\"left\">Actual vs. Actual</td><td align=\"left\">1.706</td></tr><tr><td align=\"left\">Actual vs. A-GHN Scale-0.6</td><td align=\"left\">0.841</td></tr><tr><td align=\"left\">Actual vs. A-GHN Scale-0.8</td><td align=\"left\">1.189</td></tr><tr><td align=\"left\">Actual vs. A-GHN Scale-1</td><td align=\"left\">1.312</td></tr><tr><td align=\"left\">Actual vs. A-GHN Scale-2</td><td align=\"left\">0.971</td></tr><tr><td align=\"left\">Actual vs. A-GHN Scale-4</td><td align=\"left\">0.589</td></tr><tr><td align=\"left\">Actual vs. A-GHN Scale-6</td><td align=\"left\">0.546</td></tr><tr><td align=\"left\">Actual vs. A-GHN Scale-8</td><td align=\"left\">0.443</td></tr></tbody></table></table-wrap>" ]

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stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi ^{0}=X$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:mrow><mml:msup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\rho (\\lambda _{i}) = e^{-(\\gamma \\lambda _{i})} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M32\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi>ρ</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>λ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>γ</mml:mi><mml:msub><mml:mi>λ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma \\ge 0$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:mrow><mml:mi>γ</mml:mi><mml:mo>≥</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda _{i}$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:msub><mml:mi>λ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$i^{th}$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">th</mml:mi></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Lambda$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:mi mathvariant=\"normal\">Λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq18\"><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Lambda _\\gamma = \\rho (\\Lambda ) = \\text {diag}(\\{\\rho (\\lambda _i)\\}_{i=1}^{N})$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mrow><mml:msub><mml:mi mathvariant=\"normal\">Λ</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"normal\">Λ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mtext>diag</mml:mtext><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:mi>ρ</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>λ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq19\"><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$g_{w}$$\\end{document}</tex-math><mml:math id=\"M44\"><mml:msub><mml:mi>g</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} g_{w} = \\sum _{k=0}^{K-1}w_{k}(\\Lambda _{\\gamma })^{k} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M46\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>K</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:msub><mml:mi>w</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"normal\">Λ</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi>k</mml:mi></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq20\"><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w_{k}$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:msub><mml:mi>w</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq21\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\textit{K} = 2$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:mrow><mml:mi mathvariant=\"italic\">K</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\Psi _{\\gamma }&amp;= U g_{w} U^{T} X \\nonumber \\\\&amp;= U \\left( \\sum _{k=0}^{K-1}w_{k}(\\Lambda _{\\gamma })^{k}\\right) U^{T} X \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M52\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mi>γ</mml:mi></mml:msub></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mi>U</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:msup><mml:mi>U</mml:mi><mml:mi>T</mml:mi></mml:msup><mml:mi>X</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mi>U</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>K</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:msub><mml:mi>w</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"normal\">Λ</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi>k</mml:mi></mml:msup></mml:mfenced><mml:msup><mml:mi>U</mml:mi><mml:mi>T</mml:mi></mml:msup><mml:mi>X</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\Psi _{\\gamma }&amp;= (w_{0}I_{N} + w_{1}e^{-(\\Lambda _{\\gamma })} UU^{T}) X \\nonumber \\\\&amp;= (w_{0}I_{N}+w_{1}e^{-(\\gamma L)})X \\nonumber \\\\&amp;= (W_{\\gamma }e^{-(\\gamma L)})X \\nonumber \\\\&amp;= (W_{\\gamma } H_{\\gamma })X \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M54\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mi>γ</mml:mi></mml:msub></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msub><mml:mi>I</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"normal\">Λ</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup><mml:mi>U</mml:mi><mml:msup><mml:mi>U</mml:mi><mml:mi>T</mml:mi></mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msub><mml:mi>I</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>γ</mml:mi><mml:mi>L</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>γ</mml:mi><mml:mi>L</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:msub><mml:mi>H</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq22\"><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma }^{N \\times N}$$\\end{document}</tex-math><mml:math id=\"M56\"><mml:msubsup><mml:mi>W</mml:mi><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq23\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq24\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\gamma } = e^{-\\gamma L}$$\\end{document}</tex-math><mml:math id=\"M60\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>γ</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq25\"><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi _{\\gamma }^{N \\times N}$$\\end{document}</tex-math><mml:math id=\"M62\"><mml:msubsup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq26\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma }$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:msub><mml:mi>W</mml:mi><mml:mi>γ</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq27\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w_{0}$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:msub><mml:mi>w</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq28\"><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w_{1}$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:msub><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq29\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma } (I_{N} + e^{-(\\gamma L)} )X$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>γ</mml:mi><mml:mi>L</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq30\"><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$e^{-(\\gamma L}$$\\end{document}</tex-math><mml:math id=\"M72\"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>γ</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq31\"><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$e^{-(\\gamma L}$$\\end{document}</tex-math><mml:math id=\"M74\"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>γ</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq32\"><alternatives><tex-math id=\"M75\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_{N}$$\\end{document}</tex-math><mml:math id=\"M76\"><mml:msub><mml:mi>I</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq33\"><alternatives><tex-math id=\"M77\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w_{0}$$\\end{document}</tex-math><mml:math id=\"M78\"><mml:msub><mml:mi>w</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq34\"><alternatives><tex-math id=\"M79\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{\\gamma _{1}, \\gamma _{2}, \\gamma _{3}, \\cdots , \\gamma _{m}\\}$$\\end{document}</tex-math><mml:math id=\"M80\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>⋯</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq35\"><alternatives><tex-math id=\"M81\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{H_{\\gamma _{1}}, H_{\\gamma _{2}}, H_{\\gamma _{3}},\\cdots , H_{\\gamma _{m}}\\}$$\\end{document}</tex-math><mml:math id=\"M82\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:msub><mml:mo>,</mml:mo><mml:mo>⋯</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq36\"><alternatives><tex-math id=\"M83\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$_{N}$$\\end{document}</tex-math><mml:math id=\"M84\"><mml:msub><mml:mrow/><mml:mi>N</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq37\"><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi _{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M86\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq38\"><alternatives><tex-math id=\"M87\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha = \\{\\alpha _{\\gamma _{1}}, \\alpha _{\\gamma _{2}}, \\cdots , \\alpha _{\\gamma _{m}}\\}$$\\end{document}</tex-math><mml:math id=\"M88\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:msub><mml:mo>,</mml:mo><mml:mo>⋯</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M89\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\Psi _{\\gamma _{i}}&amp;= tanh (W_{\\gamma _{i}}e^{-(\\gamma _{i} L)}X) \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M90\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>h</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mi>L</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup><mml:mi>X</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M91\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned}&amp;= tanh (W_{\\gamma _{i}}H_{\\gamma _{i}}X), i \\in [1, m]\\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M92\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd/><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>h</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:msub><mml:mi>H</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:mi>X</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M93\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\alpha&amp;= [vec(\\Psi _{\\gamma _{i}}), vec(\\Psi _{\\gamma _{i}}), \\cdots , vec(\\Psi _{\\gamma _{i}})]_{m \\times N^{2}} [W_{\\alpha }]_{N^{2} \\times 1} , i \\in [1, m] \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M94\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mi>α</mml:mi></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mo>⋯</mml:mo><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>×</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>×</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ10\"><label>10</label><alternatives><tex-math id=\"M95\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned}&amp;= [\\alpha _{\\gamma _{1}}, \\alpha _{\\gamma _{2}}, \\cdots , \\alpha _{\\gamma _{m}}]_{[m \\times 1]} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M96\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd/><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:msub><mml:mo>,</mml:mo><mml:mo>⋯</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>m</mml:mi><mml:mo>×</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq39\"><alternatives><tex-math id=\"M97\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha _{\\gamma _{i}} = vec(\\Psi _{\\gamma _{i}}) \\times W_{\\alpha }$$\\end{document}</tex-math><mml:math id=\"M98\"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:mo>=</mml:mo><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>×</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mi>α</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M99\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi _{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M100\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M101\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C_{f}$$\\end{document}</tex-math><mml:math id=\"M102\"><mml:msub><mml:mi>C</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ11\"><label>11</label><alternatives><tex-math id=\"M103\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} C_{f} = \\sum _{i=1}^{m}\\text {Softmax}(\\alpha _{\\gamma _{i}})\\Psi _{\\gamma _{i}} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M104\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:mtext>Softmax</mml:mtext><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq42\"><alternatives><tex-math id=\"M105\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\alpha }$$\\end{document}</tex-math><mml:math id=\"M106\"><mml:msub><mml:mi>W</mml:mi><mml:mi>α</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq43\"><alternatives><tex-math id=\"M107\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M108\"><mml:msub><mml:mi>W</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq44\"><alternatives><tex-math id=\"M109\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C_{f}$$\\end{document}</tex-math><mml:math id=\"M110\"><mml:msub><mml:mi>C</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ12\"><label>12</label><alternatives><tex-math id=\"M111\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} J&amp;= \\sum _{s=1}^{S}||C_{f}^{s} - \\text {FC}^{s} ||_{F}^{2} \\nonumber \\\\&amp;= \\sum _{s=1}^{S}||\\sum _{i=1}^{m} \\text {Softmax}(\\alpha _{\\gamma _{i}}^{s})\\Psi _{\\gamma _{i}}^{s} - \\text {FC}^{s} ||_{F}^{2} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M112\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mi>J</mml:mi></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>S</mml:mi></mml:munderover><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:msubsup><mml:mi>C</mml:mi><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msup><mml:mtext>FC</mml:mtext><mml:mi>s</mml:mi></mml:msup><mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>S</mml:mi></mml:munderover><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:mtext>Softmax</mml:mtext><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>α</mml:mi><mml:mrow><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mi>s</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msubsup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mi>s</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msup><mml:mtext>FC</mml:mtext><mml:mi>s</mml:mi></mml:msup><mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq45\"><alternatives><tex-math id=\"M113\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi _{\\gamma _{i}}^{s}$$\\end{document}</tex-math><mml:math id=\"M114\"><mml:msubsup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mi>s</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq46\"><alternatives><tex-math id=\"M115\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$N \\times N$$\\end{document}</tex-math><mml:math id=\"M116\"><mml:mrow><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq47\"><alternatives><tex-math id=\"M117\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M118\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq48\"><alternatives><tex-math id=\"M119\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m \\times 1$$\\end{document}</tex-math><mml:math id=\"M120\"><mml:mrow><mml:mi>m</mml:mi><mml:mo>×</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ13\"><label>13</label><alternatives><tex-math id=\"M121\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} J&amp;= \\sum _{s=1}^{S}||\\sum _{i=1}^{m}H_{i}^{s}\\Pi _{i} - \\text {FC}^{s} ||_{F}^{2} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M122\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mi>J</mml:mi></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>S</mml:mi></mml:munderover><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msubsup><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msubsup><mml:msub><mml:mi mathvariant=\"normal\">Π</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msup><mml:mtext>FC</mml:mtext><mml:mi>s</mml:mi></mml:msup><mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq49\"><alternatives><tex-math id=\"M123\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Pi _{i}$$\\end{document}</tex-math><mml:math id=\"M124\"><mml:msub><mml:mi mathvariant=\"normal\">Π</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq50\"><alternatives><tex-math id=\"M125\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{i}^{s}$$\\end{document}</tex-math><mml:math id=\"M126\"><mml:msubsup><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ14\"><label>14</label><alternatives><tex-math id=\"M127\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\hat{J}}&amp;= \\mathop {{\\textrm{argmin}}}\\limits _\\alpha \\sum _{s=1}^{S}|| \\sum _{i=1}^{m}\\alpha _{i}H_{i}^{s}- \\text {FC}^{s} ||_{F}^{2} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M128\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mover accent=\"true\"><mml:mi>J</mml:mi><mml:mo stretchy=\"false\">^</mml:mo></mml:mover></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mtext>argmin</mml:mtext><mml:mi>α</mml:mi></mml:munder><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>S</mml:mi></mml:munderover><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi>α</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msubsup><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msup><mml:mtext>FC</mml:mtext><mml:mi>s</mml:mi></mml:msup><mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq51\"><alternatives><tex-math id=\"M129\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha _{i}$$\\end{document}</tex-math><mml:math id=\"M130\"><mml:msub><mml:mi>α</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq52\"><alternatives><tex-math id=\"M131\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{i}$$\\end{document}</tex-math><mml:math id=\"M132\"><mml:msub><mml:mi>H</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq53\"><alternatives><tex-math id=\"M133\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma _{i}}^T$$\\end{document}</tex-math><mml:math id=\"M134\"><mml:msubsup><mml:mi>W</mml:mi><mml:mrow><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mi>T</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq54\"><alternatives><tex-math id=\"M135\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Pi _{i}$$\\end{document}</tex-math><mml:math id=\"M136\"><mml:msub><mml:mi mathvariant=\"normal\">Π</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq55\"><alternatives><tex-math id=\"M137\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma _{i}}^T$$\\end{document}</tex-math><mml:math id=\"M138\"><mml:msubsup><mml:mi>W</mml:mi><mml:mrow><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mi>T</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq56\"><alternatives><tex-math id=\"M139\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi _{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M140\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq57\"><alternatives><tex-math id=\"M141\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M142\"><mml:msub><mml:mi>W</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq58\"><alternatives><tex-math id=\"M143\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$87 \\times 87$$\\end{document}</tex-math><mml:math id=\"M144\"><mml:mrow><mml:mn>87</mml:mn><mml:mo>×</mml:mo><mml:mn>87</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq59\"><alternatives><tex-math id=\"M145\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\times$$\\end{document}</tex-math><mml:math id=\"M146\"><mml:mo>×</mml:mo></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq60\"><alternatives><tex-math id=\"M147\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\times$$\\end{document}</tex-math><mml:math id=\"M148\"><mml:mo>×</mml:mo></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq61\"><alternatives><tex-math id=\"M149\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m=7$$\\end{document}</tex-math><mml:math id=\"M150\"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn>7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq62\"><alternatives><tex-math id=\"M151\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$87 \\times 87$$\\end{document}</tex-math><mml:math id=\"M152\"><mml:mrow><mml:mn>87</mml:mn><mml:mo>×</mml:mo><mml:mn>87</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq63\"><alternatives><tex-math id=\"M153\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\textit{I}_{N})$$\\end{document}</tex-math><mml:math id=\"M154\"><mml:mrow><mml:msub><mml:mi mathvariant=\"italic\">I</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq64\"><alternatives><tex-math id=\"M155\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$L_2$$\\end{document}</tex-math><mml:math id=\"M156\"><mml:msub><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq65\"><alternatives><tex-math id=\"M157\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$5e^{-4}$$\\end{document}</tex-math><mml:math id=\"M158\"><mml:mrow><mml:mn>5</mml:mn><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq66\"><alternatives><tex-math id=\"M159\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M160\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq67\"><alternatives><tex-math id=\"M161\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M162\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq68\"><alternatives><tex-math id=\"M163\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M164\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq69\"><alternatives><tex-math id=\"M165\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m=7$$\\end{document}</tex-math><mml:math id=\"M166\"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn>7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq70\"><alternatives><tex-math id=\"M167\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M168\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq71\"><alternatives><tex-math id=\"M169\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M170\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq72\"><alternatives><tex-math id=\"M171\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\hbox {Mean} = 0.732$$\\end{document}</tex-math><mml:math id=\"M172\"><mml:mrow><mml:mtext>Mean</mml:mtext><mml:mo>=</mml:mo><mml:mn>0.732</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq73\"><alternatives><tex-math id=\"M173\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\hbox {Mean} = 0.645$$\\end{document}</tex-math><mml:math id=\"M174\"><mml:mrow><mml:mtext>Mean</mml:mtext><mml:mo>=</mml:mo><mml:mn>0.645</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq74\"><alternatives><tex-math id=\"M175\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p =.00007$$\\end{document}</tex-math><mml:math id=\"M176\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>00007</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq75\"><alternatives><tex-math id=\"M177\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p =.03$$\\end{document}</tex-math><mml:math id=\"M178\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>03</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq76\"><alternatives><tex-math id=\"M179\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p =.00004$$\\end{document}</tex-math><mml:math id=\"M180\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>00004</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq77\"><alternatives><tex-math id=\"M181\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p =.12$$\\end{document}</tex-math><mml:math id=\"M182\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq78\"><alternatives><tex-math id=\"M183\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\hbox {Mean} = 0.037$$\\end{document}</tex-math><mml:math id=\"M184\"><mml:mrow><mml:mtext>Mean</mml:mtext><mml:mo>=</mml:mo><mml:mn>0.037</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq79\"><alternatives><tex-math id=\"M185\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\hbox {Mean} = 0.086$$\\end{document}</tex-math><mml:math id=\"M186\"><mml:mrow><mml:mtext>Mean</mml:mtext><mml:mo>=</mml:mo><mml:mn>0.086</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq80\"><alternatives><tex-math id=\"M187\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p = 0$$\\end{document}</tex-math><mml:math id=\"M188\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq81\"><alternatives><tex-math id=\"M189\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p =.016$$\\end{document}</tex-math><mml:math id=\"M190\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>016</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq82\"><alternatives><tex-math id=\"M191\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p =.00001$$\\end{document}</tex-math><mml:math id=\"M192\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>00001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ15\"><label>15</label><alternatives><tex-math id=\"M193\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\begin{aligned} MI(X;Y) = D_{KL}(P_{(X,Y} \\parallel P_X \\otimes P_Y) \\end{aligned} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M194\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi>M</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>X</mml:mi><mml:mo>;</mml:mo><mml:mi>Y</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">KL</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">‖</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi>X</mml:mi></mml:msub><mml:mo>⊗</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi>Y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq83\"><alternatives><tex-math id=\"M195\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$D_{KL}$$\\end{document}</tex-math><mml:math id=\"M196\"><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">KL</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq84\"><alternatives><tex-math id=\"M197\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$N=250$$\\end{document}</tex-math><mml:math id=\"M198\"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>250</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq85\"><alternatives><tex-math id=\"M199\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M200\"><mml:msub><mml:mi>W</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq86\"><alternatives><tex-math id=\"M201\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M202\"><mml:msub><mml:mi>W</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq87\"><alternatives><tex-math id=\"M203\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Pi _{i}$$\\end{document}</tex-math><mml:math id=\"M204\"><mml:msub><mml:mi mathvariant=\"normal\">Π</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq88\"><alternatives><tex-math id=\"M205\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$W_{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M206\"><mml:msub><mml:mi>W</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq89\"><alternatives><tex-math id=\"M207\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi _{\\gamma _{i}}$$\\end{document}</tex-math><mml:math id=\"M208\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq90\"><alternatives><tex-math id=\"M209\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$87 \\times 87$$\\end{document}</tex-math><mml:math id=\"M210\"><mml:mrow><mml:mn>87</mml:mn><mml:mo>×</mml:mo><mml:mn>87</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq91\"><alternatives><tex-math id=\"M211\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$86 \\times 86$$\\end{document}</tex-math><mml:math id=\"M212\"><mml:mrow><mml:mn>86</mml:mn><mml:mo>×</mml:mo><mml:mn>86</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq92\"><alternatives><tex-math id=\"M213\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$333 \\times 333$$\\end{document}</tex-math><mml:math id=\"M214\"><mml:mrow><mml:mn>333</mml:mn><mml:mo>×</mml:mo><mml:mn>333</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq93\"><alternatives><tex-math id=\"M215\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$360 \\times 360$$\\end{document}</tex-math><mml:math id=\"M216\"><mml:mrow><mml:mn>360</mml:mn><mml:mo>×</mml:mo><mml:mn>360</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>" ]

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[ "<media xlink:href=\"41598_2023_50408_MOESM1_ESM.pdf\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Pancreatic cancer (PC) is one of most lethal human carcinomas worldwide, which accounts for its lowest 5-year survival rate about 8% [##REF##30463539##1##, ##REF##29717230##2##]. Furthermore, PC incidence continuously increases in both men and women in the United States, which is estimated approximately 64,050 new cases in 2023 [##REF##36633525##3##]. As possession of high aggressiveness and hidden symptoms, only 10–20% of PC patients are localized disease at diagnosis. PC patients are often treated with surgical resection and subsequently adjuvant systemic chemotherapy [##REF##30341417##4##]. And 5-year survival rate of surgical resectable PC patients only reaches to 30% after surgery and adjuvant chemotherapy treatments [##REF##30341417##4##]. Thus, it is urgent to comprehensively understand the molecular mechanisms of PC and develop novel strategies for treatment of PC.</p>", "<p id=\"Par3\">F-box protein FBXO31, functioning as the substrate recognition protein of SCF (SKP/Cullin/F-box protein) class E3 ubiquitin ligase, is responsible for mediating substrate ubiquitination and degradation [##REF##23657496##5##, ##REF##29242641##6##]. FBXO31 was identified as a tumor suppressor in breast cancer and prostate cancers and it located at chromosome 16q24.3 loss of heterozygosity region [##REF##19412162##7##, ##REF##29343641##8##]. It has been suggested that FBXO31 plays a key role in biological process of DNA repair, cell cycle, cell growth and metastasis, thus contributing to cancer development [##REF##19412162##7##, ##REF##34686346##9##–##REF##26124108##11##]. Furthermore, a small number of studies implied that FBXO31 functioned as an oncoprotein to promote oncogenesis and cancer progression in lung and esophageal cancer [##REF##31037126##12##–##REF##26175949##14##]. Therefore, the opposite role of FBXO31 in different human cancers was critically associated with its downstream substrates, acting as oncogenic or tumor suppressive role. For example, identified oncogenic substrates of FBXO31 include MDM2, DUSP6, CyclinD1 and CyclinA1 [##REF##34686346##9##, ##REF##26124108##11##, ##REF##29279382##15##, ##REF##31413110##16##]. However, the physiological function of FBXO31 and its targeted substrates in PC have not been fully elucidated.</p>", "<p id=\"Par4\">SIRT2 belongs to family members of NAD⁺-dependent type III protein deacetylase, which is predominantly localized in the cytoplasm [##REF##12620231##17##]. SIRT2 is associated with histone deacetylation (H4K16Ac) and chromosomal condensation during mitosis [##REF##31505260##18##]. Extensive research has been demonstrated that SIRT2 deacetylated APC/C activator CDH1 and CDC20 to activate APC/C, leading to Aurora-A degradation and mitosis regulation and genome integrity [##REF##22014574##19##]. Studies have suggested that SIRT2 may be a novel target for cancer treatment [##REF##31505260##18##, ##REF##32449165##20##]. Oncogenic characteristic of SIRT2 was demonstrated in some types of cancer [##REF##31324785##21##–##UREF##0##23##], while others showed the tumor suppressive role of SIRT2 [##REF##27637077##24##–##REF##33789098##28##]. Even in pancreatic cancer, the precise role of SIRT2 remains elusive and opposite [##REF##27637077##24##, ##REF##23175188##29##, ##REF##23523103##30##]. Thus, the role and molecular mechanism of SIRT2 in PC need be better understood.</p>", "<p id=\"Par5\">N⁶-methyladenosine (m6A) modification is one of the most abundant posttranscriptional modifications (PTMs) in eukaryotic mRNA [##REF##31520073##31##, ##REF##32303268##32##]. The well-known function of m6A is identified in regulating RNA metabolism, including pre-mRNA splicing, mRNA decay, mRNA translation, mRNA export [##REF##31520073##31##, ##REF##32303268##32##]. Growing body of evidence suggests that m6A modification is critically involved in tumorgenisis [##REF##32183948##33##, ##REF##32398132##34##]. In addition, m6A methylation is performed by m6A writer complex, which comprises a METTL3-METTL14 methyltransferase core and other components [##REF##31520073##31##]. METTL3 serves as a catalytic subunit and METTL14 functions as a structural basis for substrate recognition [##REF##31520073##31##]. It has been reported that METTL3 and METTL14 promote the tumor initiation and progression in PC [##REF##31606241##35##–##REF##32097728##39##]. Here, we identified a novel molecular mechanism of METTL3-FBXO31-SIRT2 signaling axis and its impact on tumor growth and metastasis in PC.</p>" ]

[ "<title>Materials and methods</title>", "<title>Human pancreatic cancer tissue and IHC</title>", "<p id=\"Par23\">Human pancreatic cancer microarray slides (HpanA150su01) were purchased from OUTDO BIOTECH (Shanghai, China). The tissue chip contains 90 cases of pancreatic cancer tissues and 60 cases of matched tumor-adjacent normal tissues. IHC stain was operated to detect the expression of FBXO31 and SIRT2 in the same tissue chips as described before [##REF##35279684##43##]. Slides were treated by deparaffinization and rehydration operation. Then, slides were pretreated with antigen retrieval, and incubated with 3% H₂O₂ for 10 min at room temperature (RT). After blocking with BSA for 1 h, slides were incubated with human FBXO31 or SIRT2 antibodies overnight at 4 °C. Slides were incubated with biotinylated secondary Ab for 1 h at RT, followed by streptavidin-conjugated horseradish peroxide for 1 h and DAB for 5 min at RT. Images were collected by Aperio Imagescope software and analyzed by two independent pathologists. IHC staining was scored as follows: score = percentage of positive staining of tumor cells (0: 0%; 1: 1–25%; 2: 26–50%; 3: 51–75%; 4: 76–100%) × staining intensity (0: negative; 1: weak; 2: medium; 3: strong). The final scores ≥4 were considered as high expression of FBXO31 or SIRT2 for statistical analysis.</p>", "<title>Cell culture, cell transfection and infection</title>", "<p id=\"Par24\">HEK293T, HeLa and human pancreatic cancer cells (Patu-8988 and Panc-1) were obtained from the Cell Bank of the Chinese Academy of Sciences (Shanghai, China). The cells were authenticated by STR profiling and tested for mycoplasma contamination. All cells were maintained in DMEM medium supplemented with 10% FBS, and 1% Penicillin/Streptomycin. Cells were cultured at 37 °C at 5% CO₂ atmosphere. Plasmid constructs or siRNAs were transfected using Lipofectamine 3000 according to manufacturer’s protocol. Lentiviral vectors loading FBXO31 cDNA or SIRT2 shRNA sequences were packaged and infected PC cells for generation of stable transfected cells.</p>", "<title>Plasmids, siRNA and sgRNA</title>", "<p id=\"Par25\">Plasmids, including FBXO31, FBXO31-Δ-Fbox, SIRT2, Del-SIRT2, METTL3 and METTL14, were obtained from Youbio Biological Technology (Hunan, China). They were constructed into pcDNA 3.1 vector carrying with different tags. FBXO31 sgRNAs were designed using guide design tools from Zhang lab (<ext-link ext-link-type=\"uri\" xlink:href=\"https://zlab.Bio/guide-design-resources\">https://zlab.Bio/guide-design-resources</ext-link>) and cloned into CRISPR V2 backbones. FBXO31-sgRNA sequence was as follows: CAG GCT TGA TGA GGT CGT CGG GG. SIRT2 shRNA sequence was cloned into lentiviral vector pHBLV-U6 (Hanbio Bio, Shanghai, China) indicated as follows: GCC AAC CAT CTG TCA CTA CTT. The siRNAs of METTL3, METTL14, YTHDF1 and YTHDF2 were purchased from Hanbio Biotechnology Co. LTD (Shanghai, China). METTL3 siRNA sequences were used as described before [##REF##30870073##44##]: siMETTL3-1, CTG CAA GTA TGT TCA CTA TGA; siMETTL3-2, GCA AGT ATG TTC ACT ATG AAA. METTL14 siRNA sequences were used as indicated before [##REF##32111213##45##]: SiMETTL14-1, GCT GGA CTT GGG ATG ATA TTA; siMETTL14-2, GAA CCT GAA ATT GGC AAT ATA. siRNA sequences of YTHDF1 and YTHDF2 were performed as described before [##REF##31818312##46##, ##REF##31409574##47##]. siYTHDF1-1, CCT CCA CCC ATA AAG CAT A; siYTHDF1-2, CCT GCT CTT CAG CGT CAA TTT-3; siYTHDF2, AAG GAC GTT CCC AAT AGC CAA.</p>", "<title>Antibodies</title>", "<p id=\"Par26\">Anti-FBXO31 antibody (#86137; 1:1000) antibody was purchased from Abcam. Anti-AuroraA antibody (#14475; 1:1,000), anti-Slug antibody (#9585; 1:1000), anti-C-myc antibody (#5605; 1:1000), anti-p-p44/42 MAPK (Erk1/2) (#4370; 1:1000) and anti-tubulin antibody (2128 S; 1:2000) antibodies were all obtained from Cell Signaling Technology. Anti-SIRT2 (66410-1-Ig; 1:1500), anti-METTL3 (15073-1-AP; 1:1500), anti-METTL14 (26158-1-Ap; 1:1500), Anti-Flag tag (20543-1-AP; 1:1500), anti-HA tag (51064-2-AP; 1:1000), Anti-β-actin (20536-1-AP; 1:2000) and anti-His tag (66005-1-Ig; 1:1,000) antibodies were all bought from Proteintech. Peroxidase-conjugated anti-mouse secondary antibody (70-GAM007, 1:5000) and peroxidase-conjugated anti-rabbit secondary antibody (70-GAR0072; 1:5,000) were purchased from MultiSciences Company.</p>", "<title>MTT assay</title>", "<p id=\"Par27\">Cell viability was conducted by MTT assay as described before [##REF##35279684##43##]. PC cells pretreated with indicated groups were seeded into 96 well plates. After 72 h, 10 μl MTT solution (0.5 mg/ml) was added into each well of plates and cultured for 4 h. After discarding the supernatant of each well, 100 μl DMSO was added. Then, OD490 value was detected and recorded.</p>", "<title>Wound healing assay</title>", "<p id=\"Par28\">Wound healing assay was performed to detect cell migration as described before [##REF##35279684##43##]. Transfected cells with indicated groups were incubated in 6-well plates. After cell confluence reached over 90%, a linear wound scratch was made by scraping the surface of plates using a pipette tip. Then, the wound scratches at 0 h and 20 h were photographed, respectively.</p>", "<title>Transwell migration and invasion assay</title>", "<p id=\"Par29\">Transwell assay was performed as mentioned previously to analyze cell migration and invasion ability [##REF##35279684##43##]. Transfected cells were seeded into Transwell upper-chamber with serum-free medium, while medium containing 10% FBS was placed into lower chamber (Corning). For Transwell invasion assay, the chamber should be precoated with a thin-layer Matrigel (BD Biosciences) before cells were seeded. Consequently, the upper cells of chambers were removed using a cotton buds, and the bottom surface cells of chambers were fixed, stained and photographed.</p>", "<title>qRT-PCR</title>", "<p id=\"Par30\">Total RNA was extracted using TRIzol (Ambion) and reverse transcribed into cDNA using PrimeScript™ RT reagent Kit (TaKaRa). Real-time PCR was carried out using SYBR Green PCR Master Mix and a LightCycler480 Instrument (Roche). The data were quantified by 2^−ΔΔCt method. Primers were described as follows: FBXO31, sense, CAT CAA GCC TGG CCT CTT C, antisense; GGT CGA TCT CCA CTG TCT G; SIRT2, sense, CAC ATC ACA CTG CGT CAG C, antisense, CTT CAC ACT TGG GCG TCA C; METTL3, sense, TTG TCT CCA ACC TTC CGT AGT, antisense, CCA GAT CAG AGA GGT GGT GTA G; METTL14, sense, AGT GCC GAC AGC ATT GGT G, antisense, GAG CAG AGG TAT CAT AGG AA; YTHDF1, sense, GCA CAC AAC CTC CAT CTT CG, antisense, AAC TGG TTC GCC CTC ATT GT; GAPDH, sense, CAG CCT CAA GAT CAG CA, antisense, TGT GGT CAT GAG TCC TTC CA.</p>", "<title>Western blotting</title>", "<p id=\"Par31\">Cells were collected and lysed in cold RIPA buffer addition of protease inhibitor cocktail (Thermo Fisher Scientific). The lysates were centrifuged at 12,000 <italic>g</italic> for 20 min at 4 °C and then the liquid supernatants were collected. The protein concentrations were estimated by BCA methods. Then, the proteins were electrophoresed using SDS-PAGE gel and transferred to PVDF membrane. The members were probed with the indicated primary antibodies overnight at 4 °C. After washing with TBST buffer for 3 times, the members were incubated proper secondary antibodies for 2 h at RT. The signals were visualized using chemiluminescence reagents (Thermo Fisher Scientific).</p>", "<title>Immunoprecipitation</title>", "<p id=\"Par32\">For Immunoprecipitation analysis, cells were lysed with cold NP40 lysate with protease inhibitor cocktail (Thermo Fisher Scientific). Then, the proteins were added and incubated with magnetic beads supplemented with HA or Flag Tag (Sino biological, China). After washing 3 times using TBST buffer, the beads were eluted by boiling in SDS loading buffer. Subsequently, the final elute was subjected to SDS-PAGE electrophoresis and western blotting analysis.</p>", "<title>In vivo ubiquitination assay</title>", "<p id=\"Par33\">To detect in vivo ubiquitination of SIRT2, cells were transfected with His-ubiquitin along with indicated plasmids. After 36 h post-transfection, cells were incubated with MG132 (10 μM, Sigma) for 6 h. Then, the cells were collected and lysed in NP40 buffer. The lysates were cultured with HA-tag magnetic beads. The beads were washed for 3 times by TBST and eluted by boiling in SDS loading buffer. Then the pull-down protein was analyzed by western blotting.</p>", "<title>Tandem mass spectrometry</title>", "<p id=\"Par34\">HEK293T cells transfected with Flag-FBXO31 or EV were immunoprecipitated with Flag magnetic beads described as Flag IP. The lysates were resolved on SDS-PAGE and stained by Coomassie blue. The band of FBXO31-associated protein was excised from the gel and sent for tandem mass spectrometric peptide analysis. The LC-MS/MS were performed at Shanghai Applied Protein Technology (China). The resulting raw data were processed using Mascot2.2 software to search specific peptide sequences from UniProt database.</p>", "<title>Protein stability analysis</title>", "<p id=\"Par35\">Cycloheximide method was performed to analyze protein half-life for protein stability studies. Cells were treated with indicated transfection. Then, cells were cultured with 20 μg/ml cycloheximide (Sigma) after 48 h post-transfection. To detect protein abundances, the cells were lysed and proteins were measured by western blotting at indicated time points.</p>", "<title>mRNA stability analysis</title>", "<p id=\"Par36\">Actinomycin D, an inhibitor of transcription, was used to detect RNA stability. The transfected cells were treated with 5 μg/ml actinomycin D (MCE, USA). Then, the cells were harvested at indicated time points and the total RNAs were extracted by TRIzol reagent. The relative expression of FBXO31 mRNA was analyzed by qRT-PCR. The half-life time of FBXO31 mRNA were calculated as described before [##REF##30154548##48##].</p>", "<title>MeRIP-qPCR assay</title>", "<p id=\"Par37\">MeRIP-PCR assay was performed as described before [##REF##32964498##49##]. Total RNA was isolated from cells treated with indicated groups, and mRNA was isolated using NEBNext Poly(A) mRNA Magnetic Isolation Module (NEB). 5 μg Puried mRNA was fragmented to 100–200 nt by NEBNext® Magnesium RNA Fragmentation Module (NEB). Next, 10% of fragmented mRNA was saved as input solution and the rest of fragmented mRNA was immunoprecipitated with m6A antibody (Abcam, ab151230) in IP binding buffer (10 mM Tris-HCl, 150 mM NaCl, 0.1% NP-40, pH 7.5) for 2 h at 4 °C. Then, 50 μl washed protein A/G magnetic beads (Thermo) were added to the immunoprecipitation mixture for 2 h at 4 °C. After incubation, the beads were collected and washed 2 times by IP binding buffer, subsequently 2 times by low-salt-reaction buffer (50 mM NaCl, 10 mM Tris–HCl, pH 7.5, 0.1% NP-40), and 2 times using high-salt-reaction buffer (500 mM NaCl, 10 mM Tris–HCl, pH 7.5, 0.1% NP-40). The bound RNA was eluted and extracted with TRIzol, and qRT-PCR was performed.</p>", "<title>RIP-qPCR assay</title>", "<p id=\"Par38\">Cells were transfected with indicated group. After 48 h, cells were collected and lysed in RIPA buffer containing protease inhibitor and RNase inhibitor. Cell lysate were collected after centrifugation at 12,000 <italic>g</italic> for 15 min, and 10% volume of lysate were used as input. Then, the rest of lysate were incubated with indicated antibody at 4 °C overnight followed by incubation with 50 μl protein A/G magnetic beads for 2 h at 4 °C. After washing the beads 3 times, RNA was extracted with TRIzol, and qRT-PCR was performed.</p>", "<title>Animal experiments</title>", "<p id=\"Par39\">Xenografted implantation model was established to estimate the in vivo effect of FBXO31 and shSIRT2. Five-weeks-old female nude mice were employed for subcutaneous injections. Panc-1 cells with stable expression of FBXO31 or shSIRT2 and their control cells were injected into the flanks of nude mice. The xenografted tumors were measured using calipers every 5 days. The recipient mice were euthanized after 4 weeks of injections and the tumor masses were resected. All animal studies were approved by the Animal Experimentation Ethical Committee of Bengbu Medical University (Bengbu, Anhui, China).</p>", "<title>Statistical analysis</title>", "<p id=\"Par40\">All data were statistically analyzed by using SPSS 21 and GraphPad Prism 9 and presented as mean ± SD. The significance was determined by two-tailed paired or unpaired t test for two groups, and ANOVA test for multiple groups. Chi‑squared test was performed to estimate the distributions of clinicopathological variables. The Kaplan–Meier method was used to analyze the overall survival of PC patients.</p>" ]

[ "<title>Results</title>", "<title>FBXO31 is aberrantly up-regulated in PC tissues and associated with poor survival in PC patients</title>", "<p id=\"Par6\">To investigated the expression profile of FBXO31 in pancreatic adenocarcinoma (PAAD), which constitutes 90–95% of PC, we analyzed TCGA and GTEx clinical datasets, including 179 cases of PAAD tissues and 171 cases of adjacent normal tissues (167 cases from GTEx and 4 cases from TCGA). We found that FBXO31 mRNA expression levels were highly elevated in PAAD tissues compared to that in adjacent normal tissues (Fig. ##FIG##0##1A##). Furthermore, we measured FBXO31 protein expression by IHC staining in tissue microarray (TMA) containing 90 cases with PAAD and 60 adjacent normal tissues (Fig. ##FIG##0##1B##). IHC data of tissue microarray showed that cytoplasmic FBXO31 expression levels were up-regulated in tumor tissues compared to their adjacent normal tissues (Fig. ##FIG##0##1C##, <italic>p</italic> &lt; 0.001). We also analyzed the overall survival of PAAD patients from tissue microarray by Kaplan–Meier analysis. The results showed that the patients with high FBXO31 expression had a shorter survival time than those with low expression of FBXO31 (Fig. ##FIG##0##1D##, <italic>p</italic> = 0.0165). Moreover, FBXO31 protein expressions were detected by Western blotting between human normal HPDE6-C7 pancreatic epithelial cell line and human PC cell lines, including Panc-1, PaTu-8988, SW1990, CFPAC-1, BxPC-3 and Capan-1 cells. The results exhibited that FBXO31 expression was higher in PC cell lines than in normal cell line (Fig. ##FIG##0##1E##). Taken together, it suggested that dysregulation of FBXO31 may be contributed to PC progression.</p>", "<title>FBXO31 promotes viability and motility of PC cells in vitro and in vivo</title>", "<p id=\"Par7\">To clarify the role of FBXO31 in PC, Patu-8988 and Panc-1 cells were transfected with FBXO31 cDNA for overexpression, and FBXO31 sgRNA for leading to FBXO31 knockdown, respectively. The mRNA expression levels of FBXO31 were verified using qRT-PCR in PC cells with FBXO31 overexpression and knockdown treatments (Fig. ##SUPPL##2##S1A##). Moreover, the results of MTT assay showed that FBXO31 knockdown obviously inhibited cell viability in PC cells. (Fig. ##FIG##1##2A##). Consistently, ectopic expression of FBXO31 significantly enhanced cell viability in PC cells (Fig. ##FIG##1##2B##).</p>", "<p id=\"Par8\">For measuring cell migratory ability, wound healing assay and Transwell migration assay were both performed in PC cells after FBXO31 modulation. The results of wound healing assay exhibited that FBXO31 deletion led to wound healing retardation compared to the control group (Fig. ##SUPPL##2##S1B##). The wound scratch closure sped up in the group of FBXO31 overexpression compared to the control group in PC cells (Fig. ##SUPPL##2##S1C##). Consistently, FBXO31 downregulation resulted in decreased migrated cells from the chamber, while FBXO31 upregulation led to increased migrated cells from the chamber (Fig. ##FIG##1##2C–F##). For Transwell invasion analysis, it was also proved that increased FBXO31 expression remarkably enhanced cell invasion capacity and decreased FBXO31 expression prominently suppressed cell invasion ability in PC cells (Fig. ##FIG##1##2C–F##). To determine whether FBXO31 promotes tumor growth in vivo, we subcutaneously injected Panc-1 cells with or without FBXO31 overexpression into the flank of nude mice. We found that FBXO31 overexpression enhanced tumor mass size, weights and volumes (Fig. ##FIG##1##2G–I##). Western blotting data showed the high expression of FBXO31 in tumor tissues (Fig. ##FIG##1##2J, K##). All of results showed that FBXO31 plays the oncogenic role in tumorigenesis and development in PC.</p>", "<title>SIRT2 is a direct target of FBXO31 in PC</title>", "<p id=\"Par9\">We therefore sought to explore the mechanisms of carcinogenic role of FBXO31 in PC. To identify novel targets of FBXO31, we screened for proteins combining with Flag-FBXO31 using a co-IP-based LC-MS/MS method in 293 T cells (Fig. ##FIG##2##3A, B##). We screened for common interacting proteins in the control and FBXO31 group through Venn diagram analysis (Fig. ##FIG##2##3B## and Supplementary File ##SUPPL##1##1##). Accordingly, SIRT2 was identified as one of FBXO31-associated protein (Fig. ##FIG##2##3A##). To this end, we found that SIRT2 protein abundance detected by western blotting was significantly increased after FBXO31 sgRNA transfection in different cell lines (Fig. ##FIG##2##3C##). Consistently, the protein abundance of SIRT2 was markedly reduced by FBXO31 cDNA transfection in a few of cell lines (Fig. ##FIG##2##3D##). Furthermore, FBXO31-deletion increased SIRT2 protein abundance in a dose-dependent manner (Fig. ##FIG##2##3E##), and similar results were also observed in FBXO31 overexpression group (Fig. ##FIG##2##3F##). We further elucidated the physical interaction between FBXO31 and SIRT2 using immunoprecipitation assay. We showed that FBXO31 specifically interacted with SIRT2 in HEK293T cells and different PC cell lines (Figs. ##FIG##2##3G–J## and ##SUPPL##2##S2##). All of results demonstrated that SIRT2 is a specific target of FBXO31.</p>", "<title>FBXO31 promotes SIRT2 ubiquitination and degradation</title>", "<p id=\"Par10\">As FBXO31 serves as substrate recognition subunit of E3 ubiquitin ligase [##REF##23657496##5##, ##REF##26124108##11##], we speculated whether FBXO31 negatively regulated SIRT2 protein abundance through proteasome-dependent degradation. To this end, we found that the endogenous SIRT2 protein expression was prominently increased upon treating HEK293T, HeLa and Panc-1 cells with proteasome inhibitor MG132 (Fig. ##FIG##3##4A##). Furthermore, FBXO31-mediated destruction of SIRT2 could be blocked by MG132 in several cell lines, which were pretreated with MG132 and co-transfection of FBXO31 and SIRT2 (Fig. ##FIG##3##4B, C##). Impressively, FBXO31 hardly changed the mRNA expression level of SIRT2 in multiple cell lines treated with either FBXO31 overexpression or FBXO31 knockdown (Figs. ##FIG##3##4D## and ##SUPPL##2##S3A–C##). Moreover, cycloheximide experiments showed the half-life time of endogenous SIRT2 protein was shortened after FBXO31 ectopic expression (Figs. ##FIG##3##4E, F## and ##SUPPL##2##S3D, E##). Consistently with these findings, half-life of SIRT2 protein was lengthened after FBXO31 deletion (Figs. ##FIG##3##4G–H## and ##SUPPL##2##S3F–G##), suggesting that FBXO31 regulated SIRT2 expression in a PTM manner. Considering the above-mentioned results, which declared that FBXO31 controlled SIRT2 expression and bound to SIRT2, we next detected whether FBXO31-mediated destruction of SIRT2 is a consequence of FBXO31-catalyzed ubiquitination. The results showed that ectopic expression of FBXO31 remarkably increased the amount of SIRT2 ubiquitination (Fig. ##FIG##3##4I–L##). Taken together, these results suggested that FBXO31 was the physiological E3 ligase that interacted with SIRT2 and promoted Sir2 ubiquitination and degradation in PC.</p>", "<title>FBXO31-mediated destruction of SIRT2 is dependent on the F-box motif of FBXO31 and the Sirtuin-type motif of SIRT2</title>", "<p id=\"Par11\">It has been reported that F-box domain of FBXO31 was required for substrate ubiquitination and degradation [##REF##19412162##7##, ##REF##26124108##11##], but not for substrate binding [##REF##24828503##40##]. It has suggested that FBXO31 interacted with SCF through its F-box domain [##REF##24828503##40##]. To determine whether FBXO31 mediated the degradation of SIRT2 through its F-box motif, we constructed FBXO31 ΔF-box-mutant plasmid. As shown in western blotting assays, FBXO31 ΔF-box mutation did not decrease the protein abundance of SIRT2 in contrast to wild-type (WT) FBXO31 (Figs. ##FIG##4##5A, B## and ##SUPPL##2##S4A##). Furthermore, we observed that FBXO31 WT, but not FBXO31 ΔF-box, essentially decreased the half-life of SIRT2 in Panc-1 cells and 293 T cells (Figs. ##FIG##4##5C, D## and ##SUPPL##2##S4B, C##). Consistently, ectopic expression of wild-type FBXO31, but not FBXO31 ΔF-box, enhanced SIRT2 ubiquitination (Fig. ##FIG##4##5E–G##). All above results suggested that FBXO31-mediated degradation of SIRT2 is dependent on its F-box domain. To test whether F-box domain of FBXO31 is necessary for binding to SIRT2, we further performed Co-IP experiments. The results showed that both FBXO31 WT and ΔF-box mutant FBXO31 could interact with SIRT2 (Fig. ##FIG##4##5H–I##), suggesting that F-box domain was not required for substrate recognition of FBXO31.</p>", "<p id=\"Par12\">As noted above, it has shown that FBXO31 acts as an upstream E3 ligase of SIRT2, thereby, we considered the binding sites of SIRT2 to specifically interact with FBXO31. Referring to the domain information of SIRT2 derived from UniProt database (UniProtKB-Q8IXJ6), we generated a truncated SIRT2 mutant containing sirtuin -type domain deletion (named as SIRT2 Δ-sirtuin). We showed that SIRT2 Δ-sirtuin blocked FBXO31-mediated SIRT2 downregulation in Panc-1 and PaTu-8988 cells (Fig. ##FIG##5##6A##). And the half-life of SIRT2 Δ-sirtuin was lengthened compared with SIRT2 WT in Panc-1 and 293 T cells (Fig. ##FIG##5##6B–E##). In support of the sirtuin-type domain of SIRT2 contributing of a key role in FBXO31-mediated SIRT2 degradation, Co-IP results showed that SIRT2 WT, instead of SIRT2 Δ-sirtuin, interacted with FBXO31 (Fig. ##FIG##5##6F–H##). Consistently, ubiquitination of SIRT2 was significantly decreased in SIRT2 Δ-sirtuin, but not in SIRT2 WT (Fig. ##FIG##5##6I–K##). These results suggested sirtuin domain of sirt2 was involved in FBXO31 binding and its ubiquitination.</p>", "<title>SIRT2 is required for FBXO31-mediated promotion effect of cell viability, migration and invasion in PC</title>", "<p id=\"Par13\">Owing to that the exact role of SIRT2 in PC remains controversial [##REF##27637077##24##, ##REF##23175188##29##, ##REF##23523103##30##], we elucidated the biological functions of SIRT2 in PC in vitro and vivo. To this end, we analyzed cell viability, migration and invasion ability after PC cells treated with SIRT2 ectopic expression or deletion (Fig. ##SUPPL##2##S5A##). We found that ectopic expression of SIRT2 significantly inhibited cell viability, while SIRT2 deletion obviously promoted cell viability in Panc-1 and PaTu-8988 cells (Fig. ##SUPPL##2##S5B, C##). Furthermore, we also showed that cell migration and invasion capacities were remarkably elevated by SIRT2 overexpression, but were depressed by SIRT2 depletion in PC cells (Fig. ##SUPPL##2##S5D–I##). Moreover, we demonstrated SIRT2 deletion in Panc-1 cells inhibited the growth of xenografted tumor in mice, revealing a significantly reduction in tumor weights and volumes (Fig. ##SUPPL##2##S6A–D##).</p>", "<p id=\"Par14\">To understand the role of FBXO31 via targeting SIRT2 degradation, we performed rescue experiments through simultaneous overexpression or deletion of FBXO31 and SIRT2 on cell viability and cell mobility. PC cells were cotransfected with FBXO31 and SIRT2, or with sgFBXO31 and shSIRT2. The protein abundances of FBXO31 and SIRT2 were detected by western blotting to verify simultaneous overexpression or deletion (Figs. ##FIG##6##7A## and ##SUPPL##2##S7A##). Moreover, overexpression of SIRT2 weakened the promotion effect of FBXO31 overexpression on diverse oncogenic phenotypes, including cell growth (Fig. ##FIG##6##7B##), cell migration (Fig. ##FIG##6##7C–F##) and cell invasion (Fig. ##FIG##6##7E, F##). In agreement with these findings, deletion of SIRT2 enhanced the inhibitory effect of FBXO31 deletion on cell viability, cell migration and cell invasiveness (Fig. ##SUPPL##2##S7B–E##).</p>", "<p id=\"Par15\">Taken together, our results showed that FBXO31 promoted PC cell viability and motility partly through mediating SIRT2 degradation. In addition, we detected the express of several downstream targets of SIRT2, including c-Myc [##REF##23175188##29##], Aurora A [##REF##22014574##19##], Slug [##REF##27783945##41##], p-ERK [##REF##27637077##24##], after cells were treated with FBXO31 ectopic expression and knockdown in multiple cells. We found only p-ERK expression, rather than c-Myc, Aurora A and Slug, was down-regulated by FBXO31 knockdown and up-regulated by FBXO31 overexpression (Fig. ##FIG##2##3C, D##). Moreover, we found that sh-Sirt2 transfection induced cell viability, migration and invasion in Panc-1 and PaTu-8988 cells, which were abrogated by ERK inhibitor treatment (Fig. S8A-F). These findings suggest that SIRT2 performed its functions in part via the ERK pathway. The results may suggest that FBXO31-mediated SIRT2 degradation and subsequently leading to p-ERK downregulation are responsible for the oncogenic function of FBXO31 in PC.</p>", "<title>METTL3/METTL14 induces FBXO31 m6A modification and promotes FBXO31 mRNA translation</title>", "<p id=\"Par16\">It has been reported that METTL3 and METTL14 serve as oncogenes in PC [##REF##31606241##35##–##REF##32843065##37##]. In agreement with other reports, we also observed that METTL3 could enhance cell viability and cell invasion in PC cells (Fig. ##SUPPL##2##S9A–D##). However, it is poorly understood whether FBXO31 mRNA could be modified by m6A readers, such as METTL3 or METTL14. To this end, we exhibited that METTL3 deletion contributed to obviously decreased protein expression of FBXO31 and increased protein expression of SIRT2 in PC cells (Fig. ##FIG##7##8A##). However, overexpression of METTL3 significantly increased FBXO31 protein abundance and subsequently decreased SIRT2 protein abundance (Fig. ##FIG##7##8B##). As known as an adaptor of METTL3 for RNA binding and allosteric activator of the enzymatic activity of METTL3 [##REF##31520073##31##], we further investigated whether METTL14 was involved in regulating FBXO31 expression. Similar results showed that METTL14 also positively regulated FBXO31 protein expression and negatively regulated SIRT2 protein expression (Fig. ##SUPPL##2##S10A, B##). Furthermore, our meRIP-qPCR results showed that METTL3 could methylate FBXO31 mRNA (Fig. ##FIG##7##8C##). However, qRT-PCR results showed that METTL3 had no significantly influence over FBXO31 mRNA level (Figs. ##SUPPL##2##S9E–G##). We also demonstrated METTL14 did not altered FBXO31 mRNA level (Fig. ##SUPPL##2##S10C, D##). Moreover, mRNA stability assay by actinomycin D showed that METTL3 didn’t change FBXO31 mRNA half-life (Fig. ##FIG##7##8D##). Taken together, these results suggested that METTL3 or METTL14-mediatied upregulation of FBXO31 might be involved in translational control rather than mRNA decay regulation.</p>", "<p id=\"Par17\">In addition, we performed cycloheximide assay to exclude whether METTL3 might influence FBXO31 protein stability. The results exhibited that FBXO31 protein elimination has no significantly change between METTL3 overexpression and the control group (Fig. ##FIG##7##8E, F##). As we known that m6A signals are recognized by m6A-binding proteins, such as YTHDF1, YTHDF2, or YTHDF3 [##REF##31520073##31##]. We therefore explored whether YTHDF-1 was involved in METTL3-mediated translation regulation. Firstly, we performed western blotting to detect FBXO31 expression in cells treated with YTHDF-1 deletion and METTL3 overexpression. The results showed that YTHDF1 deletion robustly reduced METTL3-mediated enhanced translation of FBXO31 (Fig. ##FIG##7##8G, H##). Moreover, RIP-qPCR assay showed that METTL3, YTHDF1 directly bound to FBXO31 mRNA (Fig. ##FIG##7##8I, J##). Thus, our works suggested that METTL3 upregulated FBXO31 due to enhancing translation rather than decreasing RNA decay and protein stability, and METTL3 promoted FBXO31 translation in an YTHDF1-dependent manner.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par18\">In recent decades, a variety of therapeutic strategies have been developed and substantially improvements have been received in the patient survival of some cancers. Nevertheless, to date, the treatment of PC remains a terrible challenge and has proved refractory to these new therapeutic approaches. Thus, the demand for understanding the complex molecular mechanisms and epigenetic alterations of PC is high. In the present study, we demonstrate that METTL3/METTL14 enhanced m6A modification of FBXO31 mRNA and upregulated FBXO31 protein expression, subsequently leading to SIRT2 ubiquitination and degradation (Fig. ##FIG##7##8K##). We identify a novel METTL3/METTL14-FBXO31-SIRT2 signaling axis in the regulation of PC progression, which contributes to provide new and promising targets of PC treatment.</p>", "<p id=\"Par19\">Extensive research has been indicated that E3 ligases play a critical role in tumor development and serve as therapeutic targets for tumor treatment [##REF##29242641##6##, ##REF##32226545##42##]. FBXO31 has been frequently suggested to function as tumor suppressor or oncogenic gene in different tumors [##REF##29343641##8##–##REF##27568981##10##, ##REF##28905993##13##, ##REF##26175949##14##]. However, the function and its molecular mechanism of FBXO31 in PC are fuzzy. Herein, we detected biological function of FBXO31 through IHC staining for human PC samples, in vivo and in vitro experiments. Our results showed that FBXO31 was up-regulated and associated with poor survival in PC samples. FBXO31 promoted cell viability and motility in vitro and enhanced tumor growth in vivo. Hence, we provide abundant proof to demonstrate an oncogenic role of FBXO31 in PC progression, suggesting FBXO31 may be a potential therapy target for PC.</p>", "<p id=\"Par20\">As an E3 ligase, FBXO31 targets different substrates for ubiquitination and destruction. For underlying mechanism analysis, we identified SIRT2 as a novel substrate of FBXO31 in PC. We found that FBXO31 decreased SIRT2 protein abundance, not mRNA level. Moreover, half-life time of SIRT2 was shortened by FBXO31 overexpression through Cycloheximide analysis. FBXO31 could bind to SIRT2 and strengthen SIRT2 ubiquitination and subsequent degradation. Consistent with previously report [##REF##24828503##40##], we identified that F-box domain of FBXO31 was required for FBXO31-mediated SIRT2 ubiquitination and degradation, but not for substrates recognition of FBXO31. Furthermore, we suggested that FBXO31 binds to sirtuin domain of SIRT2 and strengthens SIRT2 ubiquitination and subsequently degradation. Thus, we identified a novel substrate of FBXO31 and FBXO31 acts as an upstream E3 ligase to mediate SIRT2 degradation in a posttranslational manner.</p>", "<p id=\"Par21\">The opposite roles of SIRT2 in PC were observed in previously reports [##REF##23175188##29##]. It has been reported that c-Myc increased SIRT2 expression in MiaPaca-2 PC cells, and SIRT2 promoted c-Myc and N-Myc stabilization, leading to cell growth promotion [##REF##23175188##29##]. Consistent with this finding, other study showed that SIRT2 deacetylated LDH-A K5 and enhanced LDH-A enzyme activity and protein level, which caused significant increase of cell viability and cell migration in PC [##REF##23523103##30##]. However, another report supported SIRT2 deficiency increased KrasG12D mice tumorigenic transformation, including development of PanIN and progression to PDAC [##REF##27637077##24##]. SIRT2 loss enhanced KRAS acetylation and activity, leading to increased p-ERK expression [##REF##27637077##24##]. In this study, we demonstrated that SIRT2 plays tumor suppressive role in PC. SIRT2 inhibited cell proliferation and cell invasion in Panc-1 and PaTu-8988 cells in vitro. In addition, SIRT2 deficiency in Panc-1 cells accelerated xenografts tumor growth in vivo. More importantly, rescue experiments exhibited that SIRT2 is involved in FBXO31-mediated proliferation and motility of PC cell. Consistently, we found that FBXO31 mediated p-ERK protein expression instead of other SIRT2 downstream targets, including c-Myc and Aurora. These different conclusions regulating the role of SIRT2 in PC could be due to using various cell lines and animal models, which is required to further use Sirt2 conditional transgenic mouse models and Sirt2 conditional knockout mouse models to fully elucidate the function of SIRT2 in PC.</p>", "<p id=\"Par22\">Extensive research revealed that m6A levels were elevated in PC and higher m6A levels were correlated with poor survival of PC patients [##REF##31606241##35##, ##REF##32843065##37##]. Importantly, METTL3 had higher expression in PC tissues compared with adjacent-normal tissues [##REF##31606241##35##]. Upregulation of METTL3 promoted PC cell growth and motility [##REF##31606241##35##], and enhances chemo- and radio-resistance in PC cells [##REF##29345285##36##]. All of results suggested that m6A and METTL3 play oncogenic roles in PC. Similar results were observed in studies of the function of METTL14 in PC [##REF##32843065##37##–##REF##32097728##39##], which suggested that METTL14 contributes to oncogenic role in PC as well. Whether FBXO31 is regulated via epigenetic modification remains unclear. In this study, we found oncogenic METTL3 or METTL14 elevated FBXO31 protein expression and declined SIRT2 protein expression. These results disclosed that FBXO31 may be m6A-modified by METTL3/METTL14. It is becoming more evident that METTL3 owes methyltransferase activity and METTL14 possesses RNA-binding sites and functions as allosteric activator of METTL3 [##REF##31520073##31##]. Thus, we pursue how METTL3, the chief of m6A writer, regulates FBXO31 m6A modification. RT-PCR and mRNA stability assay exhibited that the expression of FBXO31 mediated by METTL3 was not due to METTL3-induced mRNA decay regulation. Furthermore, cycloheximide assay exclude the probability of METTL3-induced FBXO31 protein stability. Moreover, meRIP, RIP and western blotting assay demonstrated that METTL3 induced FBXO31 m6A modification through enhancing FBXO31 translation in an YTHDF1-dependent manner. Taken together, we identify an oncogenic role of FBXO31 in PC, as well as clarify its upstream epigenetics regulation and its novel downstream substrate. Our study offers novel insights into molecular basis of METTL3-FBXO31-SIRT2 axis and provides the opportunity to the development of potential therapeutic strategies for PC.</p>" ]

[]

[ "<p id=\"Par1\">FBXO31, a member of F-box family to comprise of SCF complex, contributes to a pivotal role in cancer progression. However, the possible involvements of FBXO31 in PC are unelucidated. Here, we reported that FBXO31 was overexpressed in PC patients, which was negatively associated with survival in PC patients. Furthermore, FBXO31 significantly enhanced growth, migration and invasion of PC cells in vitro. Consistently, FBXO31 overexpression promoted tumor growth in nude mice. Mechanistically, SIRT2 was a target of FBXO31 and interacted with FBXO31. Protein half-life and ubiquitination analysis demonstrated that FBXO31 promoted proteasome-dependent degradation of SIRT2. In addition, FBXO31 binds to sirtuin-type domain of SIRT2. Moreover, SIRT2 is required for the oncogenic role of FBXO31 in PC progression. Impressively, METTL3 induced m6A modification of FBXO31 and up-regulated FBXO31 expression, subsequently leading to SIRT2 down-regulation in PC cells. The results showed that METTL3 enhanced FBXO31 mRNA translation in YTHDF1-dependent manner. Taken together, we suggest that METTL3–FBXO31–SIRT2 axis was involved in PC tumorigenesis, which could identify new targets for PC treatment.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41419-024-06425-y.</p>", "<title>Author contributions</title>", "<p>KC, YW, XD, and JL conceived the work, performed the experiments, and analyzed the data. SH performed the bioinformatics analysis. ZZ and SJ performed experiments and analyzed the data. XP, JX, and YL analyzed the data. ZW edited the paper and viewed the study. JM wrote the paper, and critically viewed and supervised the study.</p>", "<title>Funding</title>", "<p id=\"Par41\">This work was supported by grant from the major project from the Natural Science Foundation of Education Department of Anhui Province (2022AH040222), Natural Science Foundation of Anhui Province (2308085MH269), and Anhui University Student Program for Innovation and Entrepreneurship (S202110367055) .</p>", "<title>Data availability</title>", "<p>The datasets supporting the conclusions of this article are included within the article and its additional files.</p>", "<title>Ethics approval and consent to participate</title>", "<p id=\"Par42\">The present study was approved the institutional Review Board of Bengbu Medical University.</p>", "<title>Consent for publication</title>", "<p id=\"Par43\">Not applicable.</p>", "<title>Competing interests</title>", "<p id=\"Par44\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>FBXO31 is up-regulated in pancreatic cancer tissues and cells.</title><p><bold>A</bold> FBXO31 mRNA expression in tumor and normal tissues from TGCA+GTEx cohort. <bold>B</bold> Representative images of FBXO31 IHC staining of human pancreatic cancer microarray slides. <bold>C</bold> IHC scores of PC tissues and adjacent normal tissues derived from human pancreatic cancer microarray slides for FBXO31 IHC staining. <bold>D</bold> Kaplan–Meier analysis of overall survival of PC patients based on FBXO31 expression (<italic>n</italic> = 87). <bold>E</bold> Western blotting analysis of FBXO31 and SIRT2 expression in different PC cells and HPDE6-C7 normal pancreatic epithelial cells.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>FBXO31 promotes PC development in vitro and in vivo.</title><p><bold>A</bold>, <bold>B</bold> MTT assays to detect cell growth of Panc-1 and Patu-8988 cells transfected with indicated FBXO31 sgRNA (<bold>A</bold>) or FBXO31 cDNA (<bold>B</bold>). Data are shown as mean ± SD of three independent experiments. **<italic>p</italic> &lt; 0.01 compared to control, ***<italic>p</italic> &lt; 0.001 compared to control. <bold>C</bold>, <bold>D</bold> Transwell assays to analyze cell migration and invasion capacity of Panc-1 cells (<bold>C</bold>) and Patu-8988 cells (<bold>D</bold>) transfected with FBXO31 sgRNAs. ***<italic>p</italic> &lt; 0.001 compared to control. <bold>E</bold>, <bold>F</bold> Transwell assays to analyze cell migration and invasion capacity of Panc-1 cells (<bold>E</bold>) and Patu-8988 cells (<bold>F</bold>) transfected with FBXO31 cDNA. *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, ***<italic>p</italic> &lt; 0.001 compared to control. <bold>G</bold> Pictures of tumor mass dissected from FBXO31-overexpressing xenografts mouse models. Stable FBXO31 overexpression of Panc-1 cells and the control cells were injected subcutaneously into the BALB/c-nu/nu mice to establish xenografts mouse models. <bold>H</bold>, <bold>I</bold> Tumor weights (<bold>H</bold>) and tumor volumes (<bold>I</bold>) of dissected tumor mass in (<bold>G</bold>). <bold>J</bold>, <bold>K</bold> IB analysis of the FBXO31 and SIRT2 protein levels in the dissected tumors (<bold>J</bold>). The protein abundance of FBXO31 and SIRT2 was quantified and plotted (<bold>K</bold>).</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>SIRT2 is a direct target of FBXO31 in PC.</title><p><bold>A</bold> Peptide sequence of SIRT2 interacting with Flag-FBXO31 identified by mass spectrometry. SIRT2 was one candidate protein. <bold>B</bold> Venn diagram analysis of candidate proteins derived from a co-IP-based mass spectrometry data in 293 T cells transfected with Flag-FBXO31 and EV. <bold>C</bold>, <bold>D</bold> IB analysis of WCLs derived from different cells transfected with FBXO31 sgRNA (<bold>C</bold>) and FBXO31 cDNA (<bold>D</bold>). <bold>E</bold>, <bold>F</bold> IB analysis of WCLs derived from different cells transfected with increased amounts of FBXO31 sgRNA (<bold>E</bold>) and FBXO31 cDNA (<bold>F</bold>). <bold>G</bold>, <bold>J</bold> IB analysis of immunoprecipitates (IPs) and WCLs derived from 293 T cells (<bold>G</bold>), Panc-1 cells (<bold>H</bold>), PaTu-8988 cells (<bold>I</bold>), and SW1990 cells (<bold>J</bold>) transfected with indicated plasmids. Cells were treated with 10 μM MG132 for 6 h before harvesting.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>FBXO31 promotes SIRT2 ubiquitination and degradation.</title><p><bold>A</bold> IB analysis of whole cell lysates (WCLs) derived from 293 T cells, Hela cells and Panc-1 cells. Where indicated, cells were treated with 10 μM MG132 for 6 h before harvesting. <bold>B</bold> IB analysis of whole cell lysates (WCLs) derived from 293 T cells, PaTu-8988 cells and Panc-1 cells transfected with indicated plasmids, which treated with 10 μM MG132 for 6 h before harvesting. <bold>C</bold> IB analysis of whole cell lysates (WCLs) derived from 293 T cells transfected with SIRT2 cDNA and increased amounts of FBXO31 cDNA with or without 10 μM MG132 treatment. <bold>D</bold> qPCR analysis to detect FBXO31 and SIRT2 mRNA levels after FBXO31 overexpression in Panc-1 cells. Data are shown as mean ± SD of three independent experiments. ***<italic>p</italic> &lt; 0.001 compared to EV. Ns nonsense. <bold>E</bold> IB analysis of WCLs derived from Panc-1 cells transfected with FBXO31 constructs. Where indicated, 100 μg/ml cycloheximide (CHX) was added and cells were harvested and lysed at indicated time points. <bold>F</bold> SIRT2 protein abundance in (<bold>E</bold>) was quantified by Image J and plotted. <bold>G</bold> IB analysis of WCLs derived from Panc-1 cells transfected with FBXO31 sgRNA. Where indicated, 100 μg/ml cycloheximide (CHX) was added and cells were harvested and lysed at indicated time points. <bold>H</bold> SIRT2 protein abundance in (<bold>G</bold>) was quantified by Image J and plotted. <bold>I</bold>–<bold>L</bold> IB analysis of products of ubiquitination and WCLs derived from 293 T cells (<bold>I</bold>), PaTu-8988 cells (<bold>J</bold>), Sw1990 cells (<bold>K</bold>) and Panc-1 cells (<bold>L</bold>) transfected with indicated constructs. Cells were treated with 10 μM MG132 for 6 h before harvesting.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>FBXO31 mediates destruction of SIRT2 through its F-box motif, but not for substrate binding.</title><p><bold>A</bold> IB analysis of WCLs derived from 293 T cells and Panc-1 cells transfected with indicated plasmids. <bold>B</bold> IB analysis of WCLs derived from Panc-1 cells transfected with indicated plasmids. <bold>C</bold> IB analysis of WCLs derived from Panc-1 cells transfected with indicated constructs. Where indicated, 100 μg/ml cycloheximide (CHX) was added and cells were harvested and lysed at indicated time points. <bold>D</bold> SIRT2 protein abundance in (<bold>C</bold>) was quantified and plotted. <bold>E</bold>, <bold>G</bold> IB analysis of products of ubiquitination and WCLs derived from PaTu-8988 cells (<bold>E</bold>), Sw1990 cells (<bold>F</bold>), and Panc-1 cells (<bold>G</bold>) transfected with indicated constructs. Cells were treated with 10 μM MG132 for 6 h before harvesting. <bold>H</bold>, <bold>I</bold> IB analysis of IPs and WCLs derived from Panc-1 cells (<bold>H</bold>) and PaTu-8988 cells (I) transfected with indicated plasmids. Cells were treated with 10 μM MG132 for 6 h before harvesting.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Sirtuin domain of SIRT2 was involved in FBXO31 binding and ubiquitination.</title><p><bold>A</bold> IB analysis of WCLs derived from Panc-1 cells and PaTu-8988 cells transfected with indicated plasmids. <bold>B</bold>, <bold>C</bold> IB analysis of WCLs derived from Panc-1 cells transfected with indicated constructs (<bold>B</bold>). Where indicated, 100 μg/ml cycloheximide (CHX) was added and cells were harvested and lysed at indicated time points. SIRT2 protein abundance in (<bold>B</bold>) was quantified and plotted as indicated (<bold>C</bold>). <bold>D</bold>, <bold>E</bold> IB analysis of WCLs derived from 293 T cells transfected with indicated constructs (<bold>D</bold>). Where indicated, 100 μg/ml cycloheximide (CHX) was added and cells were harvested and lysed at indicated time points. SIRT2 protein abundance in (<bold>D</bold>) was quantified and plotted as indicated (<bold>E</bold>). <bold>F</bold>, <bold>H</bold> IB analysis of IPs and WCLs derived from293T cells (<bold>F</bold>), Panc-1 cells (<bold>G</bold>), and PaTu-8988 cells (<bold>H</bold>) transfected with indicated plasmids. Cells were treated with 10 μM MG132 for 6 h before harvesting. <bold>I</bold>–<bold>K</bold> IB analysis of products of ubiquitination and WCLs derived from 293T cells (<bold>I</bold>), Panc-1 cells (<bold>J</bold>), and PaTu-8988 cells (<bold>K</bold>) transfected with indicated plasmids. Cells were treated with 10 μM MG132 for 6 h before harvesting.</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><title>SIRT2 is required for FBXO31-mediated promotion of cell viability, migration and invasion in PC.</title><p><bold>A</bold> IB analysis of WCLs derived from Panc-1 cells and PaTu-8988 cells transfected with indicated plasmids. <bold>B</bold> MTT assays to detect cell proliferation of Panc-1 and Patu-8988 cells transfected with indicated plasmids. Data are shown as mean ± SD of three independent experiments. **<italic>p</italic> &lt; 0.01 and ***<italic>p</italic> &lt; 0.001. <bold>C</bold>, <bold>D</bold> Wound healing assays to detect cell migration of Panc-1 cells (<bold>C</bold>) and PaTu-8988 cells (<bold>D</bold>) transfected with indicated plasmids. ***<italic>p</italic> &lt; 0.001. <bold>E</bold>, <bold>F</bold> Transwell assays to detect cell migration and invasion of Panc-1 cells (<bold>E</bold>) and PaTu-8988 cells (<bold>F</bold>) transfected with indicated plasmids. ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig8\"><label>Fig. 8</label><caption><title>METTL3 induces FBXO31 m6A modification and promotes FBXO31 mRNA translation.</title><p><bold>A</bold> IB analysis of WCLs derived from Panc-1 cells and PaTu-8988 cells transfected with METTL3 siRNAs. <bold>B</bold> IB analysis of WCLs derived from a number of cells transfected with METTL3 cDNA. <bold>C</bold> Enrichment of mRNA by A/G magnetic beads coupled with m6A antibody in Panc-1 cells, m⁶A-IP combined with RT-qPCR was used to quantify the relative m6A level of Fbxo31 mRNA. <bold>D</bold> qPCR analysis of FBXO31 mRNA levels in Panc-1 cells in the absence or presence of METTL3 overexpression, and after actinomycin D treatment. <bold>E</bold>, <bold>F</bold> IB analysis of WCLs derived from PaTu-8988 cells transfected with indicated constructs (<bold>E</bold>). Where indicated, 100 μg/ml cycloheximide (CHX) was added and cells were harvested and lysed at indicated time points. FBXO31 protein abundance in (<bold>E</bold>) was quantified and plotted as indicated (<bold>F</bold>). <bold>G</bold>, <bold>H</bold> IB analysis of WCLs derived from Panc-1 cells (<bold>G</bold>) and PaTu-8988 cells (<bold>H</bold>) transfected with indicated siRNAs. <bold>I</bold>, <bold>J</bold> The interaction between FBXO31 mRNA and METTL3 (<bold>I</bold>) or YTHDF1 (<bold>J</bold>) was analyzed by RIP from Panc-1 cells immunoprecipitated with Flag antibody. <bold>K</bold> The diagram of FBXO31 increased by METTL3 to promote PC development via regulating SIRT2 ubiquitination and degradation.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>" ]

[ "<fn-group><fn><p>Edited by Professor Stephen Tait</p></fn><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Kai Chen, Yue Wang</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41419_2024_6425_MOESM1_ESM.xlsx\"><caption><p>supplementary file</p></caption></media>", "<media xlink:href=\"41419_2024_6425_MOESM2_ESM.docx\"><caption><p>Supplementary file legends</p></caption></media>", "<media xlink:href=\"41419_2024_6425_MOESM3_ESM.pdf\"><caption><p>Supplementary figures</p></caption></media>", "<media xlink:href=\"41419_2024_6425_MOESM4_ESM.pdf\"><caption><p>Original WB Images</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Itch (AIP4) is a member of the of E3 ubiquitin ligase family that mediates lysine-29, -48 and -63-linked ubiquitin conjugation [##REF##33402750##1##]. It is associated with pro-proliferative activities and endocytic trafficking [##REF##31015455##2##]. Itch is composed of an N-terminal lipid binding C2 domain, a proline rich region, WW motifs and in the C terminus a HECT (homologous to the E6-AP C-terminus) domain. The two WW motifs mediate an intramolecular interaction that keeps Itch in an inactive conformation. Several substrates have been identified for Itch; including FLIP, Numb, SREBP2, chemokine receptor CXCR4 and Bid [##REF##20392206##3##]. Regulation of the anti-apoptotic protein FLIP is important during cell death, and it has been shown that ubiquitination by Itch promotes its degradation and reduces its protein levels [##REF##31443721##4##, ##REF##16469705##5##]. Itch also interacts with and ubiquitinates endocytic proteins including endophilin, intersectin-1, amphiphysin, Snx9, and Pacsin, which results in regulation of trafficking of cell surface receptors [##REF##14684745##6##]. Itch is highly expressed in the gastrointestinal tract, brain and skeletal muscle, and it is overexpressed in multiple types of cancers [##REF##32165318##7##].</p>", "<p id=\"Par3\">The regulation of death receptor signalling by ubiquitination has recently emerged as an important mechanism of resistance to cell death in cancer cells [##REF##34912054##8##, ##REF##29195774##9##]. Core components of the TRAIL signalling pathway have been demonstrated to be regulated by ubiquitination, namely TRAIL-R1/2, FLIP and caspase-8. To evade cell death cancer cells frequently use the ubiquitin-proteasomal system for degradation of pro-apoptotic proteins [##REF##9779994##10##, ##REF##34943974##11##]. TRAIL-mediated apoptosis is unique because it selectively induces apoptosis in cancer cells compared to untransformed cells [##REF##9930862##12##–##REF##18931688##14##]. Binding of the ligand TRAIL (TNF-related apoptosis-inducing ligand) to death receptors (TRAIL-R1, TRAIL-R2) on the cell surface results in recruitment of FADD and activation of procaspase-8 or -10 and the subsequent cleavage of Bid, which results in its translocation to mitochondria and initiation of BAX/BAK pore formation. Bid is a key mediator of both intrinsic and extrinsic apoptosis and has been proposed to define whether TRAIL-mediated apoptosis is mitochondria-dependent or -independent [##REF##12407450##15##, ##REF##10428830##16##]. A regulator of caspase-8 activity, and Bid cleavage, is the FLICE-like inhibitory protein (FLIP); FLIP is a procaspase-8 homologue that can compete with caspase-8 for binding to FADD and is itself negatively regulated by ubiquitination [##REF##20392206##3##, ##REF##16469705##5##].</p>", "<p id=\"Par4\">We hypothesized that Itch may play a role in the regulation of TRAIL-induced apoptosis by altering the abundance and/or subcellular distribution of FLIP or TRAIL receptors. In the TCGA pan-cancer atlas the three cancer types with the highest gain of copy number for ITCH were rectum, colon and oesophageal carcinoma making these interesting disease settings in which to study Itch. Consequently, we compared the expression of ITCH in cell lines from these cancers and focussed our work on the cell line with the highest expression of ITCH, OE33, an oesophageal cell line [##REF##22460905##17##]. In this study, we examined whether knockdown of Itch affects the endocytosis of TRAIL-R2/R1, FLIP expression and TRAIL-mediated signalling in the oesophageal cell line OE33 that displays a high expression of Itch. We demonstrate that the E3 ubiquitin ligase Itch regulates TRAIL-mediated cell death and trafficking of the TRAIL-R2 receptor, cholesterol trafficking to mitochondria, Bax activation and cytochrome c release. We propose a mechanism where Itch regulates import of anti-apoptotic mitochondrial cholesterol through interaction with a lipid transfer protein complex.</p>" ]

[ "<title>Materials and methods</title>", "<title>Cell Lines</title>", "<p id=\"Par5\">OE33, LIM1215 and the KM12 cell lines were maintained in RPMI media (Gibco, UK). COLO320, HCT116 and HT29 cell lines were maintained in Macoy’s5A media (Gibco, UK). Cell culture media was supplemented with 10% foetal bovine serum (Gibco, UK), 5% Penicillin/Streptomycin (Gibco, UK) and 2mM L-glutamine (Gibco, UK). All cells were maintained at 37 °C in a 5% CO₂ humidified atmosphere and were regularly screened for the presence of mycoplasma using the MycoAlert Mycoplasma Detection Kit (Lonza, Switzerland).</p>", "<title>Reagents and antibodies</title>", "<p id=\"Par6\">The following commercial antibodies were used: TRAIL-R2/DR5 (rabbit, Cat# 3696 S, Cell Signalling Technology); BID (rabbit; Cat# 2002S, Cell Signalling Technology); PARP (rabbit, Cat# 9542 S, Cell Signalling Technology); Caspase 3 (rabbit, Cat# 9662 S, Cell Signalling Technology); FLIP NF6 (mouse, Cat# AG-20B-0056-C100, Adipogen); Itch (mouse, Cat# 611198, BD Biosciences); FADD (mouse, Cat# 556402, BD Pharmigen); Caspase-8 (mouse, Cat# ALX-804-242-C100, Enzo); TRAIL-R1/DR4 (rabbit, Cat# AB16955, Calbiochem); SREBP2 (rabbit, Cat# ab30682, Abcam); beta-Actin (mouse, Cat# A5316, Sigma), cytochrome C (BD Biosciences, # 556433), BAX 6A7 (Thermo #MA5-14003), StAR (#8449; Cell Signalling Technology), VDAC2 (ab155803; AbCam), Bax (#2772; Cell Signalling Technology) and GAPDH (mouse, Cat# sc-47724, Santa Cruz). The following PE-conjugated antibodies were used in cell surface expression experiments: isotype control (Cat# 12-4714-73, eBioscience); DR5 (Cat# 12-9908-42, eBioscience) and DR4 (Cat# 12-6644-42, eBioscience). AMG655 (Conatumumab) was sourced from Amgen Inc (Thousand Oaks, CA, USA); this antibody was coupled to Dynabeads using the Dynabead Coupling Kit (Life Technologies, Paisley, UK) for use in TRAIL-R2 DISC IP assay. The secondary antibodies used for immunocytochemistry were Alexa Fluor488- and 568- conjugated goat anti-rabbit, anti-mouse and anti-sheep (Thermo Fischer Scientific); for Western blot detection goat anti-rabbit and anti-mouse IgG- HRP conjugates (Cell Signalling Technologies). The following reagents were used: Filipin III (SAE0087; Sigma-Aldrich); DAPI (#62248; Thermo Fischer Scientific); U18666A (#662015; Calbiochem); ABT-263 (#S10001; Selleckchem); Alexa488-wheat germ agglutinin (#W11261; Thermo Fischer Scientific). Human isoleucine-zipper TRAIL (izTRAIL) was expressed and purified as described and stored at -80 °C in aliquots [##REF##16638878##18##]. The smartpool siRNA (Dharmacon, USA) for ITCH were; GUUGGGAACUGCUGCAUUA, CAACAUGGGACGUAUUUAU, GAAAUUAAGAGUCAUGAUC and CGAAGACGUUUGUGGGUGA.</p>", "<title>Knockdown cell line generation</title>", "<p id=\"Par7\">To generate <italic>ITCH</italic> knockdown cell lines lentivirus expressing short hairpin RNA (shRNA) from the pLKO1.puro plasmid were generated with the targeting sequence of the <italic>ITCH</italic> gene AACACCTCGAGACAACCTC (shEE162) and the shRNA control CAACAAGATGAAGAGCACCAA (Sigma MISSION Target shRNA). Selection was carried out using 1 µg/ml of puromycin for 48 h. The efficiency of shRNA knockdown was assessed by Western blot.</p>", "<title>Immunoblotting</title>", "<p id=\"Par8\">Whole cell lysate was prepared in RIPA buffer and Western blot analysis was carried out as described previously [##UREF##0##19##]. Protein expression was detected using the Western Lighting Plus-ECL substrate (PerkinElmer, Waltham, MA) on a G:BOX Chemi6 gel doc system (Syngene). Densitometry was carried out using ImageJ software. Uncropped blots are shown in Supplementary Fig. ##SUPPL##0##4##.</p>", "<title>Flow cytometry assays</title>", "<p id=\"Par9\">To assess cell death, live cell staining with FITC-tagged AnnexinV (BD Biosciences) and addition of PI (Sigma) were analysed on a BD Accuri C6 Plus flow cytometer (BD Biosciences). Cell surface TRAIL-R1 and TRAIL-R2 expression was assessed following live cell staining with Phycoerythrin-conjugated antibodies. All experiments were gated using an isotype control antibody.</p>", "<title>Cell viability assay</title>", "<p id=\"Par10\">Cell viability was assessed using CellTiterGlo Luminescent Assay (Promega, Madison, WI) according to manufacturer’s instructions on a Biotek plate reader.</p>", "<title>Caspase activity assay</title>", "<p id=\"Par11\">Caspase activity was assessed using Caspase-3/-7 Glo Luminescent Assay (Promega, Madison, WI) according to manufacturer’s instructions on a Biotek plate reader.</p>", "<title>Cytochrome C release assay</title>", "<p id=\"Par12\">The assay was essentially performed as previously described [##REF##18166654##20##, ##REF##23545197##21##]. Cells were collected, washed in PBS, resuspended in ice cold permeabilization buffer (150 mM KCl, 1 mM EDTA, 200 μg/ml digitonin, in PBS) and incubated on ice for 5 min. Cells were washed once in PBS, fixed in 4% paraformaldehyde at room temperature for 20 minutes, washed 3 times in PBS (700 × <italic>g</italic> for 5 min at 4 °C) and resuspended in blocking buffer (2% BSA in PBS) for 30 min at room temperature. Cells were incubated with anti-cytochrome C antibodies at 1:200 dilution in blocking buffer overnight at 4 °C followed by Alexa-488 anti–mouse IgG antibody at a 1:200 dilution in blocking buffer for 1 h. Following washing 3 times in blocking buffer the samples were analysed on a BD Accuri C6 Plus flow cytometer (BD Biosciences) equipped with the BD CSampler Plus software (BD Biosciences).</p>", "<title>BAX IP</title>", "<p id=\"Par13\">Roughly 10 × 10⁶ cells were used per sample. Cells were treated for 6 h with 50 ng/ml izTRAIL, lysed in 100 μl CHAPS buffer (150 mM sodium chloride, 10 mM HEPES pH 7.4, 1.0% CHAPS) with protease inhibitors for 1 hour on ice. The lysate was centrifuged at 15,000 × <italic>g</italic> for 20 min. Each sample contained 500 µg of protein in of 500 µl lysis buffer with 2 μg of BAX 6A7 antibody. The samples were incubated at 4 °C with rotation overnight. 25 μl of protein A agarose beads were preincubated with 500 µl of CHAPS buffer at 4 °C with rotation for 3 h, and then added to the samples for 30 min. Immunoprecipitates were collected via a brief spin (2500 × <italic>g</italic> for 5 min at 4 °C), washed four times with 500 µl of CHAPS lysis buffer (with 0.2% NP-40 buffer), and then solubilized with 2× SDS–PAGE sample buffer.</p>", "<title>DISC-IP</title>", "<p id=\"Par14\">The TRAIL-R2 DISC-IP was carried out as previously described and recruitment of DISC proteins was assessed by Western blotting [##REF##24577104##22##].</p>", "<title>Immunofluorescence</title>", "<p id=\"Par15\">Immunocytochemistry was performed as described previously [##UREF##0##19##]. Confocal images were acquired of the cells at room temperature using a Leica SP8 confocal microscope equipped with a 63x objective (1.4 NA HCX PL APO lens) controlled by the Leica Application Suite-X software.</p>", "<title>Image analysis</title>", "<p id=\"Par16\">Confocal image analysis was carried out using the ImageJ software. Receptor expression was expressed as the Integrated Density of the stain at the plasma membrane divided by the area. The plasma membrane was identified using wheat germ agglutin stain and the integrated density was measured by highlighting the intensity of the receptor staining at the plasma membrane. Colocalization analysis was performed using the Pearson colocalization coefficient using the JaCOP plugin.</p>", "<title>Transmission electron microscopy</title>", "<p id=\"Par17\">Embedding and processing of samples was performed as described [##UREF##0##19##]. Images were acquired on a Jeol JEM1400plus microscope at 80 kV equipped with a JEOL Ruby (8 MPixel) bottom-mounted CCD camera.</p>", "<title>Statistical data analysis</title>", "<p id=\"Par18\">Statistical significance was calculated from distinct technical replicates (<italic>n</italic> ≥ 3; unless otherwise stated) and confirmed in at least three independent experiments either by Student’s T test (two-tailed) or two-way ANOVA in GraphPad Prism 9. Two-way ANOVA tests were performed to compare two factors (for e.g. shRNA and drug concentration). The Student’s <italic>t</italic> test was used for comparison of data with a normal distribution and equal variance. Outliers were identified by a ROUT test. Graphs were plotted as means with error bars represented as standard error of mean; statistical significance was denoted as follows: ***<italic>p</italic> &lt; 0.001, **<italic>p</italic> &lt; 0.01, *<italic>p</italic> &lt; 0.05, ns = <italic>p</italic> &gt; 0.05.</p>" ]

[ "<title>Results</title>", "<title>Itch regulates TRAIL-mediated apoptosis independently of FLIP</title>", "<p id=\"Par19\">To investigate the role of Itch in TRAIL-mediated apoptosis, we generated a stable knockdown in the oesophageal cancer cell line OE33 and subjected it to TRAIL treatment followed by quantification of cell viability and apoptosis. Western blot analysis demonstrated a reduction in protein expression of 80% in the OE33 Itch knockdown (KD) cell line with no change in the expression of pro-caspase-8 or the two FLIP splice forms (Fig. ##FIG##0##1A–C##). A similar lack of impact on FLIP expression was observed in a panel of oesophageal and colorectal cancer cell lines (Supplementary Fig. ##SUPPL##1##1##). FLIP(L) has been shown to be ubiquitinated by Itch in a few cancer cell lines and fibroblasts, while in macrophages its stability is not directly regulated by Itch [##REF##16469705##5##, ##REF##18559494##23##–##REF##19339247##26##].</p>", "<p id=\"Par20\">To assess the functional effects of Itch knockdown on TRAIL-induced apoptosis, we used recombinant isoleucine-zipper (iz) TRAIL, which maintains the trimeric nature of the cell surface TRAIL ligand and enhances its activity [##REF##17318333##27##]. The Itch KD cell line was significantly more resistant to the izTRAIL-induced apoptosis as assessed by cell viability (<italic>p</italic> &lt; 0.001; Fig. ##FIG##0##1D##) and apoptosis assays (<italic>p</italic> &lt; 0.001; Fig. ##FIG##0##1E##). The Itch KD cell line also displayed significantly reduced activity of caspase-8 (<italic>p</italic> &lt; 0.001; Fig. ##FIG##0##1F##) and caspase-3/7 (<italic>p</italic> &lt; 0.001; Fig. ##FIG##0##1G##) following treatment with izTRAIL. These results were corroborated by a reduction of cleaved caspase-8, PARP and Bid in the Itch KD cell line (Fig. ##FIG##0##1H, I##<bold>;</bold>\n<italic>p</italic> &lt; 0.001). In conclusion, our findings demonstrate that Itch regulates TRAIL-mediated apoptosis through a mechanism that is not dependent on FLIP.</p>", "<title>Itch knockdown causes a mis-localization of TRAIL-R2 in OE33 cells</title>", "<p id=\"Par21\">Next, we sought to investigate whether loss of Itch mediates TRAIL resistance through downregulation of the cell surface expression of death receptors. A major limiting factor of apoptotic TRAIL signalling is the availability of the receptor at the cell surface [##REF##22909995##28##, ##REF##15155747##29##]. Itch targets components of the endocytic machinery and regulates signalling and stability of cell surface receptors [##REF##19341794##30##]. A significant reduction in cell surface TRAIL-R2 expression was observed in the Itch knockdown compared to the control (Fig. ##FIG##1##2A##; <italic>p</italic> &lt; 0.001). In comparison, the cell surface expression of TRAIL-R1 (DR4) was found to be unaltered between the two cell lines (Fig. ##FIG##1##2B##), while Epidermal Growth Factor receptor (EGFR) was increased (<italic>p</italic> &lt; 0.05; Fig. ##FIG##1##2C##) and transferrin internalisation was unchanged (Fig. ##FIG##1##2D##). TRAIL-R1, -R2 and EGFR are internalised after ligand binding by both clathrin-dependent and -independent endocytosis while the transferrin receptor is only internalised by clathrin-mediated endocytosis [##REF##34660590##31##]. Therefore, these data suggested that clathrin-mediated receptor endocytosis was not enhanced by Itch depletion and altered receptor trafficking could not explain the reduction of TRAIL-R2 on the cell surface. Immunocytochemistry supported the finding that TRAIL-R2 cell surface expression was reduced in the Itch KD OE33 cell line (Fig. ##FIG##1##2E##). Importantly, a loss of Itch expression did not impact on total TRAIL-R1/R2 receptor (DR4/5) protein expression (Fig. ##FIG##1##2F##). To validate these findings further, a panel of oesophageal and colorectal cancer cell lines were subjected to Itch knockdown, which resulted in a reduced TRAIL-R2 cell surface expression (Supplementary Fig. ##SUPPL##2##2##). In summary, knockdown of Itch resulted in a resistance to TRAIL-mediated apoptosis and correlated with a loss of TRAIL-R2 at the plasma membrane but not TRAIL-R1. This indicated that Itch either regulates anterograde membrane trafficking of TRAIL-R2 (but not TRAIL-R1), enhances the assembly of the DISC complex, or regulates association of caspase-8 and/or Bid with mitochondria. The first option seemed unlikely as there are no data suggesting that the two TRAIL receptors traffic to the plasma membrane via independent mechanisms and we therefore focussed on exploring the other two options.</p>", "<title>TRAIL-activated DISC assembly is independent of Itch</title>", "<p id=\"Par22\">We hypothesised that Itch may be incorporated into the death receptor signalling complex (DISC) where it could regulate caspase-8 recruitment or activation. Next, we investigated whether Itch regulates the assembly of the DISC. A reduction in TRAIL-R2 recruitment into the DISC in the Itch KD cells was observed (Fig. ##FIG##2##3A##), consistent with reduced cell surface levels of TRAIL-R2 (Fig. ##FIG##1##2A##). However, this did not correlate with significantly reduced recruitment of caspase-8, FADD or FLIP(L). Furthermore, caspase-8 dependent cleavage of FLIP-L at the DISC was maintained in the OE33 Itch KD cell line, and all other components of the complex are there in equal amounts to the control suggesting that Itch does not regulate the DISC assembly or activation of caspase-8 at the DISC (Fig. ##FIG##2##3A, B##). Similar results were observed in the HT29 and HCT116 cell lines (Fig. ##FIG##2##3C, D##). Taken together, our findings indicate that Itch regulation of caspase-8 activity and apoptosis is not due to alterations in the death receptor complex at the plasma membrane.</p>", "<title>Itch knockdown regulates mitochondrial cholesterol content which implicates a novel regulatory role in apoptosis</title>", "<p id=\"Par23\">Based on our findings showing that receptor endocytosis was not significantly altered in the Itch KD cell line and the assembly of the DISC and recruitment of caspase-8 was not impaired we next investigated the role of mitochondria in apoptosis in these cells. The OE33 cell line is classified as a type II cell reliant on the intrinsic apoptotic pathway. The lipid composition of the mitochondrial outer membrane is an important regulator of caspase-8 recruitment, activity [##REF##19001123##32##, ##REF##18084240##33##], and subsequent cleavage of Bid to induce apoptosis [##REF##22448037##34##]. Furthermore, mitochondrial cholesterol mitigates against apoptosis by increasing the stiffness of the mitochondrial membrane to prevent perforations and release of cytochrome c [##REF##18084240##33##], which is significant as Itch regulates cholesterol metabolism through ubiquitination of nuclear SREBP2 and SIRT6 resulting in increased intracellular cholesterol levels [##UREF##1##35##]. We therefore investigated whether a defect in cholesterol homoeostasis in the Itch KD OE33 cell line could affect mitochondrial cholesterol content, caspase-8 activity and cell viability.</p>", "<p id=\"Par24\">While the morphology of the endoplasmic reticulum (ER) and Golgi appeared normal, the morphology of the mitochondria was significantly altered in the KD (Fig. ##FIG##3##4A, B##). Control mitochondria had a normal oblong shape, while mitochondria in the Itch KD cells were often round and significantly wider (<italic>p</italic> &lt; 0.001; Fig. ##FIG##3##4C##). Furthermore, disorganised cristae were observed indicating an accumulation of cholesterol in mitochondria [##REF##15644330##36##]. To investigate whether there was an increase in mitochondrial cholesterol in Itch KD cells they were stained with Filipin-III dye (Fig. ##FIG##3##4D##). An increase in Filipin-III staining of mitochondria was observed in OE33 Itch KD and this observation was corroborated in HT29 and HCT116 cells (Supplementary Fig. ##SUPPL##3##3##). A significant increase in colocalization of mitochondrial outer membrane with the Filipin-cholesterol stain was observed in the KD compared to control (<italic>p</italic> &lt; 0.0001; Fig. ##FIG##3##4E##). The images further illustrate the altered morphology of mitochondria in cells with reduced Itch expression. Finally, we investigated whether SREBP2 expression was altered in the OE33 knockdown cell line as it is a main regulator of cholesterol metabolism. When cholesterol levels are low SREBP2 is proteolytically activated and translocated to the nucleus to regulate transcription of genes involved in cholesterol synthesis and uptake. A reduction in the mature nuclear form of SREBP2 was observed in the knockdown compared to the control indirectly indicating elevated cholesterol levels (Fig. ##FIG##3##4F##). In summary, the data show that Itch regulates cholesterol content in mitochondria.</p>", "<title>Accumulation of cholesterol in mitochondria cause resistance to TRAIL treatment and inhibits caspase-8 cleavage</title>", "<p id=\"Par25\">Based on our findings that Itch knockdown results in an accumulation of cholesterol in mitochondria we hypothesised that this altered cholesterol trafficking was the underlying cause of the resistance to TRAIL-mediated apoptosis in the Itch knockdown cells. To test this hypothesis, control cells were treated with the drug U18666A to promote trafficking and accumulation of cholesterol in mitochondria [##REF##18084240##33##]. TRAIL-induced activation of Caspase-8 and Caspase-3/7 in control cells treated with U18666A was inhibited to levels similar to that of Itch knockdown cells (Fig. ##FIG##4##5A, B##). U18666A used as a single agent did not have any effect on Caspase-8, -3 or PARP cleavage (Fig. ##FIG##4##5C##, lanes 1–2), but together with TRAIL-treatment inhibited activation of Caspase-8, -3 and cleavage of Bid and PARP (Fig. ##FIG##4##5C##, lanes 3–4). Quantifications of the data are shown in Fig. ##FIG##4##5D–G##. The expression of TRAIL-R2 or FLIP were not altered by the treatment. Furthermore, treatment with U18666A reduced the cell surface expression of TRAIL-R2 and TRAIL-R1 (Fig. ##FIG##4##5H, I##) and increased cholesterol in mitochondria (Fig. ##FIG##4##5J##), which aligns with the Itch knockdown data. The lipid composition of the mitochondrial outer membrane is important for regulation of Bax/Bak oligomerisation, pore formation and release of cytochrome c. Lipids, such as cholesterol, that increase the stiffness of the membrane attenuate Bax/Bak activation [##REF##18084240##33##, ##REF##18259190##37##]. To investigate the impact of Itch expression on Bax, the protein in its activated conformation was immunoprecipitated with the 6A7 antibody (Fig. ##FIG##5##6A##). Significantly less active Bax was present in the Itch KD in response to TRAIL treatment (Fig. ##FIG##5##6B##; <italic>p</italic> &lt; 0.01). To further validate the observation the downstream release of cytochrome c was quantified in a FACS assay. Itch KD cells treated with two concentrations of TRAIL showed strikingly less cytochrome c release compared to the control, which further confirmed the impact of Itch on intrinsic apoptosis (Fig. ##FIG##5##6C##; <italic>p</italic> &lt; 0.001). Finally, we hypothesised that the effect of an inhibitor targeting anti-apoptotic protein Bcl-2 would be attenuated in the Itch KD. To stimulate the activation of the intrinsic apoptotic pathway directly the Bcl-2 inhibitor ABT-253 (Navitoclax) was used. It is a potent inhibitor of anti-apoptotic Bcl-2 family members (Bcl-2, Bcl-XL, Bcl-W) through its interaction with the BH3-binding groove, causing the release of Bim that activates Bax/Bak which leads to an induction of mitochondrial outer membrane permeabilization and release of cytochrome c. The Itch KD showed a significantly impaired sensitivity to the Bcl-2 inhibitor at 24 h and 48 h (Fig. ##FIG##5##6D##; <italic>p</italic> &lt; 0.001). Together, these experiments provide evidence for a regulatory role for Itch in regulation of caspase-8 activation through mitochondrial cholesterol content and suggest that Itch mediates TRAIL resistance mainly through regulation of cholesterol trafficking.</p>", "<title>Cisplatin sensitivity is regulated by Itch and mitochondrial cholesterol</title>", "<p id=\"Par26\">Because cleaved Bid synergises and primes cells for apoptosis upon cisplatin treatment, we hypothesised that OE33 Itch KD cells would be resistant to cisplatin treatment due to the reduced Bid levels [##REF##32024383##38##]. Indeed, the Itch KD cell line was significantly more resistant to cisplatin-mediated apoptosis (Fig. ##FIG##6##7A, B##). A three-fold increase in IC₅₀ value in the Itch KD cell line for cisplatin (4.27 µg/ml) compared to the control cell line (1.23 µg/ml) was observed. To investigate the impact of mitochondrial cholesterol on cisplatin-induced apoptosis OE33 cells were treated with UA18666A followed by cisplatin (Fig. ##FIG##6##7C##). Cisplatin-induced cleavage of caspase-8, -3, Bid and PARP (lanes 1-3) was abrogated by pre-treatment with UA18666A (lanes 4–6). In summary, the data supports a mechanism where Itch and mitochondrial cholesterol trafficking has and important regulatory role in TRAIL- and cisplatin-induced apoptosis. The main protein that shuttles cholesterol to mitochondria is the START domain-containing protein STARD1 that form membrane contact sites between organelles [##UREF##2##39##]. A clinical study investigating differential gene expression in oesophageal adenocarcinoma in pre- and post-treatment biopsies associated with resistance to chemotherapy [##REF##35954391##40##]. Validations of the hits in siRNA screens reduced the number to seven genes, which included STARD1. Knockdown of STARD1 alone or in combination with cisplatin reduced cell viability in four oesophageal adenocarcinoma cell lines [##REF##35954391##40##]. Thus, low level of STARD1 is a sensitiser to cisplatin treatment in oesophageal adenocarcinoma. We therefore hypothesized that Itch KD cells have increased expression of STARD1 to facilitate cholesterol transfer. Indeed, Western blotting of cell lysates showed elevated levels of STARD1 and its interaction partner VDAC2 (Fig. ##FIG##6##7D, E##). While STARD1 is not directly regulated by ubiquitination it is stabilised by VDAC2, a protein in the outer mitochondrial membranate that is ubiquitinated by Nedd4 in melanoma cells, a HECT E3 ligase with high sequence homology in the interacting WW domains to Itch [##REF##31974380##41##]. Endogenous VDAC2 from OE33 cells co-immunoprecipitated both STARD1 and Itch (Fig. ##FIG##6##7F##). Together the data supports a model where Itch negatively regulates the stability of the VDAC2/STARD1 complex at the mitochondrial outer membrane, cholesterol import and activation of apoptosis (Fig. ##FIG##6##7G##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par27\">Ubiquitination and deubiquitination have emerged as important regulators of death receptor signalling. Particularly in cancer cells the downregulation of pro-apoptotic proteins by ubiquitination have been shown to mediate resistance to cell death. For example, the ubiquitin ligases Cbl and Cbl-b have been associated with TRAIL-mediated apoptosis resistance mechanisms at the plasma membrane where they regulate receptor clustering in lipid rafts and caspase-8 activation [##REF##11741956##42##, ##REF##19223002##43##]. The fact that these ubiquitin ligases regulate both receptor trafficking to cholesterol-rich lipid domains and downstream TRAIL signalling implies that there are additional regulatory mechanisms that affect TRAIL sensitivity. Here we have investigated the function of the ubiquitin ligase Itch in this context. Itch is known to regulate receptor trafficking, intracellular cholesterol synthesis, the stability of the anti-apoptotic protein FLIP and the pro-apoptotic protein tBid [##REF##20392206##3##, ##REF##16469705##5##, ##REF##19341794##30##, ##UREF##1##35##]. Here, we show for the first time that Itch regulates TRAIL-mediated intrinsic apoptosis through regulation of caspase-8 activation and intracellular cholesterol homoeostasis.</p>", "<p id=\"Par28\">In this study, we observed that knockdown of Itch in OE33 cells results in resistance to TRAIL- and cisplatin-mediated apoptosis. This correlated with reduced TRAIL-R2 at the plasma membrane rather than the expected increased expression of the anti-apoptotic protein FLIP. The protein expression of TRAIL-R2 was not impaired and the localisation of TRAIL-R1 or EGFR were not affected. Together this strongly indicated that Itch-regulated receptor endocytosis that was not enhanced. Regulation of trafficking from the ER/Golgi to the plasma membrane is still an unresolved question for the TRAIL receptors to our knowledge. Interestingly, the exit of other transmembrane proteins that traffic from the biosecretory pathway to cholesterol-rich domains of the plasma membrane, such as the aquaporins, is regulated by cholesterol concentration [##UREF##3##44##]. The sub-cellular localisation of death receptors do have a significant impact on signalling as shown in a breast cancer cell line where the total protein remained the same, but the cell surface expression of TRAIL-R1 and -R2 was reduced [##REF##19843632##45##]. Further studies are required to dissect these mechanisms. Intracellular signalling through caspase-8 and caspase-3/7 was found to be reduced in cell lines with reduced Itch expression, but caspase-8 cleavage at the DISC was not impaired which indicated that a regulation of mitochondrial-dependent apoptosis was contributing to the phenotype. Furthermore, we observed a significant reduction of t-Bid, which after activation by caspase-8 associates with Bax and Bak and induces mitochondrial membrane pore formation and subsequent cytochrome c release [##REF##12598529##46##]. The sensitivity to TRAIL signalling is regulated by the targeting of t-Bid by the ubiquitin/proteasome system and the mitochondrial membrane composition [##REF##20392206##3##, ##REF##18166654##20##, ##REF##18084240##33##, ##REF##10801801##47##]. A significant accumulation of cholesterol was observed in mitochondria in the Itch KD, along with reduced Bid and PARP cleavage. Treatment with U18666A, a drug that promotes accumulation of cholesterol in mitochondrial membranes, resulted in a loss of caspase-8 activity and cleavage of downstream targets similar to that observed in Itch KD cells. This study provides new insights into the complexity of the intersection between receptor signalling, membrane trafficking and the significance of the ubiquitin E3 ligase Itch in regulating mechanisms of TRAIL-mediated apoptosis.</p>", "<p id=\"Par29\">An important pathway for trafficking of cholesterol to mitochondria occurs through membrane contact sites, and this can be induced by treatment with the drug U18666A [##REF##31537798##48##]. An increase in mitochondrial cholesterol has a strong anti-apoptotic activity due to the inhibition of BAX and BAK oligomerization, which prevents release of cytochrome c and induction of apoptosis [##REF##18084240##33##]. Here we show an impaired BAX activation and cytochrome c release in Itch KD cells. The lipid composition of the mitochondrial outer membrane has an important role in the recruitment and activation of caspase-8 and subsequent cleavage of Bid [##REF##19001123##32##, ##REF##22448037##34##, ##REF##21072056##49##]. A reduced membrane fluidity impairs Bax oligomerisation, resulting in apoptosis resistance [##REF##18084240##33##, ##UREF##4##50##, ##REF##18593925##51##]. Inhibition of intracellular cholesterol trafficking by the drug U18666A in the HCT116 cell line leads to a mislocalisation of TRAIL-R2 from the plasma membrane to intracellular organelles, loss of caspase-8 activation, PARP cleavage and 5-FU resistance [##REF##27506940##52##]. Chemotherapy resistance is a common issue in cancer therapy that is associated with cholesterol regulation and in particular cholesterol content in the plasma membrane and mitochondria [##REF##18084240##33##, ##REF##18593925##51##, ##REF##1516050##53##–##UREF##6##58##].</p>", "<p id=\"Par30\">Reprogrammed lipid metabolism is an established hallmark of cancer, and in particular upregulation of the mevalonate pathway [##REF##24606524##59##]. Cholesterol promotes cell proliferation and is regulated by oncogenes (myc, PTEN) and the tumour suppressor p53. The accumulation of cholesterol correlates with a reduction in either a cholesterol exporter or a stabilisation of an importer [##REF##31974380##41##, ##REF##18593925##51##]. Here we propose that Itch-mediated poly-ubiquitination regulates proteins facilitating mitochondrial cholesterol import. A recent clinical study performed a gene set enrichment analysis from oesophageal adenocarcinoma biopsies pre- and post-treatment with chemotherapy [##REF##35954391##40##]. A set of genes from responders to chemotherapy were identified and validated in a siRNA screen. One of 80 hits was STARD1, a cholesterol shuttling protein associated with mitochondria. Knockdown of STARD1 alone or in combination with cisplatin or 5-FU reduce cell viability significantly in four oesophageal cancer cell lines. Oesophageal cancer is not the only cancer type that has been associated with resistance to apoptosis and chemotherapy due to increased mitochondrial cholesterol [##REF##1516050##53##, ##REF##22981231##60##–##REF##35806209##62##]. For example, knockdown of STARD1 in hepatocellular carcinoma sensitises cells to cisplatin and reduces proliferation [##REF##18593925##51##].</p>", "<p id=\"Par31\">Here we report a novel regulatory mechanism for the ubiquitinating enzyme Itch in TRAIL-mediated apoptosis dependent on mitochondrial cholesterol (Fig. ##FIG##6##7G##). An increase in mitochondrial cholesterol decreases membrane fluidity, increases resistance to apoptosis-inducing agents, impaired caspase-8 activation, Bax activation and cytochrome c release. Trafficking of cholesterol to mitochondria is mainly mediated by STARD1/D3 at ER-mitochondria and late endosome-mitochondria membrane contact sites [##REF##25505173##63##, ##REF##19965586##64##]. Our data show a correlation between STARD1 expression, mitochondrial cholesterol and resistance to apoptosis mediated by TRAIL, cisplatin or Navitoclax. Its overexpression in oesophageal adenocarcinoma treatment-resistant clinical samples and knockdown in the OE33 cell line demonstrates that it regulates the sensitivity to cisplatin and 5-FU [##REF##35954391##40##]. It will be important to further dissect these mechanisms to map the interrelationship between Itch, mitochondrial cholesterol, membrane contact sites, apoptosis and chemotherapy resistance in order to improve patient outcomes.</p>" ]

[]

[ "<p id=\"Par1\">The activation of apoptosis signalling by TRAIL (TNF-related apoptosis-inducing ligand) through receptor binding is a fundamental mechanism of cell death induction and is often perturbed in cancer cells to enhance their cell survival and treatment resistance. Ubiquitination plays an important role in the regulation of TRAIL-mediated apoptosis, and here we investigate the role of the E3 ubiquitin ligase Itch in TRAIL-mediated apoptosis in oesophageal cancer cells. Knockdown of Itch expression results in resistance to TRAIL-induced apoptosis, caspase-8 activation, Bid cleavage and also promotes cisplatin resistance. Whilst the assembly of the death-inducing signalling complex (DISC) at the plasma membrane is not perturbed relative to the control, TRAIL-R2 is mis-localised in the Itch-knockdown cells. Further, we observe significant changes to mitochondrial morphology alongside an increased cholesterol content. Mitochondrial cholesterol is recognised as an important anti-apoptotic agent in cancer. Cells treated with a drug that increases mitochondrial cholesterol levels, U18666A, shows a protection from TRAIL-induced apoptosis, reduced caspase-8 activation, Bid cleavage and cisplatin resistance. We demonstrate that Itch knockdown cells are less sensitive to a Bcl-2 inhibitor, show impaired activation of Bax, cytochrome c release and an enhanced stability of the cholesterol transfer protein STARD1. We identify a novel protein complex composed of Itch, the mitochondrial protein VDAC2 and STARD1. We propose a mechanism where Itch regulates the stability of STARD1. An increase in STARD1 expression enhances cholesterol import to mitochondria, which inhibits Bax activation and cytochrome c release. Many cancer types display high mitochondrial cholesterol levels, and oesophageal adenocarcinoma tumours show a correlation between chemotherapy resistance and STARD1 expression which is supported by our findings. This establishes an important role for Itch in regulation of extrinsic and intrinsic apoptosis, mitochondrial cholesterol levels and provides insight to mechanisms that contribute to TRAIL, Bcl-2 inhibitor and cisplatin resistance in cancer cells.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41419-023-06417-4.</p>", "<title>Acknowledgements</title>", "<p>We thank Prof. Henning Walzcak (UCL Cancer Institute, UK) for generously sharing the bacterial expression construct for isoleucine zipper TRAIL. We thank Prof. Ian Mills and Anna Carberry for thoughtful insights and discussions. This work was supported by CRUK (C11884/A24387; DBL), MRC (MR/S021205/1; DBL) and the Northern Ireland Department for the Economy (EE). Schematic figures were created with BioRender.com.</p>", "<title>Author contributions</title>", "<p>EE, DBL and JH conceived and planned the experiments. JH, AS and NC performed the cell culture, flow cytometry sorting and Western blots. EE prepared samples and performed transmission electron microscopy. JH performed all other experiments and analysed the data. RT provided expertise on chemoresistance and oesophageal cell lines. EE, DBL and JH wrote the manuscript.</p>", "<title>Data availability</title>", "<p>The data sets generated during the current study are available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par32\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Itch knockdown increases resistance to TRAIL-mediated apoptosis in OE33 cells and impairs caspase-8 cleavage and activity.</title><p><bold>A</bold> Western blot analysis of basal expression of FLIP(L), FLIP(S), FADD, Procaspase-8, TRAIL-R1, TRAIL-R2 in OE33 Ctrl (shCTRL) and Itch knockdown (KD) cells stably expressing shRNA targeting ITCH. <bold>B</bold> Bar graph showing the densitometry of Western blot analysis of Itch expression normalised to the actin loading control in five independent experiments. <bold>C</bold> Bar graph showing the quantification for FLIP-Long and -Short expression in control shRNA and Itch knockdown (KD) cell lines. <italic>N</italic> = 5 independent experiments. <bold>D</bold> OE33 Ctrl and Itch KD cell lines were subjected to treatment with increasing doses of izTRAIL for 24 h (0–50 ng/mL). Cell viability was measured using the CellTiterGlo Assay. Data was normalised to an untreated control. <bold>E</bold> OE33 Ctrl and Itch KD cells were treated with 0–20 ng/mL TRAIL for 24 h and then stained with FITC-conjugated Annexin V and propidium iodide to assess the number of apoptotic cells under each treatment condition. Bar graph showing the percentage of apoptotic cells (Annexin V-positive cells) of the population. <bold>F</bold> Caspase -8 and (<bold>G</bold>) Caspase -3/-7 activity in OE33 Ctrl and Itch KD cell lines was measured following treatment with increasing concentrations of izTRAIL (0–50 ng/mL). Activity was measured 6 h post treatment using the Caspase -3/-7 or the Caspase -8 Glo assays. <bold>H</bold> Western blot analysis of cleaved Caspase-8, Bid and PARP in OE33 Ctrl and Itch KD cell lines following treatment for 6 or 24 h with 5 ng/ml izTRAIL. <bold>I</bold> Densitometry of the experiment in (<bold>C</bold>) in four independent repeats. Error bars represent the standard error of the mean. Statistical significance was measured by Student’s <italic>t</italic> test. *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Itch knockdown cells show reduced surface expression of TRAIL-R2 in OE33 cells.</title><p>FACS analysis of cell surface expression of (<bold>A</bold>) TRAIL-R2 and (<bold>B</bold>) TRAIL-R1 cell surface expression in OE33 Ctrl and Itch KD cell lines. Bar graphs showing the mean fluorescence intensity of cell surface staining of TRAIL-R2 in OE33 control and Itch KD cells in three independent experiments (<italic>n</italic> = 10,000 cells per experiment). <bold>C</bold> FACS analysis of cell surface expression of EGFR in serum starved cells normalised to the control cell line in three independent experiments. <bold>D</bold> FACS analysis of fluorescent transferrin uptake in serum starved cells. Three independent experiments were performed where 10,000 cells were analysed per experiment. <bold>E</bold> TRAIL-R2 cell surface expression was measured using confocal microscopy. Alexa488-tagged wheat germ agglutinin stain was used to identify the plasma membrane and anti-DR5 antibody stain was used to determine the intensity of TRAIL-R2 at the plasma membrane. Receptor expression is expressed as the Integrated Density of the stain at the plasma membrane divided by the area. <italic>N</italic> = 20. <bold>F</bold> Western blot showing the total expression levels of TRAIL-R2 and -R1 in control and Itch KD OE33 cells. Error bars represent the standard error of the mean. Statistical significance was calculated by Student’s <italic>t</italic> test; ns, not significant, *<italic>p</italic> &lt; 0.05, ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Itch is found at the death-inducing signalling complex (DISC) but does not regulate its composition or cleavage of caspase-8.</title><p><bold>A</bold> Immunoprecipitation of the DISC using an activating TRAIL-R2 antibody from OE33 cells with a stable Itch knockdown (KD) or a control. Cells were treated for 1 h to induce formation of the DISC. Proteins were separated by size on a SDS-PAGE gel prior to Western blot analysis. <bold>B</bold> Densitometry of cleaved caspase-8 normalised to the pro-caspase-8 in the DISC IP from OE33 cells from three independent experiments. <bold>C</bold> Immunoprecipitation of the DISC in HT29 cells treated with control or ITCH siRNA using the TRAIL-R2 antibody. <bold>D</bold> Immunoprecipitation of the DISC in HCT116 cells treated with control or ITCH siRNA using the TRAIL-R2 antibody. Statistical significance was measured by Student’s <italic>t</italic> test, ns represents a non-significant difference.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Itch knockdown leads to an accumulation of mitochondrial cholesterol.</title><p><bold>A</bold> Transmission electron micrographs illustrating the morphology of control and Itch KD cells. Scale bars, 5 µm. <bold>B</bold> Electron micrographs illustrating the morphology and size of mitochondria in control and Itch KD cells. Scale bar, 1 µm for all images. <bold>C</bold> Quantification of mitochondrial width from 25 cells. Mean ± SD. <bold>D</bold> Confocal images illustrating the accumulation of free cholesterol by Filipin-III staining together with outer mitochondrial membrane marker TOM20. Scale bar, 5 µm. <bold>E</bold> Tukey box plot displaying the Pearson colocalization co-efficient of TOM20 and Filipin staining to compare levels of mitochondrial cholesterol in control and Itch KD cell lines. <italic>N</italic> = 14 per group. <bold>F</bold> Western blot analysis of cell lysates showing the expression of nuclear SREBP2 (cleaved) protein in the Itch KD compared to control. Statistical significance was measured by Student’s <italic>t</italic> test. ***<italic>p</italic> &lt; 0.001, ****<italic>p</italic> &lt; 0.0001.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Cholesterol homoeostasis is an important resistance mechanism for TRAIL-induced apoptosis.</title><p><bold>A</bold> Caspase-8 activity and (<bold>B</bold>) Caspase-3/-7 activity was measured following treatment with increasing concentrations of izTRAIL (0–50 ng/mL). Activity was measured 6 h post treatment using the Caspase-3/-7 or the Caspase-8 Glo assays. Cells were treated with U18666A (1 ng/ml) for 24 h. <bold>C</bold> Western blot analysis of cell lysates after treatment with U18666A and izTRAIL for key apoptotic proteins; caspase-8, -3, Bid and PARP. <bold>D–G</bold> Quantification of an inhibition of apoptosis in OE33 cells treated with U18666A (1 ng/ml) in combination with izTRAIL, showing a significant loss of cleavage of caspase-8, -3, Bid, and PARP in three independent experiments. <bold>H</bold> Bar graph showing the mean fluorescence of cell surface expression of TRAIL-R2 stained control and cells treated with U18666A in three independent experiments. <bold>I</bold> Bar graph showing the mean fluorescence intensity of cell surface expression of TRAIL-R1 in control and U18666A-treated (1 ng/ml) OE33 cells in three independent experiments (<italic>n</italic> = 10,000 cells per experiment). <bold>J</bold> Fluorescence images of OE33 cells showing the accumulation of cholesterol, stained with Filipin-III, in mitochondria after U18666A treatment. Scale bar, 5 µm. Statistical significance was measured by Student’s <italic>t</italic> test. *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Itch regulates intrinsic apoptosis, Bax activation and cytochrome release.</title><p><bold>A</bold> Western blot analysis of an immunoprecipitation experiment using the Bax 6A7 antibody that specifically recognises the activated form of the protein. Total Bax and actin from the OE33 detergent extracts are shown below. Cells were treated with 50 ng/ml izTRAIL for 6 h. <bold>B</bold> Quantification of three independent experiments shown in (<bold>A</bold>). Statistical analysis was performed using Student’s <italic>t</italic> test. **<italic>p</italic> &lt; 0.01. <bold>C</bold> Flow analysis of cytochrome c release from OE33 control and Itch KD cell lines following stimulation with 10–20 ng/ml izTRAIL for 6 h. In total, 10,000 cells per sample were analysed in three independent experiments. Statistical analysis was performed using 2-way ANOVA. ***<italic>p</italic> &lt; 0.001. <bold>D</bold> The percentage apoptotic cells were assessed post-treatment with 5 µM Navitoclax (ABT-263) at the indicated time points. Statistical analysis was performed using 2-way ANOVA. ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><title>Cisplatin-mediated apoptosis is regulated by Itch expression and mitochondrial cholesterol.</title><p><bold>A</bold> Cell viability assay of the Itch KD cell line in response to Cisplatin treatment for 72 h at 0–6 µg/ml. <bold>B</bold> Apoptosis assay using the Itch KD cell line treated with 0–6 µg/ml Cisplatin for 72 h. Data was expressed as a percentage of control. <bold>C</bold> Analysis of apoptotic markers in whole cell lysates from cells treated with Cisplatin in U18666A. <bold>D</bold> Western blot analysis of total expression levels of STARD1 and VDAC2 (dimers) in control and Itch KD OE33 cell lines. Error bars represent the standard error of the mean. Statistical significance was calculated by Student’s <italic>t</italic> test. <bold>E</bold> Quantification of STARD1 band intensity normalised to the loading control in three independent experiments. Statistical analysis was performed using Student’s <italic>t</italic> test, ***<italic>p</italic> &lt; 0.001. <bold>F</bold> Immunoprecipitation of VDAC2 from OE33 detergent extract. The samples were incubated overnight with a control IgG and the VDAC2 antibody and washed four times. Co-immunoprecipitated proteins were separated by SDS-PAGE electrophoresis and STARD1 and Itch were detected by Western blotting. <bold>G</bold> A schematic image illustrating the suggested model for Itch in regulation of extrinsic and intrinsic apoptosis. A reduction in TRAIL-R at the cell surface impairs downstream apoptotic signalling, which moreover is not further amplified at the mitochondria. Loss of Itch expression results in an increase in mitochondrial cholesterol which impairs membrane fluidity, binding of caspase-8, subsequent activation of Bid and Bax. Together, this results in reduced pore formation in the outer mitochondrial membrane and reduced cytochrome c release. Mechanistically loss of Itch expression results in reduced ubiquitination and degradation of the STARD1/VDAC2 lipid transfer complex that mediates cholesterol import to mitochondria. A stabilisation of STARD1/VDAC2 promotes import of mitochondrial cholesterol which is anti-apoptotic. Statistical significance; *<italic>p</italic> &lt; 0.05, ***<italic>p</italic> &lt; 0.001.</p></caption></fig>" ]

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[ "<fn-group><fn><p>Edited by Dr Francesca Bernassola</p></fn><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41419_2023_6417_MOESM1_ESM.docx\"><caption><p>Supplementary figure legends</p></caption></media>", "<media xlink:href=\"41419_2023_6417_MOESM2_ESM.tif\"><caption><p>Supplementary Figure 1</p></caption></media>", "<media xlink:href=\"41419_2023_6417_MOESM3_ESM.tif\"><caption><p>Supplementary Figure 2</p></caption></media>", "<media xlink:href=\"41419_2023_6417_MOESM4_ESM.tif\"><caption><p>Supplementary Figure 3</p></caption></media>", "<media xlink:href=\"41419_2023_6417_MOESM5_ESM.pdf\"><caption><p>Original Data File</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par11\">Extracellular vesicles (EVs), including small EVs (sEVs) and large EVs(lEVs), are minute membrane-bound particles released naturally from cells and delimited by a lipid bilayer [##REF##30637094##1##]. EVs can regulate intercellular communication by delivering numerous cargoes, comprising nucleic acids, lipids, and proteins, from donor to recipient cells, thereby contributing to multifarious physiological and pathological processes [##UREF##0##2##]. EVs derived from both normal and cancer cells can respond to extracellular and intracellular stress, including pH imbalance, platelet activation, ionizing radiation, low oxygen levels, radiation, chemotherapy, and necrosis. In response to a stress factor, cells can support the evasion of cell death within the tumor microenvironment (TME) while concurrently transmitting pro-survival information via EV-mediated intercellular communication to facilitate facilitating resistance to therapy [##UREF##1##3##]. Furthermore, EVs can influence the development and progression of cancer and are involved in inflammatory responses, metastasis, angiogenesis, epithelial-mesenchymal transition, invasion, cell migration, and proliferation [##REF##29795272##4##]. EVs can also deliver a series of molecules to affect cell death in response to cellular stress stimuli [##UREF##2##5##]. For instance, a recent study revealed that sEVs can inhibit ferroptosis by facilitating the removal of iron from cells, thereby preventing cell death in the context of tumor suppression [##REF##31735663##6##].</p>", "<p id=\"Par12\">Cell death can be categorized as regulated cell death (RCD) and accidental cell death (ACD), depending on the morphology, biochemistry, and function [##REF##29362479##7##]. ACD refers to cell suicide following injury. In contrast, RCD is regulated by controlled signaling pathways and contributes to disease development and maintenance of homeostasis [##REF##36482419##8##]. RCD can be further subdivided into apoptotic and nonapoptotic types [##REF##33462123##9##, ##REF##30948788##10##]. Historically, apoptosis has been deemed the major form of RCD. However, contemporary research indicates that nonapoptotic RCD forms have not received adequate attention in the context of tumor cell biology and the mechanisms underlying cancer therapy [##REF##22078876##11##, ##REF##27048813##12##]. During the current decade, the most commonly studied types of non-apoptotic RCD have included ferroptosis, necroptosis, and pyroptosis [##REF##36482419##8##, ##REF##32778143##13##]. Furthermore, nonapoptotic RCD is closely associated with cancer development and the response to therapeutic interventions. In particular, nonapoptotic forms of RCD exhibit synergistic antitumor immune responses while possibly exerting inhibitory effects on tumor immune responses [##REF##35725836##14##].</p>", "<p id=\"Par13\">The regulation of nonapoptotic RCD by EVs provides a novel and promising strategy for addressing human diseases [##UREF##3##15##]. However, it is important to note that a comprehensive and systematic summary of nonapoptotic RCD mediated by EVs in cancer progression is currently lacking. In this context, our review aims to bridge this gap by exploring the roles of EVs in mediating ferroptosis, pyroptosis, and necroptosis across various cancer types. We believe that this exploration holds significant promise for clinical applications in the areas of cancer diagnosis and therapy.</p>" ]

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[ "<title>Conclusions and perspectives</title>", "<p id=\"Par35\">Nonapoptotic RCD forms, mainly ferroptosis, pyroptosis, and necroptosis, have gained increasing attention over the last decade. Understanding the functions of EV-mediated cell death is greatly conducive to providing a favorable technique for the diagnosis and treatment of human cancers. This review outlines the characteristics of EV-mediated non-apoptotic RCD forms and the mechanisms by which EVs transfer different cargoes to mediate tumor progression. Moreover, considering the improved biocompatibility and intrinsic targeting ability of EVs over free drugs, EV-based strategies for targeting cell death regulators shows significant potential with regard to cancer therapy. Accumulating preclinical studies on EV-mediated nonapoptotic RCD forms in cancers provide novel insights into cancer biology and pave the way for the clinical development of EV-based therapeutics.</p>", "<p id=\"Par36\">Recent advances in the expanding roles of EV-mediated cell death hold great potential for both diagnostic and therapeutic applications for cancers. However, several crucial questions remain unanswered: (i) Can the transport of bioactive molecules involved in RCD forms by sEVs in bodily fluids serve as a novel source of candidate biomarkers for cancer diagnosis and prognosis prediction? Altered ferroptosis markers in exosomes have been demonstrated to be promising and easily accessible markers for early cancer detection and prognosis in different cancers, such as HCC and PDAC [##UREF##17##116##, ##REF##31920150##117##]. Encouragingly, technical progress has led to the development of multimolecular detection platforms, which may promote the development of early cancer detection and treatment monitoring by integrating EV biomarkers [##REF##36329610##118##–##REF##35624008##120##]. (ii) Can nonapoptotic RCD triggered by sEV-based drug delivery systems be harnessed as a novel treatment strategy in cancer therapy? The ineffective delivery of a therapeutic drugs is a major obstacle in the treatment of different cancers. Exosomes have the benefit of high biocompatibility, low immunogenicity, high efficiency, and strong potential for drug delivery. Moreover, erastin@FA-exo can increase the erastin uptake efficiency into MDA‐MB‐231 cells, and ferroptosis stimulated by suppression of System X_c⁻ has a more pronounced inhibitory effect on the migration and proliferation of breast cancer [##REF##31464035##108##]. Exosome nanovesicles loaded with drugs achieve significant abscopal effects to elicit ATP-mediated antitumor immunity by triggering pyroptosis in macrophages, enhancing the maturation of DCs, and inhibiting tumor-distant metastases [##UREF##16##115##]. EV-based drug delivery systems could be developed to efficiently deliver antitumor drugs and cell death inducers, thus synergistically suppressing tumor growth. (iii) Can the utilization of sEVs to transport multiple molecules and drugs that mediate cell death serve as an innovative therapeutic approach for use in preclinical studies for cancer treatment? These questions underscore the potential for harnessing the capabilities of sEV-based strategies to improve both cancer diagnosis and treatment. A recent study uncovered a promising triple therapeutic strategy based on inhibiting tumor cell-derived exosome secretion to enhance the effects of ferroptosis-dependent cancer treatment and cancer immunotherapy [##UREF##18##121##]. Therefore, combination therapies that target multiple cell death pathways while improving therapeutic efficiency should be considered in the future.</p>", "<p id=\"Par37\">Although some research progress has been made regarding the roles of exosome-mediated nonapoptotic RCD forms in tumor progression, most studies were conducted in preclinical models. However, there is encouraging news on the horizon, with certain clinical trials evaluating the impact of key players involved in nonapoptotic RCDs in the context of solid metastatic cancer and hematological malignancies (NCT05493800, NCT04739618). This development emphasizes the growing interest in translating preclinical findings into clinical applications. Consequently, further exploration into the mechanisms associated with EV biogenesis and transport, as well as those related to EV-mediated cell death signaling mechanisms, may have the potential to enhance therapeutic safety and selectivity. This could aid in the development of more effective and targeted treatments for cancer.</p>" ]

[ "<p id=\"Par1\">Extracellular vesicles (EVs) have gained increasing recognition as significant regulators of intercellular communication in various physiological and pathological processes. These vesicles play a pivotal role in cancer progression by facilitating the transfer of diverse cargoes, including lipids, proteins, and nucleic acids. Regulated cell death (RCD), the orderly and autonomous death of cells, is controlled by a variety of biomacromolecules and, in turn, influences various biological processes and cancer progression. Recent studies have demonstrated that EV cargoes regulate diverse oncogenes and tumor suppressors to mediate different nonapoptotic forms of RCD, notably ferroptosis, pyroptosis, and necroptosis. Nevertheless, comprehensive exploration of EV-mediated nonapoptotic RCD forms in the context of cancer has not been performed. This review summarizes the progress regarding the biological functions and underlying mechanisms of EVs in mediating nonapoptotic RCD by delivery of cargoes to regulate tumor progression. Additionally, the review delves into the potential clinical applications of EV-mediated cell death and its significance in the areas of cancer diagnosis and therapy.</p>", "<p id=\"Par2\">\n\n</p>", "<title>Subject terms</title>" ]

[ "<title>Facts</title>", "<p id=\"Par3\">\n<list list-type=\"bullet\"><list-item><p id=\"Par4\">Extracellular vesicles (EVs) play a role in numerous pathophysiological processes, including nonapoptotic RCD.</p></list-item><list-item><p id=\"Par5\">EVs act as a double-edged sword in tumor progression by mediating various forms of nonapoptotic RCDs, including ferroptosis, pyroptosis, and necroptosis.</p></list-item><list-item><p id=\"Par6\">Targeting the various cargoes associated with EV-mediated cell death holds promise for advancing cancer therapy.</p></list-item></list>\n</p>", "<title>Open questions</title>", "<p id=\"Par7\">\n<list list-type=\"bullet\"><list-item><p id=\"Par8\">What are the shared characteristics and distinctions between ferroptosis, pyroptosis, and necroptosis?</p></list-item><list-item><p id=\"Par9\">What is the association between extracellular vesicle (EV)-mediated cell death and the response to cancer therapy?</p></list-item><list-item><p id=\"Par10\">In what manner do EV-based drug delivery systems influence RCD processes and contribute to their anticancer efficacy?</p></list-item></list>\n</p>", "<title>Overview of EVs</title>", "<p id=\"Par14\">EVs are heterogeneous membrane vesicles that are actively secreted by virtually all types of cells, which can be released into the extracellular environment and serve as key mediators of intercellular communication [##REF##31324871##16##–##REF##35260831##18##]. Based on biogenesis, release pathways, subcellular origin, and size, EVs can be roughly classified into three types: microvesicles (MVs) with diameters of approximately 150–1,000 nm, exosomes with diameters of 50–150 nm, and apoptotic bodies with diameters ranging between 1–5 μm [##REF##30637094##1##, ##REF##35236964##17##, ##REF##35927511##19##]. Exosomes are produced by the endosomal pathway through the endosomal sorting complex required for transport (ESCRT) mechanism, which contributes to the fusion of multivesicular bodies containing invaginated intraluminal vesicles with the plasma membrane and subsequent release into the extracellular space [##REF##35236964##17##]. MVs, also referred to as shed MVs, are directly produced through outward budding and subsequent division of the cell membrane [##REF##33753940##20##]. Apoptotic bodies, representing the largest subgroup of EVs, are generated via the apoptotic cell membrane during programmed cell death and can be phagocytosed by macrophages [##UREF##4##21##]. However, exosomes and MVs can be internalized through endocytosis [##REF##35236964##17##]. Under physiological and pathological conditions, these internalized EVs can release intraluminal contents within recipient cells to mediate intercellular communication [##REF##29339798##22##].</p>", "<p id=\"Par15\">EVs also selectively deliver various cargoes from donor cells to recipient cells, such as proteins, nucleic acids, and lipids [##REF##28524163##23##, ##REF##32457507##24##], which can mediate different diseases by influencing a variety of signaling pathways [##UREF##0##2##]. EVs are emerging as excellent liquid biopsy analytes because they can be stably detected in various bodily fluids, such as serum, plasma, and urine [##REF##33989735##25##]. Furthermore, the cargo carried by EVs can be used to assess the current disease status. Thus, EVs can be used as biomarkers for the diagnosis or detection of tumor progression [##REF##31693397##26##]. It has been widely reported that EVs exert multiple effects to mediate cell migration and proliferation, angiogenesis, immune inflammation and modulation, evasion of cell death, tumor development, and metastasis [##UREF##5##27##, ##REF##34090999##28##]. Furthermore, EVs, mainly exosomes and microparticles, participate in cancer progression and chemoresistance by mediating cell death signaling pathways [##REF##32106859##29##–##REF##32232155##32##].</p>", "<title>The main types of nonapoptotic RCDs</title>", "<title>Ferroptosis</title>", "<p id=\"Par16\">Ferroptosis is an iron-dependent form of oxidative cell death characterized by oxidative modification [##REF##22632970##33##]; it is distinct from apoptosis in terms of its biochemical, genetic, and morphological characteristics [##REF##35338310##34##]. Its morphological characteristics include cell swelling and plasma membrane rupture. Ferroptosis is a direct result of peroxidation (excessive oxidative destruction) of cell membrane-associated lipids. The process depends on reactive oxygen species (ROS), iron, and phospholipids containing polyunsaturated fatty acids (PUFAs) [##REF##33495651##35##]. Ferroptosis can be induced primarily through two distinct pathways—the transporter-dependent (extrinsic) pathway and the enzyme-regulated (intrinsic) pathway [##REF##34331036##36##]. Both of these pathways are closely linked via different subcellular organelles and a series of metabolic pathways [##REF##33462411##37##]. The extrinsic pathway is primarily induced via suppression of system X_c⁻ [##REF##22632970##33##], which is a cellular membrane amino acid transporter responsible for exporting glutamate and importing cystine, thereby regulating glutathione (GSH) biosynthesis. The intrinsic pathway can be triggered by inhibiting the activity or expression of glutathione peroxidase 4 (GPX4) via small-molecule substances [##REF##32804006##38##]. Moreover, susceptibility to ferroptosis may be influenced by other signaling pathways, including ferroptosis suppressor protein 1 (FSP1)–coenzyme Q10 [##REF##31634900##39##]. A series of antagonists and agonists orchestrate ferroptosis initiation and regulation. Lipophilic antioxidants, iron chelators, arachidonate lipoxygenase inhibitors, and acyl-CoA synthetase long-chain family member 4 (ACSL4) inhibitors block ferroptotic cell death [##REF##34331036##36##]. Therefore, inhibiting system X_c⁻, inducing consumption of GSH, and inactivating GPX4 are potentially effective treatment strategies to induce ferroptosis in cancer cells.</p>", "<title>Pyroptosis</title>", "<p id=\"Par17\">Pyroptosis, which is also referred to as inflammatory cell necrosis, is a novel type of nonapoptotic RCD. The main characteristics of pyroptosis include cell membrane pore formation, membrane rupture, and cell lysis, leading to the release of proinflammatory cytokines [##REF##30948788##10##]. Pyroptosis is mainly utilized by cells in the innate immune system in response to pathogen-induced signals and cellular perturbations triggered by inflammasomes and executed by gasdermin (GSDM) proteins, predominantly GSDMD and GSDME [##REF##19148178##40##, ##REF##18846107##41##]. Pyroptosis is generally regulated via two primary pathways, i.e., the classical and nonclassical pyroptosis pathways. The nonclassical pathway of pyroptosis is induced by direct stimulation and oligomer formation of caspase 4, caspase 5 (in humans), and caspase 11 (in mice [##REF##26375259##42##]) through the binding of their amino (N)-terminal caspase activation and recruitment domain to the gram-negative bacterial lipopolysaccharide [##REF##26655628##43##]). In contrast, the classical pathway of GSDMD activation is regulated via the activation of caspase 1 through the inflammasome signaling platform, which is assembled in response to a plethora of signals, including homeostasis-altering molecular processes, pathogen-associated molecular patterns, and damage-associated molecular patterns (DAMPs) [##REF##28163301##44##]. Caspase 1 can both cleave and activate cytokines such as interleukin (IL)-1β and IL-18 to induce formation of their mature structures, eventually resulting in inflammatory responses and pyroptosis [##REF##35673561##45##].</p>", "<title>Necroptosis</title>", "<p id=\"Par18\">Necroptosis, a form of nonapoptotic RCD and regulated necrosis, is marked by distinctive morphological characteristics such as rupture of the plasma membrane, swelling of organelles, and leakage of intracellular contents [##REF##34912054##46##]. Necroptosis is primarily regulated by receptor-interacting protein kinase (RIPK) 1, RIPK3, and even mixed lineage kinase domain-like protein (MLKL). Ligands tend to bind to specific necroptotic receptors (e.g., tumor necrosis factor [TNF] receptor 1), thus inducing necroptosis by facilitating the binding and activities of their respective cytoplasmic adaptor proteins [##REF##35288298##47##]. The oligomerization and translocation of phosphorylated MLKL produce pores in the cell membrane, and this signal transduction leads to the leakage of cellular contents, including cytokines, DAMPs, chemokines, and interferons, thereby provoking an inflammatory response [##REF##31024005##48##]. Thus, necroptosis must be strictly regulated to maintain normal tissue homeostasis [##REF##25592536##49##, ##REF##19109899##50##]. Recently, the significance of necroptosis in cancer has been increasingly appreciated, and a better understanding of necroptotic processes may be of use for developing novel cancer therapy strategies.</p>", "<title>EV-mediated RCD forms in cancers</title>", "<p id=\"Par19\">EVs mediate cancer development and propagation by influencing the crosstalk with local or remote recipient cells. Various cell-derived exosomes play crucial roles in establishing immune suppression, premetastatic niches, immune surveillance, immune escape, and maintenance of the tumor immune microenvironment [##REF##33183286##51##]. EVs can induce cell-to-cell communication by transmitting intracellular contents to orchestrate cell death in numerous cancers [##REF##36705798##52##, ##REF##35497192##53##]. In the next sections, the expanding landscape of EV-mediated ferroptosis, pyroptosis, and necroptosis in diverse cancer phenotypes is discussed, and the related topics include drug resistance, tumor metastasis, and antitumor immunity (Fig. ##FIG##0##1## and Table ##TAB##0##1##).</p>", "<title>The functions of EVs in ferroptosis</title>", "<p id=\"Par20\">Studies have demonstrated that EVs participate in and influence many cancer hallmarks, including resisting cell death, sustaining proliferative signaling, and activating invasion and metastasis [##REF##31735663##6##, ##REF##35385773##54##]. In the following section, we present the latest findings on the understanding of EV-mediated ferroptosis and its contribution to cancer chemoresistance, radioresistance, initiation, and progression (Fig. ##FIG##1##2##).</p>", "<p id=\"Par21\">EV-mediated ferroptosis affects chemoresistance and radioresistance in lung cancer. In the case of non-small cell lung cancer (NSCLC), cisplatin is the first-line chemotherapeutic medicine that induces ferroptosis [##REF##30028656##55##, ##REF##28494534##56##]. However, cisplatin resistance has become increasingly common in NSCLC patients [##REF##29653268##57##]. For instance, exosomal delivery of miR-4443 to cisplatin-sensitive NSCLC cells boosts FSP 1 expression while suppressing ferroptosis; thus, treatment of cisplatin-resistant NSCLC with antagomiR can restore responsiveness to cisplatin [##REF##33781830##58##] (Fig. ##FIG##1##2##). Lung adenocarcinoma (LUAD)-derived exosomal circRNA_101093 (cir93) increases fatty acid-binding protein 3 (FABP3) to reduce global arachidonic acid through reactions with taurine, thus inducing ferroptosis by desensitizing LUAD cells and decreasing total lipid peroxidation. PDX mouse model data revealed that poor survival of LUAD and resistance to ferroptosis were predicted by elevated levels of FABP3 and cir93 [##UREF##7##59##] (Fig. ##FIG##1##2##). In addition to their effects on chemoresistance, exosomes can also affect radioresistance by regulating ferroptosis [##REF##32106859##29##, ##REF##33781830##58##]. To date, NSCLC treatment predominantly relies on surgery, chemotherapy, immunotherapy, radiotherapy, and local interventional therapy. Although radioresistance mechanisms have been explored extensively [##REF##33071215##60##, ##REF##32528035##61##], the five-year survival rate is &lt;17% owing to tumor radioresistance [##UREF##8##62##]. The angiopoietin-like 4 (ANGPTL4) gene, an inflammatory carcinogenic regulator and a decisive angiogenesis mediator [##REF##30518876##63##–##REF##32641980##65##], has been identified as a key ferroptosis-related gene [##REF##31641008##66##]. Under hypoxia, the ANGPTL4 protein can be transferred by exosomes to bystander normoxic NSCLC, thereby suppressing the onset of ferroptosis and promoting radioresistance in bystander cells [##REF##36050447##67##].</p>", "<p id=\"Par22\">In addition to those derived from cancer cells, sEVs derived from other cell types may influence chemoresistance in preclinical tumor models of gastric cancer (GC). For example, exosome-derived miR-522 from cancer-associated fibroblasts (CAFs) could block the accumulation of lipid ROS by targeting ALOX15 in GC cells, thereby inhibiting ferroptosis and inducing chemotherapy resistance [##REF##32106859##29##] (Fig. ##FIG##1##2##). Chemotoxicity in CAFs increases the expression of ubiquitin-specific protease 7 (USP7), a promising target for antitumor drug resistance [##REF##33967786##68##, ##REF##30024656##69##]. Heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1) is associated with the exosomal secretion of multiple miRNAs [##REF##31534508##70##, ##REF##33692334##71##]. USP7 enhances the secretion of miR-522 from CAFs by mediating hnRNPA1 deubiquitination. miR-522 levels significantly decrease in the tumor microenvironment due to the knockdown of USP7 or hnRNPA1, thus causing attenuated chemosensitivity and enhanced cell death [##REF##32106859##29##] (Fig. ##FIG##1##2##). Furthermore, the pathway associated with hnRNPA1, involving stearoyl-CoA-desaturase 1 (SCD1) and ferroptosis-associated lncRNA (lncFERO), also exhibits exosome-ferroptosis effects. Chemotoxicity stimulates GC cells to secrete lncFERO through the upregulation of hnRNPA1 expression. Exo-lncFERO derived from GC cells then enters gastric cancer stem cells (GCSCs) and upregulates SCD1 expression in GCSCs by binding SCD1-associated mRNA and recruiting hnRNPA1, thereby suppressing GCSC ferroptosis and reducing chemosensitivity in GC cells. hnRNPA1 knockdown in GCSCs prevents this effect; thus, targeting the exo-lncFERO/hnRNPA1/SCD1 axis combined with chemotherapy might prove to be a promising CSC-based strategy for GC treatment [##REF##34845198##72##] (Fig. ##FIG##1##2##). Another recent study demonstrated that CAF-derived exosomal DACT3-AS1, as a GC-associated suppressive regulator, sensitized GC cells to oxaliplatin treatment via Sirtuin 1 (SIRT1)-regulated ferroptosis conferring ferroptosis-mediated oxaliplatin sensitivity [##REF##36764075##73##].</p>", "<p id=\"Par23\">Exosomes derived from other cell types can also regulate chemoresistance in other digestive system tumors. After receiving chemotherapy with gemcitabine, CAFs can secrete exosomes with high expression of miR-3173-5p, which is internalized by pancreatic ductal adenocarcinoma (PDAC) cells. Mechanistically, exosome promote resistance to gemcitabine by suppressing ferroptosis via the miR-3173-5p/ACSL4 axis [##UREF##9##74##]. Colorectal cancer (CRC)-related adipokine secretion is linked to cancer progression and chemoresistance. Microsomal triglyceride transfer protein (MTTP), a major intracellular lipid transfer protein, is delivered by adipose-derived exosomes to inhibit ferroptosis in CRC cells. Mechanistically, this study revealed that exosomes promoted oxaliplatin resistance and inhibited ferroptosis by upregulating GPX4 and xCT in CRC organoids [##REF##30323319##75##–##UREF##10##77##].</p>", "<p id=\"Par24\">Emerging studies have demonstrated a role for sEV-mediated ferroptosis in different stages of tumor development. Metastasis is the leading contributor to resultant cancer mortality in patients [##REF##31122251##78##]. Macrophages are one of the most common host immune cells in the TME and regulate metastasis [##REF##36084651##79##]. Nasopharyngeal carcinoma (NPC) is the most prevalent malignant tumor among cancers of the head and neck. Macrophage migration inhibitory factor (MIF), an inflammatory cytokine, is positively correlated with poor prognosis in NPC patients. MIF is highly expressed in NPC cells, and their secreted exosomes can be absorbed by macrophages; MIF-rich exosomes can thus suppress ferroptosis in macrophages and thereby promote NPC metastasis [##REF##35036405##80##]. Platelets are versatile cells that are part of the pathological processes of tumor cell hematogenous metastasis [##REF##27282765##81##], and platelet-derived EVs from NPC patients upregulate integrin β3 (ITGB3) while elevating the expression of solute carrier family 7 member 11 (SLC7A11) by activating the MAPK/ERK/ATF4/Nrf2 axis and increasing protein stability. This process suppresses ferroptosis, thus facilitating the distant metastasis of NPC cells through blood circulation [##REF##36263165##82##]. Interestingly, exosomes secreted by different sources mediate intercellular communication by transferring diverse cargoes, consequently exerting a discernible influence on cancer progression. Exosomal miR-22-3p is transferred from cardiomyocytes to osteosarcoma cells, thereby aggravating tumor growth by suppressing susceptibility to ferroptosis activation in myocardial infarction [##REF##36967385##83##]. Osteosarcoma tissue-derived exosomes promote ferroptosis to inhibit osteosarcoma progression via the miR-144-3p/ZEB1 axis [##REF##37461104##84##]. Asbestos-related diseases still remain a societal burden worldwide [##UREF##11##85##]. A remote, novel mutagenic mechanism of loading iron into mesothelial cells through ferroptosis-dependent EVs (FedEVs) containing ferritin was suggested. In this scenario, macrophages that engulf asbestos generate FedEVs, and ferroptotic macrophage-derived extracellular vesicles are loaded with a high level of ferritin and are received by mesothelial cells, leading to considerable oxidative DNA damage, such as 8-OHdG generation and double-strand breakage, which ultimately cause asbestos-induced mesothelial carcinogenesis [##REF##34700146##86##].</p>", "<title>EV-mediated pyroptosis in cancers</title>", "<p id=\"Par25\">EV-mediated pyroptosis contributes to the development of various diseases. For instance, an exosome-based drug delivery system targeting CD44 loaded with forsythiaside A fights disease progression by regulating NLRP3-dependent pyroptosis [##UREF##12##87##]. EV-mediated pyroptosis influences cancer progression, and EVs can transfer specific cargoes, including drugs and bioactive molecules, to target cells, leading to pyroptotic cell death and drug resistance (Fig. ##FIG##0##1## and Table ##TAB##0##1##).</p>", "<p id=\"Par26\">Accumulating evidence suggests that therapeutic resistance to nonapoptotic RCD in cancer is closely linked to exosomes and the TME, such as hypoxia [##REF##27368101##88##, ##REF##35659268##89##]. Resistance to paclitaxel is a significant challenge in treating breast cancer. Hence, paclitaxel is ineffective for breast cancer treatment, causing a worse prognosis and even recurrence in some breast cancer patients [##REF##31891780##90##]. A recent study demonstrated that hypoxic stress facilitated exosomal gp96 production and enhanced resistance to paclitaxel in paclitaxel-sensitive breast cancer cells, transformed these cells into paclitaxel-resistant breast cancer cells, and thus initiated pyroptosis-induced cell death in CD8⁺ T cells to facilitate immune escape [##REF##34988020##91##]. Another similar study indicated that exosomal endoplasmic reticulum resident protein 44 (ERp44) derived from endoplasmic reticulum-stressed cells promotes cisplatin resistance in nasopharyngeal carcinoma, thereby mediating cell apoptosis and pyroptosis [##REF##34493236##92##].</p>", "<p id=\"Par27\">Cargoes carried by exosomes mediating pyroptosis can be potentially be used as therapeutic targets for treating different types of cancer. SIRT1, a nicotinamide adenine dinucleotide-dependent deacetylase, may be a potential target for cervical cancer therapy. Since it is highly expressed in cervical cancer due to HPV infection, it is crucial for cervical cancer progression and is even linked to poor clinical outcomes. Furthermore, SIRT1 allows HPV-infected cervical cancer cells to maintain growth levels by nullifying absent in melanoma 2 (AIM2) inflammasome-mediated immunity, and silencing SIRT1 causes these cancer cells to undergo pyroptosis regulated by EVs carrying AIM2 inflammasome proteins. [##REF##29844574##30##]. These findings indicate that cancer cell-derived EVs exert potent effects on tumor progression by inducing pyroptotic cell death, which suggests a promising approach for cancer therapy.</p>", "<title>EV-mediated necroptosis in cancers</title>", "<p id=\"Par28\">Necroptosis has a dual effect of promoting and reducing tumor growth. Emerging evidence suggests that EV-mediated necroptosis can also control the migration, proliferation, and invasion of tumor cells. RIP1 and RIP3 are essential for necroptosis, and the complex mediates death receptor-dependent necroptosis [##REF##31122251##78##], Exosomal miRNAs cause necroptosis by binding and regulating RIP3. For example, in chemoresistant tumors, cotreatment with Kras-derived exosomes (circulating Kras exosomes isolated from metastatic lung cancer patients) and carboplatin induced RIP3/TNF alpha-regulated necroptosis accompanied by miR-146/miR-210 modulation in patients with metastatic lung cancer [##UREF##6##31##]. Kras-derived exosomes offer new opportunities for inhibiting metastatic neoplasia by sustaining lung immunosuppressive metabolism. Another miRNA-based therapy combinated with GW4869, an inhibitor of exosome release, has been applied in malignant pleural mesothelioma (MPM). Treatment of MPM-derived spheroids with miR-126-enriched exosomes induced antitumor effects. Treatment with exosomes enriched in miR-126 plus the inhibitor of exosome release (GW4869) led to the accumulation of miR-126 inside cells, thereby promoting necroptotic activation of MPM-stem cells [##REF##35334283##93##].</p>", "<p id=\"Par29\">The protein content of necroptotic EVs was characterized by high-throughput proteomic analyses. A study employed TNF-dependent necroptosis and apoptosis in human primary macrophages and a lymphoma cell line. The supernatants and enriched EVs were also subjected to proteomic analysis, which revealed the cell death type-specific release of cytokines as well as the underlying processes regulated during apoptosis and necroptosis [##REF##31995763##94##]. Proteomic analysis of necroptotic EVs revealed an additional regulatory mechanism during the early stage of necroptosis; this mechanism was mediated by specific EV cargoes, which reshape the tumor microenvironment and induce both adaptive and innate immune responses [##REF##34750357##95##].</p>", "<p id=\"Par30\">Further research is needed regarding the necroptotic pathways to establish their molecular mechanism as well as the relationship between downstream and upstream signaling molecules of cell death signaling pathways. This would also help researchers to explore its dual role in bilateral communication and to identify relevant targeted drugs to enhance the effect of tumor therapies.</p>", "<title>Targeting EV-regulated RCD for cancer therapy</title>", "<p id=\"Par31\">Chemotherapy, radiotherapy, surgery, and immunotherapy are the main therapeutic strategies applied to tumor treatment. Therapeutic advances in cancer immunotherapy have rapidly emerged in the past few years [##REF##31940268##96##]. The use of conventional therapy in conjunction with RCD modulators might hold significant potential for cancer treatment. EV-mediated ferroptosis is a part of tumor resistance and T-cell immunity [##REF##31424364##97##–##REF##31043744##99##]. Thus, the development of therapeutic strategies combining ferroptosis inducers with exosomal inhibitors is a promising avenue, and the combination of multiple drugs (e.g., GW4869, Fe³⁺) may enhance cancer immunotherapy effects. Complexes carrying tumor cell-derived exosomal PD-L1 (e.g., melanoma) suppress the activity of T cells and lead to resistance to tumor therapy [##REF##24188664##100##, ##REF##30951669##101##]. A hyaluronic acid-based nanoplatform (referred to as HGF NPs) was developed by combining a ferroptosis inducer (Fe³⁺) with an exosome inhibitor (GW4869) to induce antitumor responses in melanoma cells. GW4869 released from HGF NPs markedly inhibited tumor-derived exosome generation and exosomal PD-L1 and promoted T-cell activation. Furthermore, reactivated T cells release high levels of interferon-gamma (IFN-γ) to suppress the SLC7A11-GSH-GPX4 axis, thus facilitating the ferroptosis of melanoma cells [##REF##34593794##102##] (Fig. ##FIG##2##3##). Subsequently, semiconductor polymer assemblies encapsulating Fe³⁺ (ferroptosis inducers) and GW4869 (to block exosomal PD-L1) were used to establish phototheranostic metal-phenolic networks (PFG MPNs). PFG MPNs elicit a joint photothermal treatment with exosome-dependent immunotherapy, revitalizing T cells by antagonizing exosomal PD-L1-regulated suppression and boosting ferroptosis in cancer cells to evoke strong antitumor immunity in melanoma cells [##REF##34985903##103##]. These findings demonstrated that the combination of ferroptosis inducers and exosome inhibitors in tumor therapy strategies has considerable prospects for clinical application.</p>", "<p id=\"Par32\">Some compounds or drugs, such as artesunate, erastin, lycorine, FINO2, and altretamine, stimulate the ferroptosis in tumor cells [##REF##35963853##104##]. Transporting these drugs through EVs to induce ferroptosis may be more effective than free drugs. Recent studies have revealed that artificially engineered exosomes hold extensive therapeutic potential in several cancers [##REF##30452238##105##–##UREF##13##107##]. For example, exosomes targeting ferroptosis might be modified via folic acid (FA) and then used for clinical applications. Such exosomes containing the ferroptosis inducer erastin (erastin@FA-exo) confer antitumor effects by targeting folate receptor-overexpressing triple-negative breast cancer cells. Compared to free erastin, erastin@FA-exo increased the rate of erastin uptake in MDA-MB-231 cells and initiated ferroptosis by suppressing system X_c⁻ [##REF##31464035##108##]. Exosomal targeting of ferroptosis in combination with photodynamic therapy and immune modification efficiently induces antitumor effects in hepatocellular cancer (HCC) cells [##REF##34373736##109##]. Moreover, modified mesenchymal stem cell-derived exosomes induce ferroptosis in cancer cells by delivering several therapeutic agents including clinical drugs, specific siRNAs and miRNAs [##REF##37781038##110##–##REF##37777559##112##]. Engineered exosome-based treatment has also been employed in a clinical trial. EVs have been used as a vaccine adjuvant to trigger a powerful anticancer response and hence to enhance the effects of cancer immunotherapy [##UREF##15##113##]. Hu et al. developed fibroblast activation protein-α (FAP) gene–engineered tumor cell-derived exosome-like nanovesicles (eNVs-FAP) as tumor-based vaccines that inhibited tumor growth by remodeling the tumor microenvironment and promoting tumor cell ferroptosis [##REF##34506976##114##].</p>", "<p id=\"Par33\">It is now a matter of urgency to determine how to effectively use novel EV-mediated pyroptosis technology to develop new antitumor immunity schemes, improve specificity and efficiency, reduce chemotherapy resistance, and ensure safety [##REF##35963853##104##]. For example, a recent study employed cancer cell-based exosomes to supply metformin (an AMPK agonist) and POM1 (a CD39 antagonist) for targeted cancer treatment. Targeting the ATP-adenosine pathway via pharmacologically blocked of CD39 and activation of AMPK facilitates the accumulation of pro-inflammatory extracellular ATP (eATP) and reduces immunosuppressive adenosine levels. High eATP levels induce the P2X7-NLRP3 inflammasome to cause macrophage pyroptosis, which potentiates the antigen capacity and maturation of DCs to improve the cytotoxic function of natural killer cells and T cells. C-PMet-mediated immunometabolic treatment can elicit synergistic antitumor immune responses to suppress cancer progression, metastasis, and recurrence and eventually overcome anti-PD1 resistance [##UREF##16##115##] (Fig. ##FIG##3##4##). Overall, it is an innovative strategy to promote the application of eATP-dependent antitumor immunity in cancer treatment.</p>", "<p id=\"Par34\">Due to their high biocompatibility and strong bioactivity, sEVs act as a promising tool for therapeutic delivery strategies in cancer therapy. sEV-mediated delivery shows enhanced capacity to penetrate across biological barriers and through tumor blood vessels to accumulate at tumor sites, which greatly improves their therapeutic efficacy. A variety of compounds or drugs have been combined with EVs to develop efficient targeted cancer cell death treatments in numerous preclinical studies. Therefore, modified, engineered, and designer EVs represent a new development trend in this field, and these EVs could be of great clinical value if optimized and integrated properly.</p>" ]

[ "<title>Acknowledgements</title>", "<p>This work was supported by the following research grants from the National Foreign Experts Program of China (DL2023027001L); the Joint NCIS and NUS Cancer Program Seed Funding Grants [NUHSRO/2020/122/MSC/07/Cancer] (BG and LW) and the Singapore Ministry of Health’s National Medical Research Council [NMRC/CNIG/1146/2016, LW].</p>", "<title>Author contributions</title>", "<p>YCY and QJ collected the related paper and drafted the manuscript. YCY and KPY prepared the figures. LW helped to revise the manuscript. ZM acted as lead contact to conceive the review article. ZM, GS and LW designed the review and provided supervision. All authors read and approved the final manuscript.</p>", "<title>Competing interests</title>", "<p id=\"Par38\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>The emerging roles of EV-mediated non-apoptotic RCD in cancer.</title><p>EVs transfer a wide range of key regulators to mediate diverse types of cell deaths, including ferroptosis, pyroptosis, and necroptosis, which promote or inhibit tumor development and progression. AIM2 absent in melanoma 2; ANGPTL4 angiopoietin-like 4; cir93 circRNA_101093; ERp44 endoplasmic reticulum resident protein 44; eNVs-FAP exosome-like nanovesicles fibroblast activation protein; FA folic acid; GI cancers gastrointestinal cancers; HCC hepatocellular cancer; ITGB3 integrin β3; MPM malignant pleural mesothelioma; MTTP microsomal triglyceride transfer protein; MIF macrophage migration inhibitory factor; NPC nasopharyngeal carcinoma; PD-L1 programmed cell death-ligand 1.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>EVs transfer various cargoes to induce ferroptosis in cancer.</title><p>Various cell-derived EVs transfer various cargoes (e.g., miR-522, lncFERO, ferritin) to recipient cells to promote or inhibit ferroptosis by affecting ferroptotic signal transduction in various cancers. AA arachidonic acid, ALOX15 arachidonate 15-lipoxygenase, CAFs cancer-associated fibroblasts, cir93 circRNA_101093, GC gastric cancer, FSP1 ferroptosis suppressor protein 1, FABP3 fatty acid-binding protein 3, PUFAs polyunsaturated fatty acids, hnRNPA1 heterogeneous nuclear ribonucleoprotein A1, m6A N6-methyladenosine, METTL3 methyltransferase-like 3, NSCLC non-small cell lung cancer, ROS reactive oxygen species, SCD1 stearoyl-CoA-desaturase 1, USP7 ubiquitin-specific protease 7.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>HGF NPs act with anti-exosomal PD-L1 to reverse immune suppression and enhance ferroptosis.</title><p><bold>A</bold> Schematic illustration of HGF-relevant preparation and therapeutic strategy. <bold>B</bold> Scheme of in vivo experiments and western blot analysis of the exosome markers CD63 and PD-L1 in tumor tissues after treatment. <bold>C</bold> IFN-γ level and relative levels of cystine (Cys)/GSH and GPX4 activity in tumors after treatment. <bold>D</bold> Tumor growth curves during treatment. <bold>E</bold> Flow cytometric analysis of memory T cells (CD44^highCD62^low, gating on CD3⁺CD8⁺ T cells) in the spleen. Adapted with permission from [##REF##34593794##102##]; copyright 2021, Springer Nature.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Extracellular ATP-driven antitumor immunity remodels energy metabolism and triggers macrophage pyroptosis.</title><p><bold>A</bold> Schematic illustration of antitumor immune responses induced by C-PMet-based immunometabolic therapy. <bold>B</bold> Schematic illustration of immune regulation induced by POM1 and metformin. <bold>C</bold> Schematic illustration of the therapeutic schedule to inhibit tumor lung metastasis. <bold>D</bold> Primary and distant tumor growth curves after the indicated treatments and representative lung photographs. <bold>E</bold> Flow cytometric analysis of memory T cells (CD44^highCD62^low, gating on CD3⁺ CD8⁺ T cells) in the spleen. Adapted with permission from [##UREF##16##115##]; copyright 2022, John Wiley &amp; Sons, Inc.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>The roles of EV-mediated ferroptosis, pyroptosis, and necroptosis in cancers.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Cancer type</th><th>Source cell</th><th>Cargo</th><th>Role in cell death</th><th>Functions</th><th>Ref.</th></tr></thead><tbody><tr><td colspan=\"6\"><italic>EVs in ferroptosis</italic></td></tr><tr><td>Gastric cancer</td><td>CAFs</td><td>miR-522</td><td>Inhibit</td><td>Inhibits ferroptosis and enhances acquired chemoresistance</td><td>[##REF##32106859##29##]</td></tr><tr><td>Gastric cancer</td><td>GC cell</td><td>lncFERO</td><td>Inhibit</td><td>Suppresses ferroptosis in GCSCs and reduces chemosensitivity of gastric tumors</td><td>[##REF##34845198##72##]</td></tr><tr><td>Gastric cancer</td><td>CAFs</td><td>DACT3-AS1</td><td>Induce</td><td>Enhances the transformation of malignant masses and ferroptosis-mediated resistance to oxaliplatin in gastric cancer</td><td>[##REF##36764075##73##]</td></tr><tr><td>Gastric cancer</td><td>Human umbilical cord-derived adipose-derived mesenchymal stem cells</td><td>miR-149-5p and siRNA</td><td>Induce</td><td>Enhances GC cells ferroptosis via inhibition of MKL-1 expression</td><td>[##REF##37781038##110##]</td></tr><tr><td>Non-small cell lung cancer</td><td>NSCLC tumor tissue</td><td>miR-4443</td><td>Inhibit</td><td>Promotes resistance to cisplatin by regulating FSP1 m6A</td><td>[##REF##33781830##58##]</td></tr><tr><td>Non-small cell lung cancer</td><td>NSCLC cell</td><td>ANGPTL4</td><td>Inhibit</td><td>Angiopoietin-like 4-mediated radioresistance of lung cancer by suppressing ferroptosis under hypoxicmicroenvironment</td><td>[##REF##36050447##67##]</td></tr><tr><td>Lung adenocarcinoma</td><td>LUAD cell</td><td>circRNA_101093 (cir93)</td><td>Inhibit</td><td>Specifically desensitizes LUAD cells to ferroptosis and attenuates lipid peroxidation</td><td>[##UREF##7##59##]</td></tr><tr><td>Colorectal Cancer</td><td>Adipocyte</td><td>MTTP</td><td>Inhibit</td><td>Inhibits ferroptosis and promotes chemoresistance in colorectal cancer</td><td>[##UREF##10##77##]</td></tr><tr><td>Breast cancer</td><td>Breast carcinoma cells</td><td>Prominin2</td><td>Inhibit</td><td>Drives ferroptosis resistance</td><td>[##REF##31735663##6##]</td></tr><tr><td>Triple-negative breast cancer</td><td>HFL‐1 cells</td><td>erastin@FA-exo</td><td>Induce</td><td>Inhibits expression of glutathione peroxidase 4 and upregulation of cysteine dioxygenase</td><td>[##REF##31464035##108##]</td></tr><tr><td>Mesothelioma</td><td>Macrophage</td><td>Ferritin</td><td>Induce</td><td>Promotes asbestos-induced mesothelial carcinogenesis</td><td>[##REF##34700146##86##]</td></tr><tr><td>Pancreatic ductal adenocarcinoma</td><td>PDAC cells</td><td>KRAS^G12D</td><td>Induce</td><td>Inhibits of the release of KRAS^G12D from tumor cells</td><td>[##REF##31920150##117##]</td></tr><tr><td>Pancreatic ductal adenocarcinoma</td><td>CAFs</td><td>miR-3173-5p</td><td>Inhibit</td><td>CAFs inhibit ferroptosis and induce gemcitabine resistance in pancreatic cancer cells by secreting exosome-derived ACSL4-targeting miR-3173-5p</td><td>[##UREF##9##74##]</td></tr><tr><td>Nasopharyngeal carcinoma</td><td>NPC cells</td><td>MIF</td><td>Inhibit</td><td>Promotes metastasis by inhibiting the ferroptosis of macrophages</td><td>[##REF##35036405##80##]</td></tr><tr><td>Nasopharyngeal carcinoma</td><td>Platelet</td><td>ITGB3</td><td>Inhibit</td><td>Inhibits ferroptosis and enhances distant metastasis of nasopharyngeal carcinoma</td><td>[##REF##36263165##82##]</td></tr><tr><td>Osteosarcoma</td><td>Osteosarcoma tissue</td><td>miR-144-3p</td><td>Induce</td><td>Promotes ferroptosis to inhibit osteosarcoma progression via the miR-144-3p/ZEB1 axis</td><td>[##REF##37461104##84##]</td></tr><tr><td>Osteosarcoma</td><td>Cardiomyocytes</td><td>miR-22-3p</td><td>Induce</td><td>Aggravating tumor growth by suppressing the susceptibility to ferroptosis activation in myocardial infarction</td><td>[##REF##36967385##83##]</td></tr><tr><td>Osteosarcoma</td><td>Bone marrow mesenchymal stem cells</td><td>capreomycin</td><td>Induce</td><td>Induced ferroptosis of osteosarcoma cells via the Keap1/Nrf2/GPX4 axis</td><td>[##UREF##14##111##]</td></tr><tr><td>Melanoma</td><td>B16F10 tumors</td><td>PD-L1</td><td>Induce</td><td>Enhances ferroptosis for synergistic immunotherapy</td><td>[##REF##34985903##103##]</td></tr><tr><td>Melanoma</td><td>Melanoma cells</td><td>PD-L1</td><td>Induce</td><td>Reverses immune suppression and enhances ferroptosis</td><td>[##REF##34593794##102##]</td></tr><tr><td>Hepatocellular cancer</td><td>HEK293T</td><td>CD47, Erastin, and Rose Bengal</td><td>Induce</td><td>Induces obvious ferroptosis in HCC with minimized toxicity in the liver and kidney</td><td>[##REF##34373736##109##]</td></tr><tr><td>Hepatocellular cancer</td><td>Human adipose mesenchymal stem cells</td><td>miR-654-5p</td><td>Induce</td><td>Enhances sorafenib-induced ferroptosis of HCC cells via the miR-654-5p/HSPB1 axis</td><td>[##REF##37777559##112##]</td></tr><tr><td>Colon, lung, melanoma, and breast cancer</td><td>Tumor cells</td><td>FAP gene-engineered (eNVs-FAP)</td><td>Induce</td><td>eNVs-FAP vaccine-induced immune responses could stimulate tumor ferroptosis by releasing IFN-γ from cytotoxic T lymphocyte and decreasing the levels of FAP +CAFs</td><td>[##REF##34506976##114##]</td></tr><tr><td colspan=\"6\"><italic>EVs in pyroptosis</italic></td></tr><tr><td>Melanoma</td><td>B16F10 cells</td><td>POM1 and C-PMet</td><td>Induce</td><td>Remodels energy metabolism for initiating the adaptive and innate immune systems</td><td>[##UREF##16##115##]</td></tr><tr><td>Cervical cancer</td><td>SiHa cells</td><td>AIM2 inflammasome proteins</td><td>Inhibit</td><td>SIRT1-knockdown-derived EVs inhibit the growth of cervical cancer xenografts through the activation of AIM2 inflammasome</td><td>[##REF##29844574##30##]</td></tr><tr><td>Breast cancer</td><td>Paclitaxel-resistant breast cancer cells</td><td>gp96</td><td>Induce</td><td>Increases resistance to paclitaxel and promotes immune evasion in breast cancer</td><td>[##REF##34988020##91##]</td></tr><tr><td>Nasopharyngeal carcinoma</td><td>ER-stressed cells</td><td>ERp44</td><td>Inhibit</td><td>Strengthens cisplatin resistance of nasopharyngeal carcinoma</td><td>[##REF##34493236##92##]</td></tr><tr><td><italic>EVs in necroptosis</italic></td><td/><td/><td/><td/><td/></tr><tr><td>Lung cancer</td><td>KrasLung tumor samples</td><td>miR-146/miR-210</td><td>Inhibit</td><td>Downregulates immunosuppressive BACH2/GATA-3 expression through RIP-3-dependent necroptosis and miR-146/miR-210 modulation</td><td>[##UREF##6##31##]</td></tr><tr><td>Malignant pleural mesothelioma</td><td>MPM cells</td><td>miR-126</td><td>Induce</td><td>miR-126 accumulation induces protective autophagy, and the suppression of this process by GW4869 gives rise to a metabolic crisis that favors necroptosis</td><td>[##REF##35334283##93##]</td></tr></tbody></table></table-wrap>" ]

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[ "<table-wrap-foot><p><italic>ACSL4</italic> acyl-CoA synthetase long-chain family member 4, <italic>ANGPTL4</italic> angiopoietin-like 4, <italic>AIM2</italic> absent in melanoma 2, <italic>CAFs</italic> cancer-associated fibroblasts, <italic>cir93</italic> circRNA_101093, <italic>EVs</italic> extracellular vesicles, <italic>ERp44</italic> endoplasmic reticulum resident protein 44, <italic>eNVs-FAP</italic> exosome-like nanovesicles fibroblast activation protein, <italic>GC</italic> gastric cancer, <italic>GCSCs</italic> gastric cancer stem cells, <italic>HCC</italic> hepatocellular cancer, <italic>IFN-γ</italic> interferon gamma, <italic>ITGB3</italic> integrin β3, <italic>LUAD</italic> lung adenocarcinoma, <italic>m6A</italic> N6-methyladenosine, <italic>MPM</italic> malignant pleural mesothelioma, <italic>MTTP</italic> microsomal triglyceride transfer protein, <italic>MIF</italic> macrophage migration inhibitory factor, <italic>NSCLC</italic> non-small cell lung cancer, <italic>NPC</italic> nasopharyngeal carcinoma, <italic>PDAC</italic> pancreatic ductal adenocarcinoma cell, <italic>PD-L1</italic> programmed cell death-ligand 1, <italic>RIP</italic> receptor interacting protein, <italic>SIRT1</italic> sirtuin 1.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Yi-Chi Yang, Qian Jiang.</p></fn></fn-group>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par3\">All United Nation (UN) member states have implemented 17 Sustainable Development Goals (SDGs) in pursuit of peace and prosperity for all people and the planet^{##UREF##0##1##,##REF##35990172##2##}. The three main pillars of sustainability—economy, society, and environment—encompassed these goals. Sustainability is often approached from two perspectives: weak and strong sustainability^{##UREF##1##3##}. Weak sustainability posits that each of these pillars holds equal weight and that the pillars are interchangeable^{##UREF##1##3##,##UREF##2##4##}. Strong sustainability prioritises the environmental pillar^{##UREF##1##3##,##UREF##2##4##}. However, recent research has introduced a new perspective on sustainable development: integrated sustainability^{##UREF##2##4##–##UREF##4##6##}. This concept extends beyond traditional weak and strong sustainability perspectives and incorporates the spillover effects generated by the transboundary interactions across regions as a fourth pillar, alongside the original three pillars^{##UREF##4##6##}. These spillover effects represent the interplay of the three original pillars of sustainable development between two or more regions^{##UREF##3##5##,##UREF##5##7##}. In the current interconnected world, transboundary interactions across countries may positively or negatively affect SDGs in various other countries^{##UREF##6##8##}. Global sustainable development cannot be achieved by countries that act alone. Communication between countries can promote interdisciplinary programs and multilateral collaborations, help policymakers formulate coherent plans and strategies, and effectively unlock transboundary SDG interaction potential^{##REF##25722418##9##}.</p>", "<p id=\"Par4\">Widespread interactions exist between SDGs across country borders^{##UREF##0##1##,##UREF##6##8##,##UREF##7##10##–##REF##34983933##13##}, such as technological spillovers from multinational corporations and profits from international trade. These transboundary synergies may help receiving countries achieve their SDGs^{##UREF##10##14##}. Conversely, there may also be transboundary trade-offs, such as wastewater flow into transboundary rivers, which may hamper the achievement of SDGs in countries receiving wastewater^{##UREF##11##15##–##UREF##13##17##}. However, little attention has been paid to determining the impacts of these transboundary interactions on SDGs^{##UREF##14##18##}. Quantifying transboundary SDG interactions is challenging because countries are connected through different transmission channels, and the outcomes of transboundary SDG interactions can vary^{##UREF##15##19##–##REF##28358094##21##}. Regarding human-caused flows, a common channel of transboundary SDG interactions is international trade^{##UREF##17##22##}, which may have environmental and socioeconomic impacts on trade partners owing to the water^{##REF##22474363##23##,##REF##25583516##24##}, carbon^{##REF##21518879##25##}, and labour used to produce goods and embodied in trade^{##UREF##18##26##} (Fig. ##FIG##0##1a##). Additionally, nature-caused flows connect many countries (Fig. ##FIG##0##1b##). For instance, under uncontrolled pollution conditions, air and wind may transport airborne pollutants into neighbouring countries^{##UREF##19##27##} or even to distant countries through intercontinental transport^{##REF##28358094##21##,##UREF##20##28##,##UREF##21##29##}, thereby compromising air quality and human health in receiving countries^{##UREF##20##28##}. Furthermore, pollutants discarded in waterways affect local communities and neighbouring countries.</p>", "<p id=\"Par5\">This study investigates integrated sustainability in the context of the SDGs to determine whether each SDG indicator exerts positive or negative effects on the others and to quantify these effects. A conceptual framework incorporating different channels of transboundary SDG interactions was first proposed. This framework was built based on metacoupling (e.g., human–nature interactions within and between neighbouring and distant countries)^{##UREF##22##30##}, as shown in Fig. ##FIG##0##1##. This study classified these channels into two broad categories, each of which interacted with the performance of the SDGs of other countries in different ways: human-caused flows (e.g., international trade) and nature-caused flows (e.g., river flow, ocean currents, and air flow) (Fig. ##FIG##0##1##). Second, this study examined 768 pairs of SDG indicators to evaluate how an individual SDG indicator of a country interacts with other countries’ indicators through different channels^{##UREF##23##31##–##UREF##24##33##}. The pairs of indicators were identified as having causal relationships (e.g., energy intensity and CO₂ emission intensity indicators as the interaction generator and receiver, respectively), which can be derived from a database about SDG interactions^{##UREF##6##8##} (Supplementary information Tables ##SUPPL##0##S1## and ##SUPPL##0##S2##). Finally, this study proposed a spatial interaction index to quantify the overall magnitude of transboundary interactions between the performance of the SDGs in one country and those in other countries. This index can be divided into transboundary synergistic and trade-off effects and is a scorecard (score: 0–100) used to indicate the magnitude of transboundary interactions. Based on available data for 2010 to 2020, 121 countries were chosen for analysis (Supplementary information Table ##SUPPL##0##S3##). The findings of this study can aid in improving the understanding, monitoring, and careful management of transboundary SDG interactions.</p>" ]

[ "<title>Methods</title>", "<title>SDG indicator selection and data sources</title>", "<p id=\"Par18\">There are 17 SDGs with 169 targets and 231 unique indicators within the global indicator framework^{##UREF##0##1##}. This study chose the years 2010–2020 and 121 countries for analysis based on the best available data. A list of the 121 countries was included in this study (Supplementary information Table ##SUPPL##0##S3##). This study included 55 indicators constructed using robust data and applied to a broad range of countries (Supplementary information Table ##SUPPL##0##S1##). These 55 indicators were selected from the Indicators and Monitoring Framework for the Sustainable Development Goals developed by the UN Sustainable Development Solutions Network, the UN Global Indicator Framework for Sustainable Development Goals developed by the IAEG-SDGs, and some published studies^{##UREF##40##53##,##REF##31894145##54##}. The values of these indicators ranged from 0 (worst performance) to 100 (best performance)^{##REF##35990172##2##,##REF##31894145##54##}.</p>", "<title>Transboundary SDG interactions across countries</title>", "<p id=\"Par19\">This study proposed four interconnected steps to evaluate how SDG indicators interact with indicators across countries through different transmission channels.</p>", "<title>Step 1: Match SDG indicator pairs with causal relationships</title>", "<p id=\"Par20\">This study first determined whether there was a causal relationship between the SDG indicator pairs. Based on the 55 SDG indicators, 768 SDG indicator pairs showing potential causal relationships were identified, derived from an interactive repository of SDG interactions^{##UREF##6##8##} (Supplementary information Table ##SUPPL##0##S2##). By conducting a systematic literature review (65 global scientific assessments and UN flagship reports and 112 relevant scientific articles), this interactive repository recorded causal relationships across SDG targets covering the 17 SDGs^{##UREF##6##8##}. Based on the following steps, this study further quantitatively verified whether the 768 SDG indicator pairs exhibited interactions between different countries through a variety of channels.</p>", "<title>Step 2: Construct spatial weight matrices for different channels of transboundary SDG interactions</title>", "<p id=\"Par21\">Many channels connect two or more countries. This study divided these channels into human-caused and nature-caused flows (Fig. ##FIG##0##1##). This study used a spatial weight matrix (<italic>W</italic>) with diagonal elements equal to zero to represent each channel, as shown in the following equation:where indicates the weight between country <italic>i</italic> and country <italic>j</italic>. <italic>N</italic> represents the total number of countries. The channels of transboundary SDG interactions with respect to international trade in year <italic>t</italic> were constructed based on multiregional input–output (MRIO) tables , and MRIO tables from years 2010 to 2020 were obtained from the Eora26 database^{##REF##22794089##55##,##UREF##41##56##}. Several other MRIO databases exist, including EXIOBase3, WIOD, and GTAP; however, this study chose Eora26 because it has a higher country coverage (189 countries) and can provide the most up-to-date MRIO tables^{##REF##22794089##55##,##UREF##41##56##}. The value-added of international trade between one country and another is indicated in each cell of the trade weight matrix (unit: USD).</p>", "<p id=\"Par22\">This study divided the transboundary nature-caused flows into three categories: river flow, ocean currents, and air flow, as follows:</p>", "<p id=\"Par23\">(1) River flow channel : When a transboundary river crosses these countries, some water-related SDG indicators from different countries can be linked through river flow. SDG 6 relates to clean water and sanitation; therefore, 102 indicator pairs related to SDG 6 were assumed to be connected via river flow channels (Supplementary information Table ##SUPPL##0##S2##). Global geographical information of the rivers was derived from the HydroSHEDS database at a resolution of 15 arc-seconds^{##UREF##42##57##,##UREF##43##58##}. The database displays over eight million river reaches worldwide, with more than 120,000 being the most downstream reaches of connected river basins^{##UREF##42##57##,##UREF##43##58##}. These were used to identify the entire river network belonging to this basin and determine which countries share the entire river network^{##UREF##42##57##,##UREF##43##58##}. The results revealed 2126 transboundary rivers worldwide. Subsequently, a weight matrix was constructed, with each cell indicating the aggregation of river flow between the two countries. To calculate this, this study added the average long-term discharge estimates of all river reaches between the two countries, which were obtained from the HydroSHEDS database^{##UREF##42##57##,##UREF##43##58##}. The unit of the matrix was cubic meters per second. Greater river flow between the two countries indicates a stronger connection.</p>", "<p id=\"Par24\">(2) Ocean current channel : Some SDG indicators in one country may be influenced by some ocean-related SDG indicators in countries with which they share sea areas. SDG 14 is related to the preservation and sustainable exploitation of oceans, seas, and their resources to foster sustainable development; thus, the 45 indicator pairs related to SDG 14 in coastal countries were assumed to be linked via ocean current channels (Supplementary information Table ##SUPPL##0##S2##). Only coastal countries were included in the evaluation of indicators under SDG 14 (life below water). To construct a weight matrix for ocean currents across coastal countries, this study first excluded inland countries based on the Central Intelligence Agency World Factbook. Of the 121 countries, 91 were coastal and 30 were inland (Supplementary information Table ##SUPPL##0##S7##). Then, based on maritime boundaries, this study identified each coastal country’s neighbouring countries. The UN Conventions on the Law of the Sea defines maritime boundaries as territorial waters and contiguous and exclusive economic zones. Each matrix cell was filled with 1 or 0, indicating whether or not the two countries were linked by ocean currents.</p>", "<p id=\"Par25\">(3) Air flow channel : Some air-related indicators (target 11.6: fine particulate matter) from various countries can influence certain SDG indicators of a particular country due to the movement of air (Supplementary information Table ##SUPPL##0##S1##). In this study, a spatial weight matrix based on the inverse distance was constructed to represent the air flow connections between countries. This study calculated the distance between 121 countries based on their centroids. The transboundary SDG interactions of 36 indicator pairs related to the target 11.6 were estimated using this spatial weight matrix (Supplementary information Table ##SUPPL##0##S2##).</p>", "<p id=\"Par26\">This study is grounded in the metacoupling framework, an integrated conceptual construct examining the human–nature interplay within a coupled human–nature system, adjacent to that system and from distant locations^{##UREF##12##16##,##UREF##22##30##,##UREF##39##52##}. This framework encompasses all flow types relevant to human and natural systems. Determination of the spatial weight matrix is guided by four key criteria: (1) Relevance: The chosen transmission channel should mirror the real-world transmission mechanism of the SDG indicator. For example, water-related SDG indicators may be interlinked through transboundary rivers. Consequently, the spatial weight matrix, represented by river flows across countries, was utilised to examine the transboundary interactions of indicators related to SDG 6 (clean water and sanitation). (2) Timeliness: Transmission channels influenced by socio-economic conditions, such as international trade, are dynamic and frequently change over time. Consequently, data series must be updated regularly, published promptly, and be made available for the most recent years to accurately reflect these changes. (3) Coverage: The data must adequately define the relationships between any two countries included in the study. They should provide a comprehensive understanding of the interactions and connections between these countries, offering a broad scope that does not neglect critical relationships. (4) Data availability and quality: The transmission channel data must represent the most accurate measure of a specific issue. They should be obtained from reliable national or international sources to ensure credibility and reliability. Considering these selection criteria, this study incorporated different flow types that exist across countries: trade flows (human-caused flows), river flows, ocean currents, and air flows (nature-caused flows).</p>", "<title>Step 3: Construct row-standardised spatial weight matrices</title>", "<p id=\"Par27\">Row standardisation suggests that each spatial weight in a matrix is divided by its row sum, as shown below:where and indicate the weight between country <italic>i</italic> and country <italic>j</italic>, and the weight after row standardisation, respectively.</p>", "<title>Step 4: Quantify transboundary SDG interactions</title>", "<p id=\"Par28\">Spatial econometric models were used to explore the transboundary SDG interactions of SDG indicator pairs under different transmission channels. Endogeneity issues may arise in statistical analyses when an explanatory variable is correlated with an error term, leading to biased and inconsistent estimates. These complexities require specific techniques to ensure accurate and reliable results^{##UREF##44##59##–##UREF##48##63##}. Different techniques can be used to address the endogeneity problem^{##UREF##44##59##–##UREF##48##63##}. To deal with the endogeneity issues caused by the elements of the spatial weight matrix involving socioeconomic indicators^{##UREF##49##64##–##UREF##53##68##}, this study applied the 2SIV estimation method based on the control function method to explore the spatial spillover effects of SDG indicators in a panel dataset^{##UREF##49##64##}. The first stage was estimated using the following regression model:^{##UREF##49##64##}</p>", "<p id=\"Par29\"> denotes the trade flow in country <italic>i</italic> at period <italic>t</italic>. <bold>γ</bold> is a vector of the coefficients of explanatory variables. <bold>X</bold>_{<bold>1it</bold>} is a list variables measuring the economy, population, government effectiveness, access to the internet, performance of export sectors, and technological level of country <italic>i</italic>^{##UREF##54##69##} (Supplementary information Table ##SUPPL##0##S5##). Based on the residual from the first-step estimation, this study considered the following model for the second-stage estimation:^{##UREF##49##64##}</p>", "<p id=\"Par30\"> and are a pair of SDG indicators that were determined in Step 1, which respectively indicate the interaction receiver <italic>m</italic> and generator <italic>n</italic>. is the scale coefficient. is the spatial coefficient which can be used to measure the transboundary SDG interactions under the transmission channel of international trade. is a spatial weight matrix related to international trade between country <italic>i</italic> and country <italic>j</italic> in year <italic>t</italic>. <bold>β</bold> is a vector of coefficient of the explanatory variables. <bold>X</bold>_{<bold>2it</bold>} denotes the explanatory variables (Supplementary information Table ##SUPPL##0##S6##). The positive variables were transformed by taking their natural logarithms in the spatial dynamic panel data model.</p>", "<p id=\"Par31\">Multiple transmission channels could operate simultaneously^{##UREF##55##70##–##UREF##58##73##}. Indicators related to SDG 6 (clean water and sanitation), SDG 14 (life below water), and SDG target 11.6 (fine particulate matter) could be affected both through international trade and nature-caused flows (transboundary river flow, ocean currents, and air flow). This study employed higher-order spatial econometric models to account for real-world complexity. These models can incorporate more than one spatial weight matrix and, thus, characterise various types of spatial dependence. Spatial weight matrix was specifically utilised to represent channels related to nature-caused flows. <italic>λ</italic>₂ is a spatial coefficient used to evaluate transboundary SDG interactions under the transmission channel of nature-caused flows.</p>", "<title>Creating the spatial interaction index and its decomposition</title>", "<p id=\"Par32\">Domestic actions aimed at achieving SDGs may result in transboundary interactions with other countries. This study proposed a spatial interaction index to quantify the overall magnitude of transboundary interactions across all transmission channels. As the spatial coefficients (both and ) of the same explained variable (SDG indicator) from Step 4 were comparable, this study summed the absolute values of any coefficients (both positive and negative coefficients) that were significant at the 10% level or above. This provided a total impact measure of transboundary interactions on a specific SDG indicator. Subsequently, min–max normalisation was performed on each total impact value to determine the interaction magnitude of each SDG indicator. This standardisation process scaled the values to a uniform range of 0 to 100. Bringing comparable transboundary interactions onto a unified scale allowed for an easy assessment of the relative influence across different SDG indicators. Finally, the arithmetic average of all the standardised values was calculated to derive the overall spatial interaction index. Ranging from 0 to 100, a higher spatial interaction index implied stronger transboundary interactions between countries.</p>", "<p id=\"Par33\">The spatial interaction index can be divided into four distinct components: synergistic effects through nature-caused flows, trade-off effects through nature-caused flows, synergistic effects via human-caused flows, and trade-off effects via human-caused flows. First, the interaction magnitudes of the four components for each SDG indicator were determined. This was accomplished by multiplying the interaction magnitude of each SDG indicator (on a scale of 0–100) by the respective percentage shares of these components. We obtained these percentage shares from the absolute values of coefficients that were significant and calculated them as a proportion of the total sum. Subsequently, the components of the spatial interaction index were obtained by computing the arithmetic average of the interaction magnitudes for each component across all SDG indicators. This approach allows for a more nuanced understanding of the different factors contributing to transboundary SDG interactions.</p>", "<p id=\"Par34\">Using SDG indicator 7.1.1 (access to electricity) as an example, this study analysed the magnitude and direction of impacts on a country’s performance in achieving indicator 7.1.1 from progress on SDG indicators in other countries. In Step 1, it was identified that the achievement of indicator 7.1.1 could be influenced by indicator 6.4.1 (water use efficiency) and indicator 7.3.1 (energy intensity). Spatial weight matrices were constructed to represent connections between countries through river basins and trade networks. Subsequently, this study row-standardised the weight matrices. This normalisation process prepared the data for spatial econometric modelling. The last step involved using spatial econometric models to calculate the spatial coefficients. These coefficients (both and ) indicated the direction and magnitude of transboundary interactions on indicator 7.1.1 outcomes in the focal country, respectively. If both coefficients were significant at least 10%, the study would sum their absolute values and standardised this total into a single index from 0 to 100. This example shows how the performance of indicator 7.1.1 in focal countries could be influenced by other countries’ progress on indicator 6.4.1, through shared river flows powering hydropower, and indicator 7.3.1, through energy used in internationally traded goods and services.</p>", "<title>Transboundary interaction by income group</title>", "<p id=\"Par35\">This study divided 121 countries into four groups based on the World Bank country classification by income level (2022–2023) (Supplementary information Table ##SUPPL##0##S4##). Income level was measured as gross national income per capita in current USD values. Subsequently, this study compared the transboundary interactions exerted by each income group. This was achieved by constructing an updated spatial weight matrix. In this revised matrix, each row retained the value of countries belonging to a specific income group, while all other values were set to zero. Following this, Steps 3 and 4 were replicated by employing the proposed spatial interaction index to contrast the magnitude of SDG interactions across different income brackets. In this analysis, the focus was strategically directed toward the trade-related transboundary interactions of these four income groups rather than interactions facilitated by nature-caused flows. The unique nature of the sparse spatial weight matrix of ocean currents and river flows presents an intriguing challenge for quantifying transboundary interactions using spatial econometric models, which has opened new avenues for future exploration.</p>", "<title>Transboundary SDG interactions with neighbouring and non-neighbouring countries</title>", "<p id=\"Par36\">Transboundary SDG interactions between neighbouring and non-neighbouring countries may vary^{##UREF##12##16##,##UREF##35##47##}. In this study, neighbouring countries refer to countries with a common vertex, land boundary, or maritime boundary, whereas non-neighbouring countries indicate countries without any common vertex, land boundary, or maritime boundary^{##UREF##12##16##}. is a spatial weight matrix related to neighbouring countries. Each element of was filled with 1 or 0, indicating whether or not the two countries were neighbours. For the common vertex or land boundary, neighbours were identified based on a queen-contiguity-based spatial weight matrix . For the common marine boundary, neighbours were identified based on . The spatial weight matrices related to non-neighbouring countries can be obtained after excluding the neighbouring countries of each country. This study then repeated Steps 3 and 4 and used the proposed spatial interaction index to compare the SDG interaction magnitude in non-neighbouring countries to that in neighbouring countries.</p>", "<p id=\"Par37\">It is essential to acknowledge that the definitions of neighbouring and distant regions are subject to contextual variations, and there is no universally recognised measure that unequivocally designates a region as neighbouring or distant^{##UREF##59##74##}. In certain research endeavours that seek to investigate the impacts of channels closely related to distance, distant regions can be identified through the application of various distance thresholds, thereby facilitating a more comprehensive understanding of the subject matter. To gain further insight, future studies should compare the impacts of transboundary interactions using different distance thresholds to distinguish between neighbouring and distant regions.</p>" ]

[ "<title>Results</title>", "<title>Transboundary SDG interaction linkages across countries</title>", "<p id=\"Par6\">Through the transmission channels of both international trade and nature-caused flows (incorporating river flow, ocean currents, and air flow), the transboundary synergistic linkages were more pronounced than their trade-off counterparts. Specifically, amongst the transboundary linkages, which include synergistic and trade-off linkages, 73.68% of the linkages resulting from international trade were synergistic (Fig. ##FIG##1##2a, b##). Similarly, 81.82% of linkages originating form nature-caused flows were synergistic (Fig. ##FIG##1##2c, d##). These results also highlight that, compared with interaction linkages resulting from nature-caused flows, linkages originating from international trade were generally more susceptible to counterproductive effects, potentially undermining joint efforts towards the SDGs. To provide further clarity, within the sphere of international trade, trade-off linkages accounted for 26.32% (calculated as 100–73.68%) of the total SDG interaction linkages (Fig. ##FIG##1##2a, b##). This percentage is notably higher than the 18.18% (calculated as 100–81.82%) associated with nature-caused flows, as shown in Fig. ##FIG##1##2c, d##.</p>", "<p id=\"Par7\">In the international trade channel, indicators related to target 7.1 (to ensure universal access to affordable, reliable, and modern energy services) had the most (29) linkages with the SDG indicators in other countries (Fig. ##FIG##1##2a, b##). These indicators were linked to various basic human needs and the environment in other countries, such as basic drinking water and sanitation services (four linkages with target 1.4), agricultural productivity (two linkages with target 2.3), water-use efficiency (two linkages with target 6.4), housing (three linkages with target 11.1), and biodiversity (two linkages with target 15.5) (Fig. ##FIG##1##2a, b##). For instance, via the channel of international trade, the spatial lag term of target 7.1 proved to be both significant and positive in Table ##TAB##0##1##. This implies that the achievement of target 6.4 in certain countries could be promoted by synergistic effects stemming from the progress their trade partners have made towards target 7.1. This extensive network of linkages may be primarily attributed to the fundamental role of energy in many sectors. The production, distribution, and consumption of energy through international trade can have far-reaching transboundary impacts on various aspects of society and the environment.</p>", "<p id=\"Par8\">In the channel of nature-caused flows, the SDG indicator that affected the most SDG indicators in other countries was related to target 6.6. (protect and restore water-related ecosystems) (Fig. ##FIG##1##2c, d##). Attempts to improve the performance of target 6.6 in interconnected countries may interact with the performance of 19 SDG indicators in focal countries (Fig. ##FIG##1##2c, d##). For example, the spatial lag of term of target 6.6 (river flow) is 0.094, with significance at the 1% level (Table ##TAB##0##1##), suggesting the progress of SDG 1.4 of some countries can be promoted by the other countries’ actions towards achieving target 6.6 through the transboundary rivers. The actions of other countries focused on protecting and restoring water-related ecosystems may have transboundary SDG impacts, thereby creating numerous benefits for focal countries. These benefits include promoting equitable access to basic water and sanitation services (four linkages with target 1.4), contributing to the decoupling economic growth from environmental degradation (two linkages with target 8.4), and sustainable management and efficient use of natural resources (three linkages with target 12.2) (Fig. ##FIG##1##2c, d##). Furthermore, these actions can promote the conservation, restoration, and sustainable use of terrestrial and inland freshwater ecosystems and their services in focal countries (two linkages with target 15.1), as well as reduce the degradation of natural habitats and biodiversity loss (two linkages with target 15.5) (Fig. ##FIG##1##2c, d##). Fig. ##FIG##1##2## also reveals that a single SDG indicator in other countries can influence both its counterpart and various other SDG indicators in focal countries. For example, air pollutants (target 11.6) in other countries, through air flow, can profoundly impact both ambient air quality and 17 other indicators across multiple SDGs in focal countries (Fig. ##FIG##1##2c, d##). This ripple effect may influence health outcomes and economies—leading, for example, to a potential reduction in work time and productivity, which aligns with SDG 8 (promoting decent work and economic growth) (Fig. ##FIG##1##2c, d##). Moreover, it can also impact biodiversity, as represented by SDG 15 (life on land), by modifying habitats and harming wildlife (Fig. ##FIG##1##2c, d##). This discovery underscores the complex and interconnected nature of SDG interactions mediated by natural flows.</p>", "<title>Magnitude of transboundary SDG interactions of countries worldwide</title>", "<p id=\"Par9\">A spatial interaction index with a scale of 0 to 100 was devised to quantify the overall magnitude of transboundary SDG interactions. This index includes both synergistic and trade-off effects and considers transmission channels via both human-caused and nature-caused flows. A higher index indicates more substantial transboundary SDG interactions with other countries, and the index consists of four components, as shown in Fig. ##FIG##2##3a##. The aggregate of two components, namely, the transboundary synergistic effects via nature-caused flows and transboundary synergistic effects via international trade, denotes the total magnitude of the transboundary synergistic effects. For the countries worldwide, this magnitude represented 78.97% of the spatial interaction index (Fig. ##FIG##2##3a##) and was 3.76 times stronger than the total magnitude of the transboundary trade-off effects. This finding indicates that transboundary SDG interactions between countries can facilitate SDG accomplishment. Compared to the transmission channel via nature-caused flows, transboundary synergistic effects via international trade had a lower share among the countries worldwide. Specifically, the contribution of synergistic effects via nature-caused flows to the total transboundary interactions via nature-caused flows of the countries worldwide reached 90.71%, whereas the contribution of synergistic effects via international trade to the total transboundary interactions via international trade was 73.76% (Fig. ##FIG##2##3a##). Among the 17 SDGs, SDG 12 (responsible consumption and production) showed the most potent transboundary synergistic effects, scoring 39.38, followed by SDG 2 (zero hunger) and SDG 6 (clean water and sanitation), which scored 32.13 and 36.49, respectively (Fig. ##FIG##2##3b##). Among the 55 SDG indicators, target 6.6 (protect and restore water-related ecosystems) received the strongest transboundary synergistic effects (88.74), equivalent to the sum of transboundary synergistic effects through international trade (55.45) and nature-caused flows (33.29) (Fig. ##FIG##2##3c##). Considering the net effects of transboundary SDG interactions (transboundary synergistic effects minus transboundary trade-off effects), target 6.6 (protect and restore water-related ecosystems) again ranked first, demonstrating the strongest net effects (77.49) owing to its large transboundary synergistic effects (88.74) and small transboundary trade-off effects (11.25). This finding suggests that advancements in SDG indicators in other countries can significantly advance target 6.6 in the focal countries (Fig. ##FIG##2##3c##).</p>", "<title>Magnitude of transboundary SDG interactions by income group</title>", "<p id=\"Par10\">This study divided 121 countries into four groups based on the World Bank country classification (2022–2023). Compared to low, lower-middle, and upper-middle income groups, high income countries bear a greater responsibility for the influence of their domestic actions on the achievement of the 17 SDGs in other countries, as the magnitude of their transboundary SDG interactions accounted for the largest proportion of the total transboundary SDG interactions of the four income groups (sum of spatial interaction index), at 60.60% (Fig. ##FIG##3##4a##). High income countries demonstrated strong transboundary interactions with other countries; however, the population of high income countries over 2010–2020 accounted for an average of only 14.18% of the global population, based on data from the World Bank. Despite representing a relatively small fraction of the global population, high income countries are often characterised by robust economies, advanced technologies, and considerable political influence, which may amplify their roles in SDG interactions. Furthermore, when analysing the components of transboundary SDG interactions, the transboundary synergistic effects/trade-off effects of all high income countries constituted a large percentage of those globally, at 64.95% and 44.06%, respectively (Fig. ##FIG##3##4a##). High income countries showed the largest share of transboundary synergistic effects in their total transboundary SDG interactions (84.85%) compared to the other three income groups (Fig. ##FIG##3##4b##), suggesting that transboundary SDG interactions generated by high income countries may considerably promote the achievement of SDGs in their connected countries.</p>", "<title>Transboundary SDG interactions with neighbouring and non-neighbouring countries</title>", "<p id=\"Par11\">The intensity of the transboundary effects of the countries worldwide differed depending on geographic proximity. Non-neighbouring countries derived more benefits from transboundary interactions facilitated by international trade; however, neighbouring countries derived greater benefits from transboundary interactions via channels of nature-caused flows (Fig. ##FIG##4##5a##). Specifically, the transboundary synergistic effects were 14.94% more pronounced in interactions between trade partners that did not share borders compared with their neighbouring counterparts (Fig. ##FIG##4##5a##). Conversely, through the transmission channel of nature-caused flows, neighbouring countries showed transboundary synergistic effects that were 39.29% stronger than those observed between non-neighbouring countries (Fig. ##FIG##4##5a##). Transboundary trade-off effects were 17.81% stronger between neighbouring trade partners than between non-neighbouring partners (Fig. ##FIG##4##5a##). Through the nature-caused flow channel, non-neighbouring countries exhibited transboundary trade-off effects that were 1.88% stronger than those between neighbouring countries (Fig. ##FIG##4##5a##). The net effects (i.e., synergistic effects minus trade-off effects) between non-neighbouring countries through international trade were 35.46% stronger than those between neighbouring nations (Fig. ##FIG##4##5a##). Contrarily, for the transmission channel of nature-caused flows, the net effects between neighbouring countries were 45.59% more robust than those between non-neighbouring countries (Fig. ##FIG##4##5a##).</p>", "<p id=\"Par12\">An analysis of trade relationships revealed that all four income groups—high, upper-middle, lower-middle, and low income—demonstrated stronger synergistic effects than trade-off effects with both neighbouring and non-neighbouring trade partners. The share of synergistic effects among the total interactions (combining synergistic and trade-off effects) varied by income group and by whether the trading partners were neighbours. Specifically, the shares for high, upper-middle, lower-middle, and low income countries with their neighbouring partners were 72.83%, 72.46%, 72.96%, and 69.07%, respectively (Fig. ##FIG##4##5b##). In contrast, their shares with non-neighbouring partners were 86.07%, 73.61%, 56.76%, and 62.73%, respectively (Fig. ##FIG##4##5b##). Interestingly, high income countries tended to establish notably more intense synergistic relationships with trade partners outside their immediate geographic vicinity than with neighbouring trade partners (Fig. ##FIG##4##5b##). Specifically, high income countries showed 18.14% stronger synergistic effects with non-neighbouring trade partners than with neighbouring ones (Fig. ##FIG##4##5b##). This can be attributed to the extensive global practices and international influence of high income countries. High income countries often have widespread networks of investments and trade relationships worldwide, facilitating stronger interactions with non-neighbouring countries. Participation in various international accords and organisations encourages these countries to extend their relationships beyond their immediate geographic sphere, fostering more intensive interactions globally. Moreover, their relatively advanced technological infrastructure enables efficient communication and transportation over long distances.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par13\">This study quantifies transboundary interactions among 121 countries in relation to 768 SDG indicator pairs from 2010 to 2020. This assessment was conducted through various channels, including international trade, river flow, ocean currents, and air flow, by employing an integrated sustainability perspective^{##UREF##2##4##}. This study makes a key contribution by quantifying the magnitude and direction of the fourth pillar of integrated sustainability: the spillover effects caused by human–nature interactions. Therefore, sustainable development, as considered in this study, rests on four pillars: (1) social, (2) environmental, (3) economic, and (4) spillover effects^{##UREF##2##4##}. These pillars correlate with four key principles: (1) people, (2) planets, (3) prosperity, and (4) peace and partnership^{##UREF##2##4##,##UREF##4##6##}.</p>", "<p id=\"Par14\">Some research credits globalisation and openness with benefiting sustainability and economic development by invoking Ricardo’s theory of comparative advantage^{##UREF##3##5##,##UREF##4##6##,##UREF##25##34##}. However, other scholars argue that openness and globalisation run contrary to sustainability goals, based on the pollution haven hypothesis^{##UREF##4##6##,##UREF##26##35##,##UREF##27##36##}. While theories of comparative advantage highlight the welfare gains of interconnectedness, the pollution haven hypothesis introduces an important caveat regarding potential cross-border regulatory distortions and their impact on sustainability outcomes in integrated economies at different development levels. The study demonstrated that transboundary synergistic effects through international trade were the dominant form of interactions across borders, revealing the overall positive impact of globalisation and openness on advancing global sustainability in an interconnected world. While trade-offs exist in some issues, the predominance of cross-border coordination benefits underscores how collective progress is enhanced through continued cooperation at a global scale. Addressing a single SDG indicator within one country can automatically strengthen not only the same indicator but other indicators across connected nations through transboundary synergistic effects. Conversely, if these transboundary synergies develop in negative ways, such as a country failing to progress on certain indicators or regressing, they may result in vicious cycles in which setbacks are multiplied and transmitted to other countries^{##UREF##6##8##}. This highlights the risks and emphasizes the necessity to convert vicious inter-country cycles into virtuous ones. Systemic interlinkages form either virtuous or vicious cycles, indicating that transformations must be pursued intentionally to initiate desirable co-benefits and multiplication effects across borders. Pursuing progress in a coordinated manner across countries could set the stage for mutually reinforcing advances in the SDGs at a global scale.</p>", "<p id=\"Par15\">Tobler’s first law of geography—that everything is related to everything else, but near things are more related than distant ones—serves as a foundational principle in numerous research fields, including spatial analysis in epidemiology^{##REF##34579689##37##}, crime pattern analysis^{##UREF##28##38##}, economic development^{##UREF##29##39##,##UREF##30##40##}, and environmental issues^{##UREF##31##41##}. The continuing relevance and applicability of this law are evidenced by the broad range of methodologies and concepts that have been developed based on it. In modern times, as sustainability issues increasingly intersect with geographical considerations, there has been a increasing interest in revisiting and further exploring Tobler’s law, especially with respect to SDGs^{##UREF##32##42##}. While the law’s core principle remains valid in many instances, studies have illuminated the complex ways in which distance can shape interrelations, sometimes counterintuitively^{##UREF##12##16##}. For instance, some studies have highlighted habitat losses triggered by distant consumption through international trade^{##REF##31659031##43##,##REF##22678290##44##}. The negative effects of distant activities on sustainable fisheries further challenge this geographical principle^{##UREF##33##45##,##UREF##34##46##}. The results of this study suggested that the synergistic effects were 14.94% more pronounced in interactions between trade partners that did not share borders compared with those between neighbouring counterparts. Due to globalisation, different countries have become more connected and less geographically limited through international trade. Globally, non-neighbouring countries can benefit from comparative advantages by diversifying their traded goods and services, allowing them to interact more with each other than with neighbouring countries. While Tobler’s law remains valuable for understanding geographical influences, this research has revealed the importance of considering a broader array of factors, including non-proximate influences.</p>", "<p id=\"Par16\">Transboundary SDG interactions are global issues that transcend individual nations. Beyond traditional place-based governance approaches with a focus on a country’s territory, it is significant to adopt a flow-based perspective. This considers each country in the context of its associations with others by identifying, monitoring, and managing areas where key flows originate, progress between borders, and ultimately terminate^{##UREF##3##5##,##UREF##4##6##,##UREF##35##47##}. This study advocates that countries collaborate to find solutions through international organisations that act as bridges to facilitate global policymaking and support the achievement of the 2030 Agenda. Some international organisations (e.g., the UN and World Trade Organization) were formed to implement adequate measures to address global issues. Two main measures are proposed to discourage transboundary trade-off effects and encourage synergistic effects. One is to internalise the costs and benefits of transboundary SDG interactions. Countries that generate transboundary trade-off effects could be asked to provide adequate compensation, discouraging activities that impose a cost on an unrelated third party. Countries that generate transboundary synergistic effects can internalise these benefits through subsidisation, which could incentivise them to increase synergistic effects. This study evaluates the magnitude and components of transboundary SDG interactions, providing a foundation for countries worldwide to consider actions that inadvertently generate trade-offs in other countries, while reaping the benefits of synergies. The other measure is to establish a globally tradable pollution permit that presents countries with legally acceptable pollution limits. A tradable permit system has the substantial advantage of allowing efficient exchange, which helps maintain the overall level of pollution by allowing one potential polluter to purchase permits from another. A well-known example of this trading system is the Emission Trading System of the European Union, established in 2005. Thus, addressing transboundary SDG interactions requires more effective transboundary solutions and multilateral governance to achieve global sustainability.</p>", "<p id=\"Par17\">In addition to international trade, river flow, ocean currents, and air flow, other cross-border exchanges shape SDG interactions^{##REF##32890805##48##,##UREF##36##49##}. For example, owing to the high-volume nature of seaborne freight, maritime shipping is well-suited for transporting goods across international borders in regions with extensive coastlines^{##UREF##37##50##}. Cargo vessels can accommodate the bulk shipping of diverse goods across long distances in a relatively efficient manner compared with other forms of international transport^{##UREF##37##50##}. This strengthens economic cooperation and trade opportunities between coastal countries^{##UREF##37##50##}. Future studies should further explore the impacts of various human-caused transboundary flows, such as maritime transportation^{##UREF##37##50##}, technology transfer, investment, knowledge sharing, human migration, disease dissemination, and information diffusion, once data become available^{##UREF##38##51##}. The influence of nature-caused flows, including animal migration, seed dispersal, and disease spread, is also worth investigating^{##UREF##39##52##}. Capturing these additional linkages may provide deeper insights into the complex interconnected relationships between countries’ progress towards achieving the SDGs. Modelling flows such as ocean currents and wind patterns poses interesting methodological challenges given their multidirectional, changing dynamics over varying temporal and spatial scales. However, greater precision in characterising connectivity tendencies may considerably enhance our understanding of sustainability linkages. Future research should investigate novel approaches to systematically tracking variations in flow vectors—such as harnessing remote sensing data—and integrating this directional flow of information into spatial regression frameworks. This may entail simulating transport processes or calibrating networks via hydrodynamic or atmospheric modelling. Capturing the full complexity of flow regimes may provide unprecedented insights into the causal relationships among different countries.</p>" ]

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[ "<p id=\"Par1\">Domestic attempts to advance the Sustainable Development Goals (SDGs) in a country can have synergistic and/or trade-off effects on the advancement of SDGs in other countries. Transboundary SDG interactions can be delivered through various transmission channels (e.g., trade, river flow, ocean currents, and air flow). This study quantified the transboundary interactions through these channels between 768 pairs of SDG indicators. The results showed that although high income countries only comprised 14.18% of the global population, they contributed considerably to total SDG interactions worldwide (60.60%). Transboundary synergistic effects via international trade were 14.94% more pronounced with trade partners outside their immediate geographic vicinity than with neighbouring ones. Conversely, nature-caused flows (including river flow, ocean currents, and air flow) resulted in 39.29% stronger transboundary synergistic effects among neighboring countries compared to non-neighboring ones. To facilitate the achievement of SDGs worldwide, it is essential to enhance collaboration among countries and leverage transboundary synergies.</p>", "<p id=\"Par2\">Domestic attempts to advance the Sustainable Development Goals (SDGs) in a country can have synergistic and/or trade-off effects on the advancement of SDGs in other countries. Here the authors demonstrate that while high-income countries make up only 14% of the global population, they drive over 60% of worldwide SDG interactions.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41467-023-44679-w.</p>", "<title>Acknowledgements</title>", "<p>The work described in this paper was supported by a grant from Research Institute for Advanced Manufacturing (RIAM), The Hong Kong Polytechnic University (Project No. 1-CD4J, Project ID: P0041367) (J.R.), a grant from Research Centre for Resources Engineering towards Carbon Neutrality (RCRE), The Hong Kong Polytechnic University (PolyU) (Project No.1-BBEC, Project ID: P0043023) (J.R.), a grant from Research Grants Council of the Hong Kong Special Administrative Region, China-General Research Fund (Project ID: P0042030, Funding Body Ref. No: 15304222, Project No. B-Q97U) (J.R.), U.S. National Science Foundation (Grants No. 1924111, 2033507 and 2118329), Michigan AgBioResearch (J.L.), National Natural Science Foundation of China (grant #42101249), and the University of Hong Kong HKU-100 Scholars Fund (Z.X.).</p>", "<title>Author contributions</title>", "<p>J.L., Z.X., and J.R. designed and supervised the study. H.X. performed the analysis and prepared the manuscript. H.X. and S.B. established the model and compiled the code. H.X. and S.X. collected the data. J.L., Z.X., J.R., and S.X. reviewed and revised the manuscript.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par38\"><italic>Nature Communications</italic> thanks Manuel Fischer, Vahid Mohamad Taghvaee and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.</p>", "<title>Data availability</title>", "<p>The data generated in this study are available in the ##SUPPL##0##Supplementary Information##. Multiregional input-output (MRIO) tables can be obtained from the Eora26 database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://worldmrio.com/eora26/\">https://worldmrio.com/eora26/</ext-link>). The geographical information of rivers globally can be derived from the HydroSHEDS database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.hydrosheds.org/\">https://www.hydrosheds.org/</ext-link>). The data of SDG indicators can be collected from SDG Global Database by UN (<ext-link ext-link-type=\"uri\" xlink:href=\"https://unstats.un.org/sdgs/dataportal\">https://unstats.un.org/sdgs/dataportal</ext-link>), World Bank (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.worldbank.org/\">https://www.worldbank.org/</ext-link>), and Our World in Data (<ext-link ext-link-type=\"uri\" xlink:href=\"https://ourworldindata.org/\">https://ourworldindata.org/</ext-link>).</p>", "<title>Code availability</title>", "<p>All computer code used in conducting the analyses summarized in this paper is available from the corresponding author upon request. The code for the spatial econometric models can be accessed in the paper with the 10.1111/ectj.12069.</p>", "<title>Competing interests</title>", "<p id=\"Par39\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Conceptual framework of transboundary interactions of Sustainable Development Goals (SDGs) across countries.</title><p><bold>a</bold> Human-caused flows. <bold>b</bold> Nature-caused flows. Two categories of channels can create SDG interactions between countries: human-caused flows and nature-caused flows. The receiving countries of the interactions are classified as either neighbouring or non-neighbouring countries.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Transboundary synergistic and trade-off linkages across SDG indicators among countries.</title><p><bold>a</bold> Transboundary synergistic linkage across SDG indicators via international trade. <bold>b</bold> Transboundary trade-off linkage across SDG indicators via international trade. <bold>c</bold> Transboundary synergistic linkages across SDG indicators through nature-caused flows. <bold>d</bold> Transboundary trade-off linkages across SDG indicators through nature-caused flows. For better demonstration, the SDG indicators belonging to the same SDG target were grouped together based on the UN Global Indicator Framework for Sustainable Development Goals developed by the Inter-Agency and Expert Group on SDG Indicators (IAEG-SDGs). The left and right axes respectively denote the SDG targets belonging to SDG 1 to SDG 17, with the former serving as interaction generators and the latter as interaction receivers. The colour bars show the absolute values of spatial coefficients that are significant, which serve to represent the magnitude of transboundary interactions. These values were derived from 768 regression models based on spatial econometric methods, elaborated further in the Methods section. A darker colour, corresponding to a higher absolute value of the spatial coefficient, signifies stronger transboundary interactions.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Spatial interaction index and its components.</title><p><bold>a</bold> Spatial interaction index of countries worldwide. <bold>b</bold> Interaction magnitude of 17 SDGs. <bold>c</bold> Interaction magnitude of 55 SDG indicators. Both the spatial interaction index and interaction magnitude are divided into four components: synergistic effects via nature-caused flows, trade-off effects via nature-caused flows, synergistic effects via international trade, and trade-off effects via international trade. The numbers displayed on the horizontal axis of <bold>c</bold> represent the identifiers for the 55 SDG indicators included in this study (Supplementary information Table ##SUPPL##0##S1##).</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Magnitude and components of transboundary SDG interactions by income group.</title><p><bold>a</bold> Spatial interaction index by income groups. <bold>b</bold> Share of the components of spatial interaction index by income groups. The sum of synergistic effects and trade-off effects equals the spatial interaction index. There are four income groups: high, upper-middle, lower-middle, and low income groups (Supplementary information Table ##SUPPL##0##S4##). The blue in the pie charts represents the proportion of transboundary synergistic effects.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Comparison of the transboundary SDG interactions with neighbouring and non-neighbouring countries.</title><p><bold>a</bold> Magnitude of transboundary interactions with neighbouring and non-neighbouring countries. <bold>b</bold> Comparisons of the magnitude of transboundary SDG interactions among high, upper-middle, lower-middle, and low income countries. The blue and red represent the transboundary synergistic effects and transboundary trade-off effects, respectively. The light blue and dark blue colours respectively indicate the synergistic effects with neighbouring and non-neighbouring countries. In contrast, the light red and dark red indicate the trade-off effects with neighbouring and non-neighbouring countries, respectively.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Empirical results of transboundary interactions based on a two-stage instrumental variable (2SIV) estimation of the spatial econometric model</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th colspan=\"2\">First stage estimation</th><th colspan=\"2\">Explained variable: target 6.4</th><th colspan=\"2\">Explained variable: target 1.4</th></tr></thead><tbody><tr><td>GDP</td><td>0.091*** (0.033)</td><td>Spatial lag of target 7.1 (trade flow)</td><td>0.189*** (0.043)</td><td>Spatial lag of target 6.6 (trade flow)</td><td>0.038*** (0.013)</td></tr><tr><td>Population</td><td>0.071** (0.035)</td><td>Time lag</td><td>0.234*** (0.079)</td><td>Spatial lag of target 6.6 (river flow)</td><td>0.094*** (0.013)</td></tr><tr><td>Governance</td><td>0.034 (0.030)</td><td>Economy</td><td>0.020 (0.026)</td><td>Time lag</td><td>−0.003 (0.059)</td></tr><tr><td>Internet</td><td>0.028 (0.034)</td><td>Education</td><td>−0.029 (0.028)</td><td>Economy</td><td>−0.001 (0.007)</td></tr><tr><td>Export value</td><td>0.102*** (0.035)</td><td>Technology</td><td>0.053** (0.024)</td><td>Environment</td><td>0.017 (0.010)</td></tr><tr><td>Technology</td><td>0.038 (0.027)</td><td>Governance</td><td>0.045 (0.028)</td><td>Education</td><td>0.019* (0.010)</td></tr><tr><td/><td/><td>Agriculture</td><td>−0.006 (0.025)</td><td>Governance</td><td>0.018** (0.009)</td></tr><tr><td/><td/><td>Residual from the first stage</td><td>0.039* (0.023)</td><td>Population</td><td>−0.002 (0.009)</td></tr><tr><td/><td/><td/><td/><td>Residual from the first stage</td><td>−0.018** (0.007)</td></tr></tbody></table></table-wrap>" ]

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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({W}_{{air}}={[{w}_{{ij}}]}_{N\\times N})$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mi>i</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${w}_{{ij}}^{s}=\\frac{{w}_{{ij}}}{\\mathop{\\sum }\\nolimits_{j=1}^{N}{w}_{{ij}}}$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:msubsup><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq6\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${w}_{{ij}}$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq7\"><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${w}_{{ij}}^{s}$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:msubsup><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{{\\mathrm{ln}}}}}{F}_{{it}}={\\eta }_{i}+{{{{{{\\bf{X}}}}}}}_{{{{{{\\bf{1}}}}}}{{{{{\\bf{it}}}}}}}{{{{{\\boldsymbol{\\gamma }}}}}}+{\\varepsilon }_{{it}},\\,t=1,\\,2,\\,...,\\,T$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mi mathvariant=\"normal\">ln</mml:mi><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">X</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold\">1</mml:mi><mml:mi mathvariant=\"bold\">it</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant=\"bold-italic\">γ</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mspace width=\"0.25em\"/><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.25em\"/><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.25em\"/><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mspace width=\"0.25em\"/><mml:mi>T</mml:mi></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq8\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${F}_{{it}}$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq9\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\widehat{{\\varepsilon }_{{it}}}$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mover accent=\"true\"><mml:mrow><mml:msub><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{{\\mathrm{ln}}}}}{{SDG}}_{{imt}}={c}_{i}+{\\rho }_{1}{{{{\\mathrm{ln}}}}}{{SDG}}_{im,t-1}+{\\lambda }_{1}\\mathop{\\sum}\\limits_{j\\ne i}{w}_{{ijt}}^{1}{{{{\\mathrm{ln}}}}}{{SDG}}_{{jnt}}+{{{{{{\\bf{X}}}}}}}_{{{{{{\\bf{2}}}}}}{{{{{\\bf{it}}}}}}}{{{{{\\boldsymbol{\\beta }}}}}}+\\hat{\\delta {\\varepsilon }_{{it}}}+{v}_{{it}}$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:mi mathvariant=\"normal\">ln</mml:mi><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi mathvariant=\"normal\">ln</mml:mi><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:munder><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>≠</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:munder><mml:msubsup><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mi mathvariant=\"normal\">ln</mml:mi><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"bold\">X</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold\">2</mml:mi><mml:mi mathvariant=\"bold\">it</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant=\"bold-italic\">β</mml:mi><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mrow><mml:mi>δ</mml:mi><mml:msub><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>^</mml:mo></mml:mrow></mml:mover><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{SDG}}_{{imt}}$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{SDG}}_{{jnt}}$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\rho }_{1}$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\lambda }_{1}$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:msub><mml:mrow><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${w}_{{ijt}}^{1}$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:msubsup><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${w}_{{ij}}^{2}$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:msubsup><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{{\\mathrm{ln}}}}}{{SDG}}_{{imt}}=\t {c}_{i}+{\\rho }_{1}{{{{\\mathrm{ln}}}}}{{SDG}}_{im,t-1}+{{\\lambda }_{1}\\mathop{\\sum}\\limits_{j\\ne i}{w}_{{ijt}}^{1}{{{{\\mathrm{ln}}}}}{{SDG}}_{{jnt}}+\\lambda _{2}}\\mathop{\\sum}\\limits_{j\\ne i}{w}_{{ij}}^{2}{{{{\\mathrm{ln}}}}}{{SDG}}_{{jnt}}\\\\ \t+{{{{{{\\bf{X}}}}}}}_{{{{{{\\bf{2}}}}}}{{{{{\\bf{it}}}}}}}{{{{{\\boldsymbol{\\beta }}}}}}+\\hat{\\delta {\\varepsilon }_{{it}}}+{v}_{{it}}$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:mi mathvariant=\"normal\">ln</mml:mi><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi 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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>" ]

[ "<table-wrap-foot><p>The indicators chosen to represent SDG targets 7.1, 6.4, 1.4, and 6.6 are proportion of population with primary reliance on clean fuels and technology, water use efficiency, proportion of population using basic sanitation services, and lakes and rivers seasonal water area (% of total land area), respectively. Supplementary information Tables ##SUPPL##0##S5## and ##SUPPL##0##S6## show the detailed information regarding the additional variables and the rationale behind their selection. Standard errors are provided in parentheses. Significance at the 1%, 5% and 10% levels is denoted by ***, ** and *, respectively.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41467_2023_44679_MOESM1_ESM.pdf\"><caption><p>Supplementary information</p></caption></media>", "<media xlink:href=\"41467_2023_44679_MOESM2_ESM.pdf\"><caption><p>Peer Review File</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Cellular senescence is a program promoted by a myriad of stresses such as telomeres shortening, oncogenic stress-induced hyper-replication and oxidative stress-mediated damages^{##REF##31675495##1##}. This program is characterized by a permanent cell cycle arrest and a senescence-associated secretory phenotype (SASP)^{##REF##31675495##1##}, both implicated in the pathophysiological effects of senescent cells^{##REF##24954210##2##,##REF##28575665##3##}. Senescence-associated pathophysiological contexts include development, tissue regeneration, cancer and aging^{##REF##24954210##2##,##REF##28575665##3##}. Although timely regulated senescence exerts beneficial effects, the accumulation of senescent cells throughout life and upon exposure to chronic stresses exerts detrimental effects by promoting aging and its associated diseases^{##REF##16456035##4##–##REF##31097655##9##}. Mechanistically, while downstream factors and effectors, such as p53, p21^CIP1 and p16^INK4A or NF-κB and C/EBPβ, respectively blocking cell cycle progression or promoting SASP, were extensively studied^{##REF##31675495##1##–##REF##28575665##3##}, upstream molecular and subcellular mechanisms controlling these factors are less understood.</p>", "<p id=\"Par3\">Senescent cells harbour metabolic changes related to both catabolism and anabolism^{##REF##31675495##1##,##REF##12943534##10##–##REF##29090099##15##}, to the point that some metabolic specificities of senescent cells are used to target or detect them^{##REF##23945590##11##,##REF##33446552##16##,##REF##33811820##17##}. Indeed, senescent cells display metabolic rearrangements as evidenced for instance by an altered glycolytic state and glucose utilization^{##REF##23945590##11##,##REF##25690941##12##,##REF##24577087##18##}, a deregulated mitochondrial metabolism, an AMPK activation and an altered NAD⁺ metabolism^{##REF##12943534##10##,##REF##26686024##19##–##REF##30778219##22##}. Lipid metabolism is also modified in senescent cells^{##REF##29090099##15##,##REF##28012437##23##–##REF##32839400##30##}. For instance, senescent hepatocytes^{##REF##28649419##26##,##REF##28608850##27##}, fibroblasts^{##UREF##0##31##}, and T-cells^{##UREF##1##32##} display an accumulation of lipid droplets (LD), this later accounting mostly for an increase of free fatty acids^{##REF##28012437##23##} and free cholesterol^{##REF##19059270##25##,##REF##22178194##28##}, subsequently esterified and incorporated in LD via triglycerides (TG) or cholesteryl esters. The mevalonate (MVA) pathway is part of lipid anabolism and involved in the endogenous biosynthesis of poly-isoprenoids, such as prenyl groups, ubiquinone, cholesterol or dolichol^{##REF##1967820##33##}. MVA pathway is thus crucial for many cellular processes including protein-protein interactions, mitochondrial respiration, membranes fluidity or glycosylation^{##REF##1967820##33##}. Some studies using pharmacological tools, such as statins or bisphosphonates, have previously suggested an involvement of this pathway in regulating senescence, still with some contradictory effects reported^{##REF##12676819##34##,##REF##21427353##35##}. Furthermore, how endogenous cholesterol biosynthesis mechanistically regulate cellular senescence remains so far elusive. Interestingly, in a functional genetic screen of a constitutively active kinase library that we previously reported^{##REF##26583757##36##}, two kinases of the MVA pathway, mevalonate kinase (MVK) and phosphomevalonate kinase (PMVK), were identified as able to induce premature senescence when ectopically expressed. Still the mechanisms of action of these enzymes in this context and the relevance of these observations during senescence in vivo remained unknown.</p>", "<p id=\"Par4\">In this study, we assessed through the use of genetic tools whether and how the MVA pathway and the downstream biomolecules regulate cellular senescence. Unexpectedly, this work led to the identification of a new mechanism regulating senescence: a cholesterol-dependent ERRα transcriptional program leading to mitochondrial dysregulation and senescence-associated liver alterations.</p>" ]

[ "<title>Methods</title>", "<title>Cell culture and reagents</title>", "<p id=\"Par26\">MRC5 normal human fibroblasts (ATCC, Manassas, VA, USA), and kidney 293 GP cells (Clontech, Mountain View, CA, USA) were cultured in Dulbecco′s modified Eagle′s medium (DMEM, Life Technologies, Carlsbad, USA) with GlutaMax and supplemented with 10% FBS (Sigma-Aldrich, Saint-Louis, USA) and 1% penicillin/streptomycin (ThermoFisher Scientific). XCT-790 (Medchem, HY-10426/CS-2413) was used at 150 nM. N-Acetyl-Cysteine (NAC) (A9165, Sigma-Aldrich) was used directly after infection at 1 mM. These compounds were renewed every two days.</p>", "<title>Vectors, transfection and infection</title>", "<p id=\"Par27\">Retroviral vectors were used to constitutively overexpress MVK, PMVK, lamin A and progerin. MVK and PMVK plasmids were provided by Addgene in the Myristoylated Kinase Library (Kit #1000000012) described in^{##REF##17574021##37##}. K22M mutation of the kinase-dead PMVK mutant (PMVKmut) was generated using QuickChange Site-Directed Mutagenesis Kit (Agilent, Catalog # 200518). pBABE‐puro‐GFP‐wt‐lamin A (Addgene #17662) and pBABE‐puro‐GFP‐progerin (Addgene #17663) were described in^{##REF##18311132##83##}. Lentiviral particles were used to constitutively express shPMVK (pLV[shRNA]-Hygro-U6&gt; hPMVK[shRNA#4], Target sequence: GAGAACCTGATAGAATTTATC) and shFDFT1 (pLV[shRNA]-Hygro-U6 &gt; hFDFT1[shRNA#2], Target sequence CAACGATCTC CCTTGAGTTTA and pLV[shRNA]-Hygro-U6 &gt; hFDFT1[shRNA#3], Target sequence: ACC ATTTGAATGTTCGTAATA) and were provided by VectorBuilder. 293 T or 293GP virus-producing cells were transfected using the GeneJuice reagent according to the manufacturer’s recommendations (Merck Millipore). Two days after transfection, viral supernatant was collected, diluted with fresh medium (1/2) and hexadimethrine bromide was added (final concentration 8 μg/mL; Sigma-Aldrich). Target cells were then infected, centrifugated with virus particles for 30 min at 2000 rpm and subsequently incubated during 6 h at 37 °C 5% CO₂. Fresh medium was added after 6 h incubation. One day later, infected cells were selected with Geneticin at 75 µg/mL, Hygromycin at 15 µg/mL (ThermoFisher Scientific), or puromycin at 500 ng/ml (Invivogen).</p>", "<title>siRNA</title>", "<p id=\"Par28\">MRC5 fibroblasts were plated and reverse transfected with ON-TARGET plus SMART pool of small interference (si) RNAs: siCtrl (Catalog: D-001810-10-20 / Lot#2693147), siPMVK (Catalog: L-006782-00), siFNTA (Catalog: L-008807-00), siFNTB (Catalog: L-010093-00), siPGGT1B (Catalog: L-008703-00), siFDFT1 (Catalog: #L-009442-00-0005 / Lot#180518), siPDSS1 (Catalog: L-008464-01), siDHDDS (L-010399-01), siESRRA (Catalog: #L-003403-00-0005 / Lot#191211), sip53 (Catalog: #L-003329-00-0001) / Lot#180912) (Horizon Discovery) previously incubated for 20 min with Dharmafect 1 Transfection Reagent (Horizon Discovery) 0,6% in antibiotics- and serum-free medium DMEM with Glutamax. Final siRNA concentration in the well was 15 nM. The day after, cells were infected (with retroviral particles containing PMVK) as referenced previously.</p>", "<title>Animals</title>", "<p id=\"Par29\">Wild-type (WT) and ERRα^-/- male mice in a C57BL/6 J genetic background were housed and fed ad libitum with free access to water in an animal facility at McGill University. All animal experiments were conducted in accord with accepted standards of humane animal care and all protocols were approved by the McGill Facility Animal Care Committee and the Canadian Council on Animal Care. For high-fat diet (HFD) experiments, mice were separated randomly into groups of two to three mice per cage and fed either a control chow diet consisting of 10 kcal percent fat (catalog no. TD.08806; Harlan, Indianapolis, IN) or an HFD consisting of 60 kcal percent fat (catalog no. TD.06414; Harlan) and known to increase cholesterol levels according to manufacturer, during 15 weeks, initiated at 6 weeks of age. For all mouse experiments, littermates were used and mice were euthanized by cervical dislocation at Zeitgeber time (ZT) 4 for tissue isolations.</p>", "<title>RNA extraction, reverse transcription, and real-time quantitative PCR</title>", "<p id=\"Par30\">Total RNAs were extracted with phenol-chloroform using Upzol (Dutscher, Brumath, France). Synthesis of cDNA was performed using Maxima First cDNA Synthesis Kit (ThermoFisher Scientific) from 1 μg of total RNA. cDNA (50 ng/µL) was used as a template for quantitative PCR (qPCR), and mixed with primers (200 nM), SYBR™ Green PCR Master Mix (ThermoFisher Scientific) or TaqMan mix (Roche) and Universal Probe Library probes (100 µM) (ThermoFisher Scientific) for the gene of interest. Reactions were performed in triplicate. qPCR analyses were carried out with the FX96 Thermocycler (Biorad, Hercules, USA). Relative mRNA levels were calculated using the Comparative Ct (ΔΔCT) method. Gene expression was normalized with <italic>hACTB</italic> or <italic>mRplp</italic>. Primer sequences used are listed in Supplementary Table ##SUPPL##0##1##.</p>", "<title>Senescence-associated β-Galactosidase analysis and Crystal violet</title>", "<p id=\"Par31\">For SA-β-Galactosidase assay, cells were washed with PBS 1X, fixed for 5 min in 2% formaldehyde / 0.2% glutaraldehyde, rinsed twice in PBS 1X, and incubated at 37 °C overnight in SA-β-Galactosidase staining solution as previously described^{##REF##20010931##84##}. For crystal violet staining, cells were washed with PBS 1X, fixed for 15 min in 3.7% formaldehyde and stained with crystal violet.</p>", "<title>ROS and JC1 quantification</title>", "<p id=\"Par32\">Total cellular and specific mitochondrial ROS were measured respectively with CellROX™ Green Reagent (ThermoFisher Scientific) and Cell Meter™ Mitochondrial Hydroxyl Radical Detection Kit (ATT Bioquest) according to manufacturer’s recommendations. For JC1, JC1-Mitochondrial Membrane Potential Assay Kit (ab113850, Abcam) was used. JC1 monomers and aggregates were both excited at 488 nm. Detection of fluorescence for JC1 monomers and aggregates were performed respectively at 530 nm and 590 nm. Ratio F(aggregate)/F(monomer) was subsequently evaluated. Pictures acquisition was performed using Operetta CLS High-Content Analysis System (PerkinElmer). All the quantifications of ROS and JC1 were performed using Columbus Software.</p>", "<title>Cholesterol measurement</title>", "<p id=\"Par33\">Relative intracellular cholesterol concentration was measured using Cholesterol Assay Kit, based on filipin fluorescent sensor^{##REF##22325611##47##} (Cell-Based) (Abcam, ab133116) according to manufacturer’s recommendations. Quantification was performed using ImageJ Software.</p>", "<title>PMVK kinase assay</title>", "<p id=\"Par34\">The assay is based on an enzymatic coupling system using the Pyruvate kinase (PK), Pyruvate Oxidase (PO) and the Horse Radish Peroxidase (HRP). The reaction synthetizing Diphospho-mevalonate by the PMVK is measured through the ADP produced simultaneously, detected through its capacity to engage enzymatic coupling of PK, PO, and HRP through pyruvate and H₂O₂ intermediates and the oxidation of Amplex red into the fluorescent compounds Resazurin. Six days after infection, MRC5 cells were washed twice with ice-cold KH buffer (50 mM HEPES, 110 mM KOAc, pH 7.2). Then cells were transferred on ice and incubated in KHM buffer (110 mM KOAc, 20 mM HEPES, 2 mM MgOAC, pH 7.2) containing 500 µg/ml of digitonin. After 5 min the supernatants were collected on ice and frozen at -20 °C. Lysates were thawed and then mixed v/v with a buffer containing HEPES pH 7.2 30 mM, NaCl 40 mM, EGTA 2 mM, Tween 20 0.04%, MgCl₂ 20 mM, BSA 0.2%. Thirty µL of this assay buffer was deposited in black fluorescent plate (2 replicates to test the kinase activity in presence or in absence of Phosphomevalonate (PMV) in the assay). Two buffers A and B were prepared in parallel, containing respectively 50 mM KH₂PO₄ pH 7, 375 µM Amplex Red (Sigma-Aldrich, Ampliflu™ Red, 90101) and KH₂PO₄ 50 mM pH 7, MgCl₂ 2.5 mM, FAD 25 µM, Thiamine pyrophosphate 250 µM, Phosphoenol-pyruvate 2.5 mM (Megazyme), Horse Radish Peroxidase (5 U/mL) (Sigma-Aldrich, P8375), Pyruvate Kinase (15 U/mL) (from Bacillus stearothermophilus, Nipro), Pyruvate Oxidase (1.87 U/mL) (Sorachim-PYO-311). Also a solution of ATP (S1), or a mix of ATP and phospho-mevalonate (S2), was prepared in order to obtain 400 µM of each in the assay buffer by adding 5 µL of these solutions. At this step, 5 µL of S1 or S2 was first mixed with 40 µL of buffer B and then mixed again with 20 µL of buffer A. These mixtures containing either S1 or S2 were added to each tested sample and the plate was immediately incubated at 30 °C in fluorescent plate reader (Clariostar, BMG-Labtech). Real-time increase of fluorescence of rezasurin produced from Amplex red oxidation was followed during 45 min. At the end of the experiment, slopes of the curves were analyzed to retain the linear increase of fluorescence, a time window where sufficient amount of ADP has accumulated to maintain a constant activity of the enzymatic coupling system. Slope obtained with only ATP in the reaction was subtracted from that corresponding to the same sample analyzed in presence of both ATP and PMV, and plotted as a curve of PMVK-dependent fluorescence increase by unit of time.</p>", "<title>Seahorse</title>", "<p id=\"Par35\">Cells were plated in Seahorse seeding 24-well plates prior infection. Infection was performed in the 24-well plates and cells were subsequently selected for 5 days with Geneticin (ThermoFisher Scientific) at 75 µg/mL. Using Seahorse XF Cell Mito Stress Test (Agilent, Santa Clara) as described in^{##REF##33458707##44##}, fibroblasts were sequentially treated with 1,5 μM oligomycin, 1,5 μM phenylhydrazone (FCCP), and 0.5 μM Rotenone and Antimycin A. After assay, cells were stained with Hoescht for 10mn before proceeding to cell number counting and subsequent normalization. Data were obtained at SFR Biosciences AniRA-ImmO Platform, ENS de Lyon. Seahorse XFe Wave Software (Agilent) was used to subsequently analyze the data.</p>", "<title>Electron microscopy</title>", "<p id=\"Par36\">1:1 volume of glutaraldehyde 4% was added to the culture medium and cells were incubated 15 min at 4 °C. After discarding medium/glutaraldehyde, 1:1 volume of glutaraldehyde 4% / cacodylate 0.2 M pH 7.4 was added. After fixation in glutaraldehyde 2%, cells were washed three times for 1 hr at 4 °C, post-fixed with 2% OsO4 1 hr at 4 °C, and dehydrated with an increasing ethanol gradient. Impregnation was performed with Epon A (50%) plus Epon B (50%) plus DMP30 (1.7%). Inclusion was obtained by polymerisation at 60 °C for 72 h. Ultrathin sections (approximately 70 nm thick) were cut on a UCT (Leica) ultramicrotome, mounted on 200 mesh copper grids and contrasted with uranyl acetate and lead citrate. Acquisition of at least 100 mitochondria of 10–20 independent cells per condition was performed with a Jeol 1400JEM (Tokyo, Japan) transmission electron microscope equipped with an Orius 600 camera and Digital Micrograph at CIQLE platform (UCBL-Lyon).</p>", "<title>Immunoblot and Immunofluorescence</title>", "<p id=\"Par37\">For immunoblot experiments, cells were lysed in RIPA buffer. After protein quantification using Bradford assay, 30 μg of proteins were loaded and resolved by SDS-PAGE electrophoresis and transferred to nitrocellulose membranes (Bio-Rad). Membranes were blocked with TBS-Tween / Milk 5% for 1 h and incubated at 4 °C with primary antibodies overnight. Membranes were then incubated with secondary antibody for 1 h at room temperature. Detection was performed using ECL kit (Amersham). Each image of blots derive from the same experiment and all the samples of each experiment were processed in parallel. For immunofluorescence experiments, cells were washed with PBS 1X, fixed for 15 min in 3.7% formaldehyde and permeabilized with Triton 100 × 0,1% for 10 min. Blocking was performed using PBS with 20% FBS during 30 min and cells were then incubated at 4 °C with primary antibodies overnight. Cells were incubated with secondary antibody for 1 h at room temperature, and washed before proceeding to image acquisition and analyses. Quantification was performed with ImageJ software. All primary antibodies and dilutions used are listed in Supplementary Table ##SUPPL##0##2##.</p>", "<title>Statistical analysis</title>", "<p id=\"Par38\">Individual values represent mean ± SEM of n independent biological replicates for in vitro or n mice for in vivo, as mentioned in the figure legends. Shapiro-Wilk normality tests were applied to raw data before proceeding to any analyses. All further statistical analyses and tests are clearly indicated in figure legends. For groups not following normal distributions, nonparametric Mann-Whitney test was performed. For two groups both following normal distributions, parametric tests were two-tailed and performed as following Student’s t-test (equal variance) or Welch’s t-test (non-equal variance). For more than two groups, repeated measure (RM) (for paired data) or ordinary (for unpaired data) one-way ANOVA was used and Tukey’s multiple comparisons test (with a single pooled variance) was subsequently performed. For in vivo data, two-sided Grubb’s test was performed to find outliers, which were removed from further analysis if <italic>p value</italic> was below 0.05, and ordinary two-way ANOVA was used. All the statistical analyses were performed using GraphPad Prism Software 9.1.0 (<italic>ns</italic>: non-significant; *<italic>p</italic> &lt; 0.05; **<italic>p</italic> &lt; 0.01; ***<italic>p</italic> &lt; 0.001).</p>", "<title>Reporting summary</title>", "<p id=\"Par39\">Further information on research design is available in the ##SUPPL##1##Nature Research Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<title>Mevalonate pathway promotes cellular senescence</title>", "<p id=\"Par5\">In order to investigate whether the MVA pathway can regulate senescence, we expressed in MRC5 normal human fibroblasts a constitutively active PMVK^{##REF##17574021##37##} and its K22M mutant, a mutant reported to have lost its kinase activity^{##REF##16519518##38##}, to examine whether the kinase activity of PMVK is required to induce premature senescence (Fig. ##FIG##0##1a, b## and Supplementary Fig. ##SUPPL##0##1A, B##). We confirmed that K22M mutant did not display any kinase activity showing that it was indeed a PMVK kinase-dead mutant (PMVKmut) (Supplementary Fig. ##SUPPL##0##1C##). We also expressed an shRNA directed against PMVK (shPMVK) to examine the role of the MVA pathway in two relevant pro-senescence contexts, namely replicative senescence that occurs when replicative limit has been reached and progerin-induced premature senescence when compared to expression of non-mutated lamin A (Fig. ##FIG##0##1a, b## and Supplementary Fig. ##SUPPL##0##1A, B##). Progerin, a protein driving Hutchinson-Gilford progeria syndrome (HGPS), is encoded by the <italic>LMNA</italic> mutated gene. Progerin corresponds to a truncated prelamin A that is unable to be processed in a mature lamin A perturbing nuclear envelope and cell homeostasis and leading to premature senescence^{##REF##15184648##39##}. Remarkably, the constitutive overexpression of PMVK, but not the kinase-dead mutant PMVK, led to decreased cell proliferation (Fig. ##FIG##0##1c, d##). Most importantly, the knockdown of PMVK was sufficient to extend the replicative potential of normal human fibroblasts over successive passages (Fig. ##FIG##0##1c, d##) and expressing progerin, when compared to lamin A (Supplementary Fig. ##SUPPL##0##1D, E##). The overexpression of PMVK, but not its kinase-dead version, was also associated with the induction of key markers of cellular senescence: senescence-associated β-galactosidase (SA-β-gal) activity (Fig. ##FIG##0##1e##) and increased mRNA levels of <italic>p21</italic>^{<italic>CIP1</italic>} and SASP marker <italic>IL-8</italic> (Fig. ##FIG##0##1f##). On the contrary, decreasing PMVK reduced SA-β-gal activity and decreased mRNA levels of <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> in normal fibroblasts at late passages (p36) (Fig. ##FIG##0##1e, f##) and expressing progerin (Supplementary Fig. ##FIG##0##1##F, G). Together these results show that PMVK contributes to replicative and progerin-induced senescence and its kinase activity participates in senescence regulation.</p>", "<p id=\"Par6\">To further prove that this observed senescence is mediated by the MVA pathway and not the sole PMVK enzyme, we stably expressed a shRNA against PMVK and subsequently expressed the upstream enzyme MVK (Fig. ##FIG##0##1a##). As expected, constitutive overexpression of MVK (Supplementary Fig. ##SUPPL##0##1H##) induced premature cellular senescence, as shown by decreased cell density (Supplementary Fig. ##FIG##0##1##I, J), elevated SA-β-gal activity (Supplementary Fig. ##SUPPL##0##1K##) and induction of both <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> mRNA levels (Supplementary Fig. ##SUPPL##0##1L##). Noteworthy, the knockdown of PMVK abolished MVK-induced premature senescence, rescuing decreased cell density (Supplementary Fig. ##FIG##0##1##I, J), and increased SA-β-gal activity and <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> mRNA levels (Supplementary Fig. ##FIG##0##1##K, L).</p>", "<p id=\"Par7\">Taken together, these data support that the MVA pathway plays a pivotal role in promoting cellular senescence.</p>", "<title>Dysfunctional mitochondria, ROS production, DNA damage and p53 mediate mevalonate pathway-induced senescence</title>", "<p id=\"Par8\">P53 is a well-known critical effector of cellular senescence^{##REF##32182711##40##}. Its transcriptional targets such as <italic>p21</italic>^{<italic>CIP1</italic>}, <italic>GADD45A</italic> and <italic>GDF15</italic> were upregulated at mRNA levels by the constitutive expression of PMVK (Fig. ##FIG##1##2a##) and their up-regulations were p53-dependent as they were prevented by p53 knockdown using siRNA (Fig. ##FIG##1##2a##), suggesting that p53 could mediate PMVK-induced senescence. Indeed, p53 knockdown in PMVK overexpressing cells (Supplementary Fig. ##SUPPL##0##2A##) reverted several features of senescence such as PMVK-induced p53 targets and <italic>IL-8</italic> mRNA expression (Fig. ##FIG##1##2a##), decrease in cell number (Fig. ##FIG##1##2b##) and increase in SA-β-Gal activity (Fig. ##FIG##1##2c##).</p>", "<p id=\"Par9\">During cellular senescence, p53 activation can occur through oxidative stress-induced DNA damage^{##REF##31675495##1##} and its subsequent DNA damage response^{##REF##24954210##2##,##REF##28575665##3##}. Accordingly, p53 pathway activation upon PMVK constitutive expression resulted from increased oxidative stress - DNA damage pathway as cells overexpressing PMVK displayed increased DNA damage evidenced by increased γH2AX positive cells (Fig. ##FIG##1##2d##), concomitantly with increased total ROS levels (Fig. ##FIG##1##2e##). Our results support that ROS is upstream of p53 as siRNA against p53 did not decrease ROS production (Supplementary Fig. ##SUPPL##0##2B##) whereas it decreased senescence (Fig. ##FIG##1##2a–c##) upon PMVK overexpression. Of note, cells overexpressing the kinase-dead mutant PMVK displayed a limited increase of γH2AX positive cells and an absence of ROS generation (Fig. ##FIG##1##2##d, e). Importantly, NAC antioxidant treatment largely overcame PMVK-induced senescence (Fig. ##FIG##1##2f–h##) showing a critical role of ROS in mediating PMVK-induced senescence. In the context of replicative senescence, the sole knockdown of PMVK was sufficient to reduce γH2AX positive cells and ROS levels (Supplementary Fig. ##SUPPL##0##2C, D##).</p>", "<p id=\"Par10\">Mitochondria is one of the major sites of ROS production in the cell^{##REF##24024165##41##} and its dysregulation participates in cellular senescence^{##REF##25399755##13##,##REF##26686024##19##,##REF##19528227##42##}. Strikingly, constitutive overexpression of PMVK, but not of kinase-dead mutant PMVK, led to increased mitochondrial ROS generation as evidenced by enhanced intensity of specific mitochondrial ROS probe (Fig. ##FIG##1##2i##). In order to evaluate mitochondrial dysfunction in PMVK-expressing cells, we assessed mitochondrial membrane potential using cationic JC-1 dye^{##REF##30687773##43##}, but also mitochondrial oxygen consumption rate (OCR) through Seahorse mitochondrial stress test (Supplementary Fig. ##SUPPL##0##2E##)^{##REF##33458707##44##}. PMVK-induced cellular senescence is accompanied by a drop of mitochondrial membrane potential (Fig. ##FIG##1##2j##), which could be promoted by ROS production and/or increase ROS production, and a concomitant decrease of mitochondrial ETC functions, as evidenced by reduced mitochondrial basal, ATP-linked and maximal respiration (Fig. ##FIG##1##2k## and Supplementary Fig. ##SUPPL##0##2E##). Dysfunctional mitochondria may harbor changes in their morphology^{##REF##31284394##45##,##REF##32277765##46##}. Related to mitochondrial dysfunction observed in PMVK-expressing cells, we also identified atypical and persistent enlarged morphology of mitochondria in PMVK-expressing cells using electron transmission micrographs (Fig. ##FIG##1##2l##).</p>", "<p id=\"Par11\">All these results support that PMVK could promote senescence by dysregulating ETC mitochondrial functions, further inducing ROS production, DNA damage and p53 activation.</p>", "<title>The cholesterol biosynthetic branch participates in mevalonate pathway-induced senescence</title>", "<p id=\"Par12\">Farnesyl-5-pyrophosphate is the end-product of the MVA pathway and presents three isoprene units, elementary units further used either to be transferred as prenyl groups to proteins or to be condensated into more complex poly-isoprenoids, that include among others dolichol, ubiquinone or cholesterol^{##REF##1967820##33##} (Fig. ##FIG##2##3a##). In order to dissect the role of downstream branches in the PMVK-induced senescence, we knocked down the first enzyme of each branch, subsequently overexpressed PMVK and automatically counted the number of cells 4 days later. Only the knockdown of FDFT1, the first enzyme of the cholesterol biosynthesis branch, partially reverted the decreased cell number induced by PMVK overexpression (Fig. ##FIG##2##3a, b##). SiRNA-mediated FDFT1 knockdown (Supplementary Fig. ##SUPPL##0##3A##) also rescued PMVK-induced decrease in cell density (Fig. ##FIG##2##3c##), increase in SA-β-gal activity (Fig. ##FIG##2##3d##), and increase in <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> mRNA levels (Fig. ##FIG##2##3e##), without impacting <italic>PMVK</italic> mRNA level (Supplementary Fig. ##SUPPL##0##3A##). Confirming these results, stable knockdown of FDFT1 by two independent shRNA partly reverted premature senescence induced by PMVK expression (Supplementary Fig. ##SUPPL##0##3B–D##). In line with a role of the cholesterol biosynthetic branch in inducing cellular senescence, the expression of PMVK, but not the kinase-dead mutant PMVK, boosted intracellular cholesterol content, according to the fluorescence of the cholesterol sensor filipin^{##REF##22325611##47##} (Fig. ##FIG##2##3f##), and increased cholesterol-dependent LXR transcriptional targets^{##REF##29904174##48##}, namely <italic>ABCA1</italic> and <italic>ABCG1</italic> (Fig. ##FIG##2##3g##).</p>", "<p id=\"Par13\">Altogether these results indicate a functional role of the cholesterol biosynthesis pathway in the regulation of PMVK-induced senescence.</p>", "<title>Mitochondrial master regulator Estrogen-Related receptor alpha mediates mevalonate pathway-induced senescence</title>", "<p id=\"Par14\">Estrogen-Related Receptor alpha (ERRα or NR3B1) is a key regulator of mitochondrial functions and of metabolism^{##REF##25500872##49##,##REF##26777690##50##}. Noteworthy, mRNA levels of ERRα were upregulated in both replicative and progerin-induced senescence (Supplementary Fig. ##SUPPL##0##4A##). We then assessed during PMVK-induced senescence the expression of ERRα targets: ERRα itself^{##REF##14978033##51##} encoded by <italic>ESRRA</italic> gene and <italic>UQCRFS1</italic>, <italic>NDUF5A</italic>, <italic>SDHA</italic> and <italic>SDHB</italic> nuclear-encoded mitochondrial targets^{##REF##25500872##49##}. The constitutive overexpression of PMVK increased the expression of <italic>ESRRA</italic>, <italic>UQCRFS1</italic>, <italic>NDUF5A</italic>, <italic>SDHA</italic> and <italic>SDHB</italic> (Fig. ##FIG##3##4a, b## and Supplementary Fig. ##SUPPL##0##4B, C##). Remarkably, this ERRα program upregulation was partly reverted by the knockdown of FDFT1 (Fig. ##FIG##3##4c, d## and Supplementary Fig. ##SUPPL##0##4B–D##) suggesting the hypothesis of ERRα activation by the cholesterol biosynthetic pathway during PMVK-induced senescence. Further confirming an activation of ERRα during PMVK-induced senescence, its knockdown by siRNA strategy blocked PMVK-induced upregulation of various ERRα targets (Supplementary Fig. ##SUPPL##0##4E, F##), without impacting PMVK levels (Supplementary Fig. ##SUPPL##0##4G##).</p>", "<p id=\"Par15\">We next sought to determine whether cholesterol-dependent ERRα program functionally mediates the PMVK-induced senescence. Knockdown of ERRα in PMVK-overexpressing cells partially rescued the decreased cell number (Fig. ##FIG##3##4e, f##), the increased SA-β-gal activity (Fig. ##FIG##3##4g##), and the elevated <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> mRNA levels (Fig. ##FIG##3##4h##). Further supporting that ERRα mediates MVA/cholesterol biosynthetic pathway-induced senescence, its chemical inhibition using XCT-790 compound, similarly to ERRα knockdown, largely bypassed senescence induced by PMVK expression according to growth curves and SA-β-Gal activity (Supplementary Fig. ##SUPPL##0##4H, I##).</p>", "<p id=\"Par16\">To next investigate the relevance of these discoveries in a relevant pathophysiological system, we investigated the level of cellular senescence in the liver of ERRα knockout mice fed by high-fat diet (HFD), known to increase cholesterol levels and drive cellular senescence and senescence-dependent steatosis^{##REF##28608850##27##,##REF##31225436##52##}. ERRα target genes <italic>Uqcrfs1</italic>, <italic>Nduf5a</italic>, <italic>Sdha</italic> and <italic>Sdhb</italic> were only slightly induced by the HFD, potentially because some endogenous ERRα activity upon the chow diet and were accordingly reduced at mRNA levels in the liver of ERRα knockout mice, especially upon HFD (Supplementary Fig. ##SUPPL##0##4J##). As expected, HFD resulted in the accumulation of senescence markers such as <italic>p21</italic>^{<italic>Cip1</italic>} (Fig. ##FIG##3##4i, j##), <italic>Gadd45a</italic> and <italic>Gdf15</italic> p53 targets (Fig. ##FIG##3##4j##), <italic>Mmp12</italic> SASP factor (Fig. ##FIG##3##4k##), and pro-inflammatory SASP factors <italic>Cxcl1</italic> and <italic>Cxcl2</italic> (Fig. ##FIG##3##4k##), which are murine functional orthologs of human <italic>IL8</italic>^{##REF##10028286##53##}. Strikingly, increase in the expression of these senescence markers was abrogated in liver of ERRα knockout mice upon HFD (Fig. ##FIG##3##4i–k##). As previously reported^{##REF##29635284##54##}, HFD-fed ERRα knockout mice did not display hepatic steatosis, a process tightly linked to senescent cell accumulation^{##REF##28608850##27##,##REF##31225436##52##}. Examination of the same senescence markers in white adipose tissue (WAT), which can display increased senescence during HFD^{##UREF##2##55##}, displayed some similarities and differences with the liver. Indeed, <italic>p21</italic>^{<italic>Cip1</italic>}, <italic>Gdf15</italic>, <italic>Mmp12</italic>, and <italic>Cxcl2</italic> were induced whereas <italic>Gadd45a and Cxcl1</italic> were not in the control mice by the HFD (Supplementary Fig. ##SUPPL##0##4K##). Induction by the HFD of <italic>Gdf15</italic>, <italic>Mmp12</italic>, <italic>Cxcl2</italic> was decreased in the ERRα knockout mice (Supplementary Fig. ##SUPPL##0##4K##).</p>", "<p id=\"Par17\">Overall, these results highlight the importance of ERRα in mediating MVA/cholesterol biosynthetic pathway-induced cellular senescence in vitro in human cells and in vivo in mouse.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par18\">In this study, we deciphered the role of the MVA pathway, the cholesterol biosynthetic pathway and of ERRα transcription factor in mediating cellular senescence. MVA pathway activation triggers premature senescence whereas its inhibition delays replicative and progerin-induced senescence in normal human cells. PMVK-induced senescence seems to mediate, at least partly, by the biosynthetic cholesterol pathway and the activation of an ERRα transcriptional program, mitochondrial ROS accumulation, DNA damage and p53 activation. ERRα is also mediating cellular senescence in the liver, and to a lower extent in the WAT, when mice are subjected to a high fat diet (Fig. ##FIG##4##5##).</p>", "<p id=\"Par19\">Several studies depicted a role of MVA pathway in cellular senescence through the use of statins and aminobisphosphonates inhibitors but with conflicting conclusions. For instance blocking the MVA pathway with these inhibitors has been shown to delay senescence in HUVEC model^{##REF##12676819##34##}, whereas it promotes senescence in oral keratinocytes and has no obvious effect in oral fibroblasts^{##REF##21427353##35##}. Besides, statins and aminobiphosphonates have been shown both to blunt SASP, notably pro-inflammatory cytokines including IL-6, IL-8 and monocyte chemoattractant protein (MCP)-1^{##REF##12117737##56##–##REF##32257389##59##}, and some of its effects, including pro-tumorigenic activity^{##UREF##5##60##}. Dampening SASP through statins could explain their numerous anti-inflammatory outcomes in vivo^{##REF##19415282##61##,##REF##25374755##62##}. Our results using genetic tools, knockdown and/or overexpression of PMVK or MVK, clearly demonstrate that the MVA pathway promotes cellular senescence and associated SASP in normal human fibroblasts. Discrepancies with pharmacological studies might thus result from the known pleiotropic effects of the MVA inhibitors, as these inhibitors were found to exert multiple MVA pathway-independent actions^{##UREF##6##63##,##REF##17062705##64##}. For instance, bisphosphonates in addition to inhibiting FDPS enzyme and downstream pathway also induce accumulation of the upstream metabolite isopentenyl diphosphate (IPP) which can induce apoptosis, at least in some specialized cells^{##UREF##3##57##}.</p>", "<p id=\"Par20\">Although the MVA pathway contributes to senescence as its knockdown delays replicative and progerin-induced senescence, how its activity is regulated during senescence remains unknown. PMVK is up-regulated during progerin-induced senescence but not during replicative senescence, with the same trends for FDFT1, whereas MVK levels are not modified (Supplementary Fig. ##SUPPL##0##5A, B##). Nonetheless, cholesterol levels are increased during both replicative or progerin-induced senescence (Supplementary Fig. ##SUPPL##0##5C, D##). Taken together, these results suggest an accumulation of cholesterol in senescent cells, in line with two recent studies displaying this accumulation in other senescence models^{##REF##35778407##65##,##REF##36864206##66##}, and that this accumulation is not directly due to an up-regulation of PMVK and FDFT1. We can then speculate that post-translational modifications, as previously reported with two upstream MVA enzymes, namely HMGCR phosphorylation^{##REF##2369897##67##} or HGMCS sumoylation^{##REF##25187565##68##}, are involved in regulating the MVA pathway during senescence. Last but not least, cholesterol level is regulated not only by synthesis but also through transport and/or degradation^{##REF##31848472##69##}. Thus, the exact contribution of MVA pathway in the accumulation of cholesterol in these senescence models would further require deeper investigations.</p>", "<p id=\"Par21\">Our results suggest an unexpected link between the MVA pathway and the DNA damage/p53 pathway, a well-known effector pathway promoting cellular senescence^{##REF##18574463##70##}. This DNA damage/p53 pathway could be activated by an oxidative stress upon PMVK-induced senescence, probably mainly provoked by increased mitochondrial ROS production. Mitochondrial ROS are well known mediators of cellular senescence and can result from multiple mitochondrial alterations, from increased respiration and thus increased basal electron leaks during the electron transport chain activity, to decreased respiration but increased levels of electron leaks because of altered electron transport chain complex associations^{##REF##24024165##41##}. According to our findings, PMVK-induced senescence results in decreased respiration with increased mitochondrial ROS production. This is in line with previous results showing that maladaptive complex 1 assembly through increased transcriptional program of ETC components results in decreased respiration with increased mitochondrial ROS and promotes cellular senescence and aging^{##REF##24815183##71##}.</p>", "<p id=\"Par22\">Our siRNA approach to reveal which sub-branch(es) of the MVA pathway participate in PMVK-induced senescence identified an involvement of the cholesterol biosynthetic branch. Of note, this finding does not exclude that some other sub-branches could collaborate with the cholesterol biosynthetic pathway to regulate cellular senescence. Beyond the specific role of ceramide^{##REF##8530509##24##}, little is known about links between lipids and senescence except that the lipid metabolism is largely modified in senescent cells. In particular and in accordance with our results in replicative and progerin-induced senescence, it has been reported that free fatty acids and cholesterol levels are increased in senescent cells^{##REF##19059270##25##,##REF##28649419##26##,##REF##22178194##28##,##REF##28128379##29##} and that ceramides or prostaglandins regulate also the onset of senescence^{##REF##8530509##24##,##REF##17560572##72##}. In line with our findings, recent articles reported an upregulation of the expression of cholesterol synthesis genes in a model of oncogene-induced senescence^{##REF##31148378##73##} and an increased cholesterol during DNA damage-induced senescence^{##REF##36864206##66##}. During OIS, knockdown of some cholesterol synthesis genes partially bypassed cell proliferation arrest. However, the mechanisms behind these observations were not deciphered^{##REF##31148378##73##}. During DNA damage-induced senescence, cholesterol is thought to promote the SASP by increasing mTORC1 activity^{##REF##36864206##66##}. Our results underline the importance of cholesterol biosynthetic branch downstream of the MVA pathway in the regulation of cellular senescence and allow us to propose a mechanistic model through ERRα activation. Our findings and the findings of others do not exclude additional mechanisms, dependent or not on ERRα, controlled by the cholesterol in cellular senescence, including in a paracrine manner, as it has been described for some other lipids^{##REF##35370799##74##}.</p>", "<p id=\"Par23\">Our results support that ERRα participates in the pro-senescence function of the cholesterol biosynthetic pathway as its knockdown or its chemical inhibition partially overcomes PMVK-induced premature senescence. Although ablation of FDFT1, ERRα or p53 decrease PMVK-induced senescence, their effects show slight differences and not complete reversal of the phenotype suggesting that other factors and pathways could also contribute to PMVK-induced senescence. A previous study proposed that cholesterol can be an ERRα ligand^{##REF##26777690##50##}, as this is still largely debated further investigation will be needed to confirm or not this observation. As far as we know ERRα has not been associated with cellular senescence. Nevertheless, it has been shown to be activated during cancer cell death in response to PLA2R1/JAK/STAT signalling, this signalling being known to promote cellular senescence in normal human cells and in mice^{##UREF##4##58##,##REF##19197340##75##–##REF##32196928##77##}. In cancer cells, PLA2R1/JAK/STAT signalling in an ERRα-dependent manner blocks mitochondrial respiration, alters mitochondria and mediates ROS generation^{##REF##27041564##78##}, reminiscent to the observed alterations during PMVK-induced senescence in normal cell.</p>", "<p id=\"Par24\">We have previously reported that ERRα-null mice are protected from HFD-induced non-alcoholic fatty liver disease (NAFLD)^{##REF##29635284##54##}, which is characterized by liver steatosis. Senescent cells accumulate in the liver during HFD and/or aging and contribute to liver steatosis^{##REF##28608850##27##,##REF##31225436##52##}. We observed that ERRα-depleted livers are protected from increased senescence, suggesting that reduced ERRα-induced senescence could contribute to the decreased steatosis in the liver of these mice^{##REF##29635284##54##}. Adding another layer of complexity, body weight (BW) is decreased in ERRα KO mice upon HFD^{##REF##29635284##54##}, suggesting that BW decrease could contribute to decrease senescence and steatosis observed in the liver of these mice. As far as we know whether senescent cell accumulation can impact BW is currently unknown. Further studies will thus be needed to better define the complex functional connection between BW, senescence and steatosis. Still, mechanistically, it has been previously shown that ERRα loss^{##REF##29635284##54##} or elimination of senescent cells^{##REF##28608850##27##} results in change in free fatty acid metabolism decreasing liver steatosis. Beyond these observations highlighting the importance of ERRα in regulating senescence and senescence-dependent liver steatosis, we can speculate that other known pathophysiological processes regulated by ERRα could rely on its effect on cellular senescence. For instance, our results in WAT also support a decreased cellular senescence in the ERRα-null mice. ERRα-null mice display reduced osteoporosis in female mice^{##REF##19936213##79##,##REF##19608650##80##} and cellular senescence in the bone is known to promote osteoporosis^{##REF##28825716##81##}, suggesting that ERRα-promoted senescence could participate in ERRα-induced osteoporosis. In the same line, antiosteoporosis effects of MVA pathway inhibitors, aminobisphosphonates, are well-known^{##REF##18266020##82##} and may partly rely on reduced ERRα activity, though further studies need to critically test this hypothesis. Effect of ERRα in vivo on senescence can then be wide in term of tissue physiology impacted and then still needs to be deeply investigated in the future. For instance, ERRα is expressed in different cell types in the mouse liver, according to publicly available single-cell RNA sequencing, raising the question of the cells impacted by ERRα on senescence occurrence during HFD. In the context of ERRα-driven cellular senescence in vivo, it will also be critical to characterize mitochondrial phenotype in tissue as our results support it is a critical mediator of MVA pathway/ERRα-induced senescence.</p>", "<p id=\"Par25\">Overall, our results emphasize MVA pathway/cholesterol biosynthetic pathway, cholesterol levels and subsequent ERRα program as a new pathway regulating cellular senescence. As impacting cellular senescence has attracted many interests to improve various age-related diseases and health span^{##REF##22048312##7##–##REF##31097655##9##}, our work paves the way to new potential senotherapeutic strategies using drugs targeting the mevalonate pathway (statins, bisphosphonates) and in particular PMVK, and ERRα.</p>" ]

[]

[ "<p id=\"Par1\">Cellular senescence is a cell program induced by various stresses that leads to a stable proliferation arrest and to a senescence-associated secretory phenotype. Accumulation of senescent cells during age-related diseases participates in these pathologies and regulates healthy lifespan. Recent evidences point out a global dysregulated intracellular metabolism associated to senescence phenotype. Nonetheless, the functional contribution of metabolic homeostasis in regulating senescence is barely understood. In this work, we describe how the mevalonate pathway, an anabolic pathway leading to the endogenous biosynthesis of poly-isoprenoids, such as cholesterol, acts as a positive regulator of cellular senescence in normal human cells. Mechanistically, this mevalonate pathway-induced senescence is partly mediated by the downstream cholesterol biosynthetic pathway. This pathway promotes the transcriptional activity of ERRα that could lead to dysfunctional mitochondria, ROS production, DNA damage and a p53-dependent senescence. Supporting the relevance of these observations, increase of senescence in liver due to a high-fat diet regimen is abrogated in ERRα knockout mouse. Overall, this work unravels the role of cholesterol biosynthesis or level in the induction of an ERRα-dependent mitochondrial program leading to cellular senescence and related pathological alterations.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41514-023-00128-y.</p>", "<title>Acknowledgements</title>", "<p>We thank laboratory members for helpful suggestions and collaborations. This work was supported by the Ligue Régionale contre le Cancer (Comité du Rhône) (NM) and ANR (ANR‐14‐CE12‐0003) (DB). Institut Convergence PLAsCAN, ANR-17-CONV-0002 also support the project. DZ was supported by the French Ministry of Higher Education and Research and by the Fondation pour la Recherche Médicale FRM (FDT201904008259).</p>", "<title>Author contributions</title>", "<p>D.V.Z., J.C.H., M.V., A.H., A.M., C.M., A.G., A.V. and C.C. performed in vitro experiments. M.V., C.S. and J.R. performed in vivo experiments. D.V.Z., M.V., V.G., A.V., J.G., N.M. and D.B. designed the experiments and the results were analyzed by all the co-authors. D.V.Z., N.M. and D.B. designed the overall study. D.B. and N.M. co-supervised the work. D.V.Z., N.M. and D.B. wrote the manuscript with input from all authors.</p>", "<title>Data availability</title>", "<p>The data that support the findings of this study are available from the corresponding authors.</p>", "<title>Competing interests</title>", "<p id=\"Par40\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>The MVA pathway regulates cellular senescence in normal cells.</title><p><bold>a</bold> Schematic representation of the MVA pathway in eukaryotic cells. HMGCR, HMG-CoA reductase; MVK, mevalonate kinase; PMVK, phosphomevalonate kinase; MVD, mevalonate-diphosphate decarboxylase; FDPS, farnesyl diphosphate synthase. Constitutive expression (in red) or knockdown by shRNA (in orange) was performed in MRC5 fibroblasts. <bold>b</bold> Relative PMVK and Tubulin protein levels in empty vector (Ctrl), PMVK- or Kinase Dead (PMVKmut) PMVK-expressing cells and in shCtrl- or shPMVK-expressing cells. <bold>c</bold> Growth curves of Ctrl, PMVK- or PMVKmut-expressing cells, and shCtrl and shPMVK-expressing cells. Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. RM one-way ANOVA test on last time point. <bold>d</bold> Crystal violet staining of Ctrl, PMVK- or PMVKmut-expressing cells at early passage (p26), and of shCtrl- and shPMVK-expressing cells at early (p30) and late (p36) passage. <bold>e</bold> Micrographs and quantification of SA-β-gal positive cells of Ctrl, PMVK- or PMVKmut-expressing cells at early passage (p26), and of shCtrl- and shPMVK-expressing cells during passages. Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. Scale bar: 100 µm. RM one-way ANOVA test (upper panel) and paired Student’s T-test (lower panel). <bold>f</bold> RT-qPCR of <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> genes in Ctrl, PMVK- or PMVKmut-expressing cells at early passage (p26), and of shCtrl- and shPMVK-expressing cells at late passage (p36). Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. RM one-way ANOVA test (upper panel) and paired Student’s T-test (lower panel). ns (nonsignificant; *<italic>p</italic> &lt; 0.05; **<italic>p</italic> &lt; 0.01; ***<italic>p</italic> &lt; 0.001).</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>MVA pathway induction promotes mitochondrial dysfunction, ROS accumulation, DNA damage and p53-dependent senescence.</title><p><bold>a</bold> RT-qPCR of p53-regulated genes, including <italic>p21</italic>^{<italic>CIP1</italic>}, <italic>GADD45A</italic>, <italic>GDF15</italic> and <italic>IL-8</italic> in Ctrl or PMVK-expressing cells previously transfected with control non-targeting siRNA (siCtrl) or p53-targeted siRNA (sip53). Mean +/− SEM of <italic>n</italic> = 3 independent biological replicates. RM one-way ANOVA test. <bold>b</bold> Micrographs of Ctrl and PMVK-expressing cells upon sip53. Quantification of relative cell number in Ctrl and PMVK-expressing cells. Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. Scale bar: 100 µm. RM one-way ANOVA test. <bold>c</bold> Representative micrographs and quantification of SA-β-gal positive cells in Ctrl and PMVK-expressing cells upon siCtrl or sip53. Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. Scale bar: 50 µm. RM one-way ANOVA test. <bold>d</bold> Micrographs of Ctrl, PMVK- or PMVKmut-expressing cells immunostained with γH2AX antibody and DAPI stained. Scale bar: 10 µm. Number of γH2AX foci were counted manually using FiJi and divided by the number of nuclei to evaluate the mean number of foci per nucleus. Fully stained nuclei were excluded from this analysis. Mean +/− SEM of <italic>n</italic> = 3 independent biological replicates. RM one-way ANOVA test. <bold>e</bold> Quantification of relative ROS levels using CellROX™ Green Reagent probe and measuring its fluorescence intensity in Ctrl, PMVK- and PMVKmut- expressing cells. Mean +/− SEM of <italic>n</italic> = 3 independent biological replicates. RM one-way ANOVA test. <bold>f</bold> Crystal violet staining after 8 days in Ctrl and PMVK-expressing cells upon vehicle (Veh) or N-acetyl-cysteine (NAC) antioxidant treatment. <bold>g</bold> Cell count in Ctrl and PMVK-expressing cells upon vehicle or NAC treatment. Mean +/− SEM of <italic>n</italic> = 5 independent biological replicates. RM one-way ANOVA test. <bold>h</bold> Representative micrographs and quantification of SA-β-gal positive cells in Ctrl and PMVK-expressing cells upon the vehicle or NAC treatment. Mean +/− SEM of <italic>n</italic> = 5 biological replicates. Scale bar: 10 µm. RM one-way ANOVA test. <bold>i</bold> Quantification of mitochondrial ROS using mitochondrial hydroxyl radical detector and measuring its fluorescence intensity in Ctrl, PMVK-, and PMVKmut-expressing cells. Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. RM one-way ANOVA test. <bold>j</bold> Mitochondrial membrane polarisation measurement assessed by JC1-probe. Representative micrographs of JC1 in both monomer (F(530 nm)-green) or aggregate (F(590 nm)-orange) forms within Ctrl, PMVK-, and PMVKmut-expressing cells. Scale bar: 100 µm. Quantification of ratio fluorescence intensity (Monomer) / fluorescence intensity (Aggregate). Mean +/− SEM of <italic>n</italic> = 3 independent biological replicates. RM one-way ANOVA test. <bold>k</bold> Seahorse quantitative analysis of relative oxygen consumption rate (OCR). Basal OCR was evaluated in resting conditions, ATP-linked OCR upon Oligomycin treatment and Maximal OCR upon FCCP treatment. Mean +/− SEM of <italic>n</italic> = 5 independent biological replicates. Multiple paired Student’s T-tests. <bold>l</bold> Representative electron micrographs of mitochondria in Ctrl and PMVK-expressing cells and quantification of mitochondrial perimeters. M: Mitochondria. Mean +/− SD of <italic>n</italic> = 103 (Ctrl) and <italic>n</italic> = 106 (PMVK) mitochondria. Representative of <italic>n</italic> = 3 independent biological experiments. Scale bar: 300 nm. (*<italic>p</italic> &lt; 0.05; **<italic>p</italic> &lt; 0.01; ***<italic>p</italic> &lt; 0.001).</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Cholesterol biosynthetic branch participates in PMVK-induced senescence.</title><p><bold>a</bold> Schematic representation of the MVA pathway and subbranches stemming from Farnesyl-5-Pyrophosphate, including farnesylation (red), geranylation (purple), cholesterol synthesis (blue), ubiquinone synthesis (gold) and dolichol biosynthesis (green). First specific enzymes of each subbranch are indicated. <bold>b</bold> Quantification of number of cells after transfection with siRNA against PMVK and enzymes of downstream subbranches of the MVA pathway in PMVK-expressing cells. Mean +/− SEM representative of <italic>n</italic> = 4 independent biological replicates. RM one-way ANOVA test. <bold>c</bold> Representative micrographs of Ctrl and PMVK-expressing cells upon siCtrl or siFDFT1 transfection (scale bar: 100 µm) and cell number quantification. Mean +/− SEM of <italic>n</italic> = 5 independent biological replicates. RM one-way ANOVA test). <bold>d</bold> Quantification of SA-β-gal positive cells in Ctrl- and PMVK-expressing cells upon siCtrl or siFDFT1 transfection. Mean +/− SEM of <italic>n</italic> = 5 independent biological replicates. RM one-way ANOVA test. <bold>e</bold> RT-qPCR of <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> genes in Ctrl and PMVK-expressing cells upon siCtrl or siFDFT1 transfection. Mean +/− SEM of <italic>n</italic> = 6 independent biological replicates. RM one-way ANOVA test. <bold>f</bold> Cholesterol assay using filipin fluorescent sensor in Ctrl, PMVK-, and PMVKmut-expressing cells. Scale bar: 150 µm. Relative quantification of intracellular cholesterol level. Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. RM one-way ANOVA test. <bold>g</bold> RT-qPCR against <italic>ABCA1</italic> and <italic>ABCG1</italic> genes in Ctrl, PMVK-, and PMVKmut-expressing cells. Mean +/− SEM of <italic>n</italic> = 3 independent biological replicates. RM one-way ANOVA test. (*<italic>p</italic> &lt; 0.05; **<italic>p</italic> &lt; 0.01; ***<italic>p</italic> &lt; 0.001).</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Mitochondrial master regulator Estrogen-Related Receptor alpha mediates PMVK-induced senescence.</title><p><bold>a</bold>, <bold>b</bold> RT-qPCR of <italic>ESRRA</italic> and ERRα target genes (including <italic>UQCRFS1</italic>, <italic>NDUF5A</italic>, <italic>SDHA</italic>, <italic>SDHB</italic>) in empty vector (Ctrl), PMVK- or Kinase Dead (PMVKmut) PMVK-expressing cells. Mean +/− SEM of <italic>n</italic> = 4 independent biological replicates. RM one-way ANOVA test. <bold>c</bold>, <bold>d</bold> RT-qPCR of <italic>ESRRA</italic> and ERRα target genes in Ctrl and PMVK-expressing cells, upon siCtrl or siERRα transfection. Mean +/− SEM of <italic>n</italic> = 8 independent biological replicates. RM one-way ANOVA test. <bold>e</bold> Representative micrographs and cell number quantification of Ctrl and PMVK-expressing cells previously transfected with siERRα. Scale bar: 100 µm. Mean +/− SEM of <italic>n</italic> = 5 independent biological replicates. RM one-way ANOVA test. <bold>f</bold> Crystal violet staining of Ctrl and PMVK-expressing cells previously transfected with siERRα. <bold>g</bold> Quantification of SA-β-gal positive cells in Ctrl and PMVK-expressing cells upon siERRα transfection. Mean +/− SEM of <italic>n</italic> = 5 independent biological replicates. RM one-way ANOVA test. <bold>h</bold> RT-qPCR of <italic>p21</italic>^{<italic>CIP1</italic>} and <italic>IL-8</italic> genes in Ctrl and PMVK-expressing cells previously transfected with siCtrl or siERRα. Mean +/− SEM of <italic>n</italic> = 7 independent biological replicates. RM one-way ANOVA test. <bold>i</bold> Western blot on ERRα, p21^CIP1 and Tubulin in liver of ERRα WT and ERRα KO male mice fed either by chow diet (CD) or high-fat diet (HFD). Quantification of p21^CIP1 levels normalized to Tubulin levels. Mean +/− SEM of <italic>n</italic> = 3–4 male mice. Ordinary one-way ANOVA test. <bold>j</bold>, <bold>k</bold> RT-qPCR of p53 target genes (namely <italic>p21</italic>^{<italic>Cip1</italic>}, <italic>Gadd45a, Gdf15</italic>) and SASP members <italic>Cxcl1, Cxcl2 and Mmp12</italic> genes in liver of ERRα WT and ERRα KO male mice fed either by chow diet (CD) or high-fat diet (HFD). Mean +/− SEM of <italic>n</italic> = 3–4 mice. Ordinary two-way ANOVA test. (*<italic>p</italic> &lt; 0.05; **<italic>p</italic> &lt; 0.01; ***<italic>p</italic> &lt; 0.001).</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>A key role for cholesterol-ERRα axis in promoting cellular senescence.</title><p>The experimental models, human cells through manipulating the MVA pathway or WT or ERRα KO mice subjected or not to a HFD (high-fat diet), indicate that cholesterol accumulation triggers ERRα activation. In both in vitro and in vivo conditions, ERRα is determinant to mediate the subsequent cellular senescence phenotype. Mechanistically demonstrated in vitro, the upregulation of ERRα target genes enhances mitochondrial dysfunction, through electron transport chain (ETC) alteration, drop in mitochondrial membrane potential (ΔΨ) and ROS production, ultimately resulting in cellular senescence.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Nadine Martin, David Bernard.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41514_2023_128_MOESM1_ESM.pdf\"><caption><p>Supplementary file</p></caption></media>", "<media xlink:href=\"41514_2023_128_MOESM2_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Structured patient data play a key role in all types of clinical research. These data have a well-defined schema or data model with data elements that have a defined meaning and format. Structured patient data are a key component in nearly every clinical study database and are valuable for research purposes, as data points for cross-patient analysis can be easily accessed and analyzed. High-volume data (imaging, sensor, genomic) for example need to be linked to structured patient attributes (e.g., presence of disease, age, gender, etc.) for data analysis to identify features which are associated with good or poor outcome of a disease in a population. Artificial intelligence (AI) algorithms for the interpretation of medical images or sensor data also require clinical diagnoses or findings (e.g., pneumothorax) for training and validation purposes.</p>", "<p id=\"Par3\">The type of research that can be performed on structured data is significantly more powerful than on unstructured data. For example, when evidence for the efficacy of a new medical intervention needs to be established, the strongest tool is a randomized controlled trial (RCT)^{##REF##7261638##1##}. In RCTs, data are collected prospectively and they must be of high quality. While RCTs create a standardized environment for the intervention, other conditions in the patient’s experience may be very diverse. These deviations might affect efficacy, thus studies on Real-World Data (RWD) and Real World Evidence (RWE) play an increasingly important role in assessing medical products and interventions^{##REF##33063841##2##}. Potential sources for RWD include electronic health records (EHR) and insurance claims data^{##REF##31290181##3##}.</p>", "<p id=\"Par4\">Patient data cover a wide range of categories, as illustrated in Fig. ##FIG##0##1##. Structured patient data can be represented in a tabular format and consist of many different variables such as diagnosis code, therapeutic procedure, vital signs, or outcome data like response to treatment or survival time. Due to the variety of medical terminology, variables may contain thousands of different attributes. The attribute scope is best demonstrated by the systematized nomenclature of medicine (SNOMED), which contains more than 300,000 non-synonymous concepts^{##REF##19007439##4##}. In principle, each SNOMED concept can be an attribute of a structured patient data variable. Obviously, this estimate is conservative because many medical terms require post-coordination of SNOMED codes.</p>", "<p id=\"Par5\">Imaging data constitute another major category of patient data. Data are generated from imaging modalities like computer tomography or microscopy and are characterized by large data volumes per patient. Likewise, sensor data, such as electrocardiograms, have been traditionally collected in an intensive care unit or perioperative setting. Recently, wearable devices like smart watches became another source of sensor data. Genomic data are mostly generated by sequencing of human material. Resulting data sets can be very large, for example, when a patient’s whole genome is analyzed.</p>", "<p id=\"Par6\">Finally, unstructured data in patient documents are a frequently used data category. Today, a large portion of clinical information in EHR systems is still stored in free text documents such as clinical notes and discharge letters^{##UREF##0##5##}. Unstructured data do not have a predefined data model. Such data still contain valuable medical information, but this is not directly accessible for analysis. Data first have to be extracted into a structured data model, either manually or by means of natural language understanding (NLU) algorithms^{##UREF##1##6##}.</p>", "<p id=\"Par7\">Due to their importance for clinical research, structured patient data are captured within validated study databases. In contrast, most commercial EHR systems are currently not designed for clinical research and the majority of content is comprised of unstructured data^{##UREF##0##5##,##REF##31472738##7##}. Therefore, for the purpose of research, many data points are extracted by manual chart review from EHR systems and entered into study databases via electronic case report forms (eCRFs) (cf. Fig. ##FIG##1##2##), a laborious and very costly process making clinical research very expensive^{##REF##34035789##8##}. For example, Pronker et al. estimated a cost of €200,000 for the correction of erroneous data in three trials^{##REF##21284707##9##}.</p>", "<p id=\"Par8\">Development of new drugs is extremely costly (DiMasi et al. estimate capitalized cost for research and development of $2,870 million per approved drug^{##REF##26928437##10##}) and therefore is generally the sole domain of large pharmaceutical companies. A significant portion of these development costs relate to clinical studies, in particular prospective interventional trials. Developing an improved study database design with lower cost per valid data point could improve feasibility and delivery time of clinical studies. Further, it could foster investigator-initiated trials (IITs), which are driven primarily by medical needs and not by economic interests.</p>", "<p id=\"Par9\">The objectives of this manuscript are to answer the following research questions:<list list-type=\"bullet\"><list-item><p id=\"Par10\">What general characteristics are required for study databases to improve efficiency and effectiveness of the data collection process?</p></list-item><list-item><p id=\"Par11\">Is it feasible to implement and operate such an improved database in today’s setting of a university hospital?</p></list-item></list></p>", "<p id=\"Par12\">We performed our study and proof of concept implementation at the Heidelberg University Hospital, a major tertiary referral hospital in Germany with approximately 80,000 inpatient admissions and more than one million outpatient visits per year. In this context, we elicited requirements for a next-generation study database as outlined in our first objective. To test these requirements for validity and feasibility, we implemented a prototype at the Heidelberg University Hospital for 11 clinical departments.</p>" ]

[ "<title>Methods</title>", "<title>Requirements of next-generation study databases for patient data</title>", "<p id=\"Par47\">We identified desiderata for a more efficient and effective study database from ongoing study projects at Heidelberg University Hospital, Germany. Between May 2021 and July 2023, we gathered and analyzed 110 features and functionalities of electronic data capture (EDC) systems requested from the local EDC development team by data scientists and clinicians representing 11 clinical disciplines. For the process of collecting, assessing, and ordering these items, we used the <italic>issues</italic> function of our local GitLab-system (<ext-link ext-link-type=\"uri\" xlink:href=\"https://gitlab.com\">https://gitlab.com</ext-link>). Managing the software development process with this kind of system is considered best-practice since requirements can be directly linked to feature development of the EDC software. In monthly meetings, the EDC development team analyzed and summarized the requirements for improved study databases, as detailed in the results section.</p>", "<title>Technical setting for next-generation study databases in Heidelberg</title>", "<p id=\"Par48\">After defining the requirements of a next-generation study database, the next logical questions were “Is implementation of a next-generation study database with these characteristics feasible in a real university hospital setting? If so, what limitations exist presently?” To answer these questions, we conducted a proof of concept study at Heidelberg University Hospital. The main EHR system at this hospital is i.s.h.med (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.cerner.com/de/de/loesungen/ishmed\">https://www.cerner.com/de/de/loesungen/ishmed</ext-link>). We used the MDM-Portal as our FAIR infrastructure for Case Report Forms (CRFs). We selected OpenEDC^{##REF##34806987##14##} as the EDC system for the case study because it is open-source (permitting custom extensions and interfaces) and CDISC ODM-compliant. We installed OpenEDC as client-server system in the hospital’s intranet. We captured patient data (using iPad tablet computers) and medical documentation by healthcare professionals (using personal computers) in OpenEDC. We created patient-specific hyperlinks in the EHR system to the web-based graphical user interface of OpenEDC (frontend integration). For data transfer from EDC to EHR, we generated files in the Portable Document Format (PDF) and sent them to the EHR system with a Health Level 7 (HL7, <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.hl7.org\">https://www.hl7.org</ext-link>) version 2-based communication server (Orchestra version 4.10 from x-tention Informationstechnologie GmbH, <ext-link ext-link-type=\"uri\" xlink:href=\"https://x-tention.com/en/overview/orchestra-ehealth-suite\">https://x-tention.com/en/overview/orchestra-ehealth-suite</ext-link>). The Medical Data Integration Center (MeDIC) of Heidelberg University Hospital implemented a data exchange from the EHR to the EDC and provided custom ETL routes for selected clinical data elements. We developed a CDS prototype as a web service.</p>", "<title>Digital medical history proof of concept study with EHR integration</title>", "<p id=\"Par49\">To assess technical and clinical feasibility of a next-generation study database, we conducted a proof of concept study on digital medical history with EHR integration at Heidelberg University Hospital. In the eleven-month pilot phase (September 2022 – July 2023) the data for 2,217 patients were documented in 19 EDC systems by 11 clinical departments (surgery, hematology, pediatrics, anesthesiology, radiation oncology, ophthalmology, gynecology, dermatology, gastroenterology, psychosomatics, and psychiatry) using the workflow of EDC with EHR integration as presented in Fig. ##FIG##5##6##. Patients answered the medical history questions on iPads provided for this task. Collected data were transferred simultaneously into the EHR system and into a study database (CDISC ODM format).</p>" ]

[ "<title>Results</title>", "<p id=\"Par13\">Corresponding to the dual objectives of this study, two result sections are presented. First, the requirements relevant for a next-generation study database are described. They were derived from users’ requests and cover a wide variety of aspects such as data comparability, EHR integration, and patient generated data. This section is followed by the description of a prototype software implementation at Heidelberg University Hospital based on these requirements.</p>", "<title>Requirements</title>", "<p id=\"Par14\">New study results must be compared to and interpreted in the context of prior study results. Therefore, researchers should consider reuse of data structures from prior studies of the same disease at the design stage of a new study database. Following the <italic>FAIR</italic> data principles of findability, accessibility, interoperability, and reusability^{##REF##26978244##11##} can foster access to prior studies’ structural metadata (e.g., eCRFs). In conjunction with <italic>semantic annotation</italic> of data elements (to provide clear definitions for each data element), FAIR access to metadata can foster data compatibility between new studies and prior research.</p>", "<p id=\"Par15\">If clinical research is expected to be practice changing (e.g., new diagnostic or therapeutic approaches), approval from regulatory authorities is required. This means that study databases must <italic>conform to regulatory data standards</italic>. A key requirement in this context is traceability of data point origins (audit trail) to establish trust in the data, which is provided by Clinical Data Interchange Standards Consortium (CDISC, <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.cdisc.org\">https://www.cdisc.org</ext-link>) conform systems. Many other commonly used data collection tools (e.g., Microsoft Excel, IBM SPSS Statistics, or similar software) do not meet the demand for an audit trail during data capture.</p>", "<p id=\"Par16\">Ideally, EHR data should be well-structured, of high quality, and suitable for clinical research. If that is the case, electronic data capture could be done through <italic>EHR-integration</italic>, potentially bi-directionally. Import of EHR data into the electronic data capture (EDC) should be possible (e.g., extraction of laboratory results) and export should be feasible as well (e.g., a clinical note derived from a structured EDC of a patient visit into the EHR). While EHR data include all categories of clinical data (see also Fig. ##FIG##0##1##), research often mandates more data points than generated in routine clinical care (including additional diagnostic procedures or more visits for a detailed patient follow-up). Therefore, extraction, transformation, and loading (ETL) of data from an EHR system can only contribute a subset of data for a study database, requiring a combination of EHR and EDC data.</p>", "<p id=\"Par17\">EDC systems need to be disease-specific and adaptable to a specific study setting (e.g., a clinical study about acute myeloid leukemia). With more than 10,000 coarsely-grained diagnoses in the International statistical classification of diseases and related health problems (ICD)^{##UREF##2##12##}, <italic>scalable software development</italic> methods for disease-specific systems are needed to facilitate implementation of study databases. Model-driven software development is an established method and allows generating software from a model description in contrast to error-prone and laborious manual software programming.</p>", "<p id=\"Par18\">To improve outcome research, clinical study databases should not only contain comprehensive, high data quality that cover the full scope of <italic>medical documentation</italic> (e.g., inpatient and outpatient visits capturing all data generated by healthcare professionals) but also include <italic>patient generated data</italic>, such as patient reported outcome measures (PROMs)^{##REF##36990457##13##}. PROMs would permit extended plausibility checks, identification of biases in the data, and detailed assessment of diagnostic and therapeutic effects.</p>", "<p id=\"Par19\">Study databases as well as <italic>clinical decision support</italic> (CDS) used in patient care depend on high-quality structured data. Integrated systems for clinical research and routine care should avoid redundant data capture. Given the general resource constraints of clinical research and care, every data point should be documented only once and be re-used when necessary. CDS could be used to improve adherence to medical guidelines, foster patient safety, and at the same time support research study workflows.</p>", "<p id=\"Par20\">Based on the described desiderata for study databases, a <italic>next-generation study database</italic> should have the following characteristics:<list list-type=\"order\"><list-item><p id=\"Par21\">Backward Compatibility through FAIR access to eCRFs (e.g., structural metadata) with semantic annotation</p></list-item><list-item><p id=\"Par22\">Conformity with regulatory data standards and audit trail capability</p></list-item><list-item><p id=\"Par23\">Integration of EDC and EHR</p></list-item><list-item><p id=\"Par24\">Scalable EDC</p></list-item><list-item><p id=\"Par25\">Integration of clinical team documentation with the EDC system.</p></list-item><list-item><p id=\"Par26\">Collection of patient-generated data (e.g., PROMs)</p></list-item><list-item><p id=\"Par27\">Clinical decision support leveraging integrated data from EHR and EDC</p></list-item></list></p>", "<title>Prototype software implementation</title>", "<p id=\"Par28\">A key requirement for the prototype implementation is a regulatory compliant and scalable EDC software. For our case study, we used OpenEDC^{##REF##34806987##14##} as the EDC system based on CDISC’s operational data model (ODM)^{##UREF##3##15##}. OpenEDC can import eCRFs in CDISC ODM format. In addition, the portal of medical data models^{##UREF##4##16##} (MDM-Portal, <ext-link ext-link-type=\"uri\" xlink:href=\"https://medical-data-models.org/\">https://medical-data-models.org/</ext-link>) provides over 25,000 CRFs with semantic annotations, which can be imported directly into OpenEDC and adapted to study-specific documentation needs. Reuse of CRFs from MDM portal makes EDC development more scalable by allowing new studies to reuse elements, which reduces workload for medical design, programming, and testing. Since OpenEDC is based on ODM, the semantic annotations of the forms’ definitions are also included in the final data file alongside stored questionnaire responses.</p>", "<p id=\"Par29\">In order to provide FAIR access to eCRFs with semantic annotation the case study, we uploaded the eCRFs to collect the medical history to the MDM portal (Fig. ##FIG##2##3##). All data elements were annotated with Unified Medical Language System (UMLS)^{##REF##14681409##17##} codes by physicians to provide language-independent semantic annotation.</p>", "<p id=\"Par30\">Figure ##FIG##3##4## presents an example for integration of EDC and EHR data: After patient questionnaires were collected with an iPad, a PDF report was transferred into the EHR system in addition to data storage in the EDC database.</p>", "<p id=\"Par31\">In addition, EDC was integrated into the hospital’s clinical EHR workstations: In the EHR’s patient list, we implemented a web link to the EDC system for the clinical team to document in the EDC (see also Supplementary Fig. ##SUPPL##0##1##). This link contains the patient record number, current clinical user identification, and an encrypted hash. Selecting the link opens the EDC system while maintaining the context of the currently selected patient from the EHR list and the current clinical user. The encrypted hash provides a secure mechanism for logging into the EDC systems without requiring additional password entry.</p>", "<p id=\"Par32\">Patients in internal medicine completed identical questionnaires at follow-up visits as often as 15 times per patient. We developed a prototype for a patient summary as an example for clinical decision support. This overview page presents the course of symptoms over time (available from EDC). These findings are integrated with selected laboratory parameters over time (available via ETL from the EHR system) to allow CDS functionality (see Fig. ##FIG##4##5##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par33\">Today, EDC and EHR data are usually not integrated. However, data collected in clinical care and in research at university hospitals are closely related. Informed by 19 EDC projects from Heidelberg University Hospital, we collected, consolidated, analyzed, and prioritized feature requests for improved study databases. We identified seven characteristics of <italic>next-generation study databases</italic> and performed a local proof of concept study to assess technical and clinical feasibility of this approach. We engaged 11 clinical departments with this study making it more likely that our findings would be generalizable and applicable to other clinical settings. Overall, we demonstrated that next-generation study databases are feasible in the current clinical setting.</p>", "<p id=\"Par34\">We showed the feasibility of <italic>FAIR access to eCRFs</italic> by uploading medical history forms to the MDM portal. MDM and OpenEDC provide semantic annotation of data elements with UMLS codes thus meeting this criterion. Despite several public demands for FAIR principles in clinical research^{##REF##26978244##11##,##REF##26108979##18##}, at present a vast portion of clinical studies does not meet FAIR principles. At the time of manuscript preparation, clinicaltrials.gov (<ext-link ext-link-type=\"uri\" xlink:href=\"https://clinicaltrials.gov\">https://clinicaltrials.gov</ext-link>) listed more than 456,000 studies^{##REF##21366476##19##}, turning this requirement into a large-scale challenge. The feasibility of data comparison with prior research is greatly facilitated by compatible and congruent data structures in previous and new study databases. There is a paucity of available, sharable CRFs (structural metadata) and only eligibility criteria are published on clinicaltrials.gov. For some studies, subject-level data may be requested, but the usefulness of the data is limited due to the absence of related CRFs explaining the data collection. A very good exception from such “unFAIR” studies is the database of Genotypes and Phenotypes (dbGaP) from NCBI^{##REF##17898773##20##}, which provides descriptive and structural metadata for over 2,000 studies. On request, patient-level data are also available. Recently, metadata from dbGaP with semantic annotations were made available in the MDM portal for 585 studies (as of August 9, 2023). Re-use of well-proven CRFs can improve comparability of study data. Semantic annotation of data elements facilitates data integration with prior studies, as it supports mapping of data elements between different data sources by matching semantic codes. Interpretation of new study data must include comparisons with prior study results. To facilitate data integration between different studies, corresponding data elements need to be mapped, which is facilitated by semantic annotation of data elements (e.g., Logical Observation Identifier Names and Codes, LOINC, for laboratory data^{##REF##12651816##21##}).</p>", "<p id=\"Par35\">Study databases must comply with regulatory standards to enable data submissions from prospective and interventional studies to regulatory agencies such as the European Medicines Agency (EMA), United States Food and Drug Administration (FDA), Pharmaceuticals and Medical Devices Agency (PMDA) in Japan, or National Medical Products Administration (NMPA) in China. Therefore, the use of data formats endorsed by these agencies is preferable to minimize efforts for data preparation during the submission process. Regulatory agencies have agreed on standards issued by the Clinical Data Standards Interchange Consortium (CDISC, <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.cdisc.org\">https://www.cdisc.org</ext-link>). While FDA^{##UREF##5##22##}, PMDA^{##UREF##6##23##}, and NMPA^{##UREF##7##24##} have endorsed CDISC standards or even require those for data submission, EMA is preparing to adopt these standards^{##UREF##8##25##}. For EDC systems, CDISC ODM is especially suitable, since it was designed as an exchange format for clinical metadata and data^{##UREF##3##15##}. CDISC ODM also supports an audit trail, which is another key feature of regulatory-compliant data collection (traceability of data point origin).</p>", "<p id=\"Par36\">At present, the EDC remains separate from the EHR. Manual review of EHR charts is performed for source data verification. <italic>EHR and EDC data integration</italic> can have several benefits: EDC data can be used to enrich EHR data and to avoid redundant data entry, when for example patient questionnaires are transferred from the EDC into the EHR systems. Our proof-of-concept study demonstrated that this is feasible with standard functionalities of the EHR legacy systems (Fig. ##FIG##3##4##). Calling EDC data from within the EHR can simplify and enrich medical documentation for the clinical team working primarily with the EHR system. We demonstrated that access to EDC data from the EHR is feasible, but—from our experience—is technically more demanding as it requires a single-sign-on functionality for the EHR and the EDC and extended configuration capabilities to maintain patient context. However, single-sign-on is important for clinical acceptance.</p>", "<p id=\"Par37\">Further, the validity of EDC data will be improved, if they are also used directly in routine care. If data quality criteria for EDC are met, data transfer from the EHR into the EDC is possible (e.g., laboratory data). The Observational Medical Outcomes Partnership (OMOP) successfully established retrospective analysis of EHR data^{##REF##22037893##26##}. For new diagnostic and therapeutic procedures, we need prospective clinical studies. The strong regulatory requirements for interventional trials require validation procedures with a focus on data quality. Further research is needed to assess automated data transfer from the EHR into the EDC systems for interventional trials.</p>", "<p id=\"Par38\">EDC <italic>software development</italic> is complex, because it must reflect the complexity of clinical medicine with a high degree of verisimilitude. More than 10,000 diagnoses in ICD-10¹² primarily correspond to billing requirements. For each diagnosis used, specific data elements are needed in an EDC system. More finely grained terminologies such as SNOMED address more specific aspects of clinical research. As shown on clinicaltrials.gov, hundreds of thousands of clinical studies were conducted and each may have a different data structure to address the study’s protocol requirements. Typically, each study captures hundreds of disease-specific data elements making the design, development, maintenance, and quality control of the EDC resource intense. Thus, efficient implementation of study databases is a key success factor for clinical research.</p>", "<p id=\"Par39\">In EDC development, the current state-of-the-art is manual development of EDC systems’ data field by data field. Underutilized, the re-use of eCRFs from prior studies and (semi-)automatic generation of study databases instead of manual programming can make EDCs more scalable. However, the large variety of EDC systems (more than 90 systems according to G2, <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.g2.com/categories/electronic-data-capture-edc\">https://www.g2.com/categories/electronic-data-capture-edc</ext-link>) and metadata formats for eCRF design do not support the sharing of eCRFs among EDC systems. It would be highly desirable for researchers if all EDC systems would support the importing of metadata based on the FDA data standards (at present CDISC ODM) to foster re-use of CRFs. In our case study, we used OpenEDC^{##REF##34806987##14##}, because it is an open-source EDC system, which can import eCRFs in CDISC ODM format. Additionally, OpenEDC is integrated into the MDM portal and with only one click (“start data capture”) in the MDM portal, an OpenEDC database is created on the local computer allowing instant data collection.</p>", "<p id=\"Par40\"><italic>Medical documentation</italic> by healthcare professionals in the course of delivering care is a key source for data for EDC systems. While large semantic overlaps between routine documentation and study documentation can be found, study documentation is much more detailed and structured than EHR data. Therefore, it should be feasible to transfer summaries of clinically relevant aspects from the EDC data into the EHR. Re-use of patient data from other systems (e.g., laboratory information systems) also avoids error-prone redundant data entry. In our proof of concept study, we demonstrated the technical feasibility of a patient summary with EHR integration and ETL of laboratory data. As a long-term perspective, a comprehensive EHR with the full patient journey would also provide new opportunities for medical research.</p>", "<p id=\"Par41\"><italic>Patient generated data</italic> such as the medical history or patient reported outcomes (PROs) are important for routine care and research. Our proof of concept study demonstrated that non-redundant collection of these data in the EDC and the EHR systems is technically and clinically feasible using a standardized EHR interface for PDF-transfer with an HL7-based communication server (HL7-MDM-interface). Because the patients enter the data, data collection was feasible without additional clinical personnel in a resource-limited environment. A frequent non-technical problem when collecting PRO are license restrictions for PRO forms usage. Paying a license fee for a PRO form for each patient generates a large financial and administrative overhead barring large-scale implementation. Development of free PRO instruments should be encouraged through public initiatives.</p>", "<p id=\"Par42\">Currently, EDC data are collected separately from clinical data and therefore cannot contribute to <italic>clinical decision support</italic>. CDS may improve the adherence to clinical guidelines and contribute to more accurate diagnoses^{##UREF##9##27##}, patient safety, and treatment quality. CDS depends on (near) real-time, high quality clinical data. Thus, an EHR integrated EDC could contribute data required for CDS. Examples include calculations of disease scores or proposed diagnostic or therapeutic procedures for a patient^{##REF##32102108##28##}. However, at least in the European Union presenting more than basic data points makes CDS a medical device, which must be developed and placed on the market according to the medical device regulation (MDR)^{##UREF##10##29##}. The resulting workload for software manufacturers and software operations managers may be prohibitive. Further research is required to determine if CDS based on EDC data can provide additional clinical benefits justifying the additional MDR efforts.</p>", "<p id=\"Par43\">Many publications discuss the interoperability of medical information systems based on the FHIR standard allowing the re-use of EHR data in retrospective studies. The Observational Health Data Sciences and Informatics (OHDSI)^{##UREF##11##30##} community has very successfully demonstrated the power of open-source systems for large-scale health data analytics in observational settings. We propose to focus on regulatory-compliant systems in the future to enable interventional research that changes medical practice.</p>", "<p id=\"Par44\">The concepts presented in this manuscript are independent of the implementation in a German hospital. For example, Garza et al. have shown examples of prototypes for eSource-based trial data from European countries, the United States of America and beyond^{##UREF##12##31##,##UREF##13##32##}. These examples further illustrate the need for next-generation study databases.</p>", "<p id=\"Par45\">Our study has several limitations: First, our proof of concept study had a prototypic character and scalability for multi-centric trials was not assessed. We conducted our research in conjunction with a single EHR system and feasibility of developing a similar workflow in other EHR systems needs further investigation. Further, we limited our study to one university hospital and feasibility to extend our approach to other institutions still requires testing.</p>", "<p id=\"Par46\">In conclusion, next-generation study databases should be FAIR, regulatory compliant, EHR-integrated, and scalable EDC systems. Medical documentation and patient generated data should be included. EDC should support clinical decision support. We demonstrated in a proof of concept study that such systems are technically and clinically feasible.</p>" ]

[]

[ "<p id=\"Par1\">Structured patient data play a key role in all types of clinical research. They are often collected in study databases for research purposes. In order to describe characteristics of a next-generation study database and assess the feasibility of its implementation a proof-of-concept study in a German university hospital was performed. Key characteristics identified include FAIR access to electronic case report forms (eCRF), regulatory compliant Electronic Data Capture (EDC), an EDC with electronic health record (EHR) integration, scalable EDC for medical documentation, patient generated data, and clinical decision support. In a local case study, we then successfully implemented a next-generation study database for 19 EDC systems (<italic>n</italic> = 2217 patients) that linked to i.s.h.med (Oracle Cerner) with the local EDC system called OpenEDC. Desiderata of next-generation study databases for patient data were identified from ongoing local clinical study projects in 11 clinical departments at Heidelberg University Hospital, Germany, a major tertiary referral hospital. We compiled and analyzed feature and functionality requests submitted to the OpenEDC team between May 2021 and July 2023. Next-generation study databases are technically and clinically feasible. Further research is needed to evaluate if our approach is feasible in a multi-center setting as well.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41746-023-00994-6.</p>", "<title>Acknowledgements</title>", "<p>We acknowledge the generous provision of questionnaires by clinical partners from the Departments of Surgery, Hematology, Pediatrics, AnesthEsiology, Radiation Oncology, Ophthalmology, Gynecology, Dermatology, Gastroenterology, Psychosomatics, and Psychiatry at the Heidelberg University Hospital. This study received no funding. For the publication fee we acknowledge financial support by Deutsche Forschungsgemeinschaft within the funding programme “Open Access Publikationskosten” as well as by Heidelberg University.</p>", "<title>Author contributions</title>", "<p>M.D. conceptualized the study and wrote the first draft of the manuscript. M.B. programmed the integration of EDC and EHR systems. T.D., S.C.F., L.J.K., C.N., T.M.P., and N.Z. collected the requirements by collaborating with the clinical departments. U.E. supervised quality management. F.F., C.U.L., and P.K. thoroughly revised the manuscript. A.M. conceptualized, and M.K. implemented the connection to the data integration center. M.G. designed the integration between EDC and EHR and prepared the final version of the manuscript. All authors read and approved the final manuscript.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>", "<title>Data availability</title>", "<p>This study is not based on EHR-records. Instead, the basis for requirements elicitation were issues from the local GitLab systems of Heidelberg University Hospital, since these issues contain confidential information they cannot be made available outside the institution.</p>", "<title>Code availability</title>", "<p>The code of a containerized version of OpenEDC is available at <ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/OpenEDC/OpenEDC-Docker\">https://github.com/OpenEDC/OpenEDC-Docker</ext-link> along with a tutorial how to run it. On <ext-link ext-link-type=\"uri\" xlink:href=\"https://medical-data-models.org/\">https://medical-data-models.org/</ext-link> a standalone version of OpenEDC can be run directly in a web browser after registration (free of charge).</p>", "<title>Competing interests</title>", "<p id=\"Par50\">The authors declare no competing interests.</p>", "<title>Ethics approval</title>", "<p id=\"Par51\">The authors confirm that they have complied with all relevant ethical regulations. No data of individual patients were directly used for this study. Evaluation of the prototype data capture system was approved by the responsible Ethics Committee of the Medical Faculty at Heidelberg University (ethics committee study number: S-607/2023).</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Categories of patient data.</title><p>Structured patient data play a key role in nearly every clinical study database.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Manual data transfer from EHRs into study databases is currently the most frequently used method of data collection in interventional clinical trials.</title><p>It is a slow, error-prone, and expensive process.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Data model of the questionnaire with semantic annotation (UMLS codes for data elements).</title><p>Available from MDM-Portal (<ext-link ext-link-type=\"uri\" xlink:href=\"https://medical-data-models.org/45841\">https://medical-data-models.org/45841</ext-link>).</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Sample questionnaire for Digital Medical History.</title><p>Questions address fever, night sweats, weight loss, infectious diseases, lack of appetite, general performance, etc. <bold>a</bold> Representation of questionnaire on tablet. <bold>b</bold> Document in EHR generated from tablet data (in German). Both artifacts were generated from the data model in the previous figure. Note: No actual patient data are presented here.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Patient summary in the EHR generated from EDC system.</title><p>Using the report feature in the EDC system, a summary of PROM data (nausea, fatigue) and laboratory data (hemoglobin, leukocytes) is generated and displayed as a chart.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>EDC workflow with EHR integration.</title><p>Patient barcode is scanned with an iPad to identify the patient. After confirmation of patient’s name and date of birth, a suitable questionnaire is selected and the iPad is handed to the patient for data entry. When data collection is completed, data are transferred simultaneously into EHR system and into study database.</p></caption></fig>" ]

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[ "<media xlink:href=\"41746_2023_994_MOESM1_ESM.pdf\"><caption><p>Supplemental Material</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Foodborne diseases are considered an important cause of mortality and morbidity and a significant obstruction in socioeconomic development worldwide^{##UREF##0##1##}. One of the strategies used to lower the costs and incidence of foodborne diseases is the detection of foodborne pathogens to serve a safe supply of food and inhibit foodborne diseases. The nucleic acid base detection method is one of the most rapid and widely used methods in the detection of foodborne pathogens; it depends on hybridization between the target sequence of the nucleic acid and oligonucleotide primers or probes complementary to the specific nucleic acid sequence of the targeted bacteria^{##REF##24375418##2##}.</p>", "<p id=\"Par3\">The design of primers and probes is essential, especially for nucleic acid base detection methods, and it is a preliminary and critical step. This task can be challenging and requires the identification of highly unique conserved regions of target sequences and the ability to display high sensitivity, i.e., the ability to amplify its intended target, and specificity, i.e., the ability not to amplify any nontarget. In addition, the biological parameters of the primers, such as GC content, melting temperature, and the formation of secondary structures, which include self-dimers, hairpins and cross dimers, are essential for evaluating the efficient amplification of a target sequence.</p>", "<p id=\"Par4\">There are a number of software tools available to the public to design primers^{##UREF##1##3##}. However, there are no specific tools for designing primer–probe sets automated for the nucleic acid detection base method. Additionally, these software programs often have limitations in their proficiencies to perform target analysis. Users are typically required to use additional tools for testing primer specificity. They are usually not specific to detect target sequences that contain a significant number of mismatches and are consequently not suitable for application in nucleic acid detection methods. There are several simulation software programs that determine the amplification of amplicons of primer pair targets supplied by users but do not design primers^{##UREF##2##4##}, and some of them are difficult to use without bioinformatics knowledge^{##REF##23316117##5##}.</p>", "<p id=\"Par5\">To overcome these issues, we present FBPP, an open-source Python-based application supported with the SQL database for foodborne pathogen virulence factors with the ability to (i) design primers/probes using the modified Primer3 module to be suitable for detection purposes, (ii) perform PCR and gel electrophoresis photo simulations, and (iii) check the specificity of primers/probes. We believe that this application will be particularly useful in nucleic acid base detection methods.</p>" ]

[ "<title>Method, algorithm and implementation</title>", "<p id=\"Par6\">The FBPP program consists of four modules. The first module is sqlite3^{##UREF##3##6##}, which is used to create and access a database for virulence foodborne pathogen genes, while the Primer3 module^{##UREF##4##7##}, with some little bite modification to be suitable for detection purposes, is used to generate the candidate primer pairs for a given template sequence. Another module for PCR and gel electrophoresis photo simulation is created by using the Pydna module^{##UREF##5##8##}, and the last module for specificity checking uses the BLAST python module Bio. Blast from the Biopython project^{##UREF##6##9##} to look for matches between the primers and targets and not match with any nontarget region.</p>", "<p id=\"Par7\">Designing primers and probes in FBPP is accomplished in four stages: first, the target sequences are identified; in most situations, they are selected from the program database or through the input section. Next, the modified Primer3 module generates many candidate primer pairs according to the desired primer properties, which are identified by the user or using default primer properties. Then, the candidate primer pairs were subjected to PCR and gel electrophoresis simulation to calculate all amplicons from large lists of primers and ensure that the bands were not false negative results for the primers. Finally, the specificity checking process of success primers in the previous step, by default, uses the BLAST module with specific parameters that ensure high sensitivity such that it can detect a target that contains up to 35% mismatches to the primer sequence to exclude nonspecific primers to avoid false positives. The entire search process can be very long if each pair is searched with BLAST individually. To solve this problem, we saved the BLAST result in the entry database for each primer to avoid repeating the process in every run to the same target sequences, and in case unsaved primer goes to online BLAST, also to avoid being un updated program, all BLAST result for all primer will clear every three months to research again to online update BLAST.</p>", "<p id=\"Par8\">FBPP is implemented in Python and runs on an IDLE 3.7.4 platform. It accesses an SQL database over SQLite 3.10.1. The program was tested on a Windows 10 Home Server with an Intel (R) Core (TM) Processor i5-4210 U with 2.40 GHz and 4 GB RAM.moreover, an EXE file is available so that the user can run the application without the need for a python interpreter, python packages, modules, or any related program such as SQLite.</p>" ]

[ "<title>Result</title>", "<title>User interface</title>", "<p id=\"Par9\">The interface consists of two tabs; the first tab is “Add New Gene”, where users can insert new virulence genes (Fig. ##FIG##0##1##-A), and the second tab, “select primer”, has several sections where users can input the gene template, option process and other user-adjustable parameters (Fig. ##FIG##0##1##-B). In the first tab, there are two ways to enter the virulence gene information into the SQLite database: either by browsing and uploading the GenBank file from the computer or fetching it from NCBI using the accession number.</p>", "<p id=\"Par10\">In the second tab, the user has two options to predict the primer or probe: either by selecting the virulence gene from the program or by entering the sequence of the desired gene. When selecting the gene from the program, the gene information appears on a separate screen. Next, identify the desired properties of individual primers and pairs of primers. These properties include, for example, amplicon (PCR product) length, primer size, melting temperature and GC content. In addition to other options, users can also constrain the complementarity properties of primers to ensure that chosen primer candidates do not bind to themselves and that, in selected primer pairs, the forward primer does not bind to the reverse primer. For convenience, all default choices of parameters have been pretested and are likely to work well in detection applications.</p>", "<p id=\"Par11\">Users have three options: generate the candidate primer pairs for a given template, generate the candidate primer pairs with PCR &amp; gel electrophorese simulation or the specificity checking module uses BLAST in case the template is used from the program. Other options include the compare button to compare the template or gene with other sequences in the NCBI database. can be found under the “PCR Template” section.</p>", "<title>Presentation of results</title>", "<p id=\"Par12\">According to the user choice, three result reports were obtained. The report of the first option presents the specificity of the generated primers, including sequence, length, position on the consensus sequence for each oligo, Tm, GC content, self-complementarity, and self-3' complementarity (Fig. ##FIG##1##2##). The report of the second choice (Fig. ##FIG##2##3##) shows the same information of the first report plus the simulation of PCR process and figure of the observed band. The result of the third option reports the additional statement of specificity checking (Fig. ##FIG##2##3##). </p>", "<p id=\"Par13\">FBPP offers several features that are not found in other software tools. It is the only tool that specifies the prediction of primer/probe for foodborne pathogenic nucleic acid detection-based methods. In addition, it contains a database for most foodborne pathogen virulence genes; however, the program shows result simulation to avoid false negative results in detection tools.</p>", "<p id=\"Par14\">Another advantage of the FPBP program is the ability to check the specificity of the prime/probe and the number of mismatches that a specific primer pair must have to unintended targets and a custom 3’ end region where a certain number of mismatches must be present.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par15\">There are several tools available for the design of primers and probes; however, some of them have limitations that can be mentioned. One of these limitations is that some tools, such as Primer3 (Rozen and Skaletsky, 2000), cannot check specificity and make simulations, which can be accomplished by our program. Although it is a powerful and online tool for designing primers based on a single, short and conserved sequence, the same limitation was found with other software, such as BatchPrimer3^{##UREF##7##10##}, Primaclade^{##REF##15539448##11##}, PrimerIdent^{##REF##21346862##12##}, GeneFisher^{##UREF##8##13##}, Gemi^{##REF##23316117##5##} and PRISE2^{##UREF##9##14##}.</p>", "<p id=\"Par16\">Primer-BLAST^{##UREF##2##4##} is one of most famous primer design web browsers provided by NCBI. It combines Primer3 and BLAST along with the Needleman–Wunsch (NW) global alignment algorithm, which overcomes the short ages of local alignment for primer design purposes. Primer BLAST can generate candidate primer pairs and check specificity. However, Primer-BLAST inherits the limitations of Primer3. It does not specify for detection application use, and it has not contained silico PCR, GEL simulation and not define Database for foodborne pathogen which can achieved by FPBP.</p>", "<p id=\"Par17\">Other existing program packages for primer design, including Quant Prime, PRIMEGENS, PRIMEGENS, FastPCR and PrimedRPA, are specific in different applications, such as microarray analysis, DNA methylation pattern analysis of CpG islands, primer location determination, orientation, binding efficiency and primer melting temperature calculation for standard and degenerate oligonucleotides and recombinase polymerase amplification^{##UREF##10##15##–##REF##28502701##19##}.</p>", "<p id=\"Par18\">In this paper, we presented FBPP as a specific-purpose target-specific PCR primer/probe design tool that offers a group of features not found in other tools. It offers primer/probe design, PCR/gel electrophoresis simulation and checks of the specificity of the primer/probe. user-friendly graphical interface, virulence gene database included and pretested default choices for all parameters are provided to be easily usable without skill in bioinformatics or nonmolecular knowledge biologist users, while those more molecular biologists or bioinformatics can use advanced options where these parameters can be highly customized and input gene sequences.</p>", "<p id=\"Par19\">Nucleic acid‒based detection methods are gradually replacing or complementing traditional detection methods in routine microbiology laboratories. We expect FBPP to be a valuable assay design tool for application in these methods, working with highly variable sequences and DNA quality control via PCR.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par20\">In this paper, we presented FBPP as a specific-purpose target-specific PCR primer/probe design tool that offers a group of features not found in other tools. It offers primer/probe design, PCR/gel electrophoresis simulation and checks of the specificity of the primer/probe. user-friendly graphical interface, virulence gene database included and pretested default choices for all parameters are provided to be easily usable without skill in bioinformatics or nonmolecular knowledge biologist users, while those more molecular biologists or bioinformatics can use advanced options where these parameters can be highly customized and input gene sequences.</p>", "<p id=\"Par21\">Nucleic acid‒based detection methods are gradually replacing or complementing traditional detection methods in routine microbiology laboratories. We expect FBPP to be a valuable assay design tool for application in these methods, working with highly variable sequences and DNA quality control via PCR.</p>" ]

[ "<p id=\"Par1\">Foodborne pathogens can be found in various foods, and it is important to detect foodborne pathogens to provide a safe food supply and to prevent foodborne diseases. The nucleic acid base detection method is one of the most rapid and widely used methods in the detection of foodborne pathogens; it depends on hybridizing the target nucleic acid sequence to a synthetic oligonucleotide (probes or primers) that is complementary to the target sequence. Designing primers and probes for this method is a preliminary and critical step. However, new bioinformatics tools are needed to automate, specific and improve the design sets to be used in the nucleic acid‒base method. Thus, we developed foodborne pathogen primer probe design (FBPP), an open-source, user-friendly graphical interface Python-based application supported by the SQL database for foodborne pathogen virulence factors, for (i) designing primers/probes for detection purposes, (ii) PCR and gel electrophoresis photo simulation, and (iii) checking the specificity of primers/probes.</p>", "<title>Subject terms</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).</p>" ]

[]

[ "<title>Author contributions</title>", "<p>All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed M.A.S., M.S.A., H.A.H., M.M.R., M.N.A. The first draft of the manuscript was written by M.A.S. and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.</p>", "<title>Funding</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB). The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.</p>", "<title>Data availability</title>", "<p>The FBPP Design Tools Desktop application is available here: <ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/mohamedmoez1983/FBPP\">https://github.com/mohamedmoez1983/FBPP</ext-link>.</p>", "<title>Competing interests</title>", "<p id=\"Par22\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>(<bold>A</bold>): Screenshot of “Add New Gene Tab” in the FBPP program: (1) Switch from fetch to upload gene bank file, (2) entry of the accession numbers, (3) browse for the input gene bank file, and (4) the output information of file. (<bold>B</bold>): Screenshot of “Select Primer Tab” in the FBPP program. (1) Select virulence gene from Database, (2) entry of the gene Sequence, (3) click to design the primers or probe, (4) click to compare between template or gene with other sequence in NCBI database, (5) switch between the run options, (6) contains parameters specific to the selected primers and their PCR products or probe, such as the Tm of the PCR product, the primer length, the primer GC content, GC clamps at the 3’-end of the primer, and the PCR buffer conditions.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Example results of designing target-specific primers for the invA gene (virulence gene for salmonella), which contains a summary of basic properties for returned primer pairs.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Example results of option Blast for invA gene (virulence gene for salmonella), which contains (1) a summary of basic properties for returned primer pairs, (2) simulation of PCR process , (3) figure of the simulated band, (4) statement of specificity.</p></caption></fig>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Gastric cancer (GC) is one of the most prevalent digestive malignancies worldwide. A recent study shows that globally its incidence rate ranks fifth and its mortality ranks fourth^{##REF##35497064##1##}. Current treatment methods for GC include endoscopic examination, gastrectomy, and chemotherapy or adjuvant chemotherapy or neoadjuvant therapy. Although treatment efficacy has improved, outcomes are still very poor^{##REF##31521509##2##}. Finding possible biomarkers for early diagnosis or therapy targets to enhance patient outcomes for GC is therefore extremely important.</p>", "<p id=\"Par3\">The transmembrane protein PIEZO2 is a member of the PIEZO family and is crucial for the quick response of somatosensory neurons to mechanically generated currents. Its mechanical activation causes cations to flow into and activate additional Ca²⁺ channels, thus mediating Ca²⁺ influx, and regulating the cytoskeleton through RhoA activity^{##REF##29432180##3##}. Research shows that abnormal expression of PIEZO2 may be related to the prevalence and progression of cancer^{##REF##29432180##3##–##REF##30010255##5##}. Although PIEZO2 has been found linked to prognostic in patients with GC^{##REF##35991548##6##, ##UREF##0##7##}. However, there is a lack of further exploration of the value of immunotherapy, potential mechanisms of immune function, and prognostic subgroup analysis in the GC.</p>", "<p id=\"Par4\">This study uses the clinical data in the online database to conduct bioinformatics analysis on PIEZO2. We aimed to investigate the correlation of PIEZO2 with immune cell infiltration, immune-related genes, and immune checkpoint genes. Predicted the performance of PIEZO2 in immune checkpoint blocking therapy. The relationship between PIEZO2 and cancer stem cells and gene mutation in GC patients was analyzed, which saves time and work for clinical research in GC, and provides new therapeutic targets and research directions.</p>" ]

[ "<title>Methods</title>", "<title>Analysis of PIEZO2 differential expression in the TCGA and GEO databases</title>", "<p id=\"Par5\">High throughput sequencing data from the TCGA database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.cancer.gov/tcga/\">https://www.cancer.gov/tcga/</ext-link>), The expression matrix of the GSE54129 microarray was transformed into log2 in R after the original values of the data were retrieved from the GEO database. The University of California Santa Cruz (UCSC) Genome Browser Database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://xenabrowser.net/\">https://xenabrowser.net/</ext-link>) was used to retrieve the standardized pan-cancer dataset, and for each sample, the PIEZO2 gene expression data were extracted. The difference in PIEZO2 between tumor and normal tissues was assessed using the TCGA and GSE54129 datasets. We nalyse the ROC, obtained the AUC, and assessed the predictive value of PIEZO2 in tumor tissue and GC tissue using the R software package pROC (version 1.17.0.1).</p>", "<p id=\"Par6\">GC tissue samples were separated using a median split into high and low-expression groups^{##REF##35368661##8##}. Then, using the t-test function of the R software program, the significance of each gene change between the comparison and control groups was assessed. The statistically significant screening threshold was set as absolute log2-fold change (FC) &gt; 2 and adjusted <italic>P</italic> value &lt; 0.01. A volcano map was used to visualize the up and down DEGs and display the DEGs related to PIEZO2 in a heat map. To nalyse the association between PIEZO2 and OS, first-progression survival, and post-progression survival, the query probe ID 1,562,488 was examined using the online tool Kaplan–Meier Plotter (<ext-link ext-link-type=\"uri\" xlink:href=\"https://kmplot.com/analysis/index.php?p=service&amp;cancer=gastric\">https://kmplot.com/analysis/index.php?p=service&amp;cancer=gastric</ext-link>) (PPS)^{##REF##27384994##9##}.</p>", "<title>Prediction of PIEZO2 and GC stemness and gene mutation</title>", "<p id=\"Par7\">The TCGA Pan-Cancer dataset (PANCAN, N = 10,535, G = 60,499), which is unified and standardized, was acquired from the UCSC database. Each sample’s ENSG00000154864 (PIEZO2) gene expression information was taken from the database. Further, we screened the samples by methylation feature for each tumor obtained from previous research, EXPss, EREG-METHss, and RNAs tumor stemness scores^{##REF##29570990##10##}. The samples’ gene expression data and stemness index were combined. In addition, the MuTect2 program from GDC (<ext-link ext-link-type=\"uri\" xlink:href=\"https://portal.gdc.cancer.gov/\">https://portal.gdc.cancer.gov/</ext-link>) was used to process the basic nuclear variation data set of level 4 of all TCGA samples^{##REF##20164920##11##}. The samples’ gene expression data and stemness index were combined. In addition, the MuTect2 program from GDC (<ext-link ext-link-type=\"uri\" xlink:href=\"https://portal.gdc.cancer.gov/\">https://portal.gdc.cancer.gov/</ext-link>) was used to process the basic nuclear variation data set of level 4 of all TCGA samples^{##UREF##1##12##}. The purity data of each tumor was obtained from a previous study^{##REF##29343431##13##}, and the TMB, MSI, purity, and gene expression data of the sample were integrated, and each expression value was further transformed using log2 (x + 0.001). After excluding cancer types with less than three samples of a single cancer type, the expression data of 37 cancer types were obtained.</p>", "<title>The development and evaluation of a prognostic model for GC patients</title>", "<p id=\"Par8\">The data from survival time, survival status, and other pertinent features were combined using the R software package rms, and a nomogram was generated using the multifactor Cox technique to assess the predictive importance of these characteristics in 350 samples. The C index of the overall model is 0.66, 95% CI (0.61–0.71, p value = 1.4e−10).</p>", "<title>The relationship between PIEZO2 expression and immune cell infiltration and immune-related genes</title>", "<p id=\"Par9\">Each expression value was then converted using log2 (x + 0.001) utilizing the UCSC database’s unified and standardized pan-cancer dataset. Furthermore, we took the gene expression profile for GC out of the database and mapped it to the GeneSymbol. The correlation of immune-related cells in patients with GC according to gene expression was reevaluated using the R software package IOBR and the deconvo XCell approach^{##REF##34276676##14##, ##REF##29141660##15##}.</p>", "<title>Immune checkpoint analysis</title>", "<p id=\"Par10\">We further retrieved the expression data of the PIEZO2 gene’s marker genes and a total of 60 genes from the immune checkpoint pathway (inhibitory (24), stimulatory (36)) from the standardized pan-cancer dataset from the UCSC database^{##REF##29343431##13##}. Additionally, all of the normal samples were filtered, and each expression value underwent a further log2(x + 0.001) transformation. The Pearson correlation between PIEZO2 and the marker genes for five immunological pathways was then calculated.</p>", "<title>Functional analyses of PIEZO2 in GC</title>", "<p id=\"Par11\">We utilized the KEGG rest API (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.kegg.jp/kegg/rest/keggapi.html\">https://www.kegg.jp/kegg/rest/keggapi.html</ext-link>) to get the most recent gene annotation of the KEGG pathway for the functional enrichment analysis of the gene collection. The R software package org’s GO annotation of genes was utilized for the gene set function enrichment study. The background set utilized was Hs.eg.db (version 3.1.0). For GSEA, we used the GSEA software (version 3.0)^{##REF##16199517##16##}. We separated the samples into two groups based on PIEZO2 expression level (≥ 50%) and utilized c2.cp.kegg.v7.4.symbols.gmt subsets to nalyse important pathways and molecular processes^{##REF##21546393##17##}. We selected the lowest gene set as 5, the maximum gene set as 5000, and re-sampled 1000 times based on the gene expression profile and phenotypic categorization. A p-value of 0.05 and an FDR of 0.25 was regarded as statistically significant.</p>" ]

[ "<title>Results</title>", "<title>The expression level of PIEZO2 in GC tissues is correlation with stemness and gene mutation </title>", "<p id=\"Par12\">By analyzing the TCGA database and independent datasets, PIEZO2 can be used for the detection of GC tissue and is associated with late stages and worse prognosis of GC (Supplement Fig. ##SUPPL##0##S1##, Supplement Table ##SUPPL##0##S1##). And the expression of PIEZO2 is positively correlated with the gene expression of tumor progression and metastasis in GC (Supplement Fig. ##SUPPL##0##S2##). Online Kaplan Meier Plotter analysis shows that PIEZO2 is not statistically correlated with female prognosis, but has an adverse association with male prognosis. However, in GC patients with poorly differentiated tumors, the PIEZO2 overexpression group had a better prognosis compared to other subgroups (Supplement Fig. ##SUPPL##0##S3##, Supplement Table ##SUPPL##0##S2##). According to research, poorly differentiated tumor cells have increased stemness, and tumor stem cells are frequently related to malignant development and poor prognosis of tumors. As a result, we examined the important PIEZO2 and tumor stemness markers in clinical patients. PIEZO2 was shown to be inversely linked with DMPss, DNAss, ENHss, and EREG.EXPss, EREG-METHss, RNAs, MSI, purity, and TMB in GC (Fig. ##FIG##0##1##A–J) (<italic>P</italic> &lt; 0.05).</p>", "<p id=\"Par13\">This finding was supported further by an examination of the PIEZO2 mutation landscape. The findings revealed that the majority of PIEZO2 variants are missense, splice site, and frameshift insertion mutations (Fig. ##FIG##1##2##A). The waterfall graphic reveals that the PIEZO2 high expression group has much fewer mutations than the PIEZO2 low expression group (Fig. ##FIG##1##2##B). The findings imply that PIEZO2 may be adversely linked with tumor cell stemness and mutation in GC patients, resulting in a better prognosis in poorly differentiated tumors in GC patients with high PIEZO2 expression.</p>", "<title>Construction and computational validation of a nomogram model for patients with GC based on PIEZO2</title>", "<p id=\"Par14\">Multivariate Cox regression analysis showed that PIEZO2 (HR = 2.09, CI 1.45–3.02, <italic>P</italic> &lt; 0.01), M stage (HR = 2.57, CI 1.30–5.11, <italic>P</italic> &lt; 0.01), and age (HR = 1.04, CI 1.02–1.06, <italic>P</italic> &lt; 0.01) were closely related to the prognosis of patients with GC (Fig. ##FIG##2##3##A). Based on these results, a nomogram model of OS (Fig. ##FIG##2##3##B) was constructed, and a score was assigned to each variable using the 100-score scale. The total prone score was calculated by adding the points for each variable, to give a score ranging from 0 to 240 points. Calibration curves drawn from the total subscale to the survival probability line were used to obtain the estimated probability of the total survival of patients with GC patients in 1, 3, and 5 years. The C index and calibration curve were used to assess the accuracy and reliability (Fig. ##FIG##2##3##C) of the prediction of the nomogram model. The C index of the nomogram model was 0.66, and 95% CI was 0.61–0.71, indicating that the model has some accuracy and might be used to predict the OS of GC patients. In the calibration plot, the bias-corrected lines of 1, 3, and 5 years were found to be near the ideal 45° diagonal, suggesting that the theoretical value was compatible with the observed value. The following findings demonstrate that the nomograph model may be used to forecast the overall survival rate of GC patients at 1, 3, and 5 years.</p>", "<title>The interaction of PIEZO2 with immune cells in GC patients</title>", "<p id=\"Par15\">The degree of PIEZO2 expression and immune cell infiltration were compared. The findings revealed that PIEZO2 was positively associated with the majority of immune cell infiltration. The PIEZO2 high and low expression groups differed significantly (Fig. ##FIG##3##4##A,B), which was negatively correlated with Th1 cells, megakaryocyte-erythrocyte progenitors, keratinocytes, Th2 cells, basophils, pro-B-cells, epithelial cells, sebocytes, common lymphoid progenitors, plasma cells, osteoblasts, CD8⁺ naive T cells, plasmacytoid dendritic cells, gamma delta T cells, CD4⁺ effector memory T cells, and mesenchymal stem cells. The association between PIEZO2 and immune cell enrichment was investigated using Spearman correlation (Fig. ##FIG##3##4##C–F). It was shown to be favourably connected with M2-type macrophage infiltration and negatively correlated with endothelial cell and Th1 cell infiltration.</p>", "<title>The relationship between PIEZO2 and immune checkpoints in patients with GC</title>", "<p id=\"Par16\">We also looked at the link between PIEZO2 and the expression of immune-related genes in the GC microenvironment, including MHC, immune-activating and immunosuppressive genes, chemokines, and their receptors. The findings revealed that PIEZO2 was positively linked with the expression of immune-related genes, indicating that these genes may play a role in the control of immune cell infiltration (Fig. ##FIG##4##5##A). The expression of immunological checkpoint-related genes was then compared in various PIEZO2 expression groups. ENTPD1, EDNRB, SELP, TLR4, TGFB1, TNFSF4, CD28, VEGFB, IL10, and ADORA2A were found to be considerably up-regulated in the PIEZO2 overexpression groups (Fig. ##FIG##4##5##B), and PIEZO2 was shown to be positively linked with the expression of immunological checkpoint-related genes (Fig. ##FIG##4##5##D).</p>", "<title>PIEZO2 might be used as an immunotherapy target in GC</title>", "<p id=\"Par17\">To explore the value of PIEZO2 in immunotherapy. We discovered that the anticipated response rate of patients with GC in the PIEZO2 overexpression group was much lower when we used the TIDE algorithm to examine the clinical response of immune checkpoint blocking (Fig. ##FIG##4##5##C). These findings suggest that PIEZO2 might be used as an immunotherapy target.</p>", "<title>Functional analysis of PIEZO2 in GC</title>", "<p id=\"Par18\">We performed GO classification and KEGG pathway enrichment analysis of PIEZO2-related differential genes in TCGA to further understand the probable function of PIEZO2 in GC. The findings revealed that PIEZO2-related differential genes were mostly concentrated in factory transportation, neutral light receiver interaction, the calcium signaling pathway, ATP-binding cassette transporters, and extracellular matrix (ECM) receiver interaction (Fig. ##FIG##5##6##A). In biological processes, PIEZO2-related differential genes are mainly enriched in the nervous system processes, G protein-coupled receiver signaling pathways, sensory perception, detection of stimulus, and synchronous signaling. In terms of molecular function, the PIEZO2-related differential genes are mainly related to the motor transport activity, G protein-coupled receiver activity, factory receiver activity, passive transport transporter activity, and gateway channel activity (Fig. ##FIG##5##6##B).</p>", "<p id=\"Par19\">The PIEZO2-related signal pathway in GC was identified using GSEA. The path was shown to be strongly linked to tumor growth and metastasis based on the enrichment data. Finally, PIEZO2 is an immune-related gene that may participate in the TGF-, calcium, hedgehog, and extracellular signaling pathways, as well as ECM receptor interaction and growth factor binding, to enhance the incidence and development of GC (Fig. ##FIG##5##6##C–H).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par20\">The evolutionarily conserved Piezo protein composed of PIEZO1 and PIEZO2 is a large ion channel protein. PIEZO1, as a mechanical receptor, participates in the differentiation of neural stem cells and mesenchymal stem cells by sensing traction. In contrast, PIEZO2 is mainly expressed in primary sensory neurons and is related to tenderness, gentle touch, airway extension, proprioception, and heart rate regulation^{##UREF##2##18##}. In previous studies, PIEZO1 was overexpressed in GC cell lines compared to normal gastric tissue. In addition, GC patients with high expression of PIEZO1 have a poor prognosis^{##REF##34004511##19##}. However, the relationship between PIEZO2 and poor prognosis, and immune infiltration level of patients with GC has not yet been reported. This study confirmed that PIEZO2 has a role in the degree of immune infiltration. Overexpression of PIEZO2 was associated with T stage (T2 vs T1, P &lt; 0.001; T3, T4 vs T2, P &lt; 0.001), N stage (N2, N3, N4 vs N1, P &lt; 0.05), pathological stage (I vs III vs II, P &lt; 0.05), histological grade (G1 vs G2, P &lt; 0.01) (Supplement Fig. ##SUPPL##0##S1##, Supplement Table ##SUPPL##0##S1##). However, in patients with poorly differentiated GC, the high expression of PIEZO2 is related to a better prognosis. This might be because of the reduced tumor stemness and gene mutation degree in individuals with GC who express high levels of PIEZO2. According to research, PIEZO2, which is highly expressed in many tumors, can enhance tumor progression^{##REF##30010255##5##, ##UREF##3##20##, ##UREF##4##21##}. Interestingly, it has no statistical significance in the prognosis of females, but it is negatively correlated with the prognosis of males.</p>", "<p id=\"Par21\">A nomogram of PIEZO2 and other clinical variables (age, gender, and clinical stage) was produced using multivariate Cox analysis. By combining recognized risk indicators, this scoring technique aims to give a more accurate prognostic evaluation for patients with GC. The calibration curve and C index reveal that the projected and actual values of the 1, 3, and 5-year total survival rates are quite consistent. As a result, the nomograph model we developed has the potential to be a useful tool for the personalized assessment of GC patients' survival.</p>", "<p id=\"Par22\">We studied the association between immune cell infiltration and PIEZO2 expression further. The findings revealed that PIEZO2 overexpression was associated with M2 macrophages and endothelial cells. The poor prognosis of the PIEZO2 overexpression group might be attributed to an imbalance in immune function and internal environment, resulting in a loss in anti-tumor potential. The link between PIEZO2 and immune-related genes was examined to better understand the probable mechanism associated with PIEZO2 and immune cell infiltration. The findings revealed that the expression of the majority of immune-related genes was positively linked with PIEZO2. As a result, we may conclude that the poor prognosis of individuals with high PIEZO2 expression is associated with the overexpression of immunosuppressive genes. TIDE score and expression of CD274, CTLA4, HAVCR2, LAG3, PDCD1, PDCD1LG2, and TIGIT were greater in GC patients with up-regulated PIEZO2 expression than in individuals with low PIEZO2 expression. A previous study showed that higher TIDE scores in patients indicated a T cell microenvironment in dysfunctional tumors, which is not only related to the poor blocking treatment of immune checkpoints but also related to the lower survival rate under anti-PD-1 and anti-CTLA4 treatment^{##REF##30127393##22##}. The findings of these studies suggest that targeting PIEZO2 in the clinical treatment of GC patients may be a viable technique for inhibiting the treatment of immunological checkpoints.</p>", "<p id=\"Par23\">We selected DEGs linked to PIEZO2 and performed GO function annotation, GSEA, and KEGG pathway enrichment analysis to investigate the biological role of PIEZO2 in GC. The GSEA suggested that the overexpression of PIEZO2 in the calcium, Hedgehog, and TGF- β signaling pathways, ECM receptor, the activity of cell adhesion medium, calcium ion and cytokine binding, and structural composition of the extracellular mechanism are closely related. Based on the results of enrichment analysis, we can infer that PIEZO2 promotes the development of GC through such faulty processes as immune response, regulation of cell–matrix, and inflammatory response. PIEZO2 promotes the development of GC through fault processes such as immune response, regulation of cell–matrix, and inflammatory response. This provides a direction for further research on the mechanism of PIEZO2 in GC.</p>", "<p id=\"Par24\">This study revealed the role of PIEZO2 in immune cell infiltration and immune-related gene expression in GC. However, there are certain limitations to this study, as all samples are based on RNA sequencing data from internet sources. Data from several systems are diverse. Some subgroups in subgroup analysis have an insufficient sample size, therefore more samples are required for verification. The role of PIEZO2 in the prognosis of male and female patients has to be investigated further. The link between PIEZO2 expression and immune cell infiltration and immune-related gene expression has to be investigated further to ensure the veracity of the findings.</p>", "<p id=\"Par25\">This study found that PIEZO2 is associated with the poor prognosis of GC patients, which may be caused by the imbalance of the immune function internal environment caused by PIEZO2. PIEZO2 was identified as a potential new biomarker for the diagnosis and prognosis of patients with GC. In decision-making about diagnosis and treatment with GC patients, the expression of PIEZO2 in GC can predict the histological grading and treatment effectiveness of blocking treatment of immune checkpoints. The established survival model can be used as a practical tool to personalize the prognosis of patients with GC. Through enrichment analysis, it was found that PIEZO2 promotes the development of GC through fault processes such as immune response, regulation of cell–matrix, and inflammatory response, so targeting PIEZO2 may be a potential target for GC therapy. This work provides a new and feasible direction for clinical diagnosis, prognosis prediction, and immunotherapy of GC patients. Further experiments can be conducted to explore the specific mechanism of PIEZO2 in GC.</p>" ]

[]

[ "<p id=\"Par1\">Gastric cancer (GC) is one of the most prevalent malignant tumors of the gastrointestinal system in the globe. The effect of PIEZO2 on the immune function and pathological features of gastric cancer remains to be explored. The Online database of cancer genes and GSE54129 have been used to analyze the clinical characteristics of PIEZO2 expression. We looked at the relationship between PIEZO2 and the immune systems of GC patients. The TIDE algorithm was used to explore the value of PIEZO2 in immunotherapy. Investigated the enrichment of PIEZO2 gene ontology and associated signal pathways using Online gene databases. The results show that overexpression of PIEZO2 was identified as an independent risk factor for patients with GC who had poor overall survival. Individuals may have a better prognosis if they had poorly differentiated GC and increased PIEZO2 expression (<italic>P</italic> &lt; 0.05). We demonstrated a strong correlation between PIEZO2 and immune cells. The majority of immune checkpoint and immunological-related genes were associated with PIEZO2 expression. And PIEZO2 might be used as an immunotherapy target. Finally, the differential PIEZO2 genes in GC were mostly implicated in the processes of inflammation, immunological response, and tumor metastasis, according to functional analysis. PIEZO2 has a negative correlation with cell stemness and mutation levels in patients with GC and a positive correlation with immune cell infiltration and gene expression in the tumor microenvironment. These findings point to PIEZO2 as a potential new immunotherapy target of GC.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-48577-5.</p>", "<title>Acknowledgements</title>", "<p>Thanks for sharing datasets provided by public databases.</p>", "<title>Author contributions</title>", "<p>All authors directly, substantially, and intellectually contributed to the preparation of this manuscript and approved its publication.</p>", "<title>Funding</title>", "<p>This work was funded by the National Natural Science Foundation of China (Grant No. 81573762) and the Research Assistance Project of the Second Affiliated Hospital of Zhejiang Chinese Medicine University.</p>", "<title>Data availability</title>", "<p>The datasets analyzed during this study are available in the TCGA repository (<ext-link ext-link-type=\"uri\" xlink:href=\"https://portal.gdc.cancer.gov/\">https://portal.gdc.cancer.gov/</ext-link>) and the GEO database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=gse54129\">https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=gse54129</ext-link>).</p>", "<title>Competing interests</title>", "<p id=\"Par26\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Pan-cancer analysis of PIEZO2 and tumor stemness related indicators (<bold>A</bold>–<bold>I</bold>) PIEZO2 negatively correlated with DMPss, DNAss, ENHss, EREG.EXPss, EREG-METHss and RNAss, microsatellite instability, purity, and tumor mutation burden in tumors of patients with gastric cancer (<italic>P</italic> &lt; 0.05).</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>PIEZO2 mutation landscape (<bold>A</bold>) PIEZO2 mutation in gastric cancer. (<bold>B</bold>) Waterfall diagram showing the first 20 genes, mutation type, and number in the PIEZO2 high and low expression groups. *p &lt; 0.05; **p &lt; 0.01; ***p &lt; 0.001; ****p &lt; 0.0001; <italic>ns</italic> not significant.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Prognostic factor analysis and nomogram model construction. (<bold>A</bold>) Forest chart showing the influence of multivariable Cox regression analysis-related factors on the overall survival rate of patients with gastric cancer (GC). (<bold>B</bold>) Nomogram model to predict the overall survival rate of patients with GC in 1, 3, and 5 years. (<bold>C</bold>) Calibration curve of nomogram model to predict the probability of 1, 3, and 5 year total survival of patients with GC. *p &lt; 0.05; **p &lt; 0.01; ***p &lt; 0.001; ****p &lt; 0.0001; <italic>ns</italic> not significant.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>The relationship between PIEZO2 and immune cells in gastric cancer (GC) patients (<bold>A</bold>) Relationship between PIEZO2 and immune cell infiltration in GC. (<bold>B</bold>) Difference in immune cell infiltration between the PIEZO2 high and low expression groups. (<bold>C-F</bold>) Scatterplot showing PIEZO2 expression and correlation of infiltration degree of dendritic cells, TH1, M2 type macrophages, and endothelial cells. *p &lt; 0.05; **p &lt; 0.01; ***p &lt; 0.001; ****p &lt; 0.0001; <italic>ns</italic> not significant.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Relationship between PIEZO2 and immune checkpoint in patients with gastric cancer (<bold>A</bold>) Relationship between PIEZO2 and major histocompatibility complex genes, immune-activating genes, immune-suppressing genes, chemokines, and their receptors. (<bold>B</bold>) Differences in the expression of genes related to immune checkpoint between the PIEZO2 high and low expression groups. (<bold>C</bold>) Predictive response of different PIEZO2 expression groups to blocking treatment of immune checkpoint. (<bold>D</bold>) Correlation difference between PIEZO2 high and low expression groups. Expression level of genes related to the top 10 immune checkpoints. *p &lt; 0.05; **p &lt; 0.01; ***p &lt; 0.001; ****p &lt; 0.0001; <italic>ns</italic> not significant.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Gene Ontology (GO) classification and pathway analysis of PIEZO2 in gastric cancer (<bold>A</bold>) Kyoto Encyclopedia of Genes and Genomes pathway enrichment analysis identified the first 10 significant enrichment pathways. (<bold>B</bold>) GO annotations of differentially expressed genes (DEGs). (<bold>C</bold>–<bold>H</bold>) DEG Gene Set Enrichment Analysis used to identify PIEZO2 related signalling pathways and biological processes, including the TGF-β, calcium, hedgehog, and extracellular signalling pathways, extracellular matrix receptor interaction and growth factor binding. *p &lt; 0.05; **p &lt; 0.01; ***p &lt; 0.001; ****p &lt; 0.0001; <italic>ns</italic> not significant.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Yun-Chao Zhang and Min Yang.</p></fn></fn-group>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par17\">Bladder urothelial carcinoma (BLCA) is the second most common urological malignancy, with 91,893 and 84,825 new cases per year in China and the United States, respectively, and poses a fatal threat to human health, with an estimated 42,973 and 19,223 deaths in 2022, respectively^{##REF##35143424##1##,##REF##34440955##2##}. The majority of patients are diagnosed initially with nonmuscle invasive BLCA with a favorable prognosis, but progression and metastasis occur in 30% of patients with poor outcomes due to the complex and unclear mechanisms involved in the development of BLCA^{##REF##34440955##2##}. The TNM staging system, pathological differentiation degree and molecular stratification have been widely used for detecting high-risk BLCA patients but are still insufficient for precise and individualized prognostic prediction. Therefore, more attention should be focused on identifying effective biomarkers to forecast the clinical outcomes of BLCA for early management and reduce the additional therapeutic burden on patients.</p>", "<p id=\"Par18\">Inflammation is one of the ten characteristics of tumors^{##REF##35022204##3##}. Tumor-associated inflammation helps incipient neoplasia to acquire hallmark capabilities and is closely related to tumor occurrence and development^{##REF##35022204##3##}. Substantial evidence has suggested that high-risk factors such as cigarette smoking, exposure to aromatic amines, schistosome infections and endogenous irritants can induce chronic and persistent bladder inflammation, which plays a direct etiological role in carcinogenesis and promotes the progression of BLCA^{##REF##17483025##4##–##REF##12921773##6##}. In addition, tumor cells secrete inflammatory molecules connected with immune and stromal cells, including cytokines, to shape the inflammatory tumor microenvironment; growth factors, which sustain proliferative signals and prevent cell death; and extracellular matrix-modifying enzymes, which activate invasion and metastasis^{##REF##22439926##7##–##UREF##0##9##}. Recent immunotherapies have also been used in bladder cancer treatment. The tumor inflammatory environment is associated with an inhibitory immune microenvironment, which has been found in previous studies to modulate PDL1 expression and influence the efficacy of immunotherapy in patients with bladder cancer^{##REF##38053997##10##,##REF##35915245##11##}. However, tumor inflammation is a dynamic process associated with the expression of multiple genes associated with high tumor heterogeneity and has not been investigated in BLCA.</p>", "<p id=\"Par19\">In this study, we constructed a novel inflammation-related prognostic model comprising six inflammation-related genes (IRGs), TNFRSF12A, NR1H3, ITIH4, IL1R1, ELN and CYP26B1, by univariate and LASSO Cox regression analyses of data from The Cancer Genome Atlas (TCGA) database. The model was further validated with the GSE32894 dataset to determine its stability and reliability and was regarded as an independent indicator of survival in BLCA patients. In addition, somatic mutation information was obtained, a nomogram was constructed, clinical characteristic stratification was performed, and the tumor microenvironment (TME) landscape and chemotherapeutic response prediction were performed based on the risk of inflammation-related prognosis. Finally, the mRNA expression of IRGs was detected in BLCA cell lines and normal urothelial epithelial controls.</p>" ]

[ "<title>Methods</title>", "<title>Data source and preprocessing</title>", "<p id=\"Par20\">The RNA-seq expression data of BLCA patients, corresponding clinical characteristics and nucleotide variation data were downloaded from the TCGA database^{##REF##26704973##12##}. The TCGA-BLCA cohort containing 411 tumor and 19 normal tissue samples was used to construct the prognostic signature of the IRGs. The GSE32894 dataset, which included 308 tumor samples, was used as the validation cohort^{##REF##22553347##13##}. In addition, in the cohort of patients, a urothelial carcinoma cohort treated with atezolizumab was used to predict the response to immunotherapy^{##REF##29443960##14##}. For the above datasets, RNA-seq data (FPKM values) were log₂ (FPKM + 1) normalized. The panel of IRGs was combined with inflammation-associated genes from the NCBI-Gene website and a published panel.</p>", "<title>Differentially expressed IRGs screening and gene mutation analysis</title>", "<p id=\"Par21\">Differentially expressed IRGs were detected between normal and tumor tissues in the TCGA-BLCA cohort via the R package “DESeq2 v1.32.0”^{##REF##32789507##15##}. The cutoff values were regarded as |logfoldchange (FC)|&gt; 1.0 and a false discovery rate (FDR) &lt; 0.05. The differentially expressed IRGs were subsequently subjected to gene ontology (GO) and Kyoto encyclopedia of genes and genomes (KEGG) enrichment analyses via the R package “clusterProfiler v4.0.5”. The somatic mutations of the IRGs were analyzed by the R package “maftools v2.8.05” and are shown as a landscape heatmap.</p>", "<title>Gene set enrichment analysis (GSEA)</title>", "<p id=\"Par22\">GSEA was conducted on the RNA-seq data of 486 differentially expressed IRGs by GSEA tools version 4.1 (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.broadinstitute.org/gsea\">http://www.broadinstitute.org/gsea</ext-link>). We analyzed the subsets of the Molecular Signatures Database (C2 and C5) as previously described and calculated the corresponding <italic>p</italic> values.</p>", "<title>Construction and validation of the IRG prognostic model</title>", "<p id=\"Par23\">Univariate Cox regression was performed to identify overall survival-related differentially expressed IRGs. Survival analysis was performed with Kaplan–Meier survival curves, and the mean expression level of each gene was used as the cutoff. Survival-related differentially expressed IRGs were ranked according to hazard ratio (HR) and displayed in a forest plot. Subsequently, LASSO regression analyses were performed with the R package “glmnet v 4.1.1” to remove redundant factors and construct an optimal IRG signature-based prognostic model to evaluate the survival of BLCA patients. The risk score of the IRG prognostic regression model was multiplied by the expression level of the six IRGs and the corresponding coefficient, as previously described. The mean risk score was the cutoff value for distinguishing between the high- and low-risk groups and was validated in the GSE32894 cohort. The predictive value of the R package “survivalROC v1.0.3” was detected by the area under the curve (AUC). In addition, we performed correlation analysis between risk scores and clinical features using stratification analysis and nomograms. The consistency between the predicted 1-, 3-, and 5-year survival probabilities and the actual survival probabilities was evaluated using calibration plots.</p>", "<title>Estimation of cell infiltration in the tumor microenvironment (TME) and the clinical significance of the IRG prognostic model</title>", "<p id=\"Par24\">A prognostic model of six IRGs was used to evaluate cell infiltration in the BLCA TME. The immune landscape was explored by using CibersortABS and the R package “xCell v1.1.0”. Single-sample GSEA (ssGSEA) was used to calculate the difference in the cell composition in the TME between the high- and low-risk groups. To analyze the difference in immunotherapy efficacy between the high- and low-risk groups, we downloaded the IMvigor210 immunotherapy cohort and conducted Kaplan–Meier survival analysis and AUC prediction. The relationship between the IRG risk score and clinical characteristics was detected in the TCGA-BLCA cohort. A significant difference was regarded as <italic>p</italic> &lt; 0.05 according to one-way analysis of variance (ANOVA).</p>", "<title>Chemotherapy response analysis</title>", "<p id=\"Par25\">The RNA-seq data of NCI-60 cancer cell lines were downloaded from the CellMiner database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://discover.nci.nih.gov/cellminer\">https://discover.nci.nih.gov/cellminer</ext-link>) published by the National Institute of Health. The relationships of the expression of the six target IRGs between BLCA cell lines and 411 chemotherapy drugs that passed clinical trials with FDA approval were explored by Pearson correlation analysis. A <italic>p</italic> value &lt; 0.05 was considered to indicate drug susceptibility.</p>", "<title>Cell lines and culture conditions</title>", "<p id=\"Par26\">Immortalized human normal urothelial epithelial SV-HUC-1 cells were purchased from American Type Culture Collection. Urothelial carcinoma cell lines, including T24, 5637, RT4, BIU-87 and UM-UC-3 cells, were obtained from Professor Kai Yao. SV-HUC-1 cells were cultured in Ham's F-12K (Kaighn's) medium; T24 and 5637 cells were cultured in RPMI 1640 medium; and RT4, BIU-87 and UM-UC-3 cells were cultured in Dulbecco's modified Eagle’s medium. All of the media were supplemented with 10% fetal bovine serum and 1% penicillin/streptomycin and incubated at 37 °C in 5% carbon dioxide.</p>", "<title>Real-time-quantitative polymerase chain reaction (qPCR)</title>", "<p id=\"Par27\">The mRNA expression of six IRGs was detected in BLCA cell lines and SV-HUC-1 cells. Total RNA extraction (RC101, Vazyme), reverse transcription (R122-01, Vazyme) and cDNA amplification (Q711-02/03, Vazyme) were performed according to protocols described previously. Using the 2(−∆∆Ct) method, relative target gene expression was quantified and normalized against that of GAPDH. The sequences of primers used are listed in Table ##SUPPL##0##S5##.</p>", "<title>Ethics approval and consent to participate</title>", "<p id=\"Par28\">This study was approved by the Ethics Committee of SYSUCC (SZR2022-001).</p>" ]

[ "<title>Results</title>", "<title>Identification of differentially expressed IRGs and somatic mutation analysis</title>", "<p id=\"Par29\">Combined with the NVCI-Gene database and a previously reported cluster of inflammation-associated genes, a total of 2343 IRGs were included in this study and are listed in Table ##SUPPL##0##S1##. Differentially expressed IRGs were screened between 411 BLCA tumors and 19 normal tissues from the TCGA database. The detailed clinical information is listed in Table ##SUPPL##0##S2##. Genomic mutation analysis indicated that most of the BLCA patients (388/411, 94.4%) had at least one somatic mutation in an IRG, suggesting the predisposing role of IRG mutations in BLCA (Fig. ##FIG##0##1##A). The mutation frequencies of TP53 (47%), TTN (45%), KMT2D (29%), MUC16 (27%) and KDM6A were the 5 most common IRGs in BLCA (Fig. ##FIG##0##1##A). Subsequently, the differentially expressed IRGs between the tumors and normal tissues were detected, and the results revealed a total of 59 significantly upregulated and 426 downregulated IRGs (Fig. ##FIG##0##1##B and Table ##SUPPL##0##S3##). The differential IRGs were visualized by volcano plot and chromosome schematic (Fig. ##FIG##0##1##C,D).</p>", "<title>Biological function analysis of differentially expressed IRGs</title>", "<p id=\"Par30\">A total of 485 differentially expressed IRGs were obtained and subjected to GO, KEGG and GSEA to explore the enrichment of biofunctions. The results indicated that the IRGs in BLCA were enriched mainly in the activation of the inflammatory response, leukocyte secretion and regulation of tumor immunity (Fig. ##FIG##0##1##E,F). GSEA revealed that the differentially expressed IRGs were enriched in the regulation of interferon and the innate immune system (Fig. ##FIG##0##1##G). The biological functional results suggested that IRG signatures promoted an inflammatory microenvironment in BCLA patients, which might be essential for tumor progression and associated with clinical outcomes.</p>", "<title>Generation of IRG prognostic signatures in BLCA</title>", "<p id=\"Par31\">To further determine the prognostic value of the differentially expressed IRGs in BLCA, univariate survival analysis was performed, and the results indicated that 113 IRGs were associated with overall survival (Table ##SUPPL##0##S4##). To remove confounding factors, a LASSO Cox regression model was used to construct a risk stratification model of six IRG prognostic signatures, namely, TNFRSF12A, NR1H3, ITIH4, IL1R1, ELN and CYP26B1 (Fig. ##FIG##1##2##A,B). The hazard ratios (HRs) of the six survival-related IRGs are presented as forest plots (Fig. ##FIG##1##2##C). We detected that TNFRSF12A, IL1R1, ELN and CYP26B1 were unfavorable prognostic factors that were overexpressed in tumor tissues and associated with poor survival in the TCGA-BLCA cohort. However, NR1H3 and ITIH4 are protective indicators that are overexpressed in normal tissues and predict better outcomes (Fig. ##FIG##1##2##D). Similarly, qPCR was performed to detect the mRNA expression of six target genes in bladder cancer cell lines and the corresponding normal epithelial cell line SV-HUC-1. We found that TNFRSF12A, IL1R1, ELN and CYP26B1 were overexpressed in bladder cancer cell lines, while NR1H3 and ITIH4 were downregulated (Fig. ##FIG##1##2##E). Subsequently, the risk scores of the IRG prognostic signatures were calculated by the target gene expression and the corresponding coefficients (Fig. ##FIG##1##2##F). The mean risk score was 3.552 in the TCGA-BLCA cohort and was regarded as the threshold of the IRG prognostic model. Survival analysis indicated that high-risk patients had significantly poorer overall survival (OS) than did patients with lower risk scores (<italic>p</italic> &lt; 0.0001) (Fig. ##FIG##1##2##G). The area under the curve (AUC) curves showed that the predictive efficiency of the IRG prognostic signature had the highest AUC value (0.727) compared with that of traditional clinicopathological factors (Fig. ##FIG##1##2##H). In brief, we established an available IRG prognostic model to evaluate the clinical outcomes of BLCA patients.</p>", "<title>The clinical significance of the IRG prognostic model in the TCGA-BLCA cohort</title>", "<p id=\"Par32\">To further demonstrate the clinical significance of the IRG prognostic model in the TCGA-BLCA cohort, patients were divided into two groups based on clinicopathological factors. Correlation analysis indicated that advanced T stage (pT2–pT4), lymph node metastasis, pathological grade, poor clinical stage and age (≥ 60) were positively associated with high-risk IRG score, suggesting poor survival (Fig. ##FIG##2##3##A). In addition, we combined prognosis-related clinical factors and IRG signatures to construct a survival nomogram (Fig. ##FIG##2##3##B). Calibration curves from the TCGA-BLCA cohort showed that the nomogram-predicted 1-, 3- and 5-year survival rates were highly consistent with the actual survival rates, which demonstrated that the IRG prognostic signatures were stable and effective (Fig. ##FIG##2##3##C).</p>", "<title>External validation of the IRG prognostic signatures</title>", "<p id=\"Par33\">To further explore the efficacy of the IRG prognostic signatures, we used the GEO database (GSE32894) for independent external validation. In the GSE32894 cohort, 133 BLCA patients were divided into a low-risk group with an IRG risk score lower than 0.2, and 91 other patients were included in the high-risk group. The IRG signature expression map and the distribution of risk scores are shown in Fig. ##FIG##3##4##A,B. Survival analysis demonstrated that the overall survival (OS) of high-risk BLCA patients was significantly shorter than that of low-risk patients (<italic>p</italic> &lt; 0.0001) (Fig. ##FIG##3##4##C). The area under the curve (AUC) curves of the IRG prognostic model indicated even better performance, with AUC values of 0.82, 0.835 and 0.823 at 1 year, 3 years and 5 years, respectively, in predicting survival (Fig. ##FIG##3##4##D).</p>", "<title>The predictive value of the IRG prognostic signature for immune cell infiltration and immunotherapy efficacy</title>", "<p id=\"Par34\">Biological enrichment analysis revealed that the differentially expressed IRGs were associated with the regulation of tumor immunity. To further understand the relationships between the risk stratification of the IRG prognostic signatures and immune cell infiltration, we evaluated the immune cell landscape in the TCGA-BLCA cohort with the CIBERSORT tool. A heatmap indicated that the high-risk IRG group had abundant immune cell types and proportions, suggesting an inflammation-associated immune microenvironment in BLCA (Fig. ##FIG##4##5##A,B). However, in the high-risk group, the increase in naive immune cells, Treg cells, M2 TAMs, and myeloid dendritic cells and the decrease in CD8+ T cells constituted a suppressive microenvironment to evade immune surveillance, resulting in poor prognosis (Fig. ##FIG##4##5##C). Moreover, we further validated the predictive value of the IRG prognostic signature for immunotherapy efficacy in patients in the IMvigor210 cohort. Survival analysis indicated that the overall survival of urothelial carcinoma patients with high-risk IRG signatures was significantly shorter than that of patients with low-risk signatures (Fig. ##FIG##4##5##D). In the low-risk IRG group, the proportion of patients with objective response rates was greater than that in the high-risk group (11.7% vs. 29.79%, <italic>p</italic> &lt; 0.001) (Fig. ##FIG##4##5##E). Moreover, patients who responded to atezolizumab in the database had lower risk scores (Fig. ##FIG##4##5##F,G). After categorizing all patients into immune-activated and nonimmune-activated groups (including both immune exhausted and nonimmune patients) based on Meng et al.^{##UREF##1##16##}, we compared the inflammation scores between the two groups and found that lower inflammatory scores in patients with immune activation status suggested a possible benefit from immunotherapy (Fig. ##FIG##4##5##H). Among the six molecular subtypes, the basal/squamous subtype exhibited the highest degree of inflammation, which was significantly different from that of the other subtypes. (Fig. ##FIG##4##5##I) The AUC of the IRG prognostic signature was 0.607 for predicting the clinical outcome of immunotherapy (Fig. ##FIG##4##5##J). Our results demonstrated that high-risk BLCA patients in the IRG prognostic model were associated with an inhibitory immune tumor microenvironment and poor immunotherapy response.</p>", "<title>Prediction of the chemotherapy response in the signature</title>", "<p id=\"Par35\">To investigate the association between chemotherapy outcomes and the expression pattern of the IRG signature, we explored drug sensitivity data from the Cell Miner database. The results suggested a correlation between IRS-related genes and bladder cancer chemotherapy drugs (Fig. ##FIG##5##6##). In the high-risk IRG cohort, IL1R1, ELN and ITIH4 overexpression was negatively correlated with the first-line chemotherapy drugs cisplatin and gemcitabine, indicating that chemotherapy may not be effective. In contrast, the efficacy of paclitaxel was sensitive to the upregulation of ELN and ITIH4 expression; thus, paclitaxel might serve as an available chemotherapy option (Fig. ##FIG##5##6##). In brief, the IRG prognostic signatures provide additional information and a reference for individualized chemotherapy in BLCA patients.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par36\">Increasing evidence has suggested that tumor-associated inflammation, including gene toxicity, aberrant tissue repair, proliferation, invasion, and metastasis, is causally associated with cancer development^{##REF##22903521##17##,##REF##31205032##18##}. Due to the close relationship between inflammation and cancer, the correlation of inflammatory signatures with disease diagnosis or clinical endpoints has been studied in many cancer types^{##REF##22440947##19##,##REF##32455607##20##}. Qiu et al<italic>.</italic> explored a four-gene inflammation-related signature that included IL13, BDNF, PLCG2 and TIMP1 and could predict the prognosis and treatment response in patients with colon adenocarcinoma^{##REF##35003085##21##}. Zhang et al<italic>.</italic> identified 10 differentially expressed inflammation-related lncRNAs to predict individualized clinical outcomes in gastric carcinoma patients^{##REF##34819945##22##}. However, inflammation-induced carcinogenesis is the result of interactions among multiple intrinsic and extrinsic cellular processes, including genomic instability, reprogramming of the stromal environment, cytokine secretion and the immune response, which contribute to the high degree of heterogeneity among different types of tumors^{##REF##24154716##23##,##REF##25281468##24##}. BLCA is a chronic inflammation-related cancer and is also referred to as a “hot tumor” due to the increased infiltration of activated immunocytes and inflammatory-related cells^{##REF##32482511##25##,##REF##24818724##26##}. However, the potential role of inflammation-related genes in BLCA is unknown, and inflammation-related prognostic signatures for identifying effective immunotherapy strategies are lacking.</p>", "<p id=\"Par37\">Here, we constructed a novel IRG classifier that included TNFRSF12A, NR1H3, ITIH4, IL1R1, the ELN and CYP26B1 and explored its prognostic value for predicting overall survival (OS) and the response to immunotherapy. Among the six IRGs, TNFRSF12A is an aging-related gene involved in the hypoxia-driven inflammatory response and contributes to thyroid cancer^{##REF##37060824##27##,##REF##32391089##28##}. A low NR1H3 expression level has been verified to be an independent prognostic factor for poor overall survival and predicts worse recurrence-free survival in muscle-invasive bladder cancer patients^{##REF##28382148##29##}. ITIH4 is a serum inflammation biomarker for early gastric cancer diagnosis^{##REF##34687700##30##}. The immune-related genes IL1R1 and ELN predict poor survival in patients with pancreatic adenocarcinoma and bladder cancer, respectively^{##REF##34156282##31##}. CYP26B1 is required for the activation of T cells via retinoic acid-dependent signals that participate in the immune response^{##REF##21249211##32##}. These studies support that the six IRGs included in our classifier are potentially measurable indicators of prognosis in BLCA patients.</p>", "<p id=\"Par38\">To further demonstrate the clinical significance of our six-IRG signature in BLCA, we first divided patients into high-risk and low-risk groups according to the median IRG risk score. Correlation analysis indicated that advanced pT stage, pN stage, pathological grade, and clinical stage were strongly associated with high-risk IRG scores. Moreover, the six-IRG-related signature presented a strong ability to predict overall survival, with an AUC of 0.727 in the TGCA-BLCA cohort and even better performance in the GSE32894 cohort (AUC of 0.820). Compared with traditional prognostic factors such as the TNM staging system and clinical stage, our six-IRG-related signature was more effective and was an independent prognostic factor for BLCA (Fig. ##FIG##1##2##G). Previous studies have shown that the basal/squamous subtype of bladder cancer is linked to chronic inflammation of the bladder and has a poorer prognosis than other subtypes^{##REF##31563503##33##,##REF##34936229##34##}. Our findings further support this association. In recent years, improvements in whole-genome sequencing have facilitated a deeper understanding of genomic alterations in BLCA. Wang et al<italic>.</italic> identified a seven-lncRNA signature with an area under the curve (AUC) of 0.734, which has robust efficacy in predicting overall survival in patients with BLCA^{##REF##33189610##35##}. Similarly, Wu et al<italic>.</italic> established an eight-immune-related lncRNA signature for predicting patient prognosis, for which the area under the curve (AUC) values at 1, 3 and 5 years were 0.72, 0.76 and 0.76, respectively^{##REF##33221763##36##}. Compared with the above studies, our study incorporated the inflammatory drivers of BLCA to create a more concise inflammation-related prognostic signature with comparable predictive efficacy.</p>", "<p id=\"Par39\">In addition, an active inflammatory reaction recruits tumor-infiltrating lymphocytes into the tumor microenvironment through the release of cytokines, tumor necrosis factors and growth factors and leads to dramatic differences in immunotherapy responses^{##REF##24154716##23##}. We found that BLCA patients with high-risk inflammatory scores suffer from low response rates to PD-L1 blockade, which is associated with poor survival. The AUC value of our six-IRG signature was 0.607 for predicting immunotherapy response in the IMvigor210 database, and the effect was similar to that of another nine immune-relevant gene signatures (AUC = 0.64, 95% = 0.55–0.74), which was reported by Jiang et al<italic>.</italic>^{##REF##32096345##37##}. Our results also indicated that the proportion of immunosuppressive cells, such as Treg cells and M2 TAMs, was significantly increased in high-risk patients, which is key to the formation of an immunosuppressive microenvironment and tumor immune evasion. M2 TAMs recruit Treg cells by secreting CCL22 and synergistically produce IL-10 and TGF-β to inhibit the activation and proliferation of T cells^{##REF##32234529##38##,##REF##30520029##39##}. In addition, the reductions in dendritic cells and CD8+ T cells in high-risk patients inhibited antigen presentation and cytotoxicity, respectively, resulting in a low immunotherapy response and poor survival. In brief, our six-IRG signature was beneficial for identifying the tumor inflammatory microenvironment in BLCA patients and predicting the efficacy of immunotherapy.</p>", "<p id=\"Par40\">Finally, our six-IRG signature also provided evidence for the effectiveness of chemotherapy in guiding personalized treatments. Gemcitabine and cisplatin are commonly used as first-line chemotherapies in combination and have shown clinical benefit in treating BLCA^{##REF##35254888##40##,##REF##32868138##41##}. We detected that BLCA patients with high IRG risk scores, especially those with overexpression of ITIH4 and IL1R1, were less sensitive to gemcitabine and cisplatin chemotherapy. However, patients in which the oncogenes TNFR3F12A and CYP26B1 were downregulated had a better response to gemcitabine and cisplatin as well as a better prognosis. On the other hand, paclitaxel has been shown to be an active front-line and palliative therapy in BLCA^{##REF##10908842##42##,##REF##30563080##43##}. Alternative regimens, including cisplatin/paclitaxel and gemcitabine/paclitaxel, have shown modest activity in phase I-II trials^{##REF##22370319##44##,##REF##23823157##45##}. We found that high TNFR3F12A expression or low NR1H3 and ITIH4 expression was positively correlated with paclitaxel sensitivity, indicating that high-risk BLCA patients could benefit from second-line paclitaxel chemotherapy.</p>", "<p id=\"Par41\">Our study has several limitations. First, the signature has been validated retrospectively in only the GEO database, and future prospective studies are needed to confirm its clinical value. Furthermore, further in vivo and in vitro studies are needed to determine how the six selected genes contribute to the development of BLCA. Despite the limited sample size in this study, we explored an inflammation-related prognostic signature and assessed the response to immunotherapy. This model provides useful information for individualized clinical treatment and prognosis judgment.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par42\">In this study, we constructed an available six-IRG signature based on the TCGA and GEO cohorts to predict the prognosis of BLCA patients. We also examined the gene mutation status, immune landscape and drug sensitivity among the different risk groups. Our inflammation-associated signature provides additional information for individualized prognostic judgment and treatment selection.</p>" ]

[ "<p id=\"Par1\">Tumor inflammation is one of the hallmarks of tumors and is closely related to tumor occurrence and development, providing individualized prognostic prediction. However, few studies have evaluated the relationship between inflammation and the prognosis of bladder urothelial carcinoma (BLCA) patients. Therefore, we constructed a novel inflammation-related prognostic model that included six inflammation-related genes (IRGs) that can precisely predict the survival outcomes of BLCA patients. RNA-seq expression and corresponding clinical data from BLCA patients were downloaded from The Cancer Genome Atlas database. Enrichment analysis was subsequently performed to determine the enrichment of GO terms and KEGG pathways. K‒M analysis was used to compare overall survival (OS). Cox regression and LASSO regression were used to identify prognostic factors and construct the model. Finally, this prognostic model was used to evaluate cell infiltration in the BLCA tumor microenvironment and analyze the effect of immunotherapy in high- and low-risk patients. We established an IRG signature-based prognostic model with 6 IRGs (TNFRSF12A, NR1H3, ITIH4, IL1R1, ELN and CYP26B1), among which TNFRSF12A, IL1R1, ELN and CYP26B1 were unfavorable prognostic factors and NR1H3 and ITIH4 were protective indicators. High-risk score patients in the prognostic model had significantly poorer OS. Additionally, high-risk score patients were associated with an inhibitory immune tumor microenvironment and poor immunotherapy response. We also found a correlation between IRS-related genes and bladder cancer chemotherapy drugs in the drug sensitivity data. The IRG signature-based prognostic model we constructed can predict the prognosis of BLCA patients, providing additional information for individualized prognostic judgment and treatment selection.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51158-9.</p>", "<title>Author contributions</title>", "<p>W.Y.J., T.Y. and Y.K. contributed to the writing of the manuscript. T.Y. and L.Z.C. were responsible for the sample collection. L.Z.C. and T.X.L. performed the cell experiments. Z.Y.T. and L.S.H. conducted the statistical analysis. W.Y.J. and T.Y. reviewed the article data. W.Y.J. and Y.K. designed and supported the study. All the authors read and approved the final manuscript. Informed consent was obtained from all the BLCA patients (SZR2022-001). Written informed consent for publication of their clinical details was obtained from the patients. All of the authors agreed with the content of the paper and agreed to publish.</p>", "<title>Funding</title>", "<p>This study was supported by the Sun Yat-sen University Cancer Center Medical Scientist Training Program (No. 14zxqk08 to Kai Yao) and the Natural Science Foundation of Guangdong Province (No. 2022A1515012318 to Kai Yao).</p>", "<title>Data availability</title>", "<p>The datasets supporting the conclusions of this article are available from the corresponding author upon reasonable request. The authenticity of this article has been validated by uploading the key raw data onto the Research Data Deposit platform (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.researchdata.org.cn\">www.researchdata.org.cn</ext-link>).</p>", "<title>Competing interests</title>", "<p id=\"Par43\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Identification of differentially expressed IRGs in BLCA patients. (<bold>A</bold>) Among 411 patients, TP53, TTN, KMT2D, MUC16 and KDM6A were found to be the 5 most frequently mutated genes. (<bold>B</bold>–<bold>D</bold>) Among the differentially expressed IRGs between tumor tissues and normal tissues, 59 were upregulated and 426 were downregulated according to volcano plots, heatmaps and chromosome schematics. (<bold>E</bold>–<bold>F</bold>) The GO, KEGG and GSEA results showed that the IRGs in BLCA were enriched mainly in the activation of the inflammatory response, leukocyte secretion and regulation of tumor immunity. (<bold>G</bold>) GSEA showed that the differentially expressed IRGs were enriched in the regulation of interferon and the innate immune system.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>The prognostic value of differentially expressed IRGs in BLCA. (<bold>A</bold>,<bold>B</bold>) The LASSO Cox regression model was used to construct a risk stratification model of the prognostic signatures of the 6 differentially expressed IRGs. (<bold>C</bold>) Hazard ratios of the IRGs are presented with forest plots. (<bold>D</bold>) Among the 6 IRGs, TNFRSF12A, IL1R1, ELN and CYP26B1 were unfavorable prognostic factors, and NR1H3 and ITIH4 were protective factors; (<bold>E</bold>) TNFRSF12A, IL1R1, ELN and CYP26B1 were overexpressed in bladder cancer cell lines, while NR1H3 and ITIH4 were downregulated. (<bold>F</bold>) The coefficients of the six genes related to the inflammatory response that were screened by LASSO regression. (<bold>G</bold>) Survival analysis revealed that high-risk patients had significantly poorer OS than low-risk patients. (H) The IRG prognostic signature had a greater AUC than did the traditional clinicopathological factors.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>The clinical significance of the IRG prognostic model in the TCGA-BLCA cohort. (<bold>A</bold>) Advanced T stage, lymph node metastasis, pathological grade, poor clinical stage and age ≥ 60 years were positively associated with high-risk IRG scores. (<bold>B</bold>) Survival nomograms were constructed with prognosis-related clinical factors and IRG signatures. (<bold>C</bold>) The nomogram-predicted 1-, 3- and 5-year survival rates were highly consistent with the actual survival rates in the TCGA-BLCA cohort. *<italic>p</italic> &lt; 0.05; **<italic>p</italic> &lt; 0.01; ***<italic>p</italic> &lt; 0.001; ****<italic>p</italic> &lt; 0.0001. <italic>NS</italic> not significant.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>External validation of the IRG prognostic signatures. (<bold>A</bold>,<bold>B</bold>) The IRG signature expression map and the distribution of risk scores of 133 BLCA patients in the GSE32894 cohort are shown. (<bold>C</bold>) Patients in the high-risk score group had poorer OS than patients in the low-risk score group. (<bold>D</bold>) The area under the curve (AUC) of the IRG prognostic model indicated good performance in predicting patient prognosis.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>The predictive value of the IRG prognostic signature for immune cell infiltration and immunotherapy efficacy. (<bold>A</bold>,<bold>B</bold>) The high-risk IRG group had abundant immune cell types and proportions. (<bold>C</bold>) The proportions of naive immune cells, Treg cells, M2 TAMs, and myeloid dendritic cells were increased, while the percentage of CD8+ T cells was decreased in the high-risk group. (<bold>D</bold>) Survival analysis of patients in the IMvigor210 cohort showed that the OS of urothelial carcinoma patients with high-risk IRG signatures was significantly shorter than that of patients with low-risk signatures. (<bold>E</bold>) The proportion of patients with objective response rates in the low-risk group was greater than that in the high-risk group. (<bold>F</bold>–<bold>G</bold>) Patients in the database who responded to atezolizumab had lower risk scores. (<bold>H</bold>) Risk scores of IRGs between the immune-activated and nonimmune-activated groups. (<bold>I</bold>) Risk scores of IRGs in six molecular typologies. (<bold>J</bold>) The AUC of the IRG prognostic signature was 0.607.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Prediction of chemotherapy response according to the signature. In the high-risk IRG cohort, IL1R1, ELN and ITIH4 overexpression was negatively correlated with the first-line chemotherapy drugs cisplatin and gemcitabine, while the efficacy of paclitaxel was sensitive to the upregulation of ELN and ITIH4 expression.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Yanjun Wang, Yi Tang and Zhicheng Liu.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41598_2024_51158_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"41598_2024_51158_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"41598_2024_51158_Fig3_HTML\" id=\"MO3\"/>", "<graphic xlink:href=\"41598_2024_51158_Fig4_HTML\" id=\"MO4\"/>", "<graphic xlink:href=\"41598_2024_51158_Fig5_HTML\" id=\"MO5\"/>", "<graphic xlink:href=\"41598_2024_51158_Fig6_HTML\" id=\"MO6\"/>" ]

[ "<media xlink:href=\"41598_2024_51158_MOESM1_ESM.pdf\"><caption><p>Supplementary Tables.</p></caption></media>" ]

{ "acronym": [ "BLCA", "IRGs", "OS", "TME", "KEGG", "GSEA", "AUC", "ANOVA", "qPCR", "GO", "FDR", "HR", "ssGSEA", "TAMs" ], "definition": [ "Bladder urothelial carcinoma", "Inflammation-related genes", "Overall survival", "Tumor microenvironment", "Kyoto encyclopedia of genes and genomes", "Gene set enrichment analysis", "Area under the curve", "One-way analysis of variance", "Real-time quantitative polymerase chain reaction", "Gene ontology analysis", "False discovery rate", "Hazard ratio", "Single sample GSEA", "Tumor-associated macrophages" ] }

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[ "<title>Method</title>", "<title>Sample</title>", "<p id=\"Par10\">We aimed to obtain about 500 valid data sets in each of the two experiments with the help of the online panel provider <italic>mingle</italic>. Of the data files of those participants who started the Prisoner’s Dilemma game, 54 data files had to be removed because the participants did not complete the experiment and 70 data files had to be excluded due to double participation. The final sample consisted of 544 participants (305 female, 239 male) aged 18–88 (<italic>M</italic> = 49, <italic>SD</italic> = 15) years. A sensitivity analysis showed that with a sample size of <italic>N</italic> = 544 and 25 decisions per participant it was possible to detect effects of the base-rate manipulation on the cooperation and punishment parameters of the multinomial cooperation-and-punishment model (see below) of the size <italic>w</italic> = 0.03 with a statistical power of 1 − β = 0.95 at an α level of 0.05^{##REF##17695343##47##}.</p>", "<title>Base-rate manipulation</title>", "<p id=\"Par11\">At the start of the experiment, participants were assigned to either the cooperating-majority condition (<italic>n</italic> = 278) or the defecting-majority condition (<italic>n</italic> = 266). Depending on the assigned condition, participants were instructed either that most people would cooperate and only some would defect or that most people would defect and only some would cooperate. These instructions were used to ensure that participants formed a correct representation about the majority behavior even before the Prisoner’s Dilemma game started.</p>", "<p id=\"Par12\">The fact that the partners’ responses were determined by a computer program then allowed us to manipulate the proportion of cooperating and defecting partners in line with these instructions. Experimentally manipulating the partner behavior is a common approach in Experimental Psychology to generate varying base rates while maintaining control over confounding factors that may otherwise influence partner behavior^{##REF##23347495##16##,##REF##20658845##48##–##REF##21559490##54##}. In the cooperating-majority condition, partners were programmed to cooperate in 60% of the trials and to defect in 40% of the trials. In the defecting-majority condition, this ratio was reversed.</p>", "<title>Prisoner’s Dilemma game</title>", "<p id=\"Par13\">Materials and procedure of the Prisoner’s Dilemma game were parallel to those of a previous online study examining costly punishment in the Prisoner’s Dilemma game^{##REF##37673945##46##}. After giving their informed consent and answering demographic questions, participants received the instructions for the Prisoner’s Dilemma game. Participants of the online panel provider mingle are compensated with points that can be exchanged for online vouchers, charity donations or money (with 1 point corresponding to 1 Euro cent). Participants were thus informed that they were playing for points which they would be awarded by mingle at the end of the study in addition to the points they would receive for participating in the study. At the start of the experiment, participants were endowed with 150 points. Participants played 30 trials, five of which were training trials, of a simultaneous one-shot Prisoner’s Dilemma game with a costly punishment option.</p>", "<p id=\"Par14\">Each trial of the Prisoner’s Dilemma started with the display of the participant’s current account balance in the middle of the screen. Participants knew that they would interact with a different partner in every trial. Upon clicking a “Continue” button, the interaction partner was shown. To emphasize the social nature of the game, participants saw a color photograph (266 × 186 pixels) of a different partner in each trial. To this end, photographs of 30 white adult faces, half of which were female and half of which were male, were randomly drawn from the Chicago Face Database^{##REF##25582810##55##}. All faces had a neutral expression and were shown from a frontal view. The partner’s photograph was centered on-screen and surrounded by a blue frame (4 pixels, see Fig. ##FIG##1##2##).</p>", "<p id=\"Par15\">Beneath the photograph, participants could choose to cooperate or to defect by clicking the corresponding button and submitting their choice with a “Continue” button. Participants had been instructed that they and their partner would see their decisions to cooperate or to defect simultaneously. There were four different outcomes depending on both partners’ decisions, as illustrated by the payoff matrix in Fig. ##FIG##0##1##. Participants knew that mutual cooperation would lead to a gain of 10 points for each partner while mutual defection would lead to no gain or loss. They also knew that a defecting partner would gain 20 points when interacting with a cooperating partner who would in return lose 10 points. Participants received feedback about their own decision (e.g., “You cooperate.”) and their partner’s decision (e.g., “Your partner defects.”) and how these decisions affected each players’ account balance (e.g., “You lose 10 points.”, “Your partner gains 20 points.”). Feedback regarding the participant’s decision and outcome was displayed in black font color whereas feedback on the partner’s decision and outcome was shown in blue font color, corresponding to the blue frame around the partner’s photograph. The photograph and the feedback of the interaction outcome remained visible on the screen until the end of each trial.</p>", "<title>Costly-punishment option</title>", "<p id=\"Par16\">After each interaction in the Prisoner’s Dilemma, participants were offered a costly punishment option. Participants could decide either not to punish their partner or to invest 1, 2 or 3 points to deduce 10, 20 or 30 points, respectively, from their partner’s account balance. Participants were informed beforehand that their partners would simultaneously make their decision to punish the participants. As in a previous experiment^{##REF##37673945##46##}, the partners were programmed to always punish unilateral defection of the participants by deducing a randomly determined amount of 10, 20 or 30 points from the participants’ account. Upon clicking a “Continue” button, participants received feedback about their own punishment decision (e.g., “You invest 2 points to punish your partner.”) and its effect on the partner’s account balance (e.g., “20 points will be deducted from your partner’s account balance.”). Participants simultaneously learned about their partner’s punishment decision (e.g., “Your partner does not punish you.”) and its effect on their own account balance (e.g., “No fine will be deducted from your account balance.”). With a “Continue” button, participants could then start the next trial. The average final account balance was 128 (<italic>SD</italic> = 54) points.</p>", "<title>The cooperation-and-punishment model</title>", "<p id=\"Par17\">Multinomial models have become increasingly popular as they allow to estimate the latent cognitive processes that underlie observable categorical behavioral data [e.g.,^{##REF##17576147##42##,##REF##28816493##43##,##UREF##24##56##,##UREF##25##57##}]. The cooperation-and-punishment model used here has been successfully used to measure cooperation and punishment in previous studies^{##REF##33414495##44##–##REF##37673945##46##}. It is illustrated in Fig. ##FIG##2##3##. The model incorporates two trees, one for the defecting partners and one for the cooperating partners. The first latent process specified in both trees is the participant’s propensity to cooperate which is assumed to be independent of the individual partner’s behavior that is revealed only after the participant’s decision. Therefore, the same parameter <italic>C</italic> can be used for both trees: Participants may choose to cooperate with probability <italic>C</italic> or to defect with probability 1–<italic>C</italic>. Depending on whether the partner cooperates or defects, distinct types of punishment may occur. If the participant’s cooperation is met with the partner’s defection, the participant may apply moral punishment with probability <italic>P</italic>_Moral. Even if the participant does not apply moral punishment with probability 1 − <italic>P</italic>_Moral, the participant may still punish the partner because of an unspecific punishment bias with probability <italic>b</italic>. With probability 1 − <italic>b</italic>, no punishment is applied. After the mutual defection of both players, hypocritical punishment may be applied with probability <italic>P</italic>_Hypocritical. Even if no hypocritical punishment is applied with probability 1 − <italic>P</italic>_Hypocritical, punishment may still occur due to the unspecific punishment bias with probability <italic>b</italic>. With probability 1 − <italic>b</italic>, no punishment is applied. If the participant’s defection mismatches with the cooperation of the partner, the participant may apply antisocial punishment with probability <italic>P</italic>_Antisocial. If the participant does not apply antisocial punishment with probability 1–<italic>P</italic>_Antisocial, punishment may still occur due to the unspecific punishment bias with probability <italic>b</italic>. With probability 1 − <italic>b</italic>, no punishment is applied. Mutual cooperation does not provide any specific reason to punish the partner. Any punishment in this case is therefore used to estimate the punishment bias <italic>b</italic> which reflects an unspecific tendency to punish the partner irrespective of the outcome of the interaction. To illustrate, if an emotion-centered processing focus induces feelings of frustration, this may well result in the indiscriminate punishment of partners irrespective of the outcomes of the Prisoner’s Dilemma game which is then reflected in the punishment bias <italic>b</italic>^{##REF##37673945##46##}<italic>.</italic> The model implies that this punishment bias has to be distinguished from types of punishment that discriminate between different partner behaviors in a parallel way to how response bias has to be distinguished from more specific responses in other decision-making models^{##UREF##26##58##–##UREF##28##62##}. With probability 1–<italic>b</italic>, no punishment is applied.</p>" ]

[ "<title>Results</title>", "<p id=\"Par18\">When using multinomial models to test substantive hypotheses it is ideal to begin with a base model that fits the data. A multinomial model fits the data if the goodness-of-fit test assessing the discrepancy between the observed responses and the responses predicted by the model is non-significant, as indicated by a <italic>p</italic>-value larger than the α-level (usually 0.05). The corresponding goodness-of-fit statistic <italic>G</italic>² is chi-square distributed with degrees of freedom indicated in parentheses. To analyze the present data, two sets of the trees of the multinomial cooperation-and-punishment model depicted in Fig. ##FIG##2##3## are needed for the base model, one set for the cooperating-majority condition and one for the defecting-majority condition. This base model fit the data, <italic>G</italic>²(2) = 3.46, <italic>p</italic> = 0.177.</p>", "<p id=\"Par19\">Multinomial models allow hypothesis tests to be performed directly at the level of the parameters representing the cognitive processes assumed to underly observed behavior. For example, the hypothesis that the participants’ propensity to cooperate is significantly higher in the cooperating-majority condition than in the defecting-majority condition can be tested by restricting the <italic>C</italic> parameters of the two conditions to be equal. If this equality restriction significantly worsens the fit of the restricted model compared to the base model, as indicated by the Δ<italic>G</italic>² statistic which is chi-square distributed with degrees of freedom displayed in parentheses, it can be concluded that the participants’ propensity to cooperate differs between the two conditions. Figure ##FIG##3##4## displays the estimates of the cooperation parameter <italic>C</italic>. Cooperation was indeed significantly higher in the cooperating-majority condition than in the defecting-majority condition, Δ<italic>G</italic>²(1) = 272.57, <italic>p</italic> &lt; 0.001, <italic>w</italic> = 0.14.</p>", "<p id=\"Par20\">Estimates of the punishment parameters are shown in Fig. ##FIG##4##5##. In line with the conformity account, moral punishment was significantly higher in the cooperating-majority condition than in the defecting-majority condition, Δ<italic>G</italic>²(1) = 19.79, <italic>p</italic> &lt; 0.001, <italic>w</italic> = 0.04. Also consistent with the conformity account, a high base rate of cooperation in comparison to defection led to an increase in hypocritical punishment, Δ<italic>G</italic>²(1) = 7.88, <italic>p</italic> = 0.005, <italic>w</italic> = 0.02. So far, the data seem compatible with the conformity account. However, participants were much more likely to use moral punishment to punish a deviation from the cooperating-majority group than to use antisocial punishment to punish a deviation from the defecting-majority group, Δ<italic>G</italic>²(1) = 557.29, <italic>p</italic> &lt; 0.001, <italic>w</italic> = 0.20, which provides evidence against the assumption that punishment is exclusively determined by the goal to enforce conformity. Also, in direct opposition to the prediction of the conformity account, antisocial punishment was enhanced in the cooperating-majority condition compared to the defecting-majority condition, Δ<italic>G</italic>²(1) = 11.55, <italic>p</italic> = 0.001, <italic>w</italic> = 0.03. Finally, the punishment bias did not differ between the cooperating-majority condition and the defecting-majority condition, Δ<italic>G</italic>²(1) = 2.10, <italic>p</italic> = 0.147, <italic>w</italic> = 0.01.</p>" ]

[ "<title>General discussion</title>", "<p id=\"Par30\">The moral punishment of defection is integral to enforcing and maintaining cooperation in the light of the free-rider problem e.g.,^{##UREF##5##8##,##REF##11805825##13##}. It is therefore important to understand what drives people to accept the costs associated with punishing others. If punishment primarily serves to discourage defection^{##REF##25079496##14##}, people should use the punishment option primarily to morally punish unilateral defection while antisocial punishment should occur with a comparatively smaller probability regardless of whether the majority of the partners cooperates or defects. If punishment primarily serves to enforce conformity^{##UREF##9##15##–##UREF##11##18##,##UREF##21##36##}, people should punish all behaviors that do not conform to what the majority does regardless of the specific type of behavior in question. Both accounts predict that people will primarily use moral punishment when most people cooperate. However, the conformity account makes the unique prediction that moral punishment should become less prevalent when most people defect. The present study followed a previous study by Li et al.^{##UREF##22##37##} who found that moral punishment indeed decreases with decreasing cooperation rates. A limitation of the previous study was that participants conditioned their responses on instructed hypothetical base rates of cooperative behavior without experiencing them directly. In the present study, we used a Prisoner’s Dilemma game with a costly punishment option and manipulated whether the participants’ partners cooperated or defected in the majority (60%) of trials. In line with the study by Li et al.^{##UREF##22##37##}, we consistently found across two experiments that moral punishment was more prevalent in the cooperating-majority condition than in the defecting-majority condition. Extending the previous study, we found across both experiments that hypocritical punishment was also more prevalent when the base rate of cooperation was high compared to when it was low. This pattern is consistent with the idea that people may enforce conformity with the majority even when they do not share the preferences of the majority^{##UREF##21##36##}.</p>", "<p id=\"Par31\">So far, the results seem to support the conformity account. However, there are several aspects of the results that are inconsistent with this account. First, moral punishment of defection in the cooperating-majority group was much more likely than antisocial punishment of cooperation in the defecting-majority group which is inconsistent with the assumption that these types of punishment are exclusively determined by the goal to enforce conformity. If that were the case, then the probability of antisocial punishment in the defecting-majority condition should be as high as the probability of moral punishment in the cooperating-majority condition. This prediction is clearly contradicted by the data we observed. Another important prediction of the conformity account is that people should be more likely to use antisocial punishment to punish cooperation in the defecting-majority condition than in the cooperating-majority condition. However, antisocial punishment was lower in the defecting-majority condition than in the cooperating-majority condition, in direct opposition to the prediction of the conformity account.</p>", "<p id=\"Par32\">Overall, the results are thus most compatible with an integrative account according to which people primarily use punishment to discourage defection^{##REF##25079496##14##} but still adjust the punishment to the perceived cooperation levels. A high prevalence of cooperation is often believed to create or strengthen a cooperative norm^{##REF##20212120##22##,##UREF##15##23##,##UREF##33##70##}. Therefore, defection in a cooperative environment may be perceived as being more deviant and thus more deserving of punishment than defection in an environment in which defection is common^{##UREF##22##37##,##REF##28891657##71##}. Hypocritical punishment may be used to make up for one’s own failure to adhere to the cooperative norm as it has been observed that people tend to use punishment to feign sincere support of the majority group behavior despite their actual disapproval^{##UREF##21##36##}. Antisocial punishment may be assumed to be driven by an opposition to the normative pressure towards cooperation that is not shared. For instance, antisocial punishment has often been attributed to an aversion to morally superior “do-gooders”^{##REF##18323447##31##,##UREF##20##33##–##REF##29708860##35##}. People may use antisocial punishment as a retaliation for the embarrassment evoked by one’s unilateral defection. When cooperation is more prevalent, the embarrassment that is caused by the norm violation could well be amplified, causing a stronger urge to harm or devaluate the opponent for causing the embarrassment. In fact, increased levels of do-gooder derogation have been reported when the perceived number of people belonging to the morally superior group was high because a strong conformist pressure created a stronger threat to one’s moral identity ^{##UREF##34##72##,##UREF##35##73##}. It thus is psychologically plausible that antisocial punishment increases rather than decreases with a strong normative pressure towards cooperation as it may reflect a direct opposition towards cooperation.</p>", "<p id=\"Par33\">Given that the present results suggest that high cooperation levels lead to more antisocial punishment, the question arises as to why the prevalence of antisocial punishment is often negatively related to the prevalence of cooperation in cross-cultural comparisons^{##REF##16794075##28##,##REF##18323447##31##} in which participants from societies with low cooperation rates usually experience more antisocial punishment. Here it must be kept in mind that such findings are only correlational and the low cooperation levels might be a consequence of the detrimental effect of antisocial punishment on cooperation instead of the cause for the high antisocial punishment. In the present study, we used an experimental manipulation of the proportion of cooperation and defection to identify its effects on the different types of punishment without having to second-guess the direction of the effects. It also seems striking that most evidence in favor of the conformity account of costly punishment comes from the Public Goods game that examines cooperation within larger groups^{##REF##23347495##16##,##UREF##10##17##}, but see^{##UREF##15##23##}. It thus seems conceivable that the requirement to find a balance between individual and collective interests in larger group settings may create stronger conformist pressures than the dyadic interactions in the Prisoner’s Dilemma game.</p>", "<p id=\"Par34\">Finally, it seems noteworthy that a conformity effect was not only observed with respect to punishment but also with respect to cooperation. Participants’ willingness to cooperate was clearly affected by whether the majority of the partners cooperated or defected. This is in line with a bulk of studies on how participants condition their cooperation on perceived or proclaimed cooperation rates of others^{##REF##23347495##16##,##UREF##12##19##–##UREF##15##23##}. Interestingly, cooperation rates clearly exceeded the manipulated base rate when the partners applied moral punishment to discourage defection (Experiment 1). Without partner punishment (Experiment 2), participants lacked an economic incentive to cooperate. As a result, the participants’ propensity to cooperate aligned more closely with the manipulated base rates which therefore points to a conformist motive behind cooperation.</p>", "<p id=\"Par35\">The aim of the present experiments was to test whether costly punishment is affected by the prevalence of cooperation. By varying the cooperation rates of simulated interaction partners in a between-groups design we were able to experimentally manipulate the base rates of cooperation and defection while maintaining experimental control over extraneous factors that may otherwise influence the players’ behaviors. This approach differs from what is common practice in Experimental Economics but conforms to research traditions in Experimental Psychology [e.g.,^{##REF##23347495##16##,##REF##20658845##48##,##REF##26851770##50##,##REF##18187128##52##,##REF##21559490##54##}]. In this context, two observations seem worth noting. First, participants readily cooperated with, and even punished, their partners even though this implied sacrificing some of their own money. Second, the punishment rates observed in the highly controlled experiments presented here are comparable to the punishment rates reported in studies using real interaction partners [e.g.,^{##UREF##8##12##},^{##UREF##17##27##}]. Taken together, these observations suggest that the present experimental paradigm reliably activated mechanisms of social interactions. Still, it is of course an intriguing avenue for future research to test whether the present conclusions generalize to different settings in which, for instance, participants interact in human dyads.</p>", "<title>Conclusion</title>", "<p id=\"Par36\">Do we punish others for failing to conform to the majority irrespective of the specific type of behavior in question? The present results clearly demonstrate that people do not punish a specific behavior only because it is uncommon. Regardless of the prevalence of cooperation or defection, participants primarily used moral punishment to express their disapproval of a partner’s unilateral defection. This indicates that punishment is primarily used to discourage defection and not to enforce blind conformity with the majority. Nevertheless, there were several ways in which participants’ behaviors were sensitive to the proportion of cooperation and defection they experienced. The present results corroborate previous findings [cf.^{##UREF##22##37##}] suggesting that moral punishment increases with the proportion of cooperating partners in the Prisoner’s Dilemma game. In other words, defecting behavior that deviates from what the majority does is punished more. The same was found for hypocritical punishment. Nevertheless, moral punishment of deviations from a cooperating majority was much higher than antisocial punishment of deviations from a defecting majority which should not be the case if these types of punishment were exclusively determined by the goal to enforce conformity. Furthermore, antisocial punishment was increased when the prevalence of cooperation was high which suggests that antisocial punishment increases with the perceived pressure towards cooperation. Punishment is thus sensitive to the rates of cooperation and defection but, overall, the results are inconsistent with the idea that punishment primarily, let alone exclusively, serves to enforce conformity.</p>", "<title>Ethics approval and consent to participate</title>", "<p id=\"Par37\">The study was conducted in accordance with the guidelines laid down in the Declaration of Helsinki and by the German Research Foundation (DFG) including confidentiality of data and personal conduct. Informed consent was obtained prior to participation. For the noninvasive, purely behavioral research reported in the present series of experiments which carried no risk for the participants, a formal approval by the institution’s ethical board is not legally required in Germany (see: <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.dfg.de/en/research_funding/faq/faq_humanities_social_science/index.html\">https://www.dfg.de/en/research_funding/faq/faq_humanities_social_science/index.html</ext-link>).</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par36\">Do we punish others for failing to conform to the majority irrespective of the specific type of behavior in question? The present results clearly demonstrate that people do not punish a specific behavior only because it is uncommon. Regardless of the prevalence of cooperation or defection, participants primarily used moral punishment to express their disapproval of a partner’s unilateral defection. This indicates that punishment is primarily used to discourage defection and not to enforce blind conformity with the majority. Nevertheless, there were several ways in which participants’ behaviors were sensitive to the proportion of cooperation and defection they experienced. The present results corroborate previous findings [cf.^{##UREF##22##37##}] suggesting that moral punishment increases with the proportion of cooperating partners in the Prisoner’s Dilemma game. In other words, defecting behavior that deviates from what the majority does is punished more. The same was found for hypocritical punishment. Nevertheless, moral punishment of deviations from a cooperating majority was much higher than antisocial punishment of deviations from a defecting majority which should not be the case if these types of punishment were exclusively determined by the goal to enforce conformity. Furthermore, antisocial punishment was increased when the prevalence of cooperation was high which suggests that antisocial punishment increases with the perceived pressure towards cooperation. Punishment is thus sensitive to the rates of cooperation and defection but, overall, the results are inconsistent with the idea that punishment primarily, let alone exclusively, serves to enforce conformity.</p>" ]

[ "<p id=\"Par1\">Do people punish others for defecting or for failing to conform to the majority? In two experiments, we manipulated whether the participants’ partners cooperated or defected in the majority of the trials of a Prisoner’s Dilemma game. The effects of this base-rate manipulation on cooperation and punishment were assessed using a multinomial processing tree model. High compared to low cooperation rates of the partners increased participants’ cooperation. When participants’ cooperation was not enforced through partner punishment, the participants’ cooperation was closely aligned to the cooperation rates of the partners. Moral punishment of defection increased when cooperation rates were high compared to when defection rates were high. However, antisocial punishment of cooperation when defection rates were high was much less likely than moral punishment of defection when cooperation rates were high. In addition, antisocial punishment was increased when cooperation rates were high compared to when defection rates were high. The latter two results contradict the assumption that people punish conformity-violating behavior regardless of whether the behavior supports or disrupts cooperation. Punishment is thus sensitive to the rates of cooperation and defection but, overall, the results are inconsistent with the idea that punishment primarily, let alone exclusively, serves to enforce conformity with the majority.</p>", "<title>Subject terms</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>" ]

[ "<p id=\"Par2\">The capacity for large-scale cooperation has crucially fostered human evolution and the establishment of societies as we know them today. As cooperation implies accepting personal costs for achieving a long-term collective benefit, there is often an incentive to free ride on the other’s cooperation. This clash of individual and collective interests creates a social dilemma [cf.^{##UREF##0##1##}]. The free-rider problem poses a threat: If too many people free ride, cooperation continuously loses its appeal, declines and the system collapses^{##REF##15050515##2##–##UREF##2##5##}. Cooperation levels vary strongly between groups as a function of a number of different factors and may fall above or below 50%, depending on the situation^{##UREF##3##6##,##UREF##4##7##}. One factor that is often believed to support the maintenance of cooperation is the punishment of people who refuse to cooperate and instead defect^{##UREF##5##8##–##UREF##6##10##}. While punishment of defection in repeated interactions can obviously benefit the punishing individuals by enforcing cooperation of their partners in future interactions, punishment of defection in one-shot interactions is more challenging to explain. Irrespective of this, it is a fact that people punish defectors even in one-shot interactions in which there are no obvious incentives for doing so. This is evident not only in the lab^{##UREF##7##11##–##REF##11805825##13##} but also in everyday social interactions. For example, in a one-time interaction on an online shopping site, buyers who feel they were treated unfairly (e.g., because they ordered goods that later turn out to be of poorer quality than advertised) may spend time and effort to write negative reviews to punish the seller. It is thus important to gain a better understanding of this puzzling yet socially tangible behavior. Two possible explanations can be distinguished for why people punish defection in one-shot interactions. One possibility is that cooperating individuals punish others specifically for their defection^{##REF##25079496##14##}. Another possibility is that people punish behavior to enforce conformity with the majority regardless of whether it supports or disrupts cooperation^{##UREF##9##15##–##UREF##11##18##}. Here we test these accounts by examining how a manipulation of the proportions of cooperation and defection affects costly punishment in a Prisoner’s Dilemma game.</p>", "<p id=\"Par3\">The Prisoner’s Dilemma game is a classical paradigm for studying cooperation. In this game, two players simultaneously decide to either cooperate or defect which leads to different possible outcomes, as determined by the game’s payoff structure (see Fig. ##FIG##0##1##). A defecting player who interacts with a cooperating partner receives the highest outcome. A cooperating player who interacts with a defecting partner receives the lowest outcome. At an individual level, it is therefore more profitable to defect. At a collective level, however, cooperation is desirable because mutual cooperation leads to a better outcome for both interactants combined than mutual defection. This payoff structure thereby captures the basic dilemma of cooperation [cf.^{##UREF##0##1##}].</p>", "<p id=\"Par4\">People often strive to achieve mutual cooperation but try to avoid being cheated by a defecting partner who does not reciprocate cooperation. Therefore, it comes as no surprise that cooperation in economic dilemmas is often conditioned on the perceived or proclaimed prevalence of cooperation^{##REF##23347495##16##,##UREF##12##19##–##UREF##15##23##}. For example, Engel et al.^{##UREF##15##23##} provided their participants with selective information about the behavior of either very cooperative or very uncooperative groups before participating in an economic game. Participants were more likely to cooperate when they had received information about the behavior of cooperative groups than when they had received information about the behavior of uncooperative groups. These findings indicate that a person’s propensity to cooperate is influenced by the assumed prevalence of cooperation.</p>", "<p id=\"Par5\">A factor that has been shown to crucially contribute to the maintenance of cooperation within groups is moral punishment [cf.^{##REF##15050515##2##}]. Here, the term <italic>moral punishment</italic> is used to specifically refer to the punishment of defecting partners by cooperating individuals. Defection becomes unattractive when a significant proportion of people punish defection because punishment decreases the payoffs of defecting partners. Moral punishment can thus help to solve the free-rider problem by disincentivizing defection, thereby increasing the level of cooperation^{##UREF##5##8##,##UREF##7##11##,##REF##11805825##13##,##REF##7816134##24##,##REF##16601192##25##}. However, moral punishment often entails personal costs to the punisher. Therefore, moral punishment can be considered a second-order cooperative act^{##UREF##2##5##,##UREF##7##11##,##REF##11805825##13##,##UREF##16##26##,##UREF##17##27##}. Given the importance of moral punishment for the establishment and maintenance of cooperation, it is crucial to understand the factors that drive people to punish others for defection.</p>", "<p id=\"Par6\">Two broad accounts can be distinguished with regard to how the proportion of cooperation or defection should affect people’s punishment behavior. One possibility is that punishment is primarily used to discourage defection, regardless of the prevalence of defection [e.g.,^{##REF##25079496##14##}]. This seems reasonable as punishment in economic games is, as a rule, mainly directed at defectors. However, in a small proportion of cases, people may prefer not to cooperate, sometimes leading to <italic>antisocial punishment</italic> of cooperative acts^{##REF##16794075##28##–##REF##28903691##30##}. This type of punishment is termed antisocial as it undermines cooperation^{##REF##18323447##31##,##UREF##19##32##}. A possible explanation is that antisocial punishers are motivated by their disapproval of the normative pressure towards cooperation, exerted by individuals who are perceived as moral “do-gooders”^{##UREF##20##33##–##REF##29708860##35##}. While it may, at first glance, seem obvious that people should punish behaviors they disapprove of—which would explain the prevalence of both moral <italic>and</italic> antisocial punishment—it has been suggested that people do at least sometimes punish others for failing to conform to the majority regardless of their own private preferences^{##UREF##21##36##}. The <italic>conformity account</italic> implies that punishment is directed at behavior that deviates from what is typical^{##UREF##9##15##–##UREF##11##18##,##UREF##21##36##}. People may punish atypical behaviors to enforce conformity as conformity may reduce the costs that result from conflicts arising from uncertainty about the appropriate behavior. Furthermore, people may engage in punishment when they think that the punishment is justified by the fact that others approve of their punishment which also keeps the costs of punishment low^{##UREF##10##17##}. Considering the high prevalence of cooperation in human groups and societies, punishment will often be directed at defectors who fail to contribute to the collective benefit. However, there is a dark side to enforcing conformity irrespective of the consequences of the behavior: People may antisocially punish atypical behavior even when it is promoting the collective good^{##REF##23347495##16##,##UREF##10##17##} simply because it violates expectations.</p>", "<p id=\"Par7\">Here we examine how the proportion of cooperation and defection affects costly punishment in the Prisoner’s Dilemma game. This study follows a previous study by Li et al.^{##UREF##22##37##} in which participants had to decide between cooperation and defection in a Prisoner’s Dilemma game. Prior to making their punishment decision, participants received information about eleven possible scenarios regarding how many other players had previously chosen to cooperate (ranging from less than 5% to more than 95%). Each participant was then asked to make a punishment decision for defecting partners in every one of these hypothetical scenarios. Punishment increased with the percent of cooperation in the reference group. Apart from the fact that conceptual replications of important findings are always useful, there are several additional reasons to expand on the previous findings. First, Li et al.^{##UREF##22##37##} asked participants to respond to a list of eleven scenarios with different hypothetical base rates which may have accentuated the impact of the base rates on behavior. It is thus interesting to examine whether moral punishment increases with the proportion of cooperation when participants interact with partners directly. Second, Li et al.^{##UREF##22##37##} concentrated only on moral punishment by requiring participants to provide punishment decisions only for defecting partners. Here, we allow participants to make punishment decisions regardless of the outcome of the Prisoner’s Dilemma game which gives us the opportunity to distinguish between different types of punishment.</p>", "<p id=\"Par8\">To allow to cleanly distinguish between different types of punishment and a bias towards punishing, the <italic>multinomial cooperation-and-punishment model</italic> has been developed. The model belongs to the class of multinomial processing tree models. These models have become increasingly popular to measure the components of human decision making [for a review see^{##UREF##23##38##}]. Multinomial models are flexible and accessible measurement models for which easy-to-read tutorials^{##REF##37498691##39##} and user-friendly software^{##REF##20160285##40##} exists. They disambiguate observable behavior by enabling the measurement of the processes underlying overt behavior such as different strategies in decision-making tasks^{##REF##24638825##41##–##REF##28816493##43##}. The relationship between observable behavioral categories and the underlying processes can be visualized in a tree-like structure. Here, we use the multinomial cooperation-and-punishment model (see Fig. ##FIG##2##3##) which has been successfully applied and validated in previous studies^{##REF##33414495##44##–##REF##37673945##46##}. Besides the cooperation parameter <italic>C</italic>, representing the participants’ propensity to cooperate, the model entails that specific types of punishment have to be distinguished from a general punishment bias. <italic>Moral punishment</italic> is defined as the type of punishment that is specifically provoked when the participant’s cooperation is met with the partner’s defection. This type of punishment can be viewed as moral because it is aimed at retaliating the perceived violation of a cooperation norm. To illustrate, moral punishment is enhanced when the labels of the behavioral options in the Prisoner’s Dilemma game facilitate a moral interpretation of the behaviors relative to when the labels are neutral^{##REF##33414495##44##}. <italic>Hypocritical punishment</italic> is the type of punishment that is specifically provoked by an interaction in which both the participant and the partner chose to defect. This type of punishment can be viewed as hypocritical because participants punish behavior in others which they themselves have shown. <italic>Antisocial punishment</italic> is specifically provoked by an interaction in which the participant’s defection is met with a partner’s cooperation. This type of punishment can be labeled as antisocial in the sense that it reflects an opposition against cooperation norms. To illustrate, previous studies^{##REF##33414495##44##,##REF##37673945##46##} have shown that antisocial punishment is increased when participants experience normative pressure to cooperate through the moral punishment exerted by the partners. Furthermore, a proper measurement model of punishment has to take an unspecific bias to punish into account. This allows us to test whether the observed effects are distinct for the different punishment types or reflect a general increase in the willingness to punish, for example, as a way to vent frustration about factors that are unrelated to the outcome of the immediate interaction^{##REF##37673945##46##}.</p>", "<p id=\"Par9\">To test whether people primarily punish others for violating conformity, we manipulated the proportion of cooperating and defecting partners in the Prisoner’s Dilemma game between groups. In the <italic>cooperating-majority condition</italic>, partners cooperated in 60% of the trials and defected in the other 40%, thereby making cooperation the dominant behavior. In the <italic>defecting-majority condition</italic>, this ratio was reversed, thereby making defection the dominant behavior. To ensure that the behavior of the majority was correctly represented, the participants were truthfully informed prior to the start of the game whether most partners would cooperate or defect. If punishment primarily serves to discourage defection, moral punishment should prevail irrespective of the base-rate manipulation. If punishment primarily serves to enforce conformity, punishment should be highly susceptible to the base-rate manipulation. Specifically, moral punishment should be high in the cooperating-majority condition but low or even absent in the defecting-majority condition^{##UREF##22##37##}. Based on the idea that people may enforce conformity with the majority behavior regardless of their own preferences^{##UREF##21##36##}, hypocritical punishment should follow the same pattern as moral punishment. Hypocritical punishment should thus be increased in the cooperating-majority condition in comparison to the defecting-majority condition. If people punish to enforce conformity with the dominant behavior in the Prisoner’s Dilemma game, antisocial punishment, that is, the punishment of cooperation by defecting participants, should be high in the defecting-majority condition but low or even absent in the cooperating-majority condition^{##REF##23347495##16##,##UREF##10##17##}. In fact, if punishment were exclusively determined by the goal to enforce conformity, then the probability that cooperating participants use moral punishment to punish a deviation from a cooperating majority should be identical to the probability that defecting participants use antisocial punishment to punish a deviation from a defecting majority.</p>", "<title>Experiment 1</title>", "<title>Discussion</title>", "<p id=\"Par21\">The aim of the experiment was to test two accounts of punishment. If punishment serves to enforce conformity, then punishment should be directed at punishing <italic>any</italic> deviation from the majority and should therefore be affected by the proportion of cooperating and defecting partners. Specifically, moral punishment should be increased when cooperation is the dominant behavior whereas antisocial punishment should be increased when defection is the dominant behavior. In line with the conformity account, moral punishment was significantly higher in the cooperating-majority condition compared to the defecting-majority condition. In line with the idea that people punish to enforce conformity regardless of their own preferences^{##UREF##21##36##}, hypocritical punishment was also higher in the cooperating-majority condition compared to the defecting-majority condition. However, if punishment were exclusively determined by the goal to enforce conformity, then the probability that participants use moral punishment to punish a deviation from the cooperating majority should be identical to the probability that they use antisocial punishment to punish a deviation from the defecting majority. This was clearly not the case. In addition, antisocial punishment was enhanced in the cooperating-majority condition compared to the defecting-majority condition which is also not compatible with the conformity account. In other words, these results clearly rule out that people punish what is uncommon without regard to the type of behavior that is shown. The fact that moral punishment was much more likely than antisocial punishment regardless of the proportion of cooperation and defection strongly suggests that, while punishment is affected by the base rates of cooperation and defection, punishment primarily serves to discourage defection^{##REF##25079496##14##}. Finally, it seems noteworthy that the punishment bias was not affected by the base-rate manipulation, suggesting that a high proportion of defection did not generally decrease the propensity to punish.</p>", "<p id=\"Par22\">Similar to the punishment parameters, the probability of cooperation was significantly higher in the cooperating-majority condition than in the defecting-majority condition. This is in line with a bulk of studies reporting how participants condition their own cooperation on the perceived or proclaimed cooperation rates of others^{##REF##23347495##16##,##UREF##12##19##–##UREF##14##21##,##UREF##15##23##}. Interestingly, while being clearly influenced by the prevailing cooperation rates, participants’ propensity to cooperate still exceeded the base rate of cooperation in both the cooperating-majority condition and the defecting-majority condition: When partners cooperated in 60% of the trials in the cooperating-majority condition, participants cooperated in 70% of the trials, whereas when partners cooperated in 40% of the trials in the defecting-majority condition, participants nevertheless cooperated in 56% of the trials.</p>", "<p id=\"Par23\">Cooperation rates may have been elevated in Experiment 1 because the partners reliably punished the unilateral defection of the participants and thereby discouraged defection. This could potentially also explain why moral punishment remained at a high level in the cooperating-majority condition as well as the defecting-majority condition in that it seems conceivable that participants may have followed the example of their partners when deciding to apply moral punishment [cf.^{##UREF##22##37##,##REF##30626917##63##–##UREF##29##65##}]. It thus is necessary to test how the proportion of cooperation and defection affects moral punishment when participants cannot base their own punishment decisions on the example set by the partners. Therefore, we tested in Experiment 2 how the proportion of cooperating and defecting partners affects moral punishment when punishment is unilaterally available to the participants but not to the partners, as in previous experiments^{##REF##33414495##44##,##UREF##30##66##,##UREF##31##67##}. If the effects of the base-rate manipulation are independent of the presence or absence of partner punishment, the pattern of results from Experiment 1 should be replicated. To the degree that the effects of the base rate manipulation depend on the presence or absence of the partners’ moral punishment, the effects should differ between Experiments 1 and 2.</p>", "<title>Experiment 2</title>", "<title>Method</title>", "<p id=\"Par24\">Parallel to Experiment 1, we aimed at recruiting about 500 valid data sets with the help of the online panel provider <italic>mingle.</italic> Of those participants who had started the game, 54 data files had to be excluded because the participants did not complete the experiment; 48 data files had to be excluded due to double participation. The final sample consisted of <italic>N</italic> = 495 participants (209 female, 284 male, 2 non-binary) aged 18–90 years with a mean age of 49 (<italic>SD</italic> = 16) years. The slightly smaller sample size relative to that of Experiment 1 (<italic>n</italic> = 544) did not substantially affect the sensitivity of the statistical tests. It was still possible to detect effects of <italic>w</italic> = 0.03 with a statistical power of 1 – β = 0.95 at an α level of 0.05 when comparing the cooperation and punishment parameters between the cooperating-majority condition (<italic>n</italic> = 250) and the defecting-majority condition (<italic>n</italic> = 245)^{##REF##17695343##47##}.</p>", "<p id=\"Par25\">Materials and procedure were identical to those of Experiment 1 with the exception that the punishment option was unilaterally available to the participants, implying that the partners did not punish participants’ defection. Participants therefore only received feedback about their own punishment decision and its effect on the partner’s account balance. The average final account balance was 275 (<italic>SD</italic> = 100) points.</p>", "<title>Results</title>", "<p id=\"Par26\">As in Experiment 1, the data were analyzed using the multinomial cooperation-and-punishment model (see Fig. ##FIG##2##3##). The goodness-of-fit test showed that the base model provided a good fit to the data, <italic>G</italic>²(2) = 0.40, <italic>p</italic> = 0.819. The estimates of the cooperation parameter <italic>C</italic> are shown in Fig. ##FIG##5##6##. Replicating the results of Experiment 1, cooperation was significantly higher in the cooperating-majority condition in comparison to the defecting-majority condition, Δ<italic>G</italic>²(1) = 188.35, <italic>p</italic> &lt; 0.001, <italic>w</italic> = 0.12.</p>", "<p id=\"Par27\">Figure ##FIG##6##7## displays the estimates of the punishment parameters (left panel) and the punishment bias (right panel). In line with Experiment 1, moral punishment was significantly higher in the cooperating-majority condition than in the defecting-majority condition, Δ<italic>G</italic>²(1) = 10.01, <italic>p</italic> = 0.002, <italic>w</italic> = 0.03. Also consistent with Experiment 1, a high base rate of cooperation in comparison to defection led to an increase in hypocritical punishment, Δ<italic>G</italic>²(1) = 8.70, <italic>p</italic> = 0.003, <italic>w</italic> = 0.03. Further replicating Experiment 1 and in direct opposition to the prediction of the conformity account, moral punishment in the cooperating-majority group was much more likely than antisocial punishment in the defecting-majority group, Δ<italic>G</italic>²(1) = 486.20, <italic>p</italic> &lt; 0.001, <italic>w</italic> = 0.20, which is evidence against the assumption that these types of punishment are exclusively determined by the goal to enforce conformity. Parallel to the results of Experiment 1, and further disconfirming the conformity account, antisocial punishment was enhanced in the cooperating-majority condition compared to the defecting-majority condition, Δ<italic>G</italic>²(1) = 4.87, <italic>p</italic> = 0.027, <italic>w</italic> = 0.02. Finally, the punishment bias was significantly higher in the defecting-majority condition than in the cooperating-majority condition, Δ<italic>G</italic>²(1) = 11.46, <italic>p</italic> = 0.001, <italic>w</italic> = 0.03.</p>", "<title>Discussion</title>", "<p id=\"Par28\">The aim of Experiment 2 was to test whether the effects of Experiment 1 can be replicated when partners do not morally punish defection. Replicating the main findings of Experiment 1, moral, hypocritical and antisocial punishment were significantly higher in the cooperating-majority condition in comparison to the defecting-majority condition in Experiment 2. While the effects of the base-rate manipulation on moral and hypocritical punishment are partly in line with the conformity account, the effect on antisocial punishment is in direct opposition to what the conformity account implies, as is the fact that moral punishment in the cooperating-majority group was much more likely than antisocial punishment in the defecting-majority group. This necessarily leads to the conclusion that people do not punish behavior only because it deviates from what the majority does. Interestingly, moral punishment rates still remained at a high level even though, in contrast to Experiment 1, participants could not follow their partners’ example when deciding whether to use moral punishment. This supports the conclusion that when applying moral punishment people are not merely conforming to the observed punishment behavior of their partners. Instead, there seems to be an intrinsic motive for punishing defection. The present results thereby nicely fit with the recently proposed moral preference hypothesis according to which costly punishment of defection is driven by an internalized preference to act in a way that is typically considered moral^{##UREF##32##68##,##REF##33561377##69##}. Other than in Experiment 1, the punishment bias was increased in the defecting-majority condition in Experiment 2. This suggests that when mainly interacting with defecting partners, participants tend to randomly punish their partners more frequently, possibly as a way to vent frustration about the high prevalence of defection. As in Experiment 1, it can be concluded that there was no general reluctance to punish in the defecting-majority condition.</p>", "<p id=\"Par29\">The effect of the base-rate manipulation on the participants’ own inclination to cooperate was replicated in Experiment 2. Moreover, when cooperation was not enforced by moral punishment, participants’ own cooperation rates aligned more closely with the manipulated base rates than participants’ cooperation rates in Experiment 1. This points to a conformist motive behind cooperation, in line with the previous literature^{##REF##23347495##16##,##UREF##14##21##,##UREF##15##23##}.</p>" ]

[ "<title>Author contributions</title>", "<p>A.P., L.M., A.B. and R.B. contributed to the study conception and design. Material preparation, data collection and analysis were performed by A.P. All authors contributed through discussion and interpretation of the results. A.P. wrote the manuscript with subsequent input and final approval from all co-authors.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>", "<title>Data availability</title>", "<p>We provide the data used in our analyses via the Open Science Framework. The data is publicly available at <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/fycg3/\">https://osf.io/fycg3/</ext-link>.</p>", "<title>Competing interests</title>", "<p id=\"Par38\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Examples of a payoff structure of the Prisoner’s Dilemma game. The payoffs are displayed as a function of both players’ decisions in the Prisoner’s Dilemma game. Shaded cells denote the payoff to Player A, white cells denote the payoff to Player B.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Example trial of the Prisoner’s Dilemma game with costly punishment. In this example trial, the participant cooperated while the partner defected which led to a loss of 10 points for the participant and a gain of 20 points for the partner. The participant then chose to morally punish the partner by investing 2 points so that 20 points were subtracted from the partner’s account balance. The partner’s photograph was randomly selected from the Chicago Face Database^{##REF##25582810##55##}.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Multinomial cooperation-and-punishment model. Rectangles on the left represent the partner’s behavior. Rectangles on the right represent the participant’s behavior. Letters along the branches indicate the parameters of the model (<italic>C</italic> = cooperation, <italic>P</italic>_Moral = moral punishment of unilateral defection, <italic>P</italic>_Hypocritical = hypocritical punishment following mutual defection, <italic>P</italic>_Antisocial = antisocial punishment of unilateral cooperation; <italic>b</italic> = unspecific punishment bias).</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Estimates of the cooperation parameter <italic>C</italic> as a function of cooperation base rates in Experiment 1 (with partner punishment). In the cooperating-majority condition, partners cooperated in 60% of the trials and defected in the other 40%. In the defecting-majority condition, this ratio was reversed. Error bars represent standard errors.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Estimates of the parameters representing moral, hypocritical and antisocial punishment (left panel) and the punishment bias (right panel) in Experiment 1 (with partner punishment). In the cooperating-majority condition, partners cooperated in 60% of the trials and defected in the other 40%. In the defecting-majority condition, this ratio was reversed. Error bars represent standard errors.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Estimates of the cooperation parameter <italic>C</italic> as a function of cooperation base rates in Experiment 2 (without partner punishment). In the cooperating-majority condition, partners cooperated in 60% of the trials and defected in the other 40%. In the defecting-majority condition, this ratio was reversed. Error bars represent standard errors.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Estimates of the parameters representing moral, hypocritical, and antisocial punishment (left panel) and the punishment bias (right panel) in Experiment 2 (without partner punishment). In the cooperating-majority condition, partners cooperated in 60% of the trials and defected in the other 40%. In the defecting-majority condition, this ratio was reversed. Error bars represent standard errors.</p></caption></fig>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Rose was rushing to go to the dentist, and she parked in a spot that was reserved for people with disabilities. She did not know that, but she did not check either. As a result, Philip could not park in his reserved spot and missed his weekly therapy session. Is Rose responsible for that regrettable outcome? Is she responsible even though she did not know? What if Rose had very good reasons to believe that the spot was not reserved? What if checking the availability of the spot involved waiting for the parking attendant for a long time and thus missing an important meeting herself? People ascribe responsibility to agents who made a choice knowing that it would have negative consequences on others, but judgments about responsibility vary greatly when the choice is made without such knowledge^{##UREF##0##1##–##UREF##2##3##}. What underlying cognitive processes produce these judgments?</p>", "<p id=\"Par3\">In our account, people ascribe responsibility for bringing about a negative outcome not only to agents who predicted such an outcome but also to agents who did not predict it. In such cases, people ascribe responsibility by constructing counterfactuals, i.e, by reasoning about what could have been done to avoid the bad outcome. Counterfactuals are imagined alternatives to real events^{##REF##26393873##4##}. People conceive counterfactuals not only when developing causal explanations^{##UREF##3##5##,##REF##25698516##6##}, but also when ascribing blame^{##UREF##4##7##,##REF##22959289##8##} and responsibility^{##UREF##5##9##–##REF##37708602##11##}. However, previous work that examined the role of counterfactual reasoning in moral judgments focused mostly on agents’ actions^{##UREF##6##10##–##UREF##7##13##} and agents’ epistemic states^{##REF##33930783##14##–##REF##36402085##16##}. Less research emphasizes the role of counterfactual reasoning about agents’ intentions^{##REF##36402085##16##,##UREF##9##17##}.</p>", "<p id=\"Par4\">People answer questions about others’ responsibility with the goal of deciding whom to blame or praise, and, more generally, whom to hold accountable^{##UREF##10##18##–##UREF##12##20##}. With these moral goals in mind, agents’ intentions become especially relevant^{##REF##18439575##21##,##REF##23878021##22##}. One reason why intentions are especially relevant when formulating such judgments is that they are key evidence of the agents’ prosocial preferences - and, in particular, about how much they cared for others when making their choice^{##REF##35436157##23##,##UREF##13##24##}. For instance, an agent who does not throw an emergency buoy at a drowning man just because they do not want to is deemed responsible for the death of that man. An agent who does want to throw a buoy but does not find one is instead not deemed responsible unless there is another option for saving the drowning man. Furthermore, an agent who chooses not to put their own life at risk to save a drawing man is usually <italic>not</italic> deemed responsible, while an agent who chooses not to get their clothes wet to save a drowning man usually is. Counterfactuals are relevant for responsibility judgments to the extent that they reveal whether a person with minimal concern for others could have, with the right intentions, avoided the bad outcome.</p>", "<p id=\"Par5\">These considerations about the relevance of intentions for ascribing responsibility apply also to intentions that are specifically epistemic. Epistemic intentions are intentions that drive actions meant to acquire information^{##UREF##14##25##}. Counterfactuals in which the assessed agent has an alternative epistemic intention are especially relevant when the assessed agent did not predict the bad consequences of their choice. We reasoned that people ascribe responsibility if they can think of a counterfactual in which the assessed agent has an epistemic intention that initiates a causal chain of events that eventually prevents the negative outcome from happening (See Fig. ##FIG##0##1##).</p>", "<p id=\"Par6\">Epistemic intentions have a more distal causal role in bringing about the target outcome. Still, we hold that people making judgments about responsibility do conceive counterfactuals with alternative epistemic intentions. In fact, people do think of counterfactuals related to the initial instances in a specific causal sequence^{##REF##12420996##26##}, and counterfactuals can include changing the state of knowledge^{##UREF##8##15##}. Counterfactuals that form the basis for ascribing responsibility might take the form of a causal chain of events that is initiated by a counterfactual epistemic intention. The intention causes an epistemic action, which in turn informs a choice, which avoids the bad outcome. The counterfactual epistemic intention reveals whether the assessed agent acted with moral concern for others, or not^{##UREF##15##27##}. The reasoning is that, if the agent failed to have an epistemic intention that would have led to a better outcome for others, it is because that agent cared too little about their welfare. However, not all alternative epistemic intentions and the counterfactual chains of events they initiate are considered bases for responsibility ascription. We do not expect agents to pay unreasonable costs to acquire relevant information, and we do not expect them to intend epistemic actions that have very little chance to make a difference. Expectations about epistemic actions are, here, similar to expectations about non-epistemic action: we do not expect people to put their lives at risk to save a drowning man, for instance.</p>", "<p id=\"Par7\">We hypothesize that people ascribe responsibility to an agent who did not predict that their choice would have bad consequences if people think of a counterfactual that has the following properties:<list list-type=\"bullet\"><list-item><p id=\"Par8\">The assessed agent has an alternative epistemic intention that would lead to an intended epistemic action.</p></list-item><list-item><p id=\"Par9\">The intended epistemic action is not too costly for the assessed agent and it is expected to be sufficiently informative (it is sufficiently likely to lead the agent to change their mind and make a different choice).</p></list-item><list-item><p id=\"Par10\">The chain of events that causally follows from this alternative intention leads to an outcome that is better than the actual one.</p></list-item></list>We tested this hypothesis by running a series of preregistered studies in which we asked participants to read various vignettes that described events that eventually led to a bad outcome. Participants were requested to state whether they agreed that an agent, the main protagonist of the vignette, was responsible for a given outcome. The vignettes described situations in which the protagonists could, or could not predict the consequences of their actions.</p>", "<p id=\"Par11\">In the vignettes, we manipulated whether the agents knew about the potential consequences of their actions and the reasons behind their ignorance. The reasons for ignoring relevant information depended on whether the agent had the opportunity to learn (Study 1a), or the intention to learn (Study 1b), whether it was easy or difficult to acquire the information (Study 2a), and if the available epistemic action was sufficiently informative or not (Study 2b).</p>", "<p id=\"Par12\">Our goal was to show that, when ascribing responsibility to agents who did not predict the consequences of their choice, the cognitive processes include: <list list-type=\"order\"><list-item><p id=\"Par13\">Thinking of counterfactuals that start with alternative epistemic intentions. Consequently: <list list-type=\"order\"><list-item><p id=\"Par14\">Responsibility ascription depends on the opportunity that the agent had to learn the relevant information (Study 1a)</p></list-item><list-item><p id=\"Par15\">Responsibility ascription depends on the evidence about the target agent’s epistemic intentions, and whether or not the epistemic action was taken (Study 1b).</p></list-item></list></p></list-item><list-item><p id=\"Par16\">Thinking of alternative epistemic intentions that have sufficient expected value. Consequently: <list list-type=\"simple\"><list-item><label>H2a</label><p id=\"Par17\">Responsibility ascription depends on the cost of the intended epistemic action (Study 2a)</p></list-item><list-item><label>H2b</label><p id=\"Par18\">Responsibility ascription depends on the envisaged benefit of the intended epistemic action (Study 2b).</p></list-item></list></p></list-item></list></p>" ]

[ "<title>Methods</title>", "<title>Study 1a</title>", "<p id=\"Par48\">The methods and statistical plan have been preregistered. You can find the preregistration document at: <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/6ysb9\">https://osf.io/6ysb9</ext-link>.</p>", "<title>Participants</title>", "<p id=\"Par49\">The initial preregistered analysis for this study was a non-parametric Kruskal-Wallis test and we therefore determined the sample size in view of that. More information can be found in the Supplementary Note online. A power analysis using the package ‘pwr’^{##UREF##30##46##} in R^{##UREF##17##29##} indicated that a total sample size of 128 participants (i.e. 384 data points) would detect a low effect size (f = 0.1) with a predicted statistical power of using a one-way ANOVA with alpha at . If the effect size is low-to-medium (f = 0.15), the predicted power increases to . Since we initially planned to run a non-parametric one-way ANOVA, given the ordinal nature of our data^{##UREF##31##47##}, we added to our desired sample^{##UREF##32##48##}. We thus planned to recruit 150 participants. We included the data from all participants who had already begun the experiment when we reached the desired number and closed the survey collector.</p>", "<p id=\"Par50\">Participants were recruited from Prolific (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.prolific.com\">www.prolific.com</ext-link>) and compensated at a rate of 9 GBP per hour of participation, evaluated by Prolific as a good payment. All participants were older than 18 and they all gave their informed consent to participate in the study. The only selection criterion was the use of English as primary, first, and fluent language. We collected data from 151 participants. As one participant took longer than expected to complete the survey, the recruitment platform reached the final sample () before the participant completed their experimental session; we thus included them in our analysis.</p>", "<p id=\"Par51\">Data was discarded in the case of participants who did not answer correctly the attention check question related to that scenario. If there was a mistake on only one or two scenarios out of three, only data points related to those scenarios were discarded. This resulted in excluding 25 data points, leaving 142 data points in the <italic>Full Ignorance</italic> condition, 144 in the <italic>Willful Ignorance</italic> condition, and 142 in the <italic>Knowledge</italic> condition. The experiment lasted roughly five minutes (Mdn = 5 min 4s). Here and elsewhere, the methods used were in accordance with the international ethical requirements of psychological research and were approved by the Psychological Research Ethics Board (PREBO, Ref: 2022/18) from the Central European University in Vienna for conducting the study.</p>", "<title>Materials</title>", "<p id=\"Par52\">As material for this study, we used nine vignettes describing some real-life social situations. We designed three different scenarios with three different conditions. Three different conditions of one scenario differ minimally: only the crucial manipulation part of the text is changed across conditions. All vignettes were of similar length and not longer than a few short paragraphs.</p>", "<title>Procedure and design</title>", "<p id=\"Par53\">We implemented our stimuli on the Qualtrics software^{##UREF##33##49##}. Participants were instructed to read stories described in vignettes and answer a few questions. We designed three different scenarios and each of them occurred in three different conditions. We employed a between-subject design so that one participant saw only one condition of the scenario.</p>", "<p id=\"Par54\">The scenarios follow a similar structure: an introduction describing the context with main character A doing B (general); information about epistemic states and actions that we manipulated depending on the experimental condition; main character doing S; and finally, consequences. To see an example of one scenario across the three conditions, see Table ##TAB##0##1##. Each participant randomly read the three stories, and they were presented always with all of the three conditions (one condition per story). Participants were assigned the scenarios in a randomized order. The three experimental conditions are: <list list-type=\"order\"><list-item><p id=\"Par55\"><italic>Knowledge</italic> (i.e., Agent A acts knowingly); in this condition, the agent knows their action would produce a bad outcome, but they proceed with the behavior nevertheless;</p></list-item><list-item><p id=\"Par56\"><italic>Willful Ignorance</italic> (Agent A is willfully ignorant); in this condition, the agent does not know the relevant information, but has the opportunity to take a simple epistemic action to acquire such knowledge and willfully does not take it;</p></list-item><list-item><p id=\"Par57\"><italic>Full Ignorance</italic> (Agent A acting unknowingly); in this condition, the agent does not know the relevant information, nor the possibility of getting that information or a reason to search for it.</p></list-item></list></p>", "<p id=\"Par58\">After reading the story participants first were prompted to evaluate the agent’s behavior. In addition to that, we asked them to elaborate on their answer. Then, on the next page, they received an attention check question in a multiple-choice form, to ensure they read the story carefully. This attention check was also used as an exclusion criterion. The evaluation of the agent’s behavior was done by ascription of responsibility, operationalized as a prompted judgment that answers the following question (Responsibility Question):Participants were instructed to give answers on a 5-point Likert scale: ‘Strongly disagree’, ‘Somewhat disagree’, ‘Neither agree nor disagree’, ‘Somewhat agree’, and ‘Strongly agree’. For example: “To what extent do you agree with the statement: ‘Rose is responsible for the man missing his therapy’?”. Questions following each story were presented in a fixed order. It was important to present the Responsibility question and the Elaboration question immediately after the story, due to the possibility of attention check influencing the answer, although we made sure that the attention check questions were as neutral as possible. Moreover, we wanted to have the attention check on a separate page without the possibility to go back to the story. This way, we wanted to make sure participants were really paying attention to the story.</p>", "<title>Study 1b</title>", "<p id=\"Par60\">The methods and statistical plan have been preregistered. You can find the preregistration document at: <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/u9w6k\">https://osf.io/u9w6k</ext-link>.</p>", "<title>Participants</title>", "<p id=\"Par61\">Following our previous studies, as well as Kirfel and Hannikainen (2022) and Kirfel, Bunk, and Gerstenberg (2023), we planned to collect the data from 450 participants, thus approximately 150 per condition, or 50 per scenario. We included data from all participants who had already begun the experiment when we reached the desired number and closed the survey collector.</p>", "<p id=\"Par62\">Participants were recruited from Prolific (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.prolific.com\">www.prolific.com</ext-link>) and compensated at a rate of 9 GBP per hour of participation, evaluated by Prolific as a good payment. All participants were older than 18 and they all gave their informed consent to participate in the study. The only selection criterion was the use of English as primary, first, and fluent language. We collected data from 452 participants. As two participants took longer than expected to complete the survey, the recruitment platform reached the final sample () before the participant completed their experimental session; we thus included them in our analysis.</p>", "<p id=\"Par63\">Data was discarded in the case of participants who did not answer correctly the attention check question related to that scenario. This resulted in excluding 27 data points, leaving 144 data points in the <italic>Willful Ignorance</italic> condition, 142 in the <italic>Circumstantial Ignorance</italic> condition, and 138 in the <italic>Misinformed</italic> condition. The experiment lasted roughly 2 min (Mdn = 1 min 37 s).</p>", "<title>Materials</title>", "<p id=\"Par64\">Material for this study were the same vignettes used in Study 1a, adjusted to include the manipulation required by Study 1b.</p>", "<title>Procedure and design</title>", "<p id=\"Par65\">The procedure was similar to the procedure followed in Study 1a. However, participants read only one scenario and they were asked to answer different additional questions. We used the same platforms for collecting the data (Qualtrics software) and recruiting participants (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.prolific.com\">www.prolific.com</ext-link>) with the same payment rate set in Study 1a.</p>", "<p id=\"Par66\">Participants’ task was to read a story, and after the story, they first got a question to evaluate the agent’s behavior, which was our dependent variable. Then, on the next page, they first got an attention check question and then a question to evaluate the perceived agent’s care to learn the relevant information. There were three different scenarios and each of them occurred in three different conditions. To see an example of one scenario across the two conditions, see Table ##TAB##1##2##. Each participant was randomly assigned to one of the three conditions of the one randomly selected scenario. The three experimental conditions are: <list list-type=\"order\"><list-item><p id=\"Par67\"><italic>Willful Ignorance</italic> (i.e., Agent A has no prosocial epistemic intention and does not take the epistemic action); in this condition, the agent does not want to know if their action would produce the bad outcome, and they do not take the epistemic action to learn. They produce the negative consequence;</p></list-item><list-item><p id=\"Par68\"><italic>Circumstantial Ignorance</italic> (Agent A has a prosocial epistemic intention but does not take the epistemic action); in this condition, the agent wants to know if their action would produce the bad outcome, but the circumstances make it impossible for them to take the epistemic action to learn. They produce the negative consequence;</p></list-item><list-item><p id=\"Par69\"><italic>Misinformed Ignorance</italic> (Agent A has a prosocial intention and takes the epistemic action); in this condition, the agent wants to know if their action would produce the bad outcome and they take the epistemic action to learn, but due to someone else’s fault the relevant information was wrong. They produce the negative consequence.</p></list-item></list></p>", "<p id=\"Par70\">Our main dependent variable is the ascription of responsibility, and it was operationalized in the same manner as in Study 1a. Another dependent variable is the perception of the agent’s care to learn the relevant information. It was operationalized through the following question (Care Question):Participants were instructed to give their answer on a 5-point Likert scale, where 1 is ’A didn’t care at all’ and 5 is ’A cared a lot’. For example, “How much did Rose care about whether the spot was reserved?” (Rose is Agent A, whether the spot was reserved is information X).</p>", "<p id=\"Par72\">Between design was employed due to the possibility that answering the Care Question would influence the answers to the Responsibility question.</p>", "<title>Study 2a</title>", "<p id=\"Par73\">The methods and statistical plan have been preregistered. You can find the preregistration document at: <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/bzcpq\">https://osf.io/bzcpq</ext-link></p>", "<title>Participants</title>", "<p id=\"Par74\">The initial preregistered analysis for this study was a non-parametric Mann-Whitney t-test and we therefore determined the sample size in view of that. More information can be found in the Supplementary Note online. A power analysis using the package ‘pwr’^{##UREF##30##46##} in R^{##UREF##17##29##} indicated that a total sample size of 260 participants would detect a low effect size (d = 0.2) with a predicted statistical power of using an independent-measures t-test with alpha at . If the effect size is low-to-medium (), the predicted power decreases to . Since we planned to run a non-parametric test, given the nature of our data^{##UREF##31##47##}, we added to our desired sample^{##UREF##32##48##}. From this analysis, we aimed to collect data from 300 participants. We included the data from all participants who had already begun the experiment when we reached the desired number and closed the survey collector.</p>", "<p id=\"Par75\">Participants were recruited from Prolific (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.prolific.com\">www.prolific.com</ext-link>) and compensated at a rate of 9 GBP per hour of participation, evaluated by Prolific as a good payment. All participants were older than 18 and they all gave their informed consent to participate in the study. The only selection criterion was the use of English as primary, first, and fluent language. We collected the data from 308 participants, since the collector stops when the number of participants who concluded the study is 300, but discards participants who started the study but gave up before the final submission. Since Qualtrics counts in all the data points that started the questionnaire, and due to the fact that we did not collect participants’ IDs, we could not distinguish which participants gave up on Prolific in order to exclude them. After the exclusion of the data points that were not complete (answering none or only one question out of three related to the scenario), a total of 306 data points were taken into consideration. The exclusion criterion was that the data points of participants who did not answer correctly on an attention check would not be used. Since no participant made a mistake, all 306 data points were used in further analyses.</p>", "<p id=\"Par76\">Data was discarded in the case of participants who did not answer correctly the attention check question related to that scenario. This resulted in excluding 13 data points, leaving 146 data points in the <italic>Low Effort</italic> condition and 147 in the <italic>High Effort</italic> condition. The experiment lasted roughly two minutes (Mdn = 1 min 34s).</p>", "<title>Materials</title>", "<p id=\"Par77\">Material for this study were the same vignettes from Study 1a and Study 1b adjusted to include the manipulation required by Study 2a.</p>", "<title>Procedure and design</title>", "<p id=\"Par78\">The procedure was similar to the procedure followed in Study 1b. However, participants were asked to answer different additional questions. We used the same platforms for collecting the data (Qualtrics software) and recruiting participants (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.prolific.com\">www.prolific.com</ext-link>) with the same payment rate set in the previous studies.</p>", "<p id=\"Par79\">Participants’ task was to read a story, and after the story, they first got a question to evaluate the agent’s behavior, which was our dependent variable. Then, on the next page, they first got an attention check question and then a question to evaluate the perceived effort needed for the epistemic action. There were three different scenarios and each of them occurred in two different conditions. To see an example of one scenario across the two conditions, see Table ##TAB##2##3##. Each participant was randomly assigned to one of the two conditions of the one randomly selected scenario. Two conditions are: <list list-type=\"order\"><list-item><p id=\"Par80\"><italic>Low Effort</italic> (Low cost of the epistemic action): in this condition agent would need to do the simple action and put a little effort in order to acquire the relevant knowledge about the consequences of their action;</p></list-item><list-item><p id=\"Par81\"><italic>High Effort</italic> (High cost of the epistemic action): in this condition agent would need to put a lot of effort in order to acquire the relevant knowledge about the consequences of their action.</p></list-item></list></p>", "<p id=\"Par82\">Our main dependent variable is the ascription of responsibility, and it was operationalized in the same manner as in Study 1. Another dependent variable is the perception of effort needed to initiate the epistemic action. It was operationalized through the following question (Perceived Effort Question):Participants were instructed to give answers on a 5-point Likert scale: ’Very easy’, ’Somewhat easy’, ’Neither easy nor difficult’, ’Somewhat difficult’, and ’Very difficult.’ For example: “How difficult would have been for Rose to check whether the spot was reserved?” (Rose is the agent, information about whether the spot is reserved).</p>", "<p id=\"Par84\">We employed a between-subjects design due to the possibility that answering the Perceived Effort question would influence the answers to the subsequent Responsibility Question.</p>", "<title>Study 2b</title>", "<p id=\"Par85\">The methods and statistical plan have been preregistered. You can find the preregistration document at: <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/qxphg\">https://osf.io/qxphg</ext-link>.</p>", "<title>Participants</title>", "<p id=\"Par86\">Following our previous studies, as well as Kirfel and Hannikainen (2022) and Kirfel, Bunk, and Gerstenberg (2023), we planned to collect the data from 300 participants, thus approximately 150 per condition, or 50 per scenario. We included data from all participants who had already begun the experiment when we reached the desired number and closed the survey collector.</p>", "<p id=\"Par87\">Participants were recruited from Prolific (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.prolific.com\">www.prolific.com</ext-link>) and compensated at a rate of 9 GBP per hour of participation, evaluated by Prolific as a good payment. All participants were older than 18 and they all gave their informed consent to participate in the study. The only selection criterion was the use of English as primary, first, and fluent language. We collected data from 303 participants. As three participants took longer than expected to complete the survey, the recruitment platform reached the final sample () before the participant completed their experimental session; we thus included them in our analysis.</p>", "<p id=\"Par88\">Data was discarded in case of participants who did not answer correctly the attention check question related to that scenario. This resulted in excluding 20 data points, leaving 146 data points in the <italic>Improbable</italic> condition and 137 in the <italic>Probable</italic> condition. The experiment lasted roughly two minutes (Mdn = 1 min 39s).</p>", "<title>Materials</title>", "<p id=\"Par89\">Material for this study were two out of three vignettes from Study 1a, Study 1b, and Study 2a. The third vignette was a new one created for this study because one of the vignettes previously used could not be updated adequately for the manipulation in this study. All vignettes were adjusted to include the manipulation required by Study 2b.</p>", "<title>Procedure and design</title>", "<p id=\"Par90\">The procedure was similar to the procedure followed in Study 1b and Study 2a. However, participants were asked to answer different additional questions. We used the same platforms for collecting the data (Qualtrics software) and recruiting participants (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.prolific.com\">www.prolific.com</ext-link>) with the payment rate same as in the previous studies.</p>", "<p id=\"Par91\">Participants’ task was to read a story, and after the story, they first got a question to evaluate the agent’s behavior, which was our dependent variable. Then, on the next page, they first got an attention check question and then a question to evaluate the perceived likelihood of the relevant event happening. There were three different scenarios and each of them occurred in two different conditions. To see an example of one scenario across the two conditions, see Table ##TAB##3##4##. Each participant was randomly assigned to one of the two conditions of the one randomly selected scenario. The two experimental conditions are: <list list-type=\"order\"><list-item><p id=\"Par92\"><italic>Improbable</italic> (Low probability of the relevant event happening): in this condition the subjective probability of the relevant event happening is low since in the agent’s experience it happens very rarely or never;</p></list-item><list-item><p id=\"Par93\"><italic>Probable</italic> (High probability of the relevant event happening): in this condition the subjective probability of the relevant event happening is high since in the agent’s experience it happens very often or always.</p></list-item></list></p>", "<p id=\"Par94\">Our main dependent variable is the ascription of responsibility, and it was operationalized in the same manner as in the previous studies. Another dependent variable is the perceived likelihood of the relevant events. Relevant events are those that participate in causing negative consequences for other people. This likelihood can be understood as a proxy for the  agent’s beliefs about what would happen. It is operationalized through the following question (Probability Question):Participants are instructed to indicate the probability by using the slider, where 0 is ’Improbable’ and 100 is ’Probable’. For example: “How likely would you have thought it was that Karl had to work on that weekend?” (Karl working on that weekend is the relevant event X).</p>", "<p id=\"Par96\">Between design was employed due to the possibility that answering the Probability question would influence the answers to the Responsibility Question.</p>" ]

[ "<title>Results</title>", "<title>Study 1a</title>", "<p id=\"Par20\">Study 1a tests the hypothesis that the ascription of responsibility depends both on the assessment of agent’s epistemic states and on their epistemic actions. In more detail, we test whether responsibility ascription depends on the opportunity to learn the relevant information (H1a). If there is an opportunity to learn, then there is a counterfactual in which the intention to seize that opportunity gives a counterfactual in which the bad outcome is avoided. In turn, this counterfactual constitutes a basis for ascribing responsibility. By contrast, if there was no such opportunity, then the intention cannot be acted upon and the above counterfactual does not lead to avoiding the bad outcome. There is no basis for ascribing responsibility. To test this, we designed three different scenarios and across these scenarios, we compared conditions in which we manipulated these epistemic factors: in the <italic>Knowledge</italic> condition the agent knows relevant information (i.e., that their action will bring about a bad outcome); in the <italic>Full Ignorance</italic> condition the agent does not have such knowledge; and in the <italic>Willful Ignorance</italic> condition the agent does not have knowledge about the relevant information, but has the opportunity to take an epistemic action to acquire such knowledge and willfully does not take it. We measured participants’ responsibility judgments by prompting them to rate on a Likert scale to what extent they agreed that the agent was responsible for the bad outcome (Responsibility Question). We predicted that responsibility is ascribed more often when an agent brought about an undesirable outcome as a consequence of their willful ignorance in comparison to the case when the agent fully unknowingly brought about the same outcome. We further expected that responsibility is ascribed more often when the agent knowingly brought about the bad outcome.</p>", "<p id=\"Par21\">To test H1a, we built a cumulative link mixed model and compared it with a null model using a likelihood ratio test. The model showed a better fit of the data compared to the null model, , (See Supplementary Table ##SUPPL##0##S5##a online). Consistent with our prediction, the model indicates that participants’ responses differed significantly across conditions. The results of the pairwise comparisons (with p-values adjusted with Bonferroni correction) indicated that the <italic>Full Ignorance</italic> condition differs significantly from the <italic>Willful Ignorance</italic> condition ( = − 3.05, SE = 0.79, <italic>z</italic> = − 3.84, ) and Knowledge condition ( = − 3.72, SE = 0.62, <italic>z</italic> = − 5.98, ) so that participants were less likely to ascribe responsibility to fully ignorant agents than in the other conditions. Willfully ignorant agents were not significantly more likely to be given lower ratings compared to participants in the <italic>Knowledge</italic> condition ( = − 0.68, SE = 0.47, <italic>z</italic> = − 1.43, ). See Fig. ##FIG##1##2##.</p>", "<p id=\"Par22\">Our findings corroborate our first hypothesis. Participants were sensitive to the epistemic status of the agent. First, beliefs mattered: participants were more willing to ascribe responsibility to an agent who had knowingly brought about a bad outcome than to the agents who did not have this knowledge. Second, epistemic actions mattered: participants were more willing to ascribe responsibility when an agent brought about an undesirable outcome as a consequence of their lack of epistemic action in comparison to cases when the agent had no opportunity to take an epistemic action.</p>", "<p id=\"Par23\">In this study, we did not explicitly state the agent’s epistemic intentions in the scenario descriptions. We stated only the circumstances and the agent’s decision given those circumstances, and it was left to participants to infer, especially in the Willful ignorance condition, whether the agent lacked prosocial intentions or not. In the next study, we disentangle further the role of epistemic intention, action, and state. For that purpose, we created scenarios in which we provided explicit information about the agent’s epistemic intentions.</p>", "<title>Study 1b</title>", "<p id=\"Par24\">Study 1b tests the hypothesis that when assessing the responsibility of an agent, people will be sensitive to evidence about the target agent’s epistemic intentions that are given verbally and in an explicit way (H1b). For that purpose, we designed three different scenarios, and across these scenarios, we compared conditions in which we manipulated the agent’s epistemic intention and epistemic action. In the <italic>Willful Ignorance</italic> condition the agent does not want to learn the relevant information (they have no prosocial epistemic intention) and they do not take the epistemic action. This condition is the same as in Study 1a, but some intentions are explicitly stated. In the <italic>Circumstantial Ignorance</italic> condition, the agent has a prosocial epistemic intention, but the circumstances make the associated epistemic action impossible. In the <italic>Misinformed Ignorance</italic> condition, the agent has a prosocial epistemic intention and takes the associated epistemic action, but gets misinformed. In all of the three conditions, the agent’s behavior produces negative consequences. We measured participants’ responsibility judgments by prompting them to rate on a Likert scale to what extent they agreed that the agent was responsible for the bad outcome (Responsibility Question). In addition, participants were prompted to rate on a Likert scale how much the agent cared to learn the relevant information (Care Question). We predicted that participants would be less likely to ascribe responsibility in the <italic>Misinformed</italic>\n<italic>I</italic><italic>gnorance</italic> condition (i.e. when agents are described as having had a prosocial epistemic intention and took the epistemic action that led to wrong information) than in the <italic>Willful</italic>\n<italic>I</italic><italic>gnorance</italic> condition (i.e., when agents did not show any prosocial epistemic intention nor took any epistemic action). We also predicted that participants would be significantly less likely to ascribe responsibility to those agents in the <italic>Circumstantial</italic>\n<italic>I</italic><italic>gnorance</italic> condition, who showed intention to take the prosocial epistemic action if taking the action was possible, than in the <italic>Willful</italic>\n<italic>I</italic><italic>gnorance</italic> condition where no prosocial epistemic intention was present. We furthermore predicted that the more agents are perceived as they cared to learn the relevant information, the less likely they will be judged responsible.</p>", "<p id=\"Par25\">To test H1b, we built a cumulative link mixed model and compared it with a null model using a likelihood ratio test. The model showed a better fit of the data , (See Supplementary Table ##SUPPL##0##S6##a online). Consistent with our prediction, the model indicates that participants’ responses differed significantly across conditions. The results of the pairwise comparisons indicated that the <italic>Willful Ignorance</italic> condition differed significantly from the <italic>Circumstantial Ignorance</italic> condition ( = 2.15, SE = 0.30, <italic>z</italic> = 7.12, ) and <italic>Misinformed Ignorance</italic> condition ( = 3.50, SE = 0.46, <italic>z</italic> = 7.61, ); participants were more likely to ascribe responsibility to willfully ignorant agents. Finally, the <italic>Circumstantial Ignorance</italic> condition also differed significantly from the <italic>Misinformed Ignorance</italic> condition ( = 1.36, SE = 0.30, <italic>z</italic> = 4.47, ), so participants were more likely to ascribe responsibility to circumstantially ignorant agents. See Fig. ##FIG##2##3##.</p>", "<p id=\"Par26\">Finally, we ran a Spearman rank correlation test. As predicted, the test showed a significant strong negative relationship between Responsibility judgments and Care, , .</p>", "<p id=\"Par27\">Our findings corroborated our hypotheses: participants were sensitive to the evidence about the target agent’s epistemic intentions that was given explicitly. Participants ascribed responsibility more often to agents who did not have prosocial epistemic intentions, than to agents who had a prosocial epistemic intentions, regardless of whether epistemic action was taken or not.</p>", "<p id=\"Par28\">Furthermore, participants’ responsibility judgments were related to their perception of the agent’s care for learning.</p>", "<title>Study 2a</title>", "<p id=\"Par29\">In our previous experimental manipulations, agents who willingly chose to not acquire relevant information had the opportunity to easily do so (<italic>Willful Ignorance</italic> condition). This choice reveals to the observer that the agents were little concerned about the welfare of others-so little that they did not bother to check what consequences their actions might have had. However, choosing not to acquire the relevant information might be motivated by the cost of the epistemic action that must be performed to acquire this information. When the cost of the epistemic action is high enough, the observer has no evidence that the agent had too little concern for others’ welfare: the agent might be concerned by the welfare of others, but the cost of the epistemic action outweighs the potential benefits for others. In that case, would the observer ascribe responsibility to the agent? This is what we test in Study 2a.</p>", "<p id=\"Par30\">In Study 2a we test the hypothesis that, when ascribing responsibility, people weigh the agents’ costs for performing the epistemic action (H2a). We thus presented scenarios to participants that were similar to those in Study 1, except that we manipulated the costs for the agents to perform the epistemic action. We implemented such costs in terms of effort to acquire the relevant information: in the <italic>High Effort</italic> condition, the agent has an opportunity to acquire the information by putting a degree of time and effort into this inquiry; in the <italic>Low Effort</italic> condition, the agent has an opportunity to acquire the information with ease. We again measured participants’ responsibility judgments by prompting them to rate on a Likert scale to what extent they thought the agent was responsible for the bad outcome. We also measured their understanding of the agent’s costs for performing the epistemic action by prompting them to rate on a Likert scale the effort required by the agent to acquire knowledge (Perceived Effort Question). We predicted that responsibility would be ascribed less often to agents who needed to put a high degree of effort into taking an epistemic action. We further predicted that participants’ responsibility judgments would correlate with their perceived effort judgments.</p>", "<p id=\"Par31\">We first conducted a Mann-Whitney test to ensure that the manipulation worked as expected and that the effort required to undertake the epistemic action was perceived differently in the two conditions. The test showed a significant difference between conditions, , , ; participants judged the epistemic action to require effort more frequently in the <italic>High Effort</italic> condition than in the <italic>Low Effort</italic> condition.</p>", "<p id=\"Par32\">To test H2a, we ran a cumulative link mixed model to assess the effect of the experimental condition on participants’ ratings of responsibility ascription. We compared our model with a null model using a likelihood ratio test, and the model showed a better fit of the data compared to the null model, , (See Supplementary Table ##SUPPL##0##S7##a online). Consistent with our prediction, the results of the full model indicated that participants in the High Effort condition were 1.92 times more likely to give lower ratings compared to participants in the Low Effort condition, , . See Fig. ##FIG##3##4##.</p>", "<p id=\"Par33\">Finally, we ran a Spearman rank correlation test. As predicted, the test showed a significant albeit weak negative correlation between Responsibility judgments and Perceived Effort judgments, , .</p>", "<p id=\"Par34\">Our findings confirmed our hypotheses: participants were sensitive to the effort required by the agent to take an epistemic action. Participants ascribed more responsibility to an agent who had an easy opportunity to acquire knowledge (i.e., by putting in a low degree of effort) and did not, than to an agent who had to put some effort into acquiring the same knowledge. Furthermore, participants’ responsibility judgments were related to their perception of such effort: their judgments were found to be correlated to their own perceived effort judgments.</p>", "<title>Study 2b</title>", "<p id=\"Par35\">One way to interpret the results of the previous Study 2a is that people think of the costs and benefits for involved agents; they consider the utility of the epistemic action. One more variable in the expected utility calculation is the likelihood of the negative event happening. Study 2b investigates its relevance in the ascription of responsibility. Study 2b tests the hypothesis that, when ascribing responsibility in cases in which assessed agents bring about a bad outcome, people consider counterfactuals in which the expected value of the epistemic action is sufficiently high (H2b). This expected value is dependent on the perception of the probability that taking the epistemic action would lead to changing one’s mind about the best course of action. We manipulate such probability by changing the subjective prior probability that the bad outcome will follow from a given course of action (foreseeability of the event). For that purpose, we designed three different scenarios, and across these scenarios, we compared two conditions in which we manipulated the agent’s subjective prior probability of a negative outcome occurring: in the <italic>Improbable</italic> condition there is a low prior probability of the relevant event happening; in the <italic>Probable</italic> condition the prior probability of the relevant event happening is high. We measured participants’ responsibility judgments by prompting them to rate on a Likert scale to what extent they agreed that the agent was responsible for the bad outcome (Responsibility Question). We also measured their understanding of the prior probability by prompting them to rate on a Likert scale how likely they would have thought it was that the relevant event had happened (Probability Question).</p>", "<p id=\"Par36\">We predicted that participants would more likely ascribe responsibility to agents who believed it was likely that their choice would lead to a negative outcome (<italic>Probable</italic> condition), than to those agents who believed it was very unlikely that their choice would lead to this outcome (<italic>Improbable</italic> condition). The former more than the latter are expected to check the information. In other words, agents who do not take the epistemic action are more likely to be judged responsible for the bad outcome when the epistemic action is likely to change the agent’s choices. We furthermore predicted that the lower the perceived likelihood of the relevant event happening, the less likely they will be judged responsible.</p>", "<p id=\"Par37\">To test H2b, we ran a cumulative link mixed model to assess the effect of the experimental condition on participants’ ratings. We compared our model with a null model using a likelihood ratio test which indicated that the cumulative link mixed model including condition did not provide a better fit for the data than that model without it , (See Supplementary Table ##SUPPL##0##S8##a online). Our prediction that the two conditions would differ was not confirmed. See Fig. ##FIG##4##5##.</p>", "<p id=\"Par38\">Finally, we ran a Spearman rank correlation test. As predicted, the test showed a significant weak positive relationship between Responsibility judgments and Probability, , .</p>", "<p id=\"Par39\">Our findings did not confirm our hypotheses: although we spotted the trend that participants ascribed responsibility more often to agents who believed it was highly likely that their actions would produce negative outcomes, this result was not statistically significant.</p>", "<p id=\"Par40\">On the other hand, Spearman’s correlation showed that participants’ responsibility judgments were related to their perception of the likelihood of the relevant event.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par41\">Our studies investigate how and when people ascribe responsibility to agents who did not predict the consequences of their actions. We hypothesized that this process involves counterfactual thinking, which includes thinking of alternative epistemic intentions. The results from three out of four of our studies corroborate this general hypothesis. They show that people are sensitive to information about agents’ epistemic states, actions, and intentions when ascribing responsibility.</p>", "<p id=\"Par42\">Our findings show that agents who knowingly engaged in actions that caused a bad outcome are more often judged responsible than agents who did not know about these consequences; and that agents who had the opportunity to take an epistemic action to acquire relevant information were more often judged responsible compared to agents who did not have such opportunity (Study 1a). Furthermore, having prosocial epistemic intentions mitigates responsibility ascription, even when the epistemic action is not actually taken and when negative consequences still occur. By contrast, agents who do not want to learn about the risks of causing negative outcomes reveal their lack of concern for others. This allows assessors of responsibility to conceive a counterfactual where concern for others generates intentions that eventually cause a better outcome. Based on such counterfactual, assessors ascribe responsibility to agents who did not want to learn (Study 1b). Finally, we show that the perceived effort needed for the epistemic action can also mitigate responsibility ascription to ignorant agents. When the possibility of acquiring information was instead too costly, participants were less likely to hold agents responsible for bringing about a bad outcome (Study 2a). We intended to show that the expected value of an epistemic action would also be taken into account (Study 2b), but the data we gathered only showed a trend rather than strong evidence.</p>", "<p id=\"Par43\">Overall, our studies provide evidence that the causal role of epistemic intentions is decisive for responsibility ascription, even though their causal role in bringing about the bad outcome is more distal than the choice that directly causes a bad outcome. Importantly, the beliefs that the agent held are themselves considered as resulting from epistemic actions (or lack thereof). Epistemic actions are, in turn, motivated by epistemic intentions which reveal how much concern for others the agent had. People do have expectations that agents act with some minimal concern for others. If a counterfactual shows that a bad outcome could have been avoided, had the agent been more concerned and thus motivated to check the risks of creating problems for others, then the agent is deemed responsible. Langenhoff et al.’s (2021) model of responsibility ascription holds that dispositional inference and causal attributions are assessed independently and then combined to determine whether the agent assessed is responsible or not^{##REF##34303092##32##}. By contrast, our model states that the cognitive processes of responsibility ascription involve assessing which intentions could have caused a better outcome for others. This reveals whether an agent sufficiently cared for others, or not. Our cognitive model is compatible with Alicke’s (2020) “culpable control” model in which negative character inferences influence blame by increasing the perception of the agent’s control over the outcome^{##REF##10900996##33##}. In our model, however, even agents who did not assert their control over the outcome can be excused if they can be perceived as showing sufficient care for others.</p>", "<p id=\"Par44\">The results we presented are in line with recent findings that show that willfully ignorant agents are judged more harshly than those who did not suspect their choice could have bad consequences^{##UREF##20##34##}. They are also compatible with findings that show that people are more likely to ascribe responsibility to agents who intentionally remained ignorant than to agents who did not suspect there was a risk to assess^{##UREF##2##3##}. The authors explain the harsher moral judgments towards willfully ignorant agents by suggesting that people perceive their <italic>mens rea</italic> (guilty mind) and judge them to be more antisocial^{##UREF##20##34##}. In our studies, we show that agents who suspect that a bad outcome might occur and yet do not intend to further assess the risks are judged as responsible as agents who know about the negative consequences their choice will have. This finding contrasts with some previous results where knowledgeable agents were found more culpable than willfully ignorant ones^{##UREF##20##34##}. However, in our case, the dependent variable was responsibility, while Kirfel et al.’s (2023) study asked about culpability, which might be the source of the difference.</p>", "<p id=\"Par45\">Our results show the relevance of the effort needed to learn the relevant information in responsibility ascription. This result is compatible with a previous study showing that the number of epistemic actions needed to get to the relevant information is a good predictor of causality ascription^{##UREF##21##35##}. On the other hand, another study argues that the difficulty of performing the epistemic action does not excuse an agent who did not act to learn relevant information^{##UREF##20##34##}. In our Study 2a, we manipulated one factor only: the effort needed. Our results suggest that it clearly is a factor for ascribing responsibility. This is best interpreted as evidence that people weigh the costs and benefits for the agent when they consider why they failed to take an epistemic action. In our experimental manipulations, the expected utility of acquiring relevant knowledge in these conditions is informative of the agent’s concern for others. If the cost of an epistemic action is low compared to others’ expected benefit, people infer that the agent who does not perform the epistemic action has little concern for others or low prosocial preferences^{##REF##27388875##36##}; by contrast, if the cost of the epistemic action is high compared to others’ expected benefit, then people cannot conclude that the agent does not have at least some minimal concern for others. The agent might have prosocial preferences, which have been outweighed by the cost of taking the epistemic action.</p>", "<p id=\"Par46\">We hypothesized that the perceived likelihood that the bad outcome might occur would influence responsibility ascription, but we did not gather evidence for this hypothesis. We found a weak correlation between the measures of perceived likelihood and responsibility ascription, but we did not document a significant effect of our manipulation. Our prediction was motivated by the results of previous studies showing that foreseeability influences moral judgments^{##REF##18706537##37##,##UREF##22##38##}. Some more recent studies, however, do not show that the agent’s suspicion that the negative event could happen influences moral judgment^{##UREF##2##3##,##UREF##20##34##}. It seems still premature to draw conclusions about people’s sensitivity to foreseeability in responsibility ascription. There are several possible explanations for the lack of significant results in our Study 2b. First, it is possible that our hypothesis does not stand and that people expect agents to take epistemic actions even when the action is not expected to be very informative. Second, the effect of likelihood may be more important when the consequences are less severe. When stakes are not negligible, such as in our stories, agents are expected to take actions that do not ask for significant sacrifice on their part. Third, our manipulation might not have been as strong as expected. While the perceived likelihood differed between the two conditions in our manipulation check (See Supplementary Table ##SUPPL##0##S##b online), absolute likelihood in the <italic>Improbable</italic> condition might have been overestimated. As a consequence, both conditions might have been perceived as expressing a high likelihood that the epistemic action would be informative.</p>", "<p id=\"Par47\">Moral and legal philosophers have offered normative analyses on the responsibility and blameworthiness of willfully ignorant agents^{##UREF##23##39##–##UREF##25##41##}. Our studies enable us to compare lay people’s intuitions with the normative explanation of when responsibility should be ascribed. According to philosophers’ normative accounts, agents are expected to get informed before acting. This duty is called procedural epistemic obligation^{##UREF##26##42##}, or moral duty to get informed before acting^{##UREF##27##43##}. On the one hand, agents are not expected to be informed about every possible situation. Wieland (2017) argues that not fulfilling the moral duty to get informed does not necessarily make a person morally blameworthy^{##UREF##25##41##}. On the other hand, breaching the moral duty to get informed without justification qualifies as willful ignorance^{##UREF##28##44##} and is condemnable. The Quality of Will framework^{##UREF##15##27##} argues that if an agent showed moral concern in his actions, then they should be considered blameless; if they did not, they should be judged as blameworthy. Our studies show that laypeople’s intuitions are compatible with these philosophical accounts. When agents show moral concern, reflected in their intention to learn whether a choice risks hurting or causing problems to others, they are less often deemed responsible if a bad outcome happens nonetheless. Philosophers’ normative accounts also discuss an adequate threshold for the cost of epistemic action, above which the epistemic action is not expected anymore^{##UREF##25##41##}. We show that laypeople think along these lines: high effort needed for the epistemic action mitigates responsibility ascription. People are sensitive to the sacrifice the assessed agent needs to make to get informed. Finally, the normative account considers foreseeability as a relevant factor in culpability judgments. According to the ‘comparative culpability principle’ (CCP)^{##UREF##29##45##}, if all the other aspects are equal, the agent who was more confident that their action would produce some consequence should be more culpable. Participants in our study did not show sensitivity to this information, and so the topic needs to be investigated further.</p>" ]

[]

[ "<p id=\"Par1\">We investigate how people ascribe responsibility to an agent who caused a bad outcome but did not know he would. The psychological processes for making such judgments, we argue, involve finding a counterfactual in which some minimally benevolent intention initiates a course of events that leads to a better outcome than the actual one. We hypothesize that such counterfactuals can include, when relevant, epistemic intentions. With four vignette studies, we show that people consider epistemic intentions when ascribing responsibility for a bad outcome. We further investigate which epistemic intentions people are likely to consider when building counterfactuals for responsibility ascription. We find that, when an agent did not predict a bad outcome, people ascribe responsibility depending on the reasons behind the agents’ lack of knowledge. People judge agents responsible for the bad outcome they caused when they could have easily predicted the consequences of their actions but did not care to acquire the relevant information. However, when this information was hard to acquire, people are less likely to judge them responsible.</p>", "<title>Subject terms</title>" ]

[ "<title>Data analysis</title>", "<p id=\"Par19\">To test our hypotheses, we ran a series of cumulative link mixed models to assess the effect of the experimental conditions on participants’ ratings. The main models always included condition as fixed effect, and condition nested within vignettes as random effect. Study 1a only also featured participant ID as an additional random factor, to account for repeated measures. The null models included the random effects only. Model comparisons were done using likelihood ratio tests^{##UREF##16##28##}. Statistics were done using R version 4.2.3^{##UREF##17##29##} and the package ‘ordinal’^{##UREF##18##30##}. Correlation tests were done in Jamovi version 2.3^{##UREF##19##31##}. Following reviewers’ suggestions, some of the final analyses presented in the manuscript deviate from the preregistered version, with largely consistent results (See Supplementary Note online <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/y9gxj/\">https://osf.io/y9gxj/</ext-link>).</p>", "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-50961-0.</p>", "<title>Acknowledgements</title>", "<p>This publication is the result of research conducted for Central European University, Private University. It was made possible by the CEU Open Access Fund.</p>", "<title>Author contributions</title>", "<p>All authors designed the experiments and co-wrote the manuscript. K.M.K. conducted the experiments, and K.M.K. and F.B. analyzed the results.</p>", "<title>Data availability</title>", "<p>The data of Study 1a, Study 1b, Study 2a, and Study 2b is uploaded on <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/y9gxj/\">https://osf.io/y9gxj/</ext-link>.</p>", "<title>Competing interests</title>", "<p id=\"Par97\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Ascription of responsibility involves thinking of counterfactual in which alternative intentions - based on sufficient concern for others - lead to alternative outcomes. Panel A illustrates counterfactual thinking when the alternative intention is directly related to the proximal act of causing the negative outcome. Panel B illustrates counterfactual thinking when the alternative intention is of an epistemic nature and has a more distal effect on the outcome at stake.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Distributions of responsibility judgments across different epistemic status conditions: In the <italic>Full Ignorance</italic> condition, participants read scenarios in which an agent could not know what bad outcome their actions would have on others. In the <italic>Willful Ignorance</italic> condition, the agent had the opportunity to acquire the relevant information but chose not to. In the <italic>Knowledge condition</italic>, the agent knew about the possible consequences of their action. Participants answered the question: “To what extent do you agree with the statement: ‘[Agent] is responsible for [outcome]’?”. Answers were given on a five-point scale from ‘Strongly disagree’, to ‘Strongly agree’. Responsibility was ascribed significantly less often in the <italic>Full Ignorance</italic> condition than in the <italic>Willful Ignorance</italic> and the <italic>Knowledge</italic> condition.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Distributions of responsibility judgments across three different conditions: In the <italic>Willful Ignorance</italic> condition, participants read scenarios in which an agent did not want to know what bad outcome their actions would have on others, and they did not take the epistemic action. In the <italic>Circumstantial Ignorance</italic> condition, the agent wanted to acquire the relevant information, but it was impossible to take the epistemic action. In the <italic>Misinformed Ignorance</italic> condition, the agent wanted to know about the possible consequences of their action and took the epistemic action, but it led to the wrong information. Participants answered the question: “To what extent do you agree with the statement: ‘[Agent] is responsible for [outcome]’?”. Answers were given on a five-point scale from ‘Strongly disagree’, to ‘Strongly agree’. Responsibility was ascribed significantly more often in the <italic>Willful Ignorance</italic> condition than in the <italic>Circumstantial Ignorance</italic> condition, or <italic>Misinformed Ignorance</italic> condition.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Distributions of responsibility judgments when epistemic actions require low effort or high effort. In the <italic>Low Effort</italic> condition, participants read scenarios in which an agent could easily acquire information about the consequences of their action on others. In the <italic>High Effort</italic> condition, this same epistemic action requested significantly more effort. Participants answered the question: “To what extent do you agree with the statement: ‘[Agent] is responsible for [outcome]’?”. Answers were given on a five-point scale from ‘Strongly disagree’, to ‘Strongly agree’. Responsibility was ascribed significantly more often in the <italic>Low Effort</italic> condition than in the <italic>High Effort</italic> condition.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Distributions of responsibility judgments when the subjective prior probability of the relevant event happening is low and high. In the <italic>Improbable</italic> condition, participants read scenarios in which an agent’s subjective probability of the negative event happening was low. In the <italic>Probable</italic> condition, this subjective probability was high. Participants answered the question: “To what extent do you agree with the statement: ‘[Agent] is responsible for [outcome]’?”. Answers were given on a five-point scale from ‘Strongly disagree’, to ‘Strongly agree’. Responsibility ascribed was not statistically different across the two conditions.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Example of the three conditions of Study 1a in one of the scenarios.</p></caption><table frame=\"hsides\" rules=\"groups\"><tbody><tr><td align=\"left\" colspan=\"3\">Background</td></tr><tr><td align=\"left\" colspan=\"3\"> Rose was on her way to her dentist appointment at 11 am. She went by car and parked in the only available spot.</td></tr><tr><td align=\"left\">Full Ignorance</td><td align=\"left\">Willful Ignorance</td><td align=\"left\">Knowledge</td></tr><tr><td align=\"left\">The sign saying that spot is reserved was moved by someone. She didn’t know about the reservation and she parked there.</td><td align=\"left\">She saw there was a sign in front of the parking spot, saying whether and at what time during the day the spot is reserved. She didn’t stop to check what it said exactly, and she parked there.</td><td align=\"left\">She saw the sign saying the spot was reserved at that time. She parked there.</td></tr><tr><td align=\"left\" colspan=\"3\">Outcome</td></tr><tr><td align=\"left\" colspan=\"3\"> The sign indicates that the spot is reserved between 10am and 2pm for persons with disabilities. Consequently, a man couldn’t park anywhere and missed his weekly therapy.</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Example of all the three conditions of Study 1b in one of the scenarios.</p></caption><table frame=\"hsides\" rules=\"groups\"><tbody><tr><td align=\"left\" colspan=\"3\">Background</td></tr><tr><td align=\"left\" colspan=\"3\"> Rose was on her way to her dentist appointment at 11 am. She went by car and parked in the only available spot.</td></tr><tr><td align=\"left\">Willful Ignorance</td><td align=\"left\">Circumstantial Ignorance</td><td align=\"left\">Misinformed Ignorance</td></tr><tr><td align=\"left\">She saw there was a sign in front of the parking spot, saying whether and at what time of the day the spot is reserved. To check when exactly the spot is reserved, she would have needed to read the sign. She didn’t want to know whether the spot was reserved, and she didn’t read the sign; she parked there and went to her dentist appointment. The sign indicates that the spot is reserved between 10am and 2pm for persons with disabilities.</td><td align=\"left\">She saw there was a sign in front of the parking spot, saying whether and at what time of the day the spot is reserved. To check when exactly the spot is reserved, she would have needed to read the sign. She wanted to know whether the spot was reserved, but somebody took the sign from the pathway, so it was impossible for her to get the information. She parked there and went to her dentist appointment. The sign indicates that the spot is reserved between 10am and 2pm for persons with disabilities.</td><td align=\"left\">She saw there was a sign in front of the parking spot, saying whether and at what time of the day the spot is reserved. To check when exactly the spot is reserved, she needed to read the sign. She wanted to know whether the spot was reserved, so she read the sign and saw that it was not reserved at that time. She parked there and went to her dentist appointment. It turned out that the parking maintenance employee made a mistake and put the wrong information on the sign. The spot was actually reserved between 10am and 2pm for persons with disabilities.</td></tr><tr><td align=\"left\" colspan=\"3\">Outcome</td></tr><tr><td align=\"left\" colspan=\"3\"> Consequently, a man couldn’t park anywhere and missed his weekly therapy.</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Example of the two conditions of Study 2a in one of the scenarios.</p></caption><table frame=\"hsides\" rules=\"groups\"><tbody><tr><td align=\"left\" colspan=\"2\">Background</td></tr><tr><td align=\"left\" colspan=\"2\">Rose was on her way to her dentist appointment at 11 am. She went by car and parked in the only available spot.</td></tr><tr><td align=\"left\">Low Effort</td><td align=\"left\">High Effort</td></tr><tr><td align=\"left\">She saw there was a sign in front of the parking spot, saying whether and at what time of the day the spot is reserved. To check when exactly the spot is reserved, she would have needed to read the sign. She didn’t do so; she parked there and went to her dentist appointment.</td><td align=\"left\">She saw there was a sign in front of the parking spot, saying that you should check with the parking attendant whether the spot is reserved. The attendant was on a lunch break, so to check when exactly the spot is reserved she would have needed to wait for him to come back at some point. She didn’t do so; she parked there and went to her dentist appointment.</td></tr><tr><td align=\"left\" colspan=\"2\">Outcome</td></tr><tr><td align=\"left\" colspan=\"2\">The sign indicates that the spot is reserved between 10am and 2pm for persons with disabilities. Consequently, a man couldn’t park anywhere and missed his weekly therapy.</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Example of the two conditions of Study 2b in one of the scenarios.</p></caption><table frame=\"hsides\" rules=\"groups\"><tbody><tr><td align=\"left\" colspan=\"2\">Background</td></tr><tr><td align=\"left\" colspan=\"2\">Rose was on her way to her dentist’s appointment at noon. She went by car and parked in the only available spot.</td></tr><tr><td align=\"left\">Improbable</td><td align=\"left\">Probable</td></tr><tr><td align=\"left\">She saw there was a sign in front of the parking spot, saying that you should check with the parking attendant whether the spot is reserved. This sign had been there for a year, and, in her experience, that spot was actually never reserved. She didn’t check with the parking attendant whether the spot was reserved; she parked there and went to her dentist appointment.</td><td align=\"left\">She saw there was a sign in front of the parking spot, saying that you should check with the parking attendant whether the spot is reserved. This sign had been there for a year, and, in her experience, that spot was reserved in 90% of the cases. She didn’t check with the parking attendant whether the spot was reserved; she parked there and went to her dentist appointment.</td></tr><tr><td align=\"left\" colspan=\"2\">Outcome</td></tr><tr><td align=\"left\" colspan=\"2\">As it happens, the spot was reserved at that time for people with disabilities. Consequently, a man couldn’t park anywhere and missed his weekly therapy.</td></tr></tbody></table></table-wrap>" ]

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id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi ^{2}(2) = 9.64$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:mrow><mml:msup><mml:mi>χ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>9.64</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p = .008$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>008</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:mi>β</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p &lt; .001$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mo>.</mml:mo><mml:mn>001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:mi>β</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p &lt; .001$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mo>.</mml:mo><mml:mn>001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:mi>β</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p &lt; .001$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mo>.</mml:mo><mml:mn>001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r_s (423) = -0.681$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>423</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>0.681</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq18\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p &lt; 0.001$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq19\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U = 933$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:mrow><mml:mi>U</mml:mi><mml:mo>=</mml:mo><mml:mn>933</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq20\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p &lt; 0.001$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq21\"><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r_{rb}= 0.913$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">rb</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.913</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq22\"><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi ^{2}(1) = 5.19$$\\end{document}</tex-math><mml:math id=\"M44\"><mml:mrow><mml:msup><mml:mi>χ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>5.19</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq23\"><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p = .023$$\\end{document}</tex-math><mml:math id=\"M46\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mo>.</mml:mo><mml:mn>023</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq24\"><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta = -0.65, SE = 0.23$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>0.65</mml:mn><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mn>0.23</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq25\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\textit{z} = -2.88$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:mrow><mml:mi mathvariant=\"italic\">z</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>2.88</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq26\"><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r_s (291) = -0.305$$\\end{document}</tex-math><mml:math id=\"M52\"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>291</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>0.305</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq27\"><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p &lt; 0.001$$\\end{document}</tex-math><mml:math id=\"M54\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq28\"><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi ^{2}(1) = 2.32$$\\end{document}</tex-math><mml:math id=\"M56\"><mml:mrow><mml:msup><mml:mi>χ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>2.32</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq29\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p = 0.127$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0.127</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq30\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r_s (281) = 0.300$$\\end{document}</tex-math><mml:math id=\"M60\"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>281</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.300</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq31\"><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p &lt; 0.001$$\\end{document}</tex-math><mml:math id=\"M62\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq32\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$86.8 \\%$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:mrow><mml:mn>86.8</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq33\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.05$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:mrow><mml:mn>0.05</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq34\"><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$99 \\%$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:mrow><mml:mn>99</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq35\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\approx 15\\%$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:mrow><mml:mo>≈</mml:mo><mml:mn>15</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq36\"><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$N = 150$$\\end{document}</tex-math><mml:math id=\"M72\"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>150</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq37\"><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$N = 450$$\\end{document}</tex-math><mml:math id=\"M74\"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>450</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq38\"><alternatives><tex-math id=\"M75\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$62.4\\%$$\\end{document}</tex-math><mml:math id=\"M76\"><mml:mrow><mml:mn>62.4</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq39\"><alternatives><tex-math id=\"M77\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$.05$$\\end{document}</tex-math><mml:math id=\"M78\"><mml:mrow><mml:mo>.</mml:mo><mml:mn>05</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M79\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d = 0.35$$\\end{document}</tex-math><mml:math id=\"M80\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>0.35</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M81\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$97.8 \\%$$\\end{document}</tex-math><mml:math id=\"M82\"><mml:mrow><mml:mn>97.8</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq42\"><alternatives><tex-math id=\"M83\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\approx 15\\%$$\\end{document}</tex-math><mml:math id=\"M84\"><mml:mrow><mml:mo>≈</mml:mo><mml:mn>15</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq43\"><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$N = 300$$\\end{document}</tex-math><mml:math id=\"M86\"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>300</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>" ]

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[ "<disp-quote><p id=\"Par59\">To what extent do you agree with the statement: ‘Agent A is responsible for B experiencing the consequence C’?</p></disp-quote>", "<disp-quote><p id=\"Par71\">How much did Agent A care about learning information X?</p></disp-quote>", "<disp-quote><p id=\"Par83\">How difficult would have been for agent X to check the information W?</p></disp-quote>", "<disp-quote><p id=\"Par95\">How likely would you have thought it was that relevant event X had happened?</p></disp-quote>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41598_2023_50961_MOESM1_ESM.pdf\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">French Priest introduced grapes in Cumbum Valley, Tamilnadu, India, in 1832, and these grapes were rich in vitamins, tartaric acid, minerals, antioxidants and reduced the risk of some chronic illnesses. Panneer Thratchai (grapes) protect against cancer, heart, nervous diseases and treat haemorrhoids. They prevent Alzheimer’s disease, diabetes mellitus, and protect against oxidative rancidity &amp; viral/fungal infections, also improving night vision^{##UREF##0##1##}. The “Cumbum Panneer Thratchai” grapes (<italic>Vitis vinifera</italic> L., family: Vitaceae; Muscat Hamburg species) grown can be mainly used for the formulation of wine, jam, spirit, canned grape juice, and raisins. During the formulation of grape juice, wine and jam produce large quantities of grape by-products containing seeds, skin, and stalks. Grape’s by-products estimate that the pomace signifies around 20–30% of processed grapes’ weight and 38–52% of seeds^{##UREF##1##2##}. Grape pomace is one of the most common solid by-products generated during the wine-making. Grape pomace is used to recover a wide range of products, including ethanol, tartrates, citric acid, grape seed oil, hydrocolloids, bioactive compounds, and dietary fibre. Grape pomace is one of the significant research areas in the field of fibre extraction, particularly pectin^{##REF##33921097##3##}. Importantly, grape seeds are a cost-effective source of antioxidant and potential therapeutic compounds in the form of polyphenols^{##UREF##2##4##}. Grape seeds are described to consist of 11% protein, 35% fibre, 3% minerals, 7% water, 7–20% lipids, and 7% polyphenolic compounds (especially tocopherols and β-carotene)^{##UREF##3##5##}. Polyphenols and other phenolic compounds are gaining attention from scientists because of their potential benefits for human health^{##UREF##4##6##}. Polyphenolic compounds have the property of neutralizing over-generated free radicals (reactive oxygen species (ROS), reactive nitrogen species (RNS), and DNA reactive aldehyde (DRA))^{##UREF##5##7##}. Free radicals are typically generated as a by-product of oxygen metabolism, and mitochondria release it. Free radicals play a dual role; at a low level, they are vital for many cellular signaling mechanisms (i.e., regulate cellular events, like cell cycle, proliferation, migration, and programmed cell death)^{##REF##34728718##8##}. In contrast, at a high level, they lead to several pathological complications including damage to protein, nucleic acids, cell, and lipid membrane disturbances, and reduced cellular viability^{##REF##23268465##9##}.</p>", "<p id=\"Par3\">Remarkably, an elevated level of ROS causes oxidative stress and the loss of antioxidant and detoxifying enzymes in cells and tissues, as well as oxidative stress itself^{##REF##23268465##9##}. An imbalance between a biological system’s capacity to detoxify these reactive chemicals and generating and accumulating reactive oxygen species (ROS) in cells and tissues causes oxidative stress^{##UREF##6##10##}. Numerous studies have demonstrated that oxidative stress and depletion of antioxidant enzymes might have a role in developing and progressing several diseases (such as cancer, diabetes mellitus, cardiovascular diseases (coronary heart disease, atherosclerosis), metabolic disorders, arthritis, and neurodegenerative disorders)^{##UREF##7##11##–##UREF##10##14##}. Recently, bioactive ingredients from grape seeds gained more attention due to their therapeutic importance^{##REF##36140883##15##}. In addition, grape seed powder is a nutraceutical agent usually consumed as a well-being/dietary supplement and sold over-the-counter products in the United States of America^{##UREF##11##16##}. Grape seeds possess numerous polyphenolic compounds, including flavan-3-ols, which act to prevent various diseases^{##UREF##12##17##}. The flavan-3-ols (catechin, epicatechin, epigallocatechin, proanthocyanidin, trans-resveratrol, procyanidin B1, and their polymers) are natural antioxidants (eliminate ROS, RNS, DRA, stimulate detoxifying and antioxidant enzymes) that prevent cell damage and provide other benefits^{##REF##18081206##18##,##REF##33467650##19##}. Unfortunately, these bioactive ingredients are present inside the cell in meagre quantities and have a thermolabile structure/character. However, the most sophisticated extraction technique is needed to extract these bioactive compounds from plant sources completely. Compared to modern extraction techniques, traditional methods (such as soxhlation and blending) consume more solvents, take longer time to extraction, and produce less yield of active compounds^{##UREF##13##20##}.</p>", "<p id=\"Par4\">A few advanced extraction techniques, such as microwave-assisted extraction (MAE), pressurized liquid extraction (PLE), ultrasound-aided extraction (UAE), and carbon-dioxide super-critical extraction (CSCE) techniques are followed in the pharmaceutical industries and research laboratories. These advanced extraction techniques are generally called greener and environment-friendly technologies because these processes will consume less energy, permit the use of solvent alternates, renewable natural products, and ensure a safe and high-quality extract/product^{##REF##34118529##21##,##UREF##14##22##}. Carbon-dioxide super-critical extraction is one of the best techniques because it consumes less solvents or eliminates the use of solvents, computer-controllable operations with shorter extraction time, especially thermolabile compounds, are extracted from plant sources without damage^{##REF##33445028##23##}. Unfortunately, industries and research laboratories are seeking alternative extraction methods due to the unaffordable cost of carbon-dioxide super-critical extractor^{##UREF##15##24##}. The microwaves from the microwave-assisted extraction (MAE) technique heat the solvent system to enhance the solubility of bioactive compounds of plant cells^{##UREF##16##25##}. While generating heat, it is possible to disintegrate the thermosensitive compounds. This is the major issue for using MAE for thermosensitive compounds^{##UREF##17##26##}. Conversely, ultrasound-aided extraction (UAE) is an exciting and cost-effective alternative for completely extracting plant-derived bioactive ingredients^{##UREF##10##14##}. The UAE method is one of the most preferred extractions, which uses fewer solvents, can be automated at lower temperatures, requires less energy and has a higher yield. It also takes less time to extract the bioactive ingredients. Ultrasonic vibrations accelerate the release of extractable components into the solvent by enhancing mass transport. They also cause rupture of the plant cells by creating physical pressure during ultrasound cavitation^{##UREF##5##7##}.</p>", "<p id=\"Par5\">The present study aimed to maximize the extraction of bioactive ingredients from grape seeds using an ultrasound-aided extraction technique. Many extraction parameters, such as particle size, extraction solvent, solvent concentration, solid-to-liquid ratio, temperature, ultrasonic exposure time, ultrasound intensity, pulse cycle/mode, pH, etc., have potentially influenced the yield of bioactive ingredients and their free radicals scavenging properties^{##UREF##18##27##}. Combining these criteria resulted in the highest yield of bioactive compounds from plant sources, even though they fundamentally appeared unrelated^{##REF##26281720##28##}. Combining these parameters must be optimized to achieve the maximum yield of bioactive ingredients^{##REF##30990060##29##}. Under this condition, a statistical method of optimization is helpful. One effective method frequently considered for this purpose is the response surface methodology (RSM)^{##UREF##19##30##}. RSM is a statistical technique that determines and simultaneously solves multivariant equations using quantitative data from relevant studies^{##UREF##20##31##}. In RSM, a second-order polynomial equation is applied for modeling and optimization^{##UREF##21##32##}. RSM can be utilized to compare theoretical and actual variables involved in the process with the help of second-order polynomial equations generated in the experiment^{##UREF##22##33##}. Several methods, namely, central composite design (CCD), Box–Behnken design (BBD) and three-level full factorial design (FBD) have been widely applied for RSM to obtain an optimized extraction of bioactive polyphenolic compounds from natural sources^{##UREF##23##34##}. One of the designs used for the application of RSM is CCD, which provides viable models for processes^{##UREF##24##35##}. In contrast to the Box–Behnken design, which is made up of rotated lower-dimensional designs and estimates all linear effects, quadratic effects, and two-way interactions, the CCD is made up of a cube part that is a full factorial that determines main and interaction effects and a star design (α) that quantifies main and quadratic effects^{##UREF##25##36##}. It does not allow for reductions in design, being much less flexible than the CCD. The design space is devoid of any corner points. The factorial portion of the design, which generates rotability, defines the design space box, and the axial points are outside of it. This makes it possible to estimate the expected response with equal variance in any direction with respect to the design space’s centre. Therefore, many researchers have used the central composite design (CCD) to extract bioactive compounds and antioxidants^{##UREF##26##37##}. The (adaptive neuro-fuzzy inference system) and Machine learning algorithm approaches are also used to predict the optimal conditions, producing the best results for nonlinear systems^{##UREF##27##38##}. ANFIS simulates human thought processes using highly developed fuzzy and neural network computer systems^{##UREF##28##39##}. An intelligent neuro-fuzzy method called ANFIS is used to study how variables interact and have nonlinear effects^{##UREF##29##40##}. ANFIS, a hybrid intelligent system^{##UREF##30##41##}. Consequently, multivariable related ambiguous relationships can be quantified using ANFIS through the defuzzification process of the fuzzy inference system (FIS), and error is adjusted for dependable prediction using a backpropagation algorithm with a hidden layer of an artificial neural network (ANN)^{##REF##25153627##42##}. Further, a machine learning algorithm adapts the most effective extraction parameters. The aim of machine learning algorithm-based optimization is to reduce the degree of error in a machine learning model, improving its accuracy in making data predictions. Machine learning is generally used to learn the underlying relationship between input and output responses, which is learned from a set of training data^{##UREF##31##43##}. When confronted with new data in a live environment, the model can use this learned approximated function to predict an outcome from this new data. Optimization algorithms can make this process more efficient than any manual process. These algorithms optimize a machine learning model iteratively using mathematical models^{##UREF##32##44##}. The Random Forest Regressor is a simple and widely used algorithm in machine learning^{##UREF##33##45##}. For the best combinations, every hyperparameter configuration is randomly searched and combined. Ultimately, the bioactive ingredients have been recognized using GC–MS (gas chromatography-mass spectrometry) and LC–MS (liquid chromatography-mass spectrometry), indicating the potential of the chosen grape seeds to be used in the healthcare sectors.</p>" ]

[ "<title>Methods</title>", "<title>Preliminary experiments for selection of suitable solvent system</title>", "<p id=\"Par9\">The preliminary experiments were performed to identify the best solvent system for maximum yield of bioactive ingredients based on the highest total phenolic content (TPC), total flavonoid content (TFC), and %DPPH*sc from grape seeds extract. Eight solvents, namely ethanol, methanol, chloroform, petroleum ether, ethyl acetate, diethyl ether, acetone, and <italic>n</italic>-hexane were selected for this investigation. Each solvent system of the extraction process involved using 2 g of grape seed powder (particle size 0.5 mm), 10 mL of fixed solvent concentration (70% V/V in distilled water), ultrasound intensity: 60 W cm⁻², ultrasound exposure time: 10 min, and temperature: 40 °C. Using a UV–Visible spectrophotometer, Shimadzu UV-1800 series, and UV Probe 2.62 software, Japan, to measure the concentration of bioactive ingredients from grape seed extract. A rotary vacuum dryer (Buchi rotary evaporator, Mumbai, India) was used to concentrate the extracts. The concentrated extracts were then lyophilized (freeze dryer) to convert into powder form and stored in a desiccator until the experiment.</p>", "<title>Selection of relevant extraction variables</title>", "<p id=\"Par10\">Five independent extraction variables were selected, i.e., particle size (<italic>X</italic>₁; in mm), solvent concentration (<italic>X</italic>₂; in % V/V with distilled water), ultrasound exposure time (<italic>X</italic>₃; in min), temperature (<italic>X</italic>₄; in °C), and ultrasound intensity (<italic>X</italic>₅; in W cm⁻²), basis on the dependent variables, such as total phenolic content (TPC; y₁), total flavonoid content (TFC; y₂), and their antioxidant potentials (DPPH free radical scavenging (y₃), ABTS free radical scavenging (y₄), and FRAP potential (y₅)). According to the preliminary experimental findings, methanol is an ideal solvent for extracting grape seeds’ highest concentration of beneficial compounds, as shown in Table ##TAB##0##1##. The selected five independent variables were investigated at five-coded levels, such as very low (− 2), low (− 1), medium (0), high (+ 1), and very high (+ 2), and each variable range presented in Supplementary Table ##SUPPL##0##1##. The selected independent variable ranges were particle size (<italic>X</italic>₁: 0.5–1 mm), methanol concentration (<italic>X</italic>₂: 60–70% in distilled water), ultrasound exposure time (<italic>X</italic>₃: 18–28 min), temperature (<italic>X</italic>₄: 35–45 °C), and ultrasound intensity (<italic>X</italic>₅: 65–75 W cm⁻²) investigated.</p>", "<title>Procedure for ultrasound-aided extraction (UAE) of bioactive ingredients</title>", "<p id=\"Par11\">The extraction of bioactive ingredients from grape seeds powder was performed using an adjustable ultrasonic bath extractor with a sample of 2 g grape seeds powder in a closed container, which contained 10 mL solvent (miscible methanol in water), and specified particle size, ultrasound exposure time, temperature and ultrasound intensity. According to the Response Surface Methodology’s (RSM) central composite design (CCD), experiments were conducted in triplicate. After UAE, the extracts were filtered using Whatman No. 1 filter paper and filtrate was centrifuged at 3500 rpm for 30 min at 4 °C. The supernatant liquid (extract) was concentrated at 40 °C using a rotary vacuum dryer. The concentrated methanolic extract was then lyophilized (freeze dryer) to convert it into powder form to determine the TPC, TFC, and antioxidant potentials (%DPPH*sc, %ABTS*sc, and FRAP).</p>", "<title>Determination of total phenolic content (TPC)</title>", "<p id=\"Par12\">The spectrophotometric analysis determined the quantity of TPC (y₁) present in the extract according to the previously described method^{##REF##28763961##46##}. Briefly, 0.2 mL of grape seeds extract was mixed individually with 5 mL of 10% resolubilized Folin–Ciocalteu reagent. 2 min vortex the mixture, and 2 mL of 7.5% sodium carbonate (Na₂CO₃) was added to the mixture after 5 min. The samples were kept in the dark at room temperature for an hour. They used a UV–Visible spectrophotometer, Shimadzu UV-1800 series, and UV Probe 2.62 software, Japan, to measure the absorbance at 765 nm. The results were presented as mg of gallic acid equivalent (GAE) per gram of sample using gallic acid as the reference standard.</p>", "<title>Determination of total flavonoid content (TFC)</title>", "<p id=\"Par13\">The TFC (y₂) was determined by the method developed by da Silva et al.^{##REF##25709217##47##}. 1 mL of resolubilized extract sample mixed with 0.3 mL of 5% sodium nitrite. The mixture was allowed to incubate for 6 min in a dark place, and then 0.3 mL of 10% aluminium chloride solution was added. 3 mL of 1 M sodium hydroxide was added to the reaction, and the incubation was continued for 10 min. After 10 min, a UV–Visible spectrophotometer was employed to measure the absorbance at 510 nm. The results were presented as mg of rutin equivalent (RE) per gram of sample.</p>" ]

[ "<title>Results and discussion</title>", "<title>Adequacy of the models</title>", "<p id=\"Par28\">Ultrasound-aided extraction is one of the best techniques for extracting thermosensitive and minute bioactive ingredients from natural sources. This ultrasound-aided extraction delivers numerous advantages, such as consuming less solvent as well as energy for extraction, heat not generated during ultrasonic waves rupturing the cell wall, and ultrasonic waves very quickly breaking the cell wall and solubilizing the internal active ingredients by the solvent^{##REF##35688121##65##}. This study successfully optimized independent extraction variables through the CCD of RSM. This quadratic model was employed by combining ultrasound-aided extraction parameters of linear, interactions, and quadratic impacts on grape seed extract’s maximal extraction yield of bioactive compounds^{##UREF##45##66##}. CCD was flexible and effective, and could provide much information about experimental variables and errors with the least experimental cycle^{##UREF##46##67##}. Therefore, several experiments were carried out according to the central experiment design (CCD). Table ##TAB##1##2## presented the experimental values and their predicted TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc, and FRAP) values of grapes seed extract under combination extraction parameters. Based on the experimental results, the optimized condition was observed at 0.155 mm particle size (<italic>X</italic>₁), 65% methanol concentration (<italic>X</italic>₂), 23 min ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄) at 40 °C, and ultrasound intensity (<italic>X</italic>₅) was 70 W cm⁻². This situation, the optimal yields of TPC, TFC, and antioxidant scavenging potential were achieved to be 670.32 mg GAE/g, 451.45 mg RE/g, 81.23% DPPH*sc, 77.39% ABTS*sc and 71.55 μg mol (Fe(II))/g FRAP value (Raw data was presented in Related file). The interaction of extraction parameters may be the primary factor causing the maximum production of bioactive components from grape seeds. Similar results were obtained in our previous optimization experiments, such as bioactive compounds from <italic>Garcinia indica,</italic> and <italic>Hemidesmus indicus</italic> Linn. of ultrasound-assisted extraction^{##UREF##5##7##,##UREF##10##14##}. The experimental results fitted to the model of a second-order polynomial equation. ANOVA was used to analyse the regression equation that was obtained.</p>", "<p id=\"Par29\">The significance of the coefficients was ascertained at a 95% confidence level using the F and <italic>p</italic> tests. The associated variables would become highly significant if the <italic>p</italic>-value decreases and the F-value increases^{##UREF##47##68##}. The<italic> p</italic>-values were used as an essential tool to check the significance of the interactions of the variables^{##REF##30475804##69##}. Importantly, when the<italic> p</italic>-value was &lt; 0.05, then the model terms are assigned as statistically significant. While, the <italic>p</italic>-value was greater than 0.05 the model terms are called non-significant. The obtained F value for the lack of fit in this investigation was 18.49, and the present model was therefore highly significant (<italic>p</italic>-value 0.0001 and F value 18.49). The multiple regression coefficient of determination (R²) determines the model’s output response and the importance of lack-of-fit. The adequacy-output response model revealed that the quadratic model multiple regression coefficient of determination (R²) of TPC, TFC, and antioxidant scavenging potentials (DPPH*sc, ABTS*sc, and FRAP) were 0.9273, 0.9323, 0.9045, 0.8730, and 0.8800, respectively, which demonstrated good depiction of the variables by the model and satisfied Le Man et al. For this reason, a model is considered acceptable when R² &gt; 0.87. The predicted R² value (0.6930) is close to the adjusted R² value (0.8772), and the 95% confidence level shows that the quadratic models fit the experimental data well. This implied that 95% of the experimental values agree with the model’s predictions.</p>", "<title>Investigation of the response surfaces</title>", "<title>Total phenolic content (TPC)</title>", "<p id=\"Par30\">The experimental results and their predicted values of TPC using various combinations of extraction parameters in the ultrasound-aided solvent extraction method are presented in Table ##TAB##2##3##. Using the obtained experimental data, an analysis of variance (ANOVA) was performed to determine the coefficient of determination (R²) of the model’s significance. The statistical significance of the model equation was evaluated using the lack-of-fit test, coefficient of determination (R²), and <italic>p</italic>-values^{##UREF##48##70##,##UREF##49##71##}. From the analyzed data in Table ##TAB##2##3## and polynomial Eq. (##FORMU##7##7##), it was determined that the linear term of particle size has a substantial (<italic>p</italic> 0.05) contribution to the most significant yield of total phenolic content (<italic>X</italic>₁), temperature (<italic>X</italic>₄), and quadratic term <italic>X</italic>₂², <italic>X</italic>₃², <italic>X</italic>₅². As the ANOVA result in this model illustrates in Table ##TAB##2##3##, the model could reflect the relationship between the experimental values and their predicted responses with a higher F-value (18.49), and a very low probability value (<italic>p</italic> &lt; 0.0001). Additionally, sufficient precision and the coefficient of determination (R²) were significant markers of the model fitting. An R² value near one indicates that the suggested model provides a better explanation for the variability of the experimental data; in other words, there is a stronger correlation between the observed and predicted values^{##REF##37094478##72##}. The coefficient of determination of the ultrasound-aided solvent extraction of total polyphenolics was found to be R² = 0.9273, R² predicted = 0.6930, and R² adjusted = 0.8772, which indicated that this model has good reliability and fitting. The second-order polynomial equation for the fitted quadratic model for TPC in coded variables is given below Eq. (##FORMU##6##6##)</p>", "<p id=\"Par31\">The residuals were subsequently examined using the model data. Using residuals, it was possible to determine the difference between an experimental value from a response surface measurement and the value that the model anticipated. Figure ##FIG##1##2##a displays the studentized residuals of <italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄, and <italic>X</italic>₅ as a normal percent probability plot. These discovered variations do not deviate from the usual distribution. A model that fits the data well is indicated by a high coefficient of determination (R² &gt;&gt; 0.9), as seen in Fig. ##FIG##1##2##b. Figure ##FIG##1##2##c,d show 3D response surface and 2D contour plot reveal the significant effect of particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄) in maximizing yield of TPC with methanol concentration, ultrasonic exposure time and ultrasonic intensity held at a fixed level (zero level) = 65%, 23 min, 70 W cm⁻², respectively).The effects of particle size (<italic>X</italic>₁), temperature (<italic>X</italic>₄), and the extract’s highest content of total polyphenolic content was further illustrated by the 3D response surface and contour plot in Fig. ##FIG##1##2##c,d. The total polyphenolic concentrations ranged from 360.76 to 670.32 mg GAE/g, as Table ##TAB##1##2## demonstrates. The maximum yield of total polyphenolic content was achieved at 0.155 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C, and 60 W cm⁻² ultrasonic intensity.</p>", "<title>Total flavonoid content (TFC)</title>", "<p id=\"Par32\">From the ANOVA Table ##TAB##2##3## and obtained second-order polynomial Eq. (##FORMU##8##8##) illustrated that the linear term particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄) and quadratic term <italic>X</italic>₂², <italic>X</italic>₃², and <italic>X</italic>₅² are influencing significant (<italic>p</italic> &lt;&lt; 0.05) effects for the maximum extraction yield of total flavonoid content from grape seeds extract. The effect of other terms was found to be non-significant because <italic>p</italic> value was greater than 0.05. The experimental model successfully fits the data, as evidenced by the response surface analysis of the total flavonoid content of the extract, which revealed a high coefficient of determination value of R² = 0.9323, adjusted R² = 0.8856, predicted R² = 0.7567 and a least value for lack of fit <italic>p</italic> value &lt; 0.0001. Further, the adjusted R² value close to predicted R² value showed this model fitting one.</p>", "<p id=\"Par33\">Figure ##FIG##1##2##e illustrates normal % probability plot of studentized residuals of <italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄ and <italic>X</italic>₅. These variants are normally distributed without any deviations. Coefficient of determination (R²) value should be close 0.9 to have a good fit of the model. The closer the goodness of fit to 1, the better the empirical model fits the actual data^{##UREF##50##73##}. Figure ##FIG##1##2##f displayed the high coefficient of determination values (R² &gt;&gt; 0.9), which are indicative of a strong fit. Furthermore, the maximum content of total flavonoids in the grapes seeds extract is influenced by particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄). In contrast, other three variables, such as methanol concentration (<italic>X</italic>₂), ultrasonic time (<italic>X</italic>₃), and ultrasonic intensity (<italic>X</italic>₅) were kept constant (zero level) = 65%, 23 min, 70 W cm⁻², respectively, as shown by the 3D response surface and contour plot in Fig. ##FIG##1##2##g,h. Table ##TAB##1##2## showed a range of 243.17 to 451.45 mg (RE)/g for total flavonoids. The highest yield of flavonoids was produced with 0.155 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C and 60 W cm⁻² ultrasonic intensity; the lowest content was produced with 1.35 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C and 70 W cm⁻² ultrasonic intensity.</p>", "<title>Antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc and FRAP)</title>", "<p id=\"Par34\">Based on the statistical analysis of experimental data in Table ##TAB##2##3## and second-order polynomial Eqs. (##FORMU##8##8##)–(##FORMU##10##10##), the linear term <italic>X</italic>₁ interaction terms <italic>X</italic>₁<italic>X</italic>₄, <italic>X</italic>₃<italic>X</italic>₅, and quadratic terms <italic>X</italic>₁², X₂²are significantly (<italic>p</italic> &lt; 0.05) contributing to the effects for the maximum yield of all three antioxidants (%DPPH*sc, %ABTS*sc, FRAP) scavenging potential from grape seeds extract. In addition, Table ##TAB##2##3## shows the interaction terms <italic>X</italic>₂<italic>X</italic>₄, <italic>X</italic>₄<italic>X</italic>₅ contributing the highest DPPH* scavenging activity of grapes seeds extract. Similarly, linear term <italic>X</italic>₄, and interaction term <italic>X</italic>₃<italic>X</italic>₅ has a significant effect on ABTS*sc and FRAP. The coefficient of determination (R²) value of %DPPH*sc, %ABTS*sc, and FRAP are 0.9045, 0.8730, 0.8800 respectively, adjusted R² value of %DPPH*sc, %ABTS*sc, and FRAP are 0.8386, 0.7855, 0.7973 respectively, the predicted R² value of %DPPH*sc, %ABTS*sc, and FRAP are 0.6661, 0.5611, 0.5789, respectively. All three antioxidant potentials adjusted R² values very close to predicted R², with the least lack of fit <italic>p</italic> value of %DPPH*sc, %ABTS*sc, and FRAP &lt; 0.0001, &lt; 0.0001, and &lt; 0.0001, respectively. These observed data suggested that the model is significantly accurate. The second-order polynomial equation for the fitted quadratic models for %DPPH*sc, %ABTS*sc, and FRAP in coded variables is given in Eqs. (##FORMU##8##8##)–(##FORMU##10##10##).</p>", "<p id=\"Par35\">Figure ##FIG##2##3##a,e,i shows that the normal percentage probability plot of studentized residuals of <italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃ and <italic>X</italic>₄ and these variants are normally distributed and have no deviation for all three antioxidant scavenging experiments. Figure ##FIG##2##3##b,f,j displayed the high coefficient of determination (R² &gt;&gt; 0.87), which are indicative of a strong fit. The 3D response surfaces and 2D contour plots for antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc and FRAP) as responsible functional variables of particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄) are shown in Fig. ##FIG##2##3##c,d,g,h,k,l. The figures show that 0.155 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C and 60 W cm⁻² ultrasonic intensity correspond to the highest antioxidant (%DPPH*sc, %ABTS*sc, and FRAP) potential. The highest yields of antioxidant scavenging potentials are %DPPH 81.23%, %ABTS 77.39%, and FRAP 71.55 μg mol Fe (II)/g.</p>", "<title>ANFIS modelling</title>", "<p id=\"Par36\">ANFIS modelling was used to investigate further verify experimental data and predict the extraction variables of bioactive ingredients in the grape seeds extract. The same 50 experimental data sets shown in Table ##TAB##1##2## were divided into three sets to develop the ANFIS model prediction: 65% for the training data sets, 30% for the testing data sets, and 5% for validating the models. These sets were then used to construct a fuzzy inference system, the parameters of which were adjusted for the membership function using the least-squares method in conjunction with the back-propagation algorithm. The fuzzy logic toolbox in MATLAB v. R2013a was used to train ANFIS to obtain the results. To ensure accuracy, a FIS of ANFIS model with membership functions, five output responses, and five input responses must be constructed. The proposed architecture of the ANFIS model comprises five input parameters and one output value, as displayed in Fig. ##FIG##0##1##. Several parameters must be verified one at a time. For every input variable, including particle size (<italic>X</italic>₁), methanol concentration (<italic>X</italic>₂), ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄), and ultrasound intensity (<italic>X</italic>₅), there are three fuzzy sets: low, medium, and high. Similarly, experimental results on predicted output responses were TPC (670 mg gallic acid equivalents (GAE)/g), TFC (451 mg rutin equivalents (RE)/g), DPPH*sc (81.2%), ABTS*sc (77.4%), and FRAP (71.6 μg mol (Fe (II))/g) were defined in five fuzzy sets namely very low, low, medium, high and very high. Experiment data and human observation data were utilized to construct the fuzzy rule. The fuzzy inference system had a total number of fuzzy rules 324 and a number of network nodes 664 (Number of input response 5, output response 1 (at a time), and the type of membership function is Gaussian) presented. The predicted values of the responses were utilized to improve the fuzzy rules through RSM.</p>", "<title>Machine learning algorithm</title>", "<p id=\"Par37\">The inputs are the characteristics of the experimental parameters (<italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄, and <italic>X</italic>₅), and the output responses are y₁, y₂, y₃, y₄, and y₅. The dataset contains the five goal columns. Thus, the five random forest regressor models were constructed by maintaining the input data constant and changing the output response for each model. This experiment’s estimators are set to 100. The R error value is used to evaluate the models after they have been fitted to the training set of data. Subsequently, the models predict the input data (<italic>X</italic>₁: 0.1554 mm particle size, <italic>X</italic>₂: 65% methanol concentration, <italic>X</italic>₃: 23 min, <italic>X</italic>₄: 40 °C, and <italic>X</italic>₅: 70 W cm⁻² ultrasound intensity). Total polyphenolics (643.53 mg GAE/g), total flavonoids (411.64 mg RE/g), %DPPH*sc (76.84%), %ABTS*sc (71.12%), and FRAP (66.30 μg mol (Fe (II))/g) were all expected to have the desired output responses based on the experimental results. Figure ##FIG##3##4##a–e are created for each of the five models to illustrate the error variance between the predicted and actual values.</p>", "<title>Verification of the model</title>", "<p id=\"Par38\">The obtained optimized extraction condition based on the CCD of RSM was confirmed with verification experiments for maximum yield of bioactive ingredients from grapes seeds extract. The significantly influenced parameters’ values slightly changed, and verification experiments were performed individually. The obtained verification experimental results feed into the Design Espert software and analyse the verification experimental results and their predicted output responses based on the yield of TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc and FRAP) from grapes seeds. ANFIS and the machine learning algorithm used the same data for further verification. The verification experimental results exhibited that the particle size, methanol concentration, and temperature significantly affected the highest yield of bioactive ingredients from grapes seeds. Table ##TAB##3##4## displays the results of verification experiments conducted under optimized conditions and with minor modifications based on values of extraction parameters. Based on the verification experiment, 0.155 mm particle size of grapes seeds powder, 62.5% of methanol, in 23 min of ultrasonic waves exposure time, at 40 °C with 70 W cm⁻² ultrasonic intensity, under this condition while the experimental values of TPC, TFC, and antioxidant scavenging potentials were 672. 45 mg GAE/g, 454.65 mg RE/g, 81.89%, 77.85%, and 71.52 μg mol (Fe (II))/g), respectively. Further, the predicted values from RSM models are TPC, TFC, %DPPH*sc, %ABTS*sc and FRAP were 772. 64 mg GAE/g, 469.42 mg RE/g, 82.22%, 76.72%, and 71.52 μg mol (Fe (II))/g), respectively. By changing the extraction parameter (input) values, the value of the responses (output) was observed using a rule viewer plot (Fig. ##FIG##4##5##). The rule viewer is a compressed toolbox with built-in neural weight optimization and fuzzification techniques. Implementation experiments and comparing the outcomes with the model’s predicted value allowed for additional cross-validation of the model. In the grape seeds extract, the predicted responses obtained through the ANFIS model were TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc, and FRAP) were 632 mg GAE/g, 426 mg RE/g, 76.5%, 72.8%, and 67.3 μg mol (Fe (II))/g), respectively. At the same time, the machine learning algorithm model predicted the responses, the values for TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc, and FRAP) were 669.69 mg GAE/g, 455.11 mg RE/g, 81.18%, 76.93%, and 71.14 μg mol (Fe (II))/g), respectively. According to the findings, RSM, ANFIS modelling, machine learning algorithm predictions, and the experimentally obtained values and regression analyses fit well.</p>", "<title>GC–MS analysis</title>", "<p id=\"Par39\">A total of 20 peaks were observed from optimally obtained grape seed extract of the GC–MS chromatogram (Fig. ##FIG##5##6##) by comparing the peak retention time, peak area (%), height (%), and mass spectral fragmentation patterns to those of the well-known compounds listed in the National Institute of Standards and Technology (NIST) library. Among the 20 peaks, 12 bioactive compounds (based on the active nucleus of the structure) were identified. Table ##TAB##4##5## shows the identified bioactive compounds and their molecular formula, with molecular mass. The bioactive compounds present in the optimized extract of grapes seeds were found to be 3-Hexenoic acid, 5-Hydroxymethylfurfural, 2-Amino-5,6-dimethyl-3H-pyrimidine, Spiro[4.4]nonane-1,6-dione, 8-Methylnonanoic acid, 3,4-Altrosan, 1,5-Anhydro-d-mannitol, 9-Eicosenoic acid, <italic>cis</italic>-Vaccenic acid, 1,37-Octatriacontadiene, 1,3-Benzenedicarboxylic acid 2-Methyl-7-phenylindole.</p>", "<title>LC–MS analysis</title>", "<p id=\"Par40\">Liquid chromatography coupled with mass spectroscopy is one of the significant tools for the structural identification of small molecules in the grape seed extract. Both positive and negative modes of LC–MS chromatogram of optimally obtained grape seed extract were presented in Supplementary Fig. ##SUPPL##0##S1##. Further, the chromatogram (Supplementary Fig. ##SUPPL##0##S2##) both positive and negative modes showed many peaks at different retention times and specified the presence of four active compounds, in the positive three active compounds identified, namely, catechin (retention time: 6.242 min; molecular formula: C₁₅H₁₄O₆; mass 290.27 g/m), (−)-epicatechin (retention time: 5.262 min; molecular formula: C₁₅H₁₄O₆; mass 290.27 g/m), Fisetinidol (retention time: 4.983 min; molecular formula: C₁₅H1₄O₅; mass 228.24 g/m). and <italic>trans</italic>-resveratrol (retention time: 6.899 min; molecular formula: C₁₄H₁₂O₃; mass 274.27 g/m), and in the positive mode one compound identified (−)-epicatechin-3-<italic>O</italic>-gallate (retention time: 9.284 min; molecular formula: C₂₂H₁₈O₁₀; mass 442.4 g/m).</p>" ]

[ "<title>Results and discussion</title>", "<title>Adequacy of the models</title>", "<p id=\"Par28\">Ultrasound-aided extraction is one of the best techniques for extracting thermosensitive and minute bioactive ingredients from natural sources. This ultrasound-aided extraction delivers numerous advantages, such as consuming less solvent as well as energy for extraction, heat not generated during ultrasonic waves rupturing the cell wall, and ultrasonic waves very quickly breaking the cell wall and solubilizing the internal active ingredients by the solvent^{##REF##35688121##65##}. This study successfully optimized independent extraction variables through the CCD of RSM. This quadratic model was employed by combining ultrasound-aided extraction parameters of linear, interactions, and quadratic impacts on grape seed extract’s maximal extraction yield of bioactive compounds^{##UREF##45##66##}. CCD was flexible and effective, and could provide much information about experimental variables and errors with the least experimental cycle^{##UREF##46##67##}. Therefore, several experiments were carried out according to the central experiment design (CCD). Table ##TAB##1##2## presented the experimental values and their predicted TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc, and FRAP) values of grapes seed extract under combination extraction parameters. Based on the experimental results, the optimized condition was observed at 0.155 mm particle size (<italic>X</italic>₁), 65% methanol concentration (<italic>X</italic>₂), 23 min ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄) at 40 °C, and ultrasound intensity (<italic>X</italic>₅) was 70 W cm⁻². This situation, the optimal yields of TPC, TFC, and antioxidant scavenging potential were achieved to be 670.32 mg GAE/g, 451.45 mg RE/g, 81.23% DPPH*sc, 77.39% ABTS*sc and 71.55 μg mol (Fe(II))/g FRAP value (Raw data was presented in Related file). The interaction of extraction parameters may be the primary factor causing the maximum production of bioactive components from grape seeds. Similar results were obtained in our previous optimization experiments, such as bioactive compounds from <italic>Garcinia indica,</italic> and <italic>Hemidesmus indicus</italic> Linn. of ultrasound-assisted extraction^{##UREF##5##7##,##UREF##10##14##}. The experimental results fitted to the model of a second-order polynomial equation. ANOVA was used to analyse the regression equation that was obtained.</p>", "<p id=\"Par29\">The significance of the coefficients was ascertained at a 95% confidence level using the F and <italic>p</italic> tests. The associated variables would become highly significant if the <italic>p</italic>-value decreases and the F-value increases^{##UREF##47##68##}. The<italic> p</italic>-values were used as an essential tool to check the significance of the interactions of the variables^{##REF##30475804##69##}. Importantly, when the<italic> p</italic>-value was &lt; 0.05, then the model terms are assigned as statistically significant. While, the <italic>p</italic>-value was greater than 0.05 the model terms are called non-significant. The obtained F value for the lack of fit in this investigation was 18.49, and the present model was therefore highly significant (<italic>p</italic>-value 0.0001 and F value 18.49). The multiple regression coefficient of determination (R²) determines the model’s output response and the importance of lack-of-fit. The adequacy-output response model revealed that the quadratic model multiple regression coefficient of determination (R²) of TPC, TFC, and antioxidant scavenging potentials (DPPH*sc, ABTS*sc, and FRAP) were 0.9273, 0.9323, 0.9045, 0.8730, and 0.8800, respectively, which demonstrated good depiction of the variables by the model and satisfied Le Man et al. For this reason, a model is considered acceptable when R² &gt; 0.87. The predicted R² value (0.6930) is close to the adjusted R² value (0.8772), and the 95% confidence level shows that the quadratic models fit the experimental data well. This implied that 95% of the experimental values agree with the model’s predictions.</p>", "<title>Investigation of the response surfaces</title>", "<title>Total phenolic content (TPC)</title>", "<p id=\"Par30\">The experimental results and their predicted values of TPC using various combinations of extraction parameters in the ultrasound-aided solvent extraction method are presented in Table ##TAB##2##3##. Using the obtained experimental data, an analysis of variance (ANOVA) was performed to determine the coefficient of determination (R²) of the model’s significance. The statistical significance of the model equation was evaluated using the lack-of-fit test, coefficient of determination (R²), and <italic>p</italic>-values^{##UREF##48##70##,##UREF##49##71##}. From the analyzed data in Table ##TAB##2##3## and polynomial Eq. (##FORMU##7##7##), it was determined that the linear term of particle size has a substantial (<italic>p</italic> 0.05) contribution to the most significant yield of total phenolic content (<italic>X</italic>₁), temperature (<italic>X</italic>₄), and quadratic term <italic>X</italic>₂², <italic>X</italic>₃², <italic>X</italic>₅². As the ANOVA result in this model illustrates in Table ##TAB##2##3##, the model could reflect the relationship between the experimental values and their predicted responses with a higher F-value (18.49), and a very low probability value (<italic>p</italic> &lt; 0.0001). Additionally, sufficient precision and the coefficient of determination (R²) were significant markers of the model fitting. An R² value near one indicates that the suggested model provides a better explanation for the variability of the experimental data; in other words, there is a stronger correlation between the observed and predicted values^{##REF##37094478##72##}. The coefficient of determination of the ultrasound-aided solvent extraction of total polyphenolics was found to be R² = 0.9273, R² predicted = 0.6930, and R² adjusted = 0.8772, which indicated that this model has good reliability and fitting. The second-order polynomial equation for the fitted quadratic model for TPC in coded variables is given below Eq. (##FORMU##6##6##)</p>", "<p id=\"Par31\">The residuals were subsequently examined using the model data. Using residuals, it was possible to determine the difference between an experimental value from a response surface measurement and the value that the model anticipated. Figure ##FIG##1##2##a displays the studentized residuals of <italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄, and <italic>X</italic>₅ as a normal percent probability plot. These discovered variations do not deviate from the usual distribution. A model that fits the data well is indicated by a high coefficient of determination (R² &gt;&gt; 0.9), as seen in Fig. ##FIG##1##2##b. Figure ##FIG##1##2##c,d show 3D response surface and 2D contour plot reveal the significant effect of particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄) in maximizing yield of TPC with methanol concentration, ultrasonic exposure time and ultrasonic intensity held at a fixed level (zero level) = 65%, 23 min, 70 W cm⁻², respectively).The effects of particle size (<italic>X</italic>₁), temperature (<italic>X</italic>₄), and the extract’s highest content of total polyphenolic content was further illustrated by the 3D response surface and contour plot in Fig. ##FIG##1##2##c,d. The total polyphenolic concentrations ranged from 360.76 to 670.32 mg GAE/g, as Table ##TAB##1##2## demonstrates. The maximum yield of total polyphenolic content was achieved at 0.155 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C, and 60 W cm⁻² ultrasonic intensity.</p>", "<title>Total flavonoid content (TFC)</title>", "<p id=\"Par32\">From the ANOVA Table ##TAB##2##3## and obtained second-order polynomial Eq. (##FORMU##8##8##) illustrated that the linear term particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄) and quadratic term <italic>X</italic>₂², <italic>X</italic>₃², and <italic>X</italic>₅² are influencing significant (<italic>p</italic> &lt;&lt; 0.05) effects for the maximum extraction yield of total flavonoid content from grape seeds extract. The effect of other terms was found to be non-significant because <italic>p</italic> value was greater than 0.05. The experimental model successfully fits the data, as evidenced by the response surface analysis of the total flavonoid content of the extract, which revealed a high coefficient of determination value of R² = 0.9323, adjusted R² = 0.8856, predicted R² = 0.7567 and a least value for lack of fit <italic>p</italic> value &lt; 0.0001. Further, the adjusted R² value close to predicted R² value showed this model fitting one.</p>", "<p id=\"Par33\">Figure ##FIG##1##2##e illustrates normal % probability plot of studentized residuals of <italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄ and <italic>X</italic>₅. These variants are normally distributed without any deviations. Coefficient of determination (R²) value should be close 0.9 to have a good fit of the model. The closer the goodness of fit to 1, the better the empirical model fits the actual data^{##UREF##50##73##}. Figure ##FIG##1##2##f displayed the high coefficient of determination values (R² &gt;&gt; 0.9), which are indicative of a strong fit. Furthermore, the maximum content of total flavonoids in the grapes seeds extract is influenced by particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄). In contrast, other three variables, such as methanol concentration (<italic>X</italic>₂), ultrasonic time (<italic>X</italic>₃), and ultrasonic intensity (<italic>X</italic>₅) were kept constant (zero level) = 65%, 23 min, 70 W cm⁻², respectively, as shown by the 3D response surface and contour plot in Fig. ##FIG##1##2##g,h. Table ##TAB##1##2## showed a range of 243.17 to 451.45 mg (RE)/g for total flavonoids. The highest yield of flavonoids was produced with 0.155 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C and 60 W cm⁻² ultrasonic intensity; the lowest content was produced with 1.35 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C and 70 W cm⁻² ultrasonic intensity.</p>", "<title>Antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc and FRAP)</title>", "<p id=\"Par34\">Based on the statistical analysis of experimental data in Table ##TAB##2##3## and second-order polynomial Eqs. (##FORMU##8##8##)–(##FORMU##10##10##), the linear term <italic>X</italic>₁ interaction terms <italic>X</italic>₁<italic>X</italic>₄, <italic>X</italic>₃<italic>X</italic>₅, and quadratic terms <italic>X</italic>₁², X₂²are significantly (<italic>p</italic> &lt; 0.05) contributing to the effects for the maximum yield of all three antioxidants (%DPPH*sc, %ABTS*sc, FRAP) scavenging potential from grape seeds extract. In addition, Table ##TAB##2##3## shows the interaction terms <italic>X</italic>₂<italic>X</italic>₄, <italic>X</italic>₄<italic>X</italic>₅ contributing the highest DPPH* scavenging activity of grapes seeds extract. Similarly, linear term <italic>X</italic>₄, and interaction term <italic>X</italic>₃<italic>X</italic>₅ has a significant effect on ABTS*sc and FRAP. The coefficient of determination (R²) value of %DPPH*sc, %ABTS*sc, and FRAP are 0.9045, 0.8730, 0.8800 respectively, adjusted R² value of %DPPH*sc, %ABTS*sc, and FRAP are 0.8386, 0.7855, 0.7973 respectively, the predicted R² value of %DPPH*sc, %ABTS*sc, and FRAP are 0.6661, 0.5611, 0.5789, respectively. All three antioxidant potentials adjusted R² values very close to predicted R², with the least lack of fit <italic>p</italic> value of %DPPH*sc, %ABTS*sc, and FRAP &lt; 0.0001, &lt; 0.0001, and &lt; 0.0001, respectively. These observed data suggested that the model is significantly accurate. The second-order polynomial equation for the fitted quadratic models for %DPPH*sc, %ABTS*sc, and FRAP in coded variables is given in Eqs. (##FORMU##8##8##)–(##FORMU##10##10##).</p>", "<p id=\"Par35\">Figure ##FIG##2##3##a,e,i shows that the normal percentage probability plot of studentized residuals of <italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃ and <italic>X</italic>₄ and these variants are normally distributed and have no deviation for all three antioxidant scavenging experiments. Figure ##FIG##2##3##b,f,j displayed the high coefficient of determination (R² &gt;&gt; 0.87), which are indicative of a strong fit. The 3D response surfaces and 2D contour plots for antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc and FRAP) as responsible functional variables of particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄) are shown in Fig. ##FIG##2##3##c,d,g,h,k,l. The figures show that 0.155 mm particle size, 65% methanol concentration, 23 min ultrasonic exposure time, temperature at 40 °C and 60 W cm⁻² ultrasonic intensity correspond to the highest antioxidant (%DPPH*sc, %ABTS*sc, and FRAP) potential. The highest yields of antioxidant scavenging potentials are %DPPH 81.23%, %ABTS 77.39%, and FRAP 71.55 μg mol Fe (II)/g.</p>", "<title>ANFIS modelling</title>", "<p id=\"Par36\">ANFIS modelling was used to investigate further verify experimental data and predict the extraction variables of bioactive ingredients in the grape seeds extract. The same 50 experimental data sets shown in Table ##TAB##1##2## were divided into three sets to develop the ANFIS model prediction: 65% for the training data sets, 30% for the testing data sets, and 5% for validating the models. These sets were then used to construct a fuzzy inference system, the parameters of which were adjusted for the membership function using the least-squares method in conjunction with the back-propagation algorithm. The fuzzy logic toolbox in MATLAB v. R2013a was used to train ANFIS to obtain the results. To ensure accuracy, a FIS of ANFIS model with membership functions, five output responses, and five input responses must be constructed. The proposed architecture of the ANFIS model comprises five input parameters and one output value, as displayed in Fig. ##FIG##0##1##. Several parameters must be verified one at a time. For every input variable, including particle size (<italic>X</italic>₁), methanol concentration (<italic>X</italic>₂), ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄), and ultrasound intensity (<italic>X</italic>₅), there are three fuzzy sets: low, medium, and high. Similarly, experimental results on predicted output responses were TPC (670 mg gallic acid equivalents (GAE)/g), TFC (451 mg rutin equivalents (RE)/g), DPPH*sc (81.2%), ABTS*sc (77.4%), and FRAP (71.6 μg mol (Fe (II))/g) were defined in five fuzzy sets namely very low, low, medium, high and very high. Experiment data and human observation data were utilized to construct the fuzzy rule. The fuzzy inference system had a total number of fuzzy rules 324 and a number of network nodes 664 (Number of input response 5, output response 1 (at a time), and the type of membership function is Gaussian) presented. The predicted values of the responses were utilized to improve the fuzzy rules through RSM.</p>", "<title>Machine learning algorithm</title>", "<p id=\"Par37\">The inputs are the characteristics of the experimental parameters (<italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄, and <italic>X</italic>₅), and the output responses are y₁, y₂, y₃, y₄, and y₅. The dataset contains the five goal columns. Thus, the five random forest regressor models were constructed by maintaining the input data constant and changing the output response for each model. This experiment’s estimators are set to 100. The R error value is used to evaluate the models after they have been fitted to the training set of data. Subsequently, the models predict the input data (<italic>X</italic>₁: 0.1554 mm particle size, <italic>X</italic>₂: 65% methanol concentration, <italic>X</italic>₃: 23 min, <italic>X</italic>₄: 40 °C, and <italic>X</italic>₅: 70 W cm⁻² ultrasound intensity). Total polyphenolics (643.53 mg GAE/g), total flavonoids (411.64 mg RE/g), %DPPH*sc (76.84%), %ABTS*sc (71.12%), and FRAP (66.30 μg mol (Fe (II))/g) were all expected to have the desired output responses based on the experimental results. Figure ##FIG##3##4##a–e are created for each of the five models to illustrate the error variance between the predicted and actual values.</p>", "<title>Verification of the model</title>", "<p id=\"Par38\">The obtained optimized extraction condition based on the CCD of RSM was confirmed with verification experiments for maximum yield of bioactive ingredients from grapes seeds extract. The significantly influenced parameters’ values slightly changed, and verification experiments were performed individually. The obtained verification experimental results feed into the Design Espert software and analyse the verification experimental results and their predicted output responses based on the yield of TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc and FRAP) from grapes seeds. ANFIS and the machine learning algorithm used the same data for further verification. The verification experimental results exhibited that the particle size, methanol concentration, and temperature significantly affected the highest yield of bioactive ingredients from grapes seeds. Table ##TAB##3##4## displays the results of verification experiments conducted under optimized conditions and with minor modifications based on values of extraction parameters. Based on the verification experiment, 0.155 mm particle size of grapes seeds powder, 62.5% of methanol, in 23 min of ultrasonic waves exposure time, at 40 °C with 70 W cm⁻² ultrasonic intensity, under this condition while the experimental values of TPC, TFC, and antioxidant scavenging potentials were 672. 45 mg GAE/g, 454.65 mg RE/g, 81.89%, 77.85%, and 71.52 μg mol (Fe (II))/g), respectively. Further, the predicted values from RSM models are TPC, TFC, %DPPH*sc, %ABTS*sc and FRAP were 772. 64 mg GAE/g, 469.42 mg RE/g, 82.22%, 76.72%, and 71.52 μg mol (Fe (II))/g), respectively. By changing the extraction parameter (input) values, the value of the responses (output) was observed using a rule viewer plot (Fig. ##FIG##4##5##). The rule viewer is a compressed toolbox with built-in neural weight optimization and fuzzification techniques. Implementation experiments and comparing the outcomes with the model’s predicted value allowed for additional cross-validation of the model. In the grape seeds extract, the predicted responses obtained through the ANFIS model were TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc, and FRAP) were 632 mg GAE/g, 426 mg RE/g, 76.5%, 72.8%, and 67.3 μg mol (Fe (II))/g), respectively. At the same time, the machine learning algorithm model predicted the responses, the values for TPC, TFC, and antioxidant scavenging potentials (%DPPH*sc, %ABTS*sc, and FRAP) were 669.69 mg GAE/g, 455.11 mg RE/g, 81.18%, 76.93%, and 71.14 μg mol (Fe (II))/g), respectively. According to the findings, RSM, ANFIS modelling, machine learning algorithm predictions, and the experimentally obtained values and regression analyses fit well.</p>", "<title>GC–MS analysis</title>", "<p id=\"Par39\">A total of 20 peaks were observed from optimally obtained grape seed extract of the GC–MS chromatogram (Fig. ##FIG##5##6##) by comparing the peak retention time, peak area (%), height (%), and mass spectral fragmentation patterns to those of the well-known compounds listed in the National Institute of Standards and Technology (NIST) library. Among the 20 peaks, 12 bioactive compounds (based on the active nucleus of the structure) were identified. Table ##TAB##4##5## shows the identified bioactive compounds and their molecular formula, with molecular mass. The bioactive compounds present in the optimized extract of grapes seeds were found to be 3-Hexenoic acid, 5-Hydroxymethylfurfural, 2-Amino-5,6-dimethyl-3H-pyrimidine, Spiro[4.4]nonane-1,6-dione, 8-Methylnonanoic acid, 3,4-Altrosan, 1,5-Anhydro-d-mannitol, 9-Eicosenoic acid, <italic>cis</italic>-Vaccenic acid, 1,37-Octatriacontadiene, 1,3-Benzenedicarboxylic acid 2-Methyl-7-phenylindole.</p>", "<title>LC–MS analysis</title>", "<p id=\"Par40\">Liquid chromatography coupled with mass spectroscopy is one of the significant tools for the structural identification of small molecules in the grape seed extract. Both positive and negative modes of LC–MS chromatogram of optimally obtained grape seed extract were presented in Supplementary Fig. ##SUPPL##0##S1##. Further, the chromatogram (Supplementary Fig. ##SUPPL##0##S2##) both positive and negative modes showed many peaks at different retention times and specified the presence of four active compounds, in the positive three active compounds identified, namely, catechin (retention time: 6.242 min; molecular formula: C₁₅H₁₄O₆; mass 290.27 g/m), (−)-epicatechin (retention time: 5.262 min; molecular formula: C₁₅H₁₄O₆; mass 290.27 g/m), Fisetinidol (retention time: 4.983 min; molecular formula: C₁₅H1₄O₅; mass 228.24 g/m). and <italic>trans</italic>-resveratrol (retention time: 6.899 min; molecular formula: C₁₄H₁₂O₃; mass 274.27 g/m), and in the positive mode one compound identified (−)-epicatechin-3-<italic>O</italic>-gallate (retention time: 9.284 min; molecular formula: C₂₂H₁₈O₁₀; mass 442.4 g/m).</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par41\">The most effective extraction parameters for a high yield of bioactive components from powdered grape seeds were optimized using a statistical analysis technique based on the CCD of RSM. The experiments were performed per the design of a well-fitted model for extracting the highest yield of TPC, TFC and free radical scavenging potentials (%DPPH*sc, %ABTS*sc, and FRAP) from graph seeds powder. The optimized parameters are further verified through robust ANFIS and machine learning algorithm techniques. The obtained results demonstrated that the independent variables of linear term (particle size (<italic>X</italic>₁) and temperature (<italic>X</italic>₄), interaction terms (<italic>X</italic>₂<italic>X</italic>₄, <italic>X</italic>₃<italic>X</italic>₅, and <italic>X</italic>₄<italic>X</italic>₅), and quadratic terms <italic>X</italic>₂², <italic>X</italic>₃², and <italic>X</italic>₅²) potentially contributed to the maximum yield of bioactive ingredients from grape seeds powder. Combining all five parameters significantly enhances the yield of bioactive ingredients. The observed ideal experimental values were verified and found to fit both the observed and anticipated values using second-order polynomial equations. The design’s high R² value (&gt;&gt; 0.8) confirmed the model’s reliability. The optimal condition was observed at 0.155 mm particle size (<italic>X</italic>₁), 65% methanol concentration (<italic>X</italic>₂), 23 min ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄) at 40 °C, and ultrasound intensity (<italic>X</italic>₅) was 70 W cm⁻². Under this optimal condition, the highest yield of TPC, TFC, and antioxidant activities was 670.32 mg GAE/g of TPC, 451.45 mg RE/g of TFC, 81.23% DPPH*sc, 77.39% ABTS*sc and 71.55 μg mol (Fe(II))/g FRAP obtained. The optimized variable values were well matched with predicted values of RSM, ANFIS, and machine learning algorithm models. Furthermore, 12 volatile and five non-volatile natures of the bioactive compounds were recognized from the optimized extract of grape seed powder with the help of GC–MS and LC–MS spectroscopy. The optimization results from RSM coupled with ANFIS and machine learning algorithm is anticipated to help develop industrial-scale extraction procedures for the bioactive ingredients under research from grape seeds powder and related plant materials.</p>" ]

[ "<p id=\"Par1\">Plant materials are a rich source of polyphenolic compounds with interesting health-beneficial effects. The present study aimed to determine the optimized condition for maximum extraction of polyphenols from grape seeds through RSM (response surface methodology), ANFIS (adaptive neuro-fuzzy inference system), and machine learning (ML) algorithm models. Effect of five independent variables and their ranges, particle size (<italic>X</italic>₁: 0.5–1 mm), methanol concentration (<italic>X</italic>₂: 60–70% in distilled water), ultrasound exposure time (<italic>X</italic>₃: 18–28 min), temperature (<italic>X</italic>₄: 35–45 °C), and ultrasound intensity (<italic>X</italic>₅: 65–75 W cm⁻²) at five levels (− 2, − 1, 0, + 1, and + 2) concerning dependent variables, total phenolic content (y₁; TPC), total flavonoid content (y₂; TFC), 2, 2-diphenyl-1-picrylhydrazyl free radicals scavenging (y₃; %DPPH*sc), 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) free radicals scavenging (y₄; %ABTS*sc) and Ferric ion reducing antioxidant potential (y₅; FRAP) were selected. The optimized condition was observed at <italic>X</italic>₁ = 0.155 mm, <italic>X</italic>₂ = 65% methanol in water, <italic>X</italic>₃ = 23 min ultrasound exposure time, <italic>X</italic>₄ = 40 °C, and <italic>X</italic>₅ = 70 W cm⁻² ultrasound intensity. Under this situation, the optimal yields of TPC, TFC, and antioxidant scavenging potential were achieved to be 670.32 mg GAE/g, 451.45 mg RE/g, 81.23% DPPH*sc, 77.39% ABTS*sc and 71.55 μg mol (Fe(II))/g FRAP. This optimal condition yielded equal experimental and expected values. A well-fitted quadratic model was recommended. Furthermore, the validated extraction parameters were optimized and compared using the ANFIS and random forest regressor-ML algorithm. Gas chromatography-mass spectroscopy (GC–MS) and liquid chromatography–mass spectroscopy (LC–MS) analyses were performed to find the existence of the bioactive compounds in the optimized extract.</p>", "<title>Subject terms</title>" ]

[ "<title>Experimental section</title>", "<title>Materials</title>", "<title>Grape seeds</title>", "<p id=\"Par6\">Fresh fruits of grapes “Cumbum Panneer Thratchai” (<italic>Vitis vinifera</italic> L., family: Vitaceae; Muscat Hamburg variety) personally collected as a gift sample from grapes farm, Cumbum valley (latitude: 9.734426°, and longitude: 77.280739°), Cumbum (is known as the ‘Grapes city of South India’), Theni District, Tamilnadu, India, on April 2023. The plant material was collected with the consent of the Swamy Vivekanandha College of Pharmacy, Tiruchengode, Tamilnadu, India. No further regulation was required for the collection of this plant. In addition, the collection of plant material complied with the relevant institutional (Swamy Vivekanandha College of Pharmacy), national, and international guidelines and legislation. A pharmacognosist, Professor Murugananthan Gopal M. Pharm., PhD., Principal, Department of Pharmacognosy, Swamy Vivekanandha College of Pharmacy, Tiruchengode, Tamilnadu, India was authenticated grape seeds collected Cumbum (Specimen Number: VV/HER/COG-002). It was deposited at the herbarium, Swamy Vivekanandha College of Pharmacy, Tiruchengode, Tamilnadu, India. The grape seeds were removed from the fruits, and then the separated seeds were washed with tap water and shade-dried for seven days. Thoroughly dried grape seeds were ground into a fine powder using a kitchen mixer grinder (Butterfly Gandhimathi Home Appliances Ltd., Chennai, India). Then, the powdered sample was screened into specified particle size powders (0.15, 0.5, 0.75, 1.0, and 1.35 mm) using an exact sieve (Mesh No. 100, 35, 20, 18, and 14). The powder samples were stored under an airtight container until the start of the experiment (moisture content: 10 ± 2%).</p>", "<title>Chemicals</title>", "<p id=\"Par7\">Ethanol, methanol, chloroform, petroleum ether, ethyl acetate, diethyl ether, acetone, <italic>n</italic>-hexane, gallic acid standard, rutin standard, ascorbic acid, Folin–Ciocalteu’s phenol reagent, sodium carbonate, sodium nitrite, sodium hydroxide, aluminium chloride, ferric chloride, and potassium persulfate were obtained from Himedia Laboratories, Mumbai, India. 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS), 2,4,6-tripyridyl-s-triazine (TPTZ), 2, 2-diphenyl-1-picrylhydrazyl (DPPH) were obtained from Sigma Aldrich, Bengaluru, India. All other analytical grade chemicals and reagents were obtained from Himedia Laboratories, Mumbai, India. Distilled water was used for all experiments.</p>", "<title>Ultrasound-aided solvent extractor set-up</title>", "<p id=\"Par8\">The extraction of bioactive ingredients from grape seed powder was performed with an ultrasonic bath extractor (designed by PCI Analytics Ltd., Mumbai, India) having an optimal capacity of 250 mL. The ultrasonic bath has a temperature controller device (accuracy of ± 1.0 °C) with degassing, ultrasound power (220 V), 33 ± 3 kHz operating frequency, continuous mode at 40 kHz high-intensity ultrasound processor, and input voltage range between 200VAC-230VAC, single phase. The ultrasound-instrument produced maximum ultrasound intensity (220 W cm⁻²) with 25 mm titanium probe.</p>", "<title>Determination of antioxidant potential</title>", "<title>%DPPH scavenging assay</title>", "<p id=\"Par14\">The DPPH free radical scavenging potential (y₃) of grape seed extracts was determined according to Musa et al.^{##REF##26471610##48##}. Concisely, 3 mL of DPPH free radical solution (0.1 mM DPPH in ethanol) was mixed with 0.1 mL of grapes seeds extract; the mixture was then incubated at 37 °C for 30 min. After incubation, a UV–Visible spectrophotometer was used to quantify the absorbance at 517 nm. Methanol and DPPH were both employed as controls. The % DPPH radical scavenging ability was calculated as Eq. (##FORMU##0##1##):where A₀—absorbance of the control and A₁—absorbance of the sample.</p>", "<title>%ABTS scavenging assay</title>", "<p id=\"Par15\">The ABTS free radical scavenging potential (y₄) of grape seed extract was determined according to Canabady-Rochelle et al.^{##REF##25863620##49##}. Concisely, 2.45 mM of potassium persulfate was mixed with 7 mM ABTS radical solution, and the resultant reaction mixture was stored in the dark for 16 h at room temperature. Then, ethanol was used to adjust the reaction mixture’s absorbance to 0.70 ± 0.05 at 734 nm. 1 mL of this reaction mixture was mixed with 10 µL of grape seed extract. The absorbance was measured against the blank reagent at 734 nm. The inhibition activity was determined by the following Eq. (##FORMU##1##2##):where A0—absorbance of the control and A1—absorbance of the sample.</p>", "<title>The ferric-reducing antioxidant potential (FRAP) assay</title>", "<p id=\"Par16\">The FRAP (y5) of grapes seed extract was carried out based on the FRAP technique^{##REF##8660627##50##} and modified by Pulido et al.^{##REF##10956123##51##}. The FRAP reagent was prepared using 300 mM acetate buffer (3.1 g sodium acetate in 16 mL acetic acid at pH 3.6), 10 mmol TPTZ, and 20 mmol FeCl₃·6H₂O and 4mMol hydrochloric acid in the ratio of 10:1:1. 0.1 mL of grapes seed extract was mixed with 3.0 mL FRAP reagent and incubated in darkness for 30 min at 37 °C. The absorbance was read at 595 nm using a UV–Vis Spectrophotometer. The standard curve was linear through 200 and 1000 μM FeSO₄. Results calculated in μM Fe (II)/g dry mass were compared with ascorbic acid as a standard.</p>", "<title>Experimental design and optimization using RSM</title>", "<p id=\"Par17\">A five-level, five-coded variable central composite design (CCD) in Response surface methodology (RSM) was applied to optimize the effective extraction parameters of ultrasound-aided extraction technique concerning TPC, TFC, and antioxidant potentials (DPPH*sc, ABTS*sc, and FRAP) from grape seed extract. The selected five-coded variables were particle size (<italic>X</italic>₁: 0.5–1 mm), methanol concentration (<italic>X</italic>₂: 60–70% in distilled water), ultrasound exposure time (<italic>X</italic>₃: 18–28 min), temperature (<italic>X</italic>₄: 35–45 °C), and ultrasound intensity (<italic>X</italic>₅: 65–75 W cm⁻²) at five levels deficient (− 2), low (− 1), medium (0), high (+ 1), and very high (+ 2) investigated for maximum yield of bioactive ingredients from grape seeds extract. The independent variables were coded based on the below Eq. (##FORMU##2##3##):where <italic>xi</italic> is the dimensionless value of the independent parameter; <italic>X</italic>i, is the actual value of an independent parameter; <italic>Xz</italic>, is the actual value of an independent parameter at the central point; and Δ<italic>Xi</italic>, is the step change of the actual value of the parameter <italic>i</italic> representing to a variation of a unit for the dimensionless value of the parameter <italic>i.</italic> The total number of experiments was calculated from Eq. (##FORMU##3##4##), which is given below:where N is the total number of experiments, k is the independent variable number, and n₀ is the replicate number at the central points, resulting in an experimental design of 50 runs. Fitting experimental data determined the correlation between the dependent and independent variables in a second-order polynomial regression model. In the case of these 50 experimental runs comprised of 32 factorial points, 8 repeated levels of central points, and 10 axial points (α) at a distance of ± 2 from centre points is shown in Table ##TAB##1##2##. The results of the CCD studies (Table ##TAB##1##2##) were analysed employing the multiple regression equation.</p>", "<p id=\"Par18\">The above Eq. (##FORMU##4##5##) could be converted, which is given below based on the value of five variables,where <italic>Y</italic> is the dependent response, α₀ is the coefficients-constant of the intercept, αi is linear, αii is quadratic, and αij are interaction terms. <italic>X</italic>i and <italic>X</italic>j are coded values of independent variables of particle size (<italic>X</italic>₁), methanol concentration (<italic>X</italic>₂), ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄), and ultrasound intensity (<italic>X</italic>₅), and ε is an error. Model significance (<italic>p</italic> value), coefficient of determination (R²), predicted coefficient of determination (R² pred), adjusted coefficient of determination (R² adj), and the adequacy of the models by the statistic lack-of-fit value were all determined by analysis of variance (ANOVA). Only significant coefficients (<italic>p</italic> &lt; 0.05) or those necessary for the hierarchy were considered when creating the models. Further analysis was performed to determine the accuracy of the extraction parameters.</p>", "<title>Modeling an adaptive neuro-fuzzy inference system (ANFIS) for optimization</title>", "<p id=\"Par19\">Adaptive neuro‑fuzzy inference system (ANFIS) has an advantage over artificial neural networks (ANN) because it combines the best features of neural networks and fuzzy logic to model complex systems more accurately and precisely^{##UREF##34##52##}. They are inspired by the properties of biological neural networks that resemble the human brain; these networks learn from experience and are used in data processing for categorization and prediction^{##UREF##35##53##}. It is also suitable for various applications, such as optimizing significant extraction variables, thanks to its ability to analyse both numerical and linguistic data^{##UREF##36##54##}. Additionally, merging ANN with fuzzy-set theory helps address the benefits and limitations of both approaches^{##UREF##37##55##}. Jang can develop the intelligent computer tool ANFIS, which can be used to solve complex and nonlinear issues^{##UREF##38##56##}. Both linear and nonlinear relationships between input and output responses can be analysed with this method^{##UREF##39##57##}. This method employs a rule-based fuzzy logic model, which is trained with the help of rules generated during the procedure^{##REF##29673601##58##}. Data is used to inform the training process^{##UREF##40##59##}. Furthermore, training datasets are provided by least squares and backpropagation modeling in this system. Backpropagation of ANN is used as the first step in training data for the adaptive network-based fuzzy inference system (ANFIS)^{##UREF##41##60##}. The output response of ANN will then be used to fuzzy logic membership functions as the input parameters of particle size (<italic>X</italic>₁), methanol concentration (<italic>X</italic>₂), ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄), and ultrasound intensity (<italic>X</italic>₅). These variable optimizations are performed with greater precision thanks to the fuzzy inference system (FIS). The backpropagation algorithm is employed as the initial training strategy in the adaptive network-based fuzzy inference system (ANFIS) for data training purposes. The input parameters of particle size (<italic>X</italic>₁), methanol concentration (<italic>X</italic>₂), ultrasound exposure time (<italic>X</italic>₃), temperature (<italic>X</italic>₄), and ultrasound intensity (<italic>X</italic>₅) will be utilized as input variables for the artificial neural network (ANN). The output response of the ANN will subsequently be employed in the application of fuzzy logic membership functions. Utilizing the fuzzy inference system (FIS) enhances the accuracy of the optimizations pertaining to these variables. The analysis of each predicted output responses of yield of TPC, TFC and percentage antioxidant scavenging potential (DPPH*sc, ABTS*sc, and FRAP) was done using the optimization of ANFIS modeling and data from similar CCD of RSM experiments.</p>", "<p id=\"Par20\">In this study, the Sugeno-type fuzzy inference model was employed for the ANFIS modeling to get multiple inputs (<italic>X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄, and <italic>X</italic>₅) and a single output response (y1/y2/y3/y4/y5). Because the Sugeno-type fuzzy inference system is more computationally efficient than the Mamdani type. The Mamdani type depends more on specialized knowledge. Nonetheless, actual data is used to train the Sugeno type. The ANFIS architecture (Fig. ##FIG##0##1##) shows the design displayed multiple inputs and a single output response at a time. A Sugeno-Fuzzy Inference System (FIS) has one output response, “z,” and two inputs, “x” and “y”. Two fuzzy if–then rules for a first-order Sugeno fuzzy model can be expressed as follows:<list list-type=\"bullet\"><list-item><p id=\"Par21\">Rule 1: If x is A₁ and y is B₁, then f₁ = p₁x + q₁y + r₁,</p></list-item><list-item><p id=\"Par22\">Rule 2: If x is A₂ and y is B₂, then f₂ = p₂x + q₂y + r₂,</p></list-item></list>where A₁ and B₁ are the fuzzy sets, f₁ is the output response, and p₁, q₁, and r₁ are the design parameters determined during the training process. The number of membership functions for each given input variable was determined by a procedure of trial and error. To predict the outcome of the extraction of the majority of bioactive components from grape seeds extract, the experimental data was divided into training, testing, and validation of the network model using MATLAB v. R2013a Fuzzy logic toolbox.</p>", "<title>Optimization using machine learning algorithm</title>", "<p id=\"Par23\">The technique of continuously increasing a machine learning model’s accuracy and decreasing its error rate is known as machine learning optimization^{##REF##31751262##61##}. Most machine learning models use training data to understand the link between input and output responses. After this, the models can be applied to categorize fresh incoming data or predict trends. Since the target values of the experiment are continuous, a Random Forest Regressor is employed^{##UREF##42##62##}. This ensemble learning approach combines different decision trees to create a more accurate model^{##UREF##43##63##}. A subset of the training data and a randomly selected subset of the characteristics are used to train each decision tree. This randomization helps to improve the model’s prediction accuracy and reduce overfitting. The Random Forest algorithm generates many decision trees and then aggregates their forecasts to obtain a more accurate and reliable prediction^{##UREF##44##64##}. The primary benefit of the random forest regressor is its ability to handle high-dimensional data with a nonlinear relationship between the input and target values. The data set for this investigation has experimental values<italic> X</italic>₁, <italic>X</italic>₂, <italic>X</italic>₃, <italic>X</italic>₄, and <italic>X</italic>₅ as inputs and y₁, y₂, y₃, y₄, and y₅ as output responses. In order to generate the predictions, the experimental values are the dataset that is initially imported. It is then preprocessed to see if there are any missing or noisy data in the dataset.</p>", "<title>Verification optimized condition</title>", "<p id=\"Par24\">By evaluating the dependability of the optimization findings, the applicability of the experiment was confirmed. Under optimal conditions, a triplicate experiment was carried out based on the combination of response and minor deviation. The mean experimental results were compared to assess the model’s reasonableness about the predicted values.</p>", "<title>Utilizing GC–MS for volatile bioactive compounds identification</title>", "<p id=\"Par25\">Gas chromatography and mass spectrometry (GC–MS) was used to determine the volatile nature of the bioactive components in the optimized grape seed extract^{##UREF##5##7##}. The GC–MS analysis was performed in gas chromatography that also served as a mass spectrophotometer (Shimadzu Make QP-2010 GC–MS system), equipped with a non-polar 60 M RTX 5MS column and helium gas as the carrier gas, with a constant pressure of 15 psi and an adjusted column flow velocity of 1.00 mL × min⁻¹ with initial oven temperature at 40 °C held for 3 min and the final temperature of the oven was 480 °C. with the rate at 10 °C [min × sup⁻¹]. A 2 μL sample was injected with split-less mode. Mass spectra was recorded over 35–650 amu range with electron impact ionization energy 70 eV. The total running time for a sample is 45 min. Identification of bioactive ingredients was achieved based on their retention time of chromatographic peaks utilizing a Quadrapole detector and the NIST 2014 (National Institute of Standards and Technology, 2014) library to relative retention indices. NIST library database contains more than 62,000 patterns of well-known compounds. The spectra of the unknown bioactive ingredients of grape seeds extract fraction obtained were compared to the reference mass spectra of recognised components deposited in the NIST library collection (NIST).</p>", "<title>Utilizing LC–MS for non-volatile bioactive compounds identification</title>", "<p id=\"Par26\">Liquid chromatography and mass spectrometry (LC–MS) was used to determine the non-volatile nature of the bioactive components in the optimized grape seed extract. The LC–MS analysis was performed using the 1290 Infinity UHPLC System, and 6550 iFunnel Q-TOFs (Agilent Technologies, USA). For separations Zorbax-SB-C-18 column (2.1 × 50 mm, 1.8 µM particle size, Agilent Technologies, USA). Two mobile phases were used: A-0.1% formic acid in water and B-90% of acetonitrile in water, at a flow rate of 500 µL min⁻¹. The LC conditions were maintained at 5% at 0–3 min in B, a linear increase from 5 to 20% between 3 and 25 min, 20 to 40% during 25–40 min, and from 40 to 50% between 40 and 55 min, finally, it reached 50 to 95% at 55–63 min. The peak detection was performed through direct injection mode with an Electron Spray Ionization (ESI) probe, both positive and negative modes. The non-volatile nature of bioactive compounds was identified by obtaining the molecular mass and structural formula of compounds with the help of online libraries.</p>", "<title>Statistical analysis</title>", "<p id=\"Par27\">All the experiments were performed based on RSM’s CCD and repeated three times. Design expert software (trial version 8.0.7.1, Stat-Ease, Inc., 2021 East Hennepin Ave, Suite 480, Minneapolis, MN 55413, USA) used for the experimental design, optimization, data analysis, prediction, and quadratic model building. In regression model, the goodness of fit was evaluated based on the R² (coefficients of determination). Further, the statistical analysis was assessed by one-way analysis of variance (ANOVA), with <italic>p</italic>-values less than 0.05 considered significant. The optimal extraction conditions were analysed by contour plots and three-dimensional (3D) response surface plots. Microsoft Excel (Microsoft Office Professional Plus 2021) was used for statistical analysis and the Adaptive neuro-fuzzy logic toolbox in the MATLAB (Mathematical Laboratory) v R2013b software.</p>", "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-49839-y.</p>", "<title>Acknowledgements</title>", "<p>The authors are grateful to the managements of Kalasalingam Academy of Research and Education, Vellore Institute of Technology, M.S. Ramaiah Institute of Applied Sciences, and Swamy Vivekanandha College of Pharmacy for the research facilities and financial aids.</p>", "<title>Author contributions</title>", "<p>The project was led by S.K., L.K.R., S.K. (3rd author), P.P., T.P. and P.P. (6th author). S.K., P.P. (6th author) took care of the data curation. The training pipeline was built by L.K.R., S.K. (3rd author), S.K., P.P. (6th author) handled model training and hyperparameter search. The present paper was written by S.K. and P.P. (6th author).</p>", "<title>Data availability</title>", "<p>All data generated or analysed during this study are included in this published article [and its Supplementary Information files].</p>", "<title>Competing interests</title>", "<p id=\"Par42\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>The architecture of the ANFIS input and output response model.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Normal percentage probability plot for the studentized residuals for highest yield of TPC (<bold>a</bold>), and TFC (<bold>e</bold>). Relationship between experimental and predicted value for highest yield of TPC (<bold>b</bold>), and TFC (<bold>f</bold>), Response surface and contour plot showing the combined effects of methanol concentration (<italic>X</italic>₁) and temperature (<italic>X</italic>₂) for highest yield of TPC, and TFC, when time and particle size were held at fixed level (<bold>c,g,d,h</bold>), respectively.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Normal percentage probability plot for the studentized residuals for highest yield of %DPPHsc (<bold>a</bold>), %ABTSsc (<bold>e</bold>) and FRAP (<bold>i</bold>). Relationship between experimental and predicted value for highest yield of %DPPHsc (<bold>b</bold>), %ABTSsc (<bold>f</bold>) and FRAP (<bold>j</bold>). Response surface and contour plot showing the combined effects of methanol concentration (<italic>X</italic>₁) and temperature (<italic>X</italic>₂) for highest yield of %DPPHsc, %ABTSsc and FRAP when time and particle size were held at fixed level (<bold>c,g,k,d,h,l</bold>), respectively.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Machine learning algorithm validated the experimental and predicted values.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>ANFIS rule viewer for the effect of extraction parameters on responses for extraction of TPC, TFC and antioxidants from grape seeds extract.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>GC–MS spectra of optimally optimized extract of grape seeds. List of bioactive phytocompounds presence in the optimally obtained extract.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Preliminary selection of appropriate extraction solvent.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Solvents</th><th align=\"left\">TPC* in mg GAE/g</th><th align=\"left\">TFC* in mg RE/g</th><th align=\"left\">%DPPHsc*</th></tr></thead><tbody><tr><td align=\"left\">Ethanol</td><td char=\"±\" align=\"char\">543.36 ± 2.57</td><td char=\"±\" align=\"char\">348.64 ± 2.5</td><td char=\"±\" align=\"char\">65.34 ± 1.04</td></tr><tr><td align=\"left\">Methanol</td><td char=\"±\" align=\"char\">548.52 ± 7.15</td><td char=\"±\" align=\"char\">354.28 ± 2.85</td><td char=\"±\" align=\"char\">67.28 ± 1.95</td></tr><tr><td align=\"left\">Chloroform</td><td char=\"±\" align=\"char\">474.72 ± 4.05</td><td char=\"±\" align=\"char\">301.43 ± 1.04</td><td char=\"±\" align=\"char\">53.34 ± 1.17</td></tr><tr><td align=\"left\">Petroleum ether</td><td char=\"±\" align=\"char\">523.56 ± 1.19</td><td char=\"±\" align=\"char\">335.72 ± 2.16</td><td char=\"±\" align=\"char\">58.43 ± 0.76</td></tr><tr><td align=\"left\">Ethyl acetate</td><td char=\"±\" align=\"char\">518.34 ± 1.77</td><td char=\"±\" align=\"char\">321.26 ± 3.68</td><td char=\"±\" align=\"char\">55.76 ± 0.51</td></tr><tr><td align=\"left\">Diethyl ether</td><td char=\"±\" align=\"char\">528.35 ± 2.65</td><td char=\"±\" align=\"char\">338.39 ± 1.95</td><td char=\"±\" align=\"char\">59.53 ± 1.14</td></tr><tr><td align=\"left\">Acetone</td><td char=\"±\" align=\"char\">504.2 ± 2.04</td><td char=\"±\" align=\"char\">307.32 ± 0.72</td><td char=\"±\" align=\"char\">52.38 ± 1.07</td></tr><tr><td align=\"left\"><italic>n</italic>-Hexane</td><td char=\"±\" align=\"char\">472.23 ± 2.08</td><td char=\"±\" align=\"char\">303.85 ± 1.17</td><td char=\"±\" align=\"char\">51.56 ± 1.06</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Central composite design (CCD) with experimental responses and predicted responses.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">S.No</th><th align=\"left\" colspan=\"5\">Parameters</th><th align=\"left\" colspan=\"5\">Experimental value*</th><th align=\"left\" colspan=\"5\">RSM prediction</th><th align=\"left\" colspan=\"5\">ANFIS prediction</th><th align=\"left\" colspan=\"5\">Machine learning algorithm prediction</th></tr><tr><th align=\"left\"><italic>X</italic>₁</th><th align=\"left\"><italic>X</italic>₂</th><th align=\"left\"><italic>X</italic>₃</th><th align=\"left\"><italic>X</italic>₄</th><th align=\"left\"><italic>X</italic>₅</th><th align=\"left\">y₁</th><th align=\"left\">y₂</th><th align=\"left\">y₃</th><th align=\"left\">y₄</th><th align=\"left\">y₅</th><th align=\"left\">y₁</th><th align=\"left\">y₂</th><th align=\"left\">y₃</th><th align=\"left\">y₄</th><th align=\"left\">y₅</th><th align=\"left\">y₁</th><th align=\"left\">y₂</th><th align=\"left\">y₃</th><th align=\"left\">y₄</th><th align=\"left\">y₅</th><th align=\"left\">y₁</th><th align=\"left\">y₂</th><th align=\"left\">y₃</th><th align=\"left\">y₄</th><th align=\"left\">y₅</th></tr></thead><tbody><tr><td align=\"left\">1</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">432.26</td><td char=\".\" align=\"char\">312.34</td><td char=\".\" align=\"char\">62.65</td><td char=\".\" align=\"char\">59.45</td><td char=\".\" align=\"char\">54.67</td><td char=\".\" align=\"char\">432.03</td><td align=\"left\">298.47</td><td align=\"left\">62.04</td><td char=\".\" align=\"char\">58.87</td><td char=\".\" align=\"char\">53.90</td><td align=\"left\">432</td><td align=\"left\">312</td><td align=\"left\">62.7</td><td align=\"left\">59.5</td><td char=\".\" align=\"char\">54.7</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">2</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">462.56</td><td char=\".\" align=\"char\">325.58</td><td char=\".\" align=\"char\">65.43</td><td char=\".\" align=\"char\">61.92</td><td char=\".\" align=\"char\">56.58</td><td char=\".\" align=\"char\">447.98</td><td align=\"left\">309.29</td><td align=\"left\">62.20</td><td char=\".\" align=\"char\">58.14</td><td char=\".\" align=\"char\">53.02</td><td align=\"left\">463</td><td align=\"left\">326</td><td align=\"left\">65.4</td><td align=\"left\">61.9</td><td char=\".\" align=\"char\">56.6</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">3</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">599.06</td><td char=\".\" align=\"char\">391.56</td><td char=\".\" align=\"char\">72.34</td><td char=\".\" align=\"char\">66.45</td><td char=\".\" align=\"char\">61.06</td><td char=\".\" align=\"char\">600.04</td><td align=\"left\">382.65</td><td align=\"left\">73.64</td><td char=\".\" align=\"char\">67.52</td><td char=\".\" align=\"char\">62.77</td><td align=\"left\">599</td><td align=\"left\">392</td><td align=\"left\">72.3</td><td align=\"left\">66.4</td><td char=\".\" align=\"char\">61.1</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">4</td><td align=\"left\">0.155</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">670.32</td><td char=\".\" align=\"char\">451.45</td><td char=\".\" align=\"char\">81.23</td><td char=\".\" align=\"char\">77.39</td><td char=\".\" align=\"char\">71.55</td><td char=\".\" align=\"char\">739.73</td><td align=\"left\">466.89</td><td align=\"left\">83.08</td><td char=\".\" align=\"char\">77.92</td><td char=\".\" align=\"char\">72.81</td><td align=\"left\">670</td><td align=\"left\">451</td><td align=\"left\">81.2</td><td align=\"left\">77.4</td><td char=\".\" align=\"char\">71.6</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">5</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">562.56</td><td char=\".\" align=\"char\">353.03</td><td char=\".\" align=\"char\">68.03</td><td char=\".\" align=\"char\">65.4</td><td char=\".\" align=\"char\">60.48</td><td char=\".\" align=\"char\">511.45</td><td align=\"left\">336.76</td><td align=\"left\">66.65</td><td char=\".\" align=\"char\">62.19</td><td char=\".\" align=\"char\">57.47</td><td align=\"left\">563</td><td align=\"left\">353</td><td align=\"left\">68</td><td align=\"left\">65.4</td><td char=\".\" align=\"char\">60.5</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">6</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">653.28</td><td char=\".\" align=\"char\">403.06</td><td char=\".\" align=\"char\">76.27</td><td char=\".\" align=\"char\">72.04</td><td char=\".\" align=\"char\">68.76</td><td char=\".\" align=\"char\">616.82</td><td align=\"left\">393.6</td><td align=\"left\">75.529</td><td char=\".\" align=\"char\">71.296</td><td char=\".\" align=\"char\">66.94</td><td align=\"left\">653</td><td align=\"left\">403</td><td align=\"left\">76.3</td><td align=\"left\">72</td><td char=\".\" align=\"char\">68.8</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">7</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">28.11</td><td align=\"left\">70</td><td char=\".\" align=\"char\">498.34</td><td char=\".\" align=\"char\">334.56</td><td char=\".\" align=\"char\">67.83</td><td char=\".\" align=\"char\">63.45</td><td char=\".\" align=\"char\">57.46</td><td char=\".\" align=\"char\">495.19</td><td align=\"left\">328.22</td><td align=\"left\">64.787</td><td char=\".\" align=\"char\">59.87</td><td char=\".\" align=\"char\">54.62</td><td align=\"left\">498</td><td align=\"left\">335</td><td align=\"left\">67.8</td><td align=\"left\">63.5</td><td char=\".\" align=\"char\">57.5</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">8</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">427.56</td><td char=\".\" align=\"char\">319.48</td><td char=\".\" align=\"char\">65.84</td><td char=\".\" align=\"char\">61.5</td><td char=\".\" align=\"char\">57.36</td><td char=\".\" align=\"char\">449.98</td><td align=\"left\">314.75</td><td align=\"left\">64.64</td><td char=\".\" align=\"char\">61.48</td><td char=\".\" align=\"char\">57.24</td><td align=\"left\">428</td><td align=\"left\">319</td><td align=\"left\">65.8</td><td align=\"left\">61.3</td><td char=\".\" align=\"char\">57.4</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">9</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">431.67</td><td char=\".\" align=\"char\">320.25</td><td char=\".\" align=\"char\">65.82</td><td char=\".\" align=\"char\">62.87</td><td char=\".\" align=\"char\">58.26</td><td char=\".\" align=\"char\">432.81</td><td align=\"left\">291.18</td><td align=\"left\">61.55</td><td char=\".\" align=\"char\">56.50</td><td char=\".\" align=\"char\">52.15</td><td align=\"left\">432</td><td align=\"left\">320</td><td align=\"left\">65.8</td><td align=\"left\">62.9</td><td char=\".\" align=\"char\">58.3</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.03</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">10</td><td align=\"left\">0.75</td><td align=\"left\">76.89</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">513.63</td><td char=\".\" align=\"char\">367.58</td><td char=\".\" align=\"char\">66.61</td><td char=\".\" align=\"char\">63.65</td><td char=\".\" align=\"char\">59.34</td><td char=\".\" align=\"char\">552.59</td><td align=\"left\">364.22</td><td align=\"left\">66. 4</td><td char=\".\" align=\"char\">63.330</td><td char=\".\" align=\"char\">59.21</td><td align=\"left\">514</td><td align=\"left\">368</td><td align=\"left\">66.6</td><td align=\"left\">63.7</td><td char=\".\" align=\"char\">59.3</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">11</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">423.78</td><td char=\".\" align=\"char\">321.25</td><td char=\".\" align=\"char\">61.64</td><td char=\".\" align=\"char\">57.72</td><td char=\".\" align=\"char\">52.08</td><td char=\".\" align=\"char\">458.15</td><td align=\"left\">311.1</td><td align=\"left\">60.17</td><td char=\".\" align=\"char\">55.92</td><td char=\".\" align=\"char\">51.12</td><td align=\"left\">424</td><td align=\"left\">321</td><td align=\"left\">61.6</td><td align=\"left\">57.7</td><td char=\".\" align=\"char\">52.1</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">12</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">659.43</td><td char=\".\" align=\"char\">413.76</td><td char=\".\" align=\"char\">77.59</td><td char=\".\" align=\"char\">73.04</td><td char=\".\" align=\"char\">68.56</td><td char=\".\" align=\"char\">629.26</td><td align=\"left\">401.48</td><td align=\"left\">78.11</td><td char=\".\" align=\"char\">73.21</td><td char=\".\" align=\"char\">68.54</td><td align=\"left\">659</td><td align=\"left\">414</td><td align=\"left\">77.6</td><td align=\"left\">73</td><td char=\".\" align=\"char\">68.6</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">13</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">642.57</td><td char=\".\" align=\"char\">396.56</td><td char=\".\" align=\"char\">76.06</td><td char=\".\" align=\"char\">71.43</td><td char=\".\" align=\"char\">65.33</td><td char=\".\" align=\"char\">647.3</td><td align=\"left\">399.68</td><td align=\"left\">73.18</td><td char=\".\" align=\"char\">69.23</td><td char=\".\" align=\"char\">63.91</td><td align=\"left\">643</td><td align=\"left\">397</td><td align=\"left\">76.1</td><td align=\"left\">71.4</td><td char=\".\" align=\"char\">65.3</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.03</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">14</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">660.12</td><td char=\".\" align=\"char\">422.6</td><td char=\".\" align=\"char\">63.45</td><td char=\".\" align=\"char\">59.93</td><td char=\".\" align=\"char\">55.52</td><td char=\".\" align=\"char\">629.26</td><td align=\"left\">401.58</td><td align=\"left\">66.50</td><td char=\".\" align=\"char\">62.43</td><td char=\".\" align=\"char\">57.43</td><td align=\"left\">660</td><td align=\"left\">423</td><td align=\"left\">63.5</td><td align=\"left\">59.9</td><td char=\".\" align=\"char\">55.6</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">15</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">414.56</td><td char=\".\" align=\"char\">299.39</td><td char=\".\" align=\"char\">52.02</td><td char=\".\" align=\"char\">48.93</td><td char=\".\" align=\"char\">43.78</td><td char=\".\" align=\"char\">408.63</td><td align=\"left\">284.88</td><td align=\"left\">55.78</td><td char=\".\" align=\"char\">51.62</td><td char=\".\" align=\"char\">47.28</td><td align=\"left\">415</td><td align=\"left\">299</td><td align=\"left\">52</td><td align=\"left\">48.9</td><td char=\".\" align=\"char\">43.8</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.03</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">16</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">398.76</td><td char=\".\" align=\"char\">286.48</td><td char=\".\" align=\"char\">51.72</td><td char=\".\" align=\"char\">46.67</td><td char=\".\" align=\"char\">41.37</td><td char=\".\" align=\"char\">420.15</td><td align=\"left\">291.17</td><td align=\"left\">56.39</td><td char=\".\" align=\"char\">52.79</td><td char=\".\" align=\"char\">47.56</td><td align=\"left\">399</td><td align=\"left\">286</td><td align=\"left\">51.7</td><td align=\"left\">46.7</td><td char=\".\" align=\"char\">41.4</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">17</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">656.45</td><td char=\".\" align=\"char\">412.92</td><td char=\".\" align=\"char\">77.54</td><td char=\".\" align=\"char\">73.85</td><td char=\".\" align=\"char\">68.67</td><td char=\".\" align=\"char\">619.4</td><td align=\"left\">400.83</td><td align=\"left\">75.90</td><td char=\".\" align=\"char\">72.02</td><td char=\".\" align=\"char\">67.17</td><td align=\"left\">656</td><td align=\"left\">413</td><td align=\"left\">77.5</td><td align=\"left\">73.9</td><td char=\".\" align=\"char\">68.7</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">18</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">51.89</td><td align=\"left\">70</td><td char=\".\" align=\"char\">556.34</td><td char=\".\" align=\"char\">366.45</td><td char=\".\" align=\"char\">69.6</td><td char=\".\" align=\"char\">65.73</td><td char=\".\" align=\"char\">61.32</td><td char=\".\" align=\"char\">553.18</td><td align=\"left\">366.19</td><td align=\"left\">69.89</td><td char=\".\" align=\"char\">65.54</td><td char=\".\" align=\"char\">60.56</td><td align=\"left\">556</td><td align=\"left\">366</td><td align=\"left\">69.6</td><td align=\"left\">65.7</td><td char=\".\" align=\"char\">56.1</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">19</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">482.67</td><td char=\".\" align=\"char\">325.67</td><td char=\".\" align=\"char\">72.74</td><td char=\".\" align=\"char\">68.63</td><td char=\".\" align=\"char\">63.65</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">20</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">34.89</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">536.32</td><td char=\".\" align=\"char\">367.34</td><td char=\".\" align=\"char\">69.43</td><td char=\".\" align=\"char\">65.91</td><td char=\".\" align=\"char\">61.27</td><td char=\".\" align=\"char\">559.71</td><td align=\"left\">360</td><td align=\"left\">66.64</td><td char=\".\" align=\"char\">63.10</td><td char=\".\" align=\"char\">58.07</td><td align=\"left\">536</td><td align=\"left\">367</td><td align=\"left\">69.4</td><td align=\"left\">65.9</td><td char=\".\" align=\"char\">61.3</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">21</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">404.45</td><td char=\".\" align=\"char\">278.31</td><td char=\".\" align=\"char\">56.71</td><td char=\".\" align=\"char\">51.76</td><td char=\".\" align=\"char\">46.64</td><td char=\".\" align=\"char\">447.98</td><td align=\"left\">309.3</td><td align=\"left\">62.20</td><td char=\".\" align=\"char\">58.14</td><td char=\".\" align=\"char\">53.02</td><td align=\"left\">404</td><td align=\"left\">278</td><td align=\"left\">56.7</td><td align=\"left\">51.8</td><td char=\".\" align=\"char\">46.6</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">22</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">395.67</td><td char=\".\" align=\"char\">264.37</td><td char=\".\" align=\"char\">53.56</td><td char=\".\" align=\"char\">47.62</td><td char=\".\" align=\"char\">42.27</td><td char=\".\" align=\"char\">403.45</td><td align=\"left\">277.84</td><td align=\"left\">54.12</td><td char=\".\" align=\"char\">49.77</td><td char=\".\" align=\"char\">44.72</td><td align=\"left\">396</td><td align=\"left\">264</td><td align=\"left\">53.6</td><td align=\"left\">47.7</td><td char=\".\" align=\"char\">42.3</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">23</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">481.36</td><td char=\".\" align=\"char\">326.54</td><td char=\".\" align=\"char\">74.75</td><td char=\".\" align=\"char\">70.74</td><td char=\".\" align=\"char\">64.18</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">24</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">654.34</td><td char=\".\" align=\"char\">432.64</td><td char=\".\" align=\"char\">78.56</td><td char=\".\" align=\"char\">74.74</td><td char=\".\" align=\"char\">70.46</td><td char=\".\" align=\"char\">626.1</td><td align=\"left\">412.88</td><td align=\"left\">72.99</td><td char=\".\" align=\"char\">69.27</td><td char=\".\" align=\"char\">64.96</td><td align=\"left\">654</td><td align=\"left\">433</td><td align=\"left\">78.6</td><td align=\"left\">74.7</td><td char=\".\" align=\"char\">70.5</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">25</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">422.53</td><td char=\".\" align=\"char\">293.08</td><td char=\".\" align=\"char\">58.93</td><td char=\".\" align=\"char\">53.41</td><td char=\".\" align=\"char\">48.45</td><td char=\".\" align=\"char\">419.15</td><td align=\"left\">276.39</td><td align=\"left\">57.47</td><td char=\".\" align=\"char\">52.18</td><td char=\".\" align=\"char\">47.54</td><td align=\"left\">423</td><td align=\"left\">293</td><td align=\"left\">58.9</td><td align=\"left\">53.4</td><td char=\".\" align=\"char\">48.4</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.03</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">26</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">81.892</td><td char=\".\" align=\"char\">602.37</td><td char=\".\" align=\"char\">399.45</td><td char=\".\" align=\"char\">73.72</td><td char=\".\" align=\"char\">69.86</td><td char=\".\" align=\"char\">65.78</td><td char=\".\" align=\"char\">573.3</td><td align=\"left\">379.18</td><td align=\"left\">69.72</td><td char=\".\" align=\"char\">65.10</td><td char=\".\" align=\"char\">60.9</td><td align=\"left\">602</td><td align=\"left\">399</td><td align=\"left\">73.7</td><td align=\"left\">69.9</td><td char=\".\" align=\"char\">65.8</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.91</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">27</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">11.11</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">574.32</td><td char=\".\" align=\"char\">348.52</td><td char=\".\" align=\"char\">68.56</td><td char=\".\" align=\"char\">65.82</td><td char=\".\" align=\"char\">60.43</td><td char=\".\" align=\"char\">544.66</td><td align=\"left\">349.29</td><td align=\"left\">68.60</td><td char=\".\" align=\"char\">64.88</td><td char=\".\" align=\"char\">60.04</td><td align=\"left\">574</td><td align=\"left\">349</td><td align=\"left\">68.6</td><td align=\"left\">65.8</td><td char=\".\" align=\"char\">60.4</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">28</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">484.65</td><td char=\".\" align=\"char\">324.07</td><td char=\".\" align=\"char\">71.85</td><td char=\".\" align=\"char\">64.74</td><td char=\".\" align=\"char\">59.78</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">29</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">562.12</td><td char=\".\" align=\"char\">371.74</td><td char=\".\" align=\"char\">73.54</td><td char=\".\" align=\"char\">67.84</td><td char=\".\" align=\"char\">63.28</td><td char=\".\" align=\"char\">575.57</td><td align=\"left\">376.85</td><td align=\"left\">70.90</td><td char=\".\" align=\"char\">66.44</td><td char=\".\" align=\"char\">61.67</td><td align=\"left\">562</td><td align=\"left\">372</td><td align=\"left\">73.5</td><td align=\"left\">67.8</td><td char=\".\" align=\"char\">63.3</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">30</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">485.34</td><td char=\".\" align=\"char\">325.94</td><td char=\".\" align=\"char\">69.93</td><td char=\".\" align=\"char\">65.34</td><td char=\".\" align=\"char\">62.54</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">31</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">660.12</td><td char=\".\" align=\"char\">418.6</td><td char=\".\" align=\"char\">79.45</td><td char=\".\" align=\"char\">74.93</td><td char=\".\" align=\"char\">70.52</td><td char=\".\" align=\"char\">624.86</td><td align=\"left\">406.96</td><td align=\"left\">76.26</td><td char=\".\" align=\"char\">71.99</td><td char=\".\" align=\"char\">67.21</td><td align=\"left\">660</td><td align=\"left\">419</td><td align=\"left\">79.4</td><td align=\"left\">74.9</td><td char=\".\" align=\"char\">70.5</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">32</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">641.32</td><td char=\".\" align=\"char\">401.83</td><td char=\".\" align=\"char\">75.34</td><td char=\".\" align=\"char\">73.32</td><td char=\".\" align=\"char\">68.56</td><td char=\".\" align=\"char\">627.62</td><td align=\"left\">405.62</td><td align=\"left\">76.03</td><td char=\".\" align=\"char\">72.93</td><td char=\".\" align=\"char\">68.37</td><td align=\"left\">641</td><td align=\"left\">402</td><td align=\"left\">75.3</td><td align=\"left\">73.3</td><td char=\".\" align=\"char\">68.6</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">33</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">633.35</td><td char=\".\" align=\"char\">401.162</td><td char=\".\" align=\"char\">72.23</td><td char=\".\" align=\"char\">70.89</td><td char=\".\" align=\"char\">66.28</td><td char=\".\" align=\"char\">616.9</td><td align=\"left\">406.52</td><td align=\"left\">77.16</td><td char=\".\" align=\"char\">74.04</td><td char=\".\" align=\"char\">69.19</td><td align=\"left\">633</td><td align=\"left\">401</td><td align=\"left\">72.2</td><td align=\"left\">70.9</td><td char=\".\" align=\"char\">66.3</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">34</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">65</td><td char=\".\" align=\"char\">421.65</td><td char=\".\" align=\"char\">274.92</td><td char=\".\" align=\"char\">55.63</td><td char=\".\" align=\"char\">51.62</td><td char=\".\" align=\"char\">47.31</td><td char=\".\" align=\"char\">437.91</td><td align=\"left\">299.48</td><td align=\"left\">60.36</td><td char=\".\" align=\"char\">55.51</td><td char=\".\" align=\"char\">51.13</td><td align=\"left\">422</td><td align=\"left\">275</td><td align=\"left\">55.6</td><td align=\"left\">51.6</td><td char=\".\" align=\"char\">47.3</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">35</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">636.45</td><td char=\".\" align=\"char\">392.43</td><td char=\".\" align=\"char\">74.98</td><td char=\".\" align=\"char\">67.56</td><td char=\".\" align=\"char\">63.45</td><td char=\".\" align=\"char\">660.13</td><td align=\"left\">403.42</td><td align=\"left\">78.5</td><td char=\".\" align=\"char\">72.92</td><td char=\".\" align=\"char\">67.96</td><td align=\"left\">636</td><td align=\"left\">392</td><td align=\"left\">75</td><td align=\"left\">67.6</td><td char=\".\" align=\"char\">63.5</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">36</td><td align=\"left\">0.75</td><td align=\"left\">53.11</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">586.05</td><td char=\".\" align=\"char\">348.65</td><td char=\".\" align=\"char\">64.76</td><td char=\".\" align=\"char\">61.43</td><td char=\".\" align=\"char\">56.34</td><td char=\".\" align=\"char\">540.82</td><td align=\"left\">345.43</td><td align=\"left\">62.22</td><td char=\".\" align=\"char\">57.88</td><td char=\".\" align=\"char\">52.87</td><td align=\"left\">586</td><td align=\"left\">349</td><td align=\"left\">64.8</td><td align=\"left\">61.4</td><td char=\".\" align=\"char\">56.3</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">37</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">418.9</td><td char=\".\" align=\"char\">268.06</td><td char=\".\" align=\"char\">53.78</td><td char=\".\" align=\"char\">48.04</td><td char=\".\" align=\"char\">44.36</td><td char=\".\" align=\"char\">427.11</td><td align=\"left\">291.69</td><td align=\"left\">58.33</td><td char=\".\" align=\"char\">53.76</td><td char=\".\" align=\"char\">50.01</td><td align=\"left\">419</td><td align=\"left\">268</td><td align=\"left\">53.8</td><td align=\"left\">48</td><td char=\".\" align=\"char\">44.4</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">38</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">485.76</td><td char=\".\" align=\"char\">323.54</td><td char=\".\" align=\"char\">75.89</td><td char=\".\" align=\"char\">70.05</td><td char=\".\" align=\"char\">66.88</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">39</td><td align=\"left\">0.5</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">645.34</td><td char=\".\" align=\"char\">404.72</td><td char=\".\" align=\"char\">77.84</td><td char=\".\" align=\"char\">69.42</td><td char=\".\" align=\"char\">65.24</td><td char=\".\" align=\"char\">666.48</td><td align=\"left\">431.18</td><td align=\"left\">80.95</td><td char=\".\" align=\"char\">76.42</td><td char=\".\" align=\"char\">72.43</td><td align=\"left\">645</td><td align=\"left\">405</td><td align=\"left\">77.8</td><td align=\"left\">69.4</td><td char=\".\" align=\"char\">65.2</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">40</td><td align=\"left\">1</td><td align=\"left\">70</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">423.76</td><td char=\".\" align=\"char\">278.43</td><td char=\".\" align=\"char\">55.58</td><td char=\".\" align=\"char\">51.56</td><td char=\".\" align=\"char\">46.65</td><td char=\".\" align=\"char\">449.81</td><td align=\"left\">301.07</td><td align=\"left\">57.05</td><td char=\".\" align=\"char\">53.74</td><td char=\".\" align=\"char\">48.43</td><td align=\"left\">424</td><td align=\"left\">278</td><td align=\"left\">55.6</td><td align=\"left\">51.6</td><td char=\".\" align=\"char\">46.7</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.03</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">41</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">483.72</td><td char=\".\" align=\"char\">324.65</td><td char=\".\" align=\"char\">72.86</td><td char=\".\" align=\"char\">66.83</td><td char=\".\" align=\"char\">62.41</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.03</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">42</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">638.34</td><td char=\".\" align=\"char\">401.61</td><td char=\".\" align=\"char\">76.45</td><td char=\".\" align=\"char\">69.49</td><td char=\".\" align=\"char\">65.56</td><td char=\".\" align=\"char\">630.09</td><td align=\"left\">391.51</td><td align=\"left\">75.03</td><td char=\".\" align=\"char\">68.95</td><td char=\".\" align=\"char\">64.16</td><td align=\"left\">638</td><td align=\"left\">402</td><td align=\"left\">76.4</td><td align=\"left\">69.5</td><td char=\".\" align=\"char\">65.6</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.82</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">43</td><td align=\"left\">1.35</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">360.76</td><td char=\".\" align=\"char\">243.17</td><td char=\".\" align=\"char\">50.51</td><td char=\".\" align=\"char\">45.76</td><td char=\".\" align=\"char\">41.07</td><td char=\".\" align=\"char\">286.35</td><td align=\"left\">221.78</td><td align=\"left\">46.18</td><td char=\".\" align=\"char\">41.73</td><td char=\".\" align=\"char\">36.48</td><td align=\"left\">361</td><td align=\"left\">243</td><td align=\"left\">50.5</td><td align=\"left\">45.8</td><td char=\".\" align=\"char\">41.1</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">44</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">58.11</td><td char=\".\" align=\"char\">534.63</td><td char=\".\" align=\"char\">345.92</td><td char=\".\" align=\"char\">66.76</td><td char=\".\" align=\"char\">62.56</td><td char=\".\" align=\"char\">58.26</td><td char=\".\" align=\"char\">557.44</td><td align=\"left\">359.62</td><td align=\"left\">68.01</td><td char=\".\" align=\"char\">63.56</td><td char=\".\" align=\"char\">59.54</td><td align=\"left\">535</td><td align=\"left\">346</td><td align=\"left\">66.8</td><td align=\"left\">62.6</td><td char=\".\" align=\"char\">58.3</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">45</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">485.65</td><td char=\".\" align=\"char\">325.73</td><td char=\".\" align=\"char\">71.03</td><td char=\".\" align=\"char\">68.45</td><td char=\".\" align=\"char\">64.07</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">572.68</td><td char=\".\" align=\"char\">346.90</td><td char=\".\" align=\"char\">66.05</td><td char=\".\" align=\"char\">62.83</td><td char=\".\" align=\"char\">57.70</td></tr><tr><td align=\"left\">46</td><td align=\"left\">0.75</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">484.38</td><td char=\".\" align=\"char\">324.23</td><td char=\".\" align=\"char\">70.98</td><td char=\".\" align=\"char\">65.43</td><td char=\".\" align=\"char\">61.68</td><td char=\".\" align=\"char\">483.67</td><td align=\"left\">324.5</td><td align=\"left\">72.28</td><td char=\".\" align=\"char\">67.22</td><td char=\".\" align=\"char\">62.85</td><td align=\"left\">484</td><td align=\"left\">325</td><td align=\"left\">72.5</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">63.1</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.02</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">47</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">396.06</td><td char=\".\" align=\"char\">256.34</td><td char=\".\" align=\"char\">54.76</td><td char=\".\" align=\"char\">50.56</td><td char=\".\" align=\"char\">45.56</td><td char=\".\" align=\"char\">522.2</td><td align=\"left\">334.46</td><td align=\"left\">67.52</td><td char=\".\" align=\"char\">62.47</td><td char=\".\" align=\"char\">57.34</td><td align=\"left\">396</td><td align=\"left\">256</td><td align=\"left\">54.8</td><td align=\"left\">50.6</td><td char=\".\" align=\"char\">45.6</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr><tr><td align=\"left\">48</td><td align=\"left\">1</td><td align=\"left\">60</td><td align=\"left\">18</td><td align=\"left\">35</td><td align=\"left\">75</td><td char=\".\" align=\"char\">380.76</td><td char=\".\" align=\"char\">268.04</td><td char=\".\" align=\"char\">52.56</td><td char=\".\" align=\"char\">47.58</td><td char=\".\" align=\"char\">43.34</td><td char=\".\" align=\"char\">497.88</td><td align=\"left\">332.57</td><td align=\"left\">65.7</td><td char=\".\" align=\"char\">60.41</td><td char=\".\" align=\"char\">55.77</td><td align=\"left\">381</td><td align=\"left\">268</td><td align=\"left\">52.6</td><td align=\"left\">47.6</td><td char=\".\" align=\"char\">43.3</td><td char=\".\" align=\"char\">417.93</td><td char=\".\" align=\"char\">301.02</td><td char=\".\" align=\"char\">61.55</td><td char=\".\" align=\"char\">57.98</td><td char=\".\" align=\"char\">53.38</td></tr><tr><td align=\"left\">49</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">45</td><td align=\"left\">75</td><td char=\".\" align=\"char\">642.82</td><td char=\".\" align=\"char\">402.63</td><td char=\".\" align=\"char\">73.67</td><td char=\".\" align=\"char\">69.67</td><td char=\".\" align=\"char\">65.34</td><td char=\".\" align=\"char\">650.8</td><td align=\"left\">415.85</td><td align=\"left\">74.23</td><td char=\".\" align=\"char\">69.04</td><td char=\".\" align=\"char\">64.97</td><td align=\"left\">643</td><td align=\"left\">403</td><td align=\"left\">73.7</td><td align=\"left\">69.7</td><td char=\".\" align=\"char\">65.3</td><td char=\".\" align=\"char\">643.54</td><td char=\".\" align=\"char\">411.64</td><td char=\".\" align=\"char\">76.84</td><td char=\".\" align=\"char\">71.12</td><td char=\".\" align=\"char\">66.30</td></tr><tr><td align=\"left\">50</td><td align=\"left\">0.5</td><td align=\"left\">60</td><td align=\"left\">28</td><td align=\"left\">35</td><td align=\"left\">65</td><td char=\".\" align=\"char\">636.42</td><td char=\".\" align=\"char\">393.95</td><td char=\".\" align=\"char\">74.76</td><td char=\".\" align=\"char\">68.72</td><td char=\".\" align=\"char\">63.34</td><td char=\".\" align=\"char\">646.2</td><td align=\"left\">405.29</td><td align=\"left\">75.24</td><td char=\".\" align=\"char\">70.51</td><td char=\".\" align=\"char\">65.12</td><td align=\"left\">636</td><td align=\"left\">394</td><td align=\"left\">74.8</td><td align=\"left\">68.7</td><td char=\".\" align=\"char\">63.3</td><td char=\".\" align=\"char\">631.10</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">68.02</td><td char=\".\" align=\"char\">63.66</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Analysis of variance (ANOVA) for the quadratic polynomial mode.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Source</th><th align=\"left\">Sum of squares</th><th align=\"left\">df^a</th><th align=\"left\">Mean square</th><th align=\"left\">F-value^b</th><th align=\"left\">p-value^c</th></tr></thead><tbody><tr><td align=\"left\" colspan=\"6\">TPC (y₁)^d</td></tr><tr><td align=\"left\"> Model</td><td align=\"left\">439,900</td><td char=\".\" align=\"char\">20</td><td align=\"left\">21,993.66</td><td char=\".\" align=\"char\">18.49</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₁</td><td align=\"left\">395,800</td><td char=\".\" align=\"char\">1</td><td align=\"left\">3.96E+05</td><td char=\".\" align=\"char\">332.8</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₂</td><td align=\"left\">270.07</td><td char=\".\" align=\"char\">1</td><td align=\"left\">270.07</td><td char=\".\" align=\"char\">0.2271</td><td char=\".\" align=\"char\">0.6373</td></tr><tr><td align=\"left\"> <italic>X</italic>₃</td><td align=\"left\">440.06</td><td char=\".\" align=\"char\">1</td><td align=\"left\">440.06</td><td char=\".\" align=\"char\">0.37</td><td char=\".\" align=\"char\">0.5477</td></tr><tr><td align=\"left\"> <italic>X</italic>₄</td><td align=\"left\">6447.81</td><td char=\".\" align=\"char\">1</td><td align=\"left\">6447.81</td><td char=\".\" align=\"char\">5.42</td><td char=\".\" align=\"char\">0.0271</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>5</italic>}</td><td align=\"left\">489.66</td><td char=\".\" align=\"char\">1</td><td align=\"left\">489.66</td><td char=\".\" align=\"char\">0.4118</td><td char=\".\" align=\"char\">0.5261</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₂</td><td align=\"left\">2830.15</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2830.15</td><td char=\".\" align=\"char\">2.38</td><td char=\".\" align=\"char\">0.1337</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₃</td><td align=\"left\">222.29</td><td char=\".\" align=\"char\">1</td><td align=\"left\">222.29</td><td char=\".\" align=\"char\">0.1869</td><td char=\".\" align=\"char\">0.6687</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₄</td><td align=\"left\">290.77</td><td char=\".\" align=\"char\">1</td><td align=\"left\">290.77</td><td char=\".\" align=\"char\">0.2445</td><td char=\".\" align=\"char\">0.6247</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X5</italic></td><td align=\"left\">2198.84</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2198.84</td><td char=\".\" align=\"char\">1.85</td><td char=\".\" align=\"char\">0.1844</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₃</td><td align=\"left\">545</td><td char=\".\" align=\"char\">1</td><td align=\"left\">545</td><td char=\".\" align=\"char\">0.4583</td><td char=\".\" align=\"char\">0.5038</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₄</td><td align=\"left\">1117.46</td><td char=\".\" align=\"char\">1</td><td align=\"left\">1117.46</td><td char=\".\" align=\"char\">0.9397</td><td char=\".\" align=\"char\">0.3404</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₄</td><td align=\"left\">710.46</td><td char=\".\" align=\"char\">1</td><td align=\"left\">710.46</td><td char=\".\" align=\"char\">0.5974</td><td char=\".\" align=\"char\">0.4458</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₅</td><td align=\"left\">33.74</td><td char=\".\" align=\"char\">1</td><td align=\"left\">33.74</td><td char=\".\" align=\"char\">0.0284</td><td char=\".\" align=\"char\">0.8674</td></tr><tr><td align=\"left\"> <italic>X</italic>₄<italic>X</italic>₅</td><td align=\"left\">3002.74</td><td char=\".\" align=\"char\">1</td><td align=\"left\">3002.74</td><td char=\".\" align=\"char\">2.53</td><td char=\".\" align=\"char\">0.1229</td></tr><tr><td align=\"left\"> <italic>X</italic>₁²</td><td align=\"left\">3677.82</td><td char=\".\" align=\"char\">1</td><td align=\"left\">3677.82</td><td char=\".\" align=\"char\">3.09</td><td char=\".\" align=\"char\">0.0892</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>2</italic>}²</td><td align=\"left\">1430.88</td><td char=\".\" align=\"char\">1</td><td align=\"left\">1430.88</td><td char=\".\" align=\"char\">1.2</td><td char=\".\" align=\"char\">0.2817</td></tr><tr><td align=\"left\"> <italic>X</italic>₃²</td><td align=\"left\">6893.43</td><td char=\".\" align=\"char\">1</td><td align=\"left\">6893.43</td><td char=\".\" align=\"char\">5.8</td><td char=\".\" align=\"char\">0.0226</td></tr><tr><td align=\"left\"> <italic>X</italic>₄^{<italic>2</italic>}</td><td align=\"left\">8144.72</td><td char=\".\" align=\"char\">1</td><td align=\"left\">8144.72</td><td char=\".\" align=\"char\">6.85</td><td char=\".\" align=\"char\">0.0139</td></tr><tr><td align=\"left\"> <italic>X</italic>₅^{<italic>2</italic>}</td><td align=\"left\">2849.08</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2849.08</td><td char=\".\" align=\"char\">2.4</td><td char=\".\" align=\"char\">0.1325</td></tr><tr><td align=\"left\"> Residual</td><td align=\"left\">11,581.3</td><td char=\".\" align=\"char\">1</td><td align=\"left\">11,581.28</td><td char=\".\" align=\"char\">9.74</td><td char=\".\" align=\"char\">0.0041</td></tr><tr><td align=\"left\"> Lack of fit</td><td align=\"left\">34,486.8</td><td char=\".\" align=\"char\">29</td><td align=\"left\">1189.2</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Pure error</td><td align=\"left\">34,470.1</td><td char=\".\" align=\"char\">22</td><td align=\"left\">1566.82</td><td char=\".\" align=\"char\">656.48</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> Cor total</td><td align=\"left\">16.71</td><td char=\".\" align=\"char\">7</td><td align=\"left\">2.39</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" colspan=\"6\">TFC (y₂)^e</td></tr><tr><td align=\"left\"> Model</td><td align=\"left\">129,800</td><td char=\".\" align=\"char\">20</td><td align=\"left\">6491.91</td><td char=\".\" align=\"char\">19.96</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₁</td><td align=\"left\">115,600</td><td char=\".\" align=\"char\">1</td><td align=\"left\">1.16E+05</td><td char=\".\" align=\"char\">355.45</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₂</td><td align=\"left\">679.09</td><td char=\".\" align=\"char\">1</td><td align=\"left\">679.09</td><td char=\".\" align=\"char\">2.09</td><td char=\".\" align=\"char\">0.1592</td></tr><tr><td align=\"left\"> <italic>X</italic>₃</td><td align=\"left\">221.21</td><td char=\".\" align=\"char\">1</td><td align=\"left\">221.21</td><td char=\".\" align=\"char\">0.6801</td><td char=\".\" align=\"char\">0.4163</td></tr><tr><td align=\"left\"> <italic>X</italic>₄</td><td align=\"left\">2763.7</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2763.7</td><td char=\".\" align=\"char\">8.5</td><td char=\".\" align=\"char\">0.0068</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>5</italic>}</td><td align=\"left\">737.91</td><td char=\".\" align=\"char\">1</td><td align=\"left\">737.91</td><td char=\".\" align=\"char\">2.27</td><td char=\".\" align=\"char\">0.1428</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₂</td><td align=\"left\">213.72</td><td char=\".\" align=\"char\">1</td><td align=\"left\">213.72</td><td char=\".\" align=\"char\">0.657</td><td char=\".\" align=\"char\">0.4242</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₃</td><td align=\"left\">1015</td><td char=\".\" align=\"char\">1</td><td align=\"left\">1015</td><td char=\".\" align=\"char\">3.12</td><td char=\".\" align=\"char\">0.0878</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₄</td><td align=\"left\">243.55</td><td char=\".\" align=\"char\">1</td><td align=\"left\">243.55</td><td char=\".\" align=\"char\">0.7488</td><td char=\".\" align=\"char\">0.394</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X5</italic></td><td align=\"left\">720.84</td><td char=\".\" align=\"char\">1</td><td align=\"left\">720.84</td><td char=\".\" align=\"char\">2.22</td><td char=\".\" align=\"char\">0.1474</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₃</td><td align=\"left\">57.46</td><td char=\".\" align=\"char\">1</td><td align=\"left\">57.46</td><td char=\".\" align=\"char\">0.1767</td><td char=\".\" align=\"char\">0.6774</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₄</td><td align=\"left\">496.9</td><td char=\".\" align=\"char\">1</td><td align=\"left\">496.9</td><td char=\".\" align=\"char\">1.53</td><td char=\".\" align=\"char\">0.2264</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₄</td><td align=\"left\">32.37</td><td char=\".\" align=\"char\">1</td><td align=\"left\">32.37</td><td char=\".\" align=\"char\">0.0995</td><td char=\".\" align=\"char\">0.7547</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₅</td><td align=\"left\">0.0021</td><td char=\".\" align=\"char\">1</td><td align=\"left\">0.0021</td><td char=\".\" align=\"char\">6.40E-06</td><td char=\".\" align=\"char\">0.998</td></tr><tr><td align=\"left\"> <italic>X</italic>₄<italic>X</italic>₅</td><td align=\"left\">1006.91</td><td char=\".\" align=\"char\">1</td><td align=\"left\">1006.91</td><td char=\".\" align=\"char\">3.1</td><td char=\".\" align=\"char\">0.0891</td></tr><tr><td align=\"left\"> <italic>X</italic>₁²</td><td align=\"left\">317.76</td><td char=\".\" align=\"char\">1</td><td align=\"left\">317.76</td><td char=\".\" align=\"char\">0.9769</td><td char=\".\" align=\"char\">0.3311</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>2</italic>}²</td><td align=\"left\">660.42</td><td char=\".\" align=\"char\">1</td><td align=\"left\">660.42</td><td char=\".\" align=\"char\">2.03</td><td char=\".\" align=\"char\">0.1649</td></tr><tr><td align=\"left\"> <italic>X</italic>₃²</td><td align=\"left\">1594.97</td><td char=\".\" align=\"char\">1</td><td align=\"left\">1594.97</td><td char=\".\" align=\"char\">4.9</td><td char=\".\" align=\"char\">0.0348</td></tr><tr><td align=\"left\"> <italic>X</italic>₄^{<italic>2</italic>}</td><td align=\"left\">1575.56</td><td char=\".\" align=\"char\">1</td><td align=\"left\">1575.56</td><td char=\".\" align=\"char\">4.84</td><td char=\".\" align=\"char\">0.0359</td></tr><tr><td align=\"left\"> <italic>X</italic>₅^{<italic>2</italic>}</td><td align=\"left\">894.54</td><td char=\".\" align=\"char\">1</td><td align=\"left\">894.54</td><td char=\".\" align=\"char\">2.75</td><td char=\".\" align=\"char\">0.108</td></tr><tr><td align=\"left\"> Residual</td><td align=\"left\">3497.2</td><td char=\".\" align=\"char\">1</td><td align=\"left\">3497.2</td><td char=\".\" align=\"char\">10.75</td><td char=\".\" align=\"char\">0.0027</td></tr><tr><td align=\"left\"> Lack of fit</td><td align=\"left\">9432.79</td><td char=\".\" align=\"char\">29</td><td align=\"left\">325.27</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Pure error</td><td align=\"left\">9424.85</td><td char=\".\" align=\"char\">22</td><td align=\"left\">428.4</td><td char=\".\" align=\"char\">378.08</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> Cor total</td><td align=\"left\">7.93</td><td char=\".\" align=\"char\">7</td><td align=\"left\">1.13</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" colspan=\"6\">%DPPH*sc (y₃)^f</td></tr><tr><td align=\"left\"> Model</td><td align=\"left\">3314.9</td><td char=\".\" align=\"char\">20</td><td align=\"left\">165.74</td><td char=\".\" align=\"char\">13.73</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₁</td><td align=\"left\">2645.01</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2645.01</td><td char=\".\" align=\"char\">219.12</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₂</td><td align=\"left\">33.29</td><td char=\".\" align=\"char\">1</td><td align=\"left\">33.29</td><td char=\".\" align=\"char\">2.76</td><td char=\".\" align=\"char\">0.1076</td></tr><tr><td align=\"left\"> <italic>X</italic>₃</td><td align=\"left\">7.45</td><td char=\".\" align=\"char\">1</td><td align=\"left\">7.45</td><td char=\".\" align=\"char\">0.617</td><td char=\".\" align=\"char\">0.4385</td></tr><tr><td align=\"left\"> <italic>X</italic>₄</td><td align=\"left\">49.66</td><td char=\".\" align=\"char\">1</td><td align=\"left\">49.66</td><td char=\".\" align=\"char\">4.11</td><td char=\".\" align=\"char\">0.0518</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>5</italic>}</td><td align=\"left\">5.49</td><td char=\".\" align=\"char\">1</td><td align=\"left\">5.49</td><td char=\".\" align=\"char\">0.455</td><td char=\".\" align=\"char\">0.5053</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₂</td><td align=\"left\">0.1164</td><td char=\".\" align=\"char\">1</td><td align=\"left\">0.1164</td><td char=\".\" align=\"char\">0.0096</td><td char=\".\" align=\"char\">0.9224</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₃</td><td align=\"left\">3.06</td><td char=\".\" align=\"char\">1</td><td align=\"left\">3.06</td><td char=\".\" align=\"char\">0.2532</td><td char=\".\" align=\"char\">0.6186</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₄</td><td align=\"left\">67.48</td><td char=\".\" align=\"char\">1</td><td align=\"left\">67.48</td><td char=\".\" align=\"char\">5.59</td><td char=\".\" align=\"char\">0.025</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X5</italic></td><td align=\"left\">5.64</td><td char=\".\" align=\"char\">1</td><td align=\"left\">5.64</td><td char=\".\" align=\"char\">0.4669</td><td char=\".\" align=\"char\">0.4998</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₃</td><td align=\"left\">26.44</td><td char=\".\" align=\"char\">1</td><td align=\"left\">26.44</td><td char=\".\" align=\"char\">2.19</td><td char=\".\" align=\"char\">0.1496</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₄</td><td align=\"left\">67.77</td><td char=\".\" align=\"char\">1</td><td align=\"left\">67.77</td><td char=\".\" align=\"char\">5.61</td><td char=\".\" align=\"char\">0.0247</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₄</td><td align=\"left\">0.1093</td><td char=\".\" align=\"char\">1</td><td align=\"left\">0.1093</td><td char=\".\" align=\"char\">0.0091</td><td char=\".\" align=\"char\">0.9249</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₅</td><td align=\"left\">23.38</td><td char=\".\" align=\"char\">1</td><td align=\"left\">23.38</td><td char=\".\" align=\"char\">1.94</td><td char=\".\" align=\"char\">0.1746</td></tr><tr><td align=\"left\"> <italic>X</italic>₄<italic>X</italic>₅</td><td align=\"left\">69.24</td><td char=\".\" align=\"char\">1</td><td align=\"left\">69.24</td><td char=\".\" align=\"char\">5.74</td><td char=\".\" align=\"char\">0.0233</td></tr><tr><td align=\"left\"> <italic>X</italic>₁²</td><td align=\"left\">90.01</td><td char=\".\" align=\"char\">1</td><td align=\"left\">90.01</td><td char=\".\" align=\"char\">7.46</td><td char=\".\" align=\"char\">0.0106</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>2</italic>}²</td><td align=\"left\">105.14</td><td char=\".\" align=\"char\">1</td><td align=\"left\">105.14</td><td char=\".\" align=\"char\">8.71</td><td char=\".\" align=\"char\">0.0062</td></tr><tr><td align=\"left\"> <italic>X</italic>₃²</td><td align=\"left\">110.2</td><td char=\".\" align=\"char\">1</td><td align=\"left\">110.2</td><td char=\".\" align=\"char\">9.13</td><td char=\".\" align=\"char\">0.0052</td></tr><tr><td align=\"left\"> <italic>X</italic>₄^{<italic>2</italic>}</td><td align=\"left\">37.65</td><td char=\".\" align=\"char\">1</td><td align=\"left\">37.65</td><td char=\".\" align=\"char\">3.12</td><td char=\".\" align=\"char\">0.0879</td></tr><tr><td align=\"left\"> <italic>X</italic>₅^{<italic>2</italic>}</td><td align=\"left\">42.31</td><td char=\".\" align=\"char\">1</td><td align=\"left\">42.31</td><td char=\".\" align=\"char\">3.51</td><td char=\".\" align=\"char\">0.0713</td></tr><tr><td align=\"left\"> Residual</td><td align=\"left\">20.21</td><td char=\".\" align=\"char\">1</td><td align=\"left\">20.21</td><td char=\".\" align=\"char\">1.67</td><td char=\".\" align=\"char\">0.2059</td></tr><tr><td align=\"left\"> Lack of fit</td><td align=\"left\">350.06</td><td char=\".\" align=\"char\">29</td><td align=\"left\">12.07</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Pure error</td><td align=\"left\">321.82</td><td char=\".\" align=\"char\">22</td><td align=\"left\">14.63</td><td char=\".\" align=\"char\">3.63</td><td char=\".\" align=\"char\">0.0431</td></tr><tr><td align=\"left\"> Cor total</td><td align=\"left\">28.24</td><td char=\".\" align=\"char\">7</td><td align=\"left\">4.03</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" colspan=\"6\">%ABTS*sc (y₄)^g</td></tr><tr><td align=\"left\"> Model</td><td align=\"left\">3196.49</td><td char=\".\" align=\"char\">20</td><td align=\"left\">159.82</td><td char=\".\" align=\"char\">9.97</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₁</td><td align=\"left\">2543.85</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2543.85</td><td char=\".\" align=\"char\">158.7</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₂</td><td align=\"left\">58.62</td><td char=\".\" align=\"char\">1</td><td align=\"left\">58.62</td><td char=\".\" align=\"char\">3.66</td><td char=\".\" align=\"char\">0.0658</td></tr><tr><td align=\"left\"> <italic>X</italic>₃</td><td align=\"left\">6.13</td><td char=\".\" align=\"char\">1</td><td align=\"left\">6.13</td><td char=\".\" align=\"char\">0.3825</td><td char=\".\" align=\"char\">0.5411</td></tr><tr><td align=\"left\"> <italic>X</italic>₄</td><td align=\"left\">61.36</td><td char=\".\" align=\"char\">1</td><td align=\"left\">61.36</td><td char=\".\" align=\"char\">3.83</td><td char=\".\" align=\"char\">0.0601</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>5</italic>}</td><td align=\"left\">4.51</td><td char=\".\" align=\"char\">1</td><td align=\"left\">4.51</td><td char=\".\" align=\"char\">0.2812</td><td char=\".\" align=\"char\">0.6</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₂</td><td align=\"left\">2.43</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2.43</td><td char=\".\" align=\"char\">0.1513</td><td char=\".\" align=\"char\">0.7001</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₃</td><td align=\"left\">10.66</td><td char=\".\" align=\"char\">1</td><td align=\"left\">10.66</td><td char=\".\" align=\"char\">0.6651</td><td char=\".\" align=\"char\">0.4214</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₄</td><td align=\"left\">73.84</td><td char=\".\" align=\"char\">1</td><td align=\"left\">73.84</td><td char=\".\" align=\"char\">4.61</td><td char=\".\" align=\"char\">0.0403</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X5</italic></td><td align=\"left\">0.4209</td><td char=\".\" align=\"char\">1</td><td align=\"left\">0.4209</td><td char=\".\" align=\"char\">0.0263</td><td char=\".\" align=\"char\">0.8724</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₃</td><td align=\"left\">19.58</td><td char=\".\" align=\"char\">1</td><td align=\"left\">19.58</td><td char=\".\" align=\"char\">1.22</td><td char=\".\" align=\"char\">0.2782</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₄</td><td align=\"left\">56.9</td><td char=\".\" align=\"char\">1</td><td align=\"left\">56.9</td><td char=\".\" align=\"char\">3.55</td><td char=\".\" align=\"char\">0.0696</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₄</td><td align=\"left\">0.5913</td><td char=\".\" align=\"char\">1</td><td align=\"left\">0.5913</td><td char=\".\" align=\"char\">0.0369</td><td char=\".\" align=\"char\">0.849</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₅</td><td align=\"left\">38.43</td><td char=\".\" align=\"char\">1</td><td align=\"left\">38.43</td><td char=\".\" align=\"char\">2.4</td><td char=\".\" align=\"char\">0.1324</td></tr><tr><td align=\"left\"> <italic>X</italic>₄<italic>X</italic>₅</td><td align=\"left\">94.57</td><td char=\".\" align=\"char\">1</td><td align=\"left\">94.57</td><td char=\".\" align=\"char\">5.9</td><td char=\".\" align=\"char\">0.0216</td></tr><tr><td align=\"left\"> <italic>X</italic>₁²</td><td align=\"left\">52.56</td><td char=\".\" align=\"char\">1</td><td align=\"left\">52.56</td><td char=\".\" align=\"char\">3.28</td><td char=\".\" align=\"char\">0.0806</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>2</italic>}²</td><td align=\"left\">98.26</td><td char=\".\" align=\"char\">1</td><td align=\"left\">98.26</td><td char=\".\" align=\"char\">6.13</td><td char=\".\" align=\"char\">0.0194</td></tr><tr><td align=\"left\"> <italic>X</italic>₃²</td><td align=\"left\">74.67</td><td char=\".\" align=\"char\">1</td><td align=\"left\">74.67</td><td char=\".\" align=\"char\">4.66</td><td char=\".\" align=\"char\">0.0393</td></tr><tr><td align=\"left\"> <italic>X</italic>₄^{<italic>2</italic>}</td><td align=\"left\">18.14</td><td char=\".\" align=\"char\">1</td><td align=\"left\">18.14</td><td char=\".\" align=\"char\">1.13</td><td char=\".\" align=\"char\">0.2961</td></tr><tr><td align=\"left\"> <italic>X</italic>₅^{<italic>2</italic>}</td><td align=\"left\">35.28</td><td char=\".\" align=\"char\">1</td><td align=\"left\">35.28</td><td char=\".\" align=\"char\">2.2</td><td char=\".\" align=\"char\">0.1487</td></tr><tr><td align=\"left\"> Residual</td><td align=\"left\">14.48</td><td char=\".\" align=\"char\">1</td><td align=\"left\">14.48</td><td char=\".\" align=\"char\">0.9032</td><td char=\".\" align=\"char\">0.3498</td></tr><tr><td align=\"left\"> Lack of fit</td><td align=\"left\">464.86</td><td char=\".\" align=\"char\">29</td><td align=\"left\">16.03</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Pure error</td><td align=\"left\">428.67</td><td char=\".\" align=\"char\">22</td><td align=\"left\">19.48</td><td char=\".\" align=\"char\">3.77</td><td char=\".\" align=\"char\">0.039</td></tr><tr><td align=\"left\"> Cor total</td><td align=\"left\">36.19</td><td char=\".\" align=\"char\">7</td><td align=\"left\">5.17</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" colspan=\"6\">FRAP (y₅)^h</td></tr><tr><td align=\"left\"> Model</td><td align=\"left\">3282.89</td><td char=\".\" align=\"char\">20</td><td align=\"left\">164.14</td><td char=\".\" align=\"char\">10.64</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₁</td><td align=\"left\">2564.2</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2564.2</td><td char=\".\" align=\"char\">166.17</td><td char=\".\" align=\"char\"> &lt; 0.0001</td></tr><tr><td align=\"left\"> <italic>X</italic>₂</td><td align=\"left\">76.61</td><td char=\".\" align=\"char\">1</td><td align=\"left\">76.61</td><td char=\".\" align=\"char\">4.96</td><td char=\".\" align=\"char\">0.0338</td></tr><tr><td align=\"left\"> <italic>X</italic>₃</td><td align=\"left\">7.49</td><td char=\".\" align=\"char\">1</td><td align=\"left\">7.49</td><td char=\".\" align=\"char\">0.4854</td><td char=\".\" align=\"char\">0.4915</td></tr><tr><td align=\"left\"> <italic>X</italic>₄</td><td align=\"left\">67.35</td><td char=\".\" align=\"char\">1</td><td align=\"left\">67.35</td><td char=\".\" align=\"char\">4.36</td><td char=\".\" align=\"char\">0.0456</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>5</italic>}</td><td align=\"left\">3.5</td><td char=\".\" align=\"char\">1</td><td align=\"left\">3.5</td><td char=\".\" align=\"char\">0.2269</td><td char=\".\" align=\"char\">0.6374</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₂</td><td align=\"left\">2.48</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2.48</td><td char=\".\" align=\"char\">0.1608</td><td char=\".\" align=\"char\">0.6914</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₃</td><td align=\"left\">14.62</td><td char=\".\" align=\"char\">1</td><td align=\"left\">14.62</td><td char=\".\" align=\"char\">0.9475</td><td char=\".\" align=\"char\">0.3384</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X</italic>₄</td><td align=\"left\">67.31</td><td char=\".\" align=\"char\">1</td><td align=\"left\">67.31</td><td char=\".\" align=\"char\">4.36</td><td char=\".\" align=\"char\">0.0456</td></tr><tr><td align=\"left\"> <italic>X</italic>₁<italic>X5</italic></td><td align=\"left\">2.57</td><td char=\".\" align=\"char\">1</td><td align=\"left\">2.57</td><td char=\".\" align=\"char\">0.1666</td><td char=\".\" align=\"char\">0.6862</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₃</td><td align=\"left\">18.93</td><td char=\".\" align=\"char\">1</td><td align=\"left\">18.93</td><td char=\".\" align=\"char\">1.23</td><td char=\".\" align=\"char\">0.2772</td></tr><tr><td align=\"left\"> <italic>X</italic>₂<italic>X</italic>₄</td><td align=\"left\">59.98</td><td char=\".\" align=\"char\">1</td><td align=\"left\">59.98</td><td char=\".\" align=\"char\">3.89</td><td char=\".\" align=\"char\">0.0583</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₄</td><td align=\"left\">0.0109</td><td char=\".\" align=\"char\">1</td><td align=\"left\">0.0109</td><td char=\".\" align=\"char\">0.0007</td><td char=\".\" align=\"char\">0.979</td></tr><tr><td align=\"left\"> <italic>X</italic>₃<italic>X</italic>₅</td><td align=\"left\">26.48</td><td char=\".\" align=\"char\">1</td><td align=\"left\">26.48</td><td char=\".\" align=\"char\">1.72</td><td char=\".\" align=\"char\">0.2005</td></tr><tr><td align=\"left\"> <italic>X</italic>₄<italic>X</italic>₅</td><td align=\"left\">106.32</td><td char=\".\" align=\"char\">1</td><td align=\"left\">106.32</td><td char=\".\" align=\"char\">6.89</td><td char=\".\" align=\"char\">0.0137</td></tr><tr><td align=\"left\"> <italic>X</italic>₁²</td><td align=\"left\">59.32</td><td char=\".\" align=\"char\">1</td><td align=\"left\">59.32</td><td char=\".\" align=\"char\">3.84</td><td char=\".\" align=\"char\">0.0596</td></tr><tr><td align=\"left\"> <italic>X</italic>_{<italic>2</italic>}²</td><td align=\"left\">120.83</td><td char=\".\" align=\"char\">1</td><td align=\"left\">120.83</td><td char=\".\" align=\"char\">7.83</td><td char=\".\" align=\"char\">0.009</td></tr><tr><td align=\"left\"> <italic>X</italic>₃²</td><td align=\"left\">80.57</td><td char=\".\" align=\"char\">1</td><td align=\"left\">80.57</td><td char=\".\" align=\"char\">5.22</td><td char=\".\" align=\"char\">0.0298</td></tr><tr><td align=\"left\"> <italic>X</italic>₄²</td><td align=\"left\">25.1</td><td char=\".\" align=\"char\">1</td><td align=\"left\">25.1</td><td char=\".\" align=\"char\">1.63</td><td char=\".\" align=\"char\">0.2123</td></tr><tr><td align=\"left\"> <italic>X</italic>₅²</td><td align=\"left\">48.08</td><td char=\".\" align=\"char\">1</td><td align=\"left\">48.08</td><td char=\".\" align=\"char\">3.12</td><td char=\".\" align=\"char\">0.0881</td></tr><tr><td align=\"left\"> Residual</td><td align=\"left\">12.03</td><td char=\".\" align=\"char\">1</td><td align=\"left\">12.03</td><td char=\".\" align=\"char\">0.7794</td><td char=\".\" align=\"char\">0.3846</td></tr><tr><td align=\"left\"> Lack of fit</td><td align=\"left\">447.5</td><td char=\".\" align=\"char\">29</td><td align=\"left\">15.43</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Pure error</td><td align=\"left\">416.99</td><td char=\".\" align=\"char\">22</td><td align=\"left\">18.95</td><td char=\".\" align=\"char\">4.35</td><td char=\".\" align=\"char\">0.0264</td></tr><tr><td align=\"left\"> Cor total</td><td align=\"left\">30.51</td><td char=\".\" align=\"char\">7</td><td align=\"left\">4.36</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Central composite design (CCD) with experimental responses and predicted responses.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">S.No</th><th align=\"left\" colspan=\"5\">Parameters</th><th align=\"left\" colspan=\"5\">Experimental value*</th><th align=\"left\" colspan=\"5\">RSM prediction</th><th align=\"left\" colspan=\"5\">ANFIS prediction</th><th align=\"left\" colspan=\"5\">Machine learning algorithm prediction</th></tr><tr><th align=\"left\">X1</th><th align=\"left\">X2</th><th align=\"left\">X3</th><th align=\"left\">X4</th><th align=\"left\">X5</th><th align=\"left\">y1</th><th align=\"left\">y2</th><th align=\"left\">y3</th><th align=\"left\">y4</th><th align=\"left\">y5</th><th align=\"left\">y1</th><th align=\"left\">y2</th><th align=\"left\">y3</th><th align=\"left\">y4</th><th align=\"left\">y5</th><th align=\"left\">y1</th><th align=\"left\">y2</th><th align=\"left\">y3</th><th align=\"left\">y4</th><th align=\"left\">y5</th><th align=\"left\">y1</th><th align=\"left\">y2</th><th align=\"left\">y3</th><th align=\"left\">y4</th><th align=\"left\">y5</th></tr></thead><tbody><tr><td align=\"left\">1</td><td char=\".\" align=\"char\">0.25</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">667.67</td><td char=\".\" align=\"char\">445.65</td><td char=\".\" align=\"char\">78.95</td><td char=\".\" align=\"char\">75.65</td><td char=\".\" align=\"char\">70.04</td><td char=\".\" align=\"char\">695.15</td><td char=\".\" align=\"char\">441.62</td><td char=\".\" align=\"char\">82.41</td><td char=\".\" align=\"char\">77.2256</td><td char=\".\" align=\"char\">72.3434</td><td align=\"left\">717</td><td align=\"left\">471</td><td char=\".\" align=\"char\">85.6</td><td align=\"left\">81.3</td><td char=\".\" align=\"char\">75.7</td><td char=\".\" align=\"char\">666.87</td><td char=\".\" align=\"char\">449.63</td><td char=\".\" align=\"char\">79.57</td><td char=\".\" align=\"char\">75.66</td><td char=\".\" align=\"char\">70.28</td></tr><tr><td align=\"left\">2</td><td char=\".\" align=\"char\">0.155</td><td align=\"left\">62.5</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">672.45</td><td char=\".\" align=\"char\">454.65</td><td char=\".\" align=\"char\">81.89</td><td char=\".\" align=\"char\">77.85</td><td char=\".\" align=\"char\">71.52</td><td char=\".\" align=\"char\">752.64</td><td char=\".\" align=\"char\">469.42</td><td char=\".\" align=\"char\">82.22</td><td char=\".\" align=\"char\">76.72</td><td char=\".\" align=\"char\">71.52</td><td align=\"left\">632</td><td align=\"left\">426</td><td char=\".\" align=\"char\">76.5</td><td align=\"left\">72.8</td><td char=\".\" align=\"char\">67.3</td><td char=\".\" align=\"char\">669.70</td><td char=\".\" align=\"char\">455.11</td><td char=\".\" align=\"char\">81.18</td><td char=\".\" align=\"char\">76.93</td><td char=\".\" align=\"char\">71.14</td></tr><tr><td align=\"left\">3</td><td char=\".\" align=\"char\">0.155</td><td align=\"left\">67.5</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">70</td><td char=\".\" align=\"char\">670.13</td><td char=\".\" align=\"char\">448.76</td><td char=\".\" align=\"char\">79.05</td><td char=\".\" align=\"char\">76.45</td><td char=\".\" align=\"char\">70.43</td><td char=\".\" align=\"char\">732.76</td><td char=\".\" align=\"char\">467.24</td><td char=\".\" align=\"char\">83.24</td><td char=\".\" align=\"char\">78.544</td><td char=\".\" align=\"char\">73.5081</td><td align=\"left\">634</td><td align=\"left\">427</td><td char=\".\" align=\"char\">76.8</td><td align=\"left\">73.3</td><td char=\".\" align=\"char\">67.8</td><td char=\".\" align=\"char\">668.34</td><td char=\".\" align=\"char\">451.40</td><td char=\".\" align=\"char\">79.52</td><td char=\".\" align=\"char\">76.10</td><td char=\".\" align=\"char\">70.49</td></tr><tr><td align=\"left\">4</td><td char=\".\" align=\"char\">0.155</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">67.5</td><td char=\".\" align=\"char\">658.65</td><td char=\".\" align=\"char\">463.34</td><td char=\".\" align=\"char\">80.34</td><td char=\".\" align=\"char\">73.78</td><td char=\".\" align=\"char\">70.37</td><td char=\".\" align=\"char\">751.71</td><td char=\".\" align=\"char\">472.56</td><td char=\".\" align=\"char\">82.26</td><td char=\".\" align=\"char\">77.4991</td><td char=\".\" align=\"char\">72.2171</td><td align=\"left\">635</td><td align=\"left\">427</td><td char=\".\" align=\"char\">76.7</td><td align=\"left\">73.1</td><td char=\".\" align=\"char\">67.6</td><td char=\".\" align=\"char\">662.44</td><td char=\".\" align=\"char\">458.40</td><td char=\".\" align=\"char\">80.11</td><td char=\".\" align=\"char\">74.71</td><td char=\".\" align=\"char\">70.42</td></tr><tr><td align=\"left\">5</td><td char=\".\" align=\"char\">0.155</td><td align=\"left\">65</td><td align=\"left\">23</td><td align=\"left\">40</td><td align=\"left\">72.5</td><td char=\".\" align=\"char\">659.67</td><td char=\".\" align=\"char\">462.34</td><td char=\".\" align=\"char\">81.32</td><td char=\".\" align=\"char\">74.71</td><td char=\".\" align=\"char\">70.24</td><td char=\".\" align=\"char\">735.34</td><td char=\".\" align=\"char\">465.39</td><td char=\".\" align=\"char\">83.61</td><td char=\".\" align=\"char\">78.0947</td><td char=\".\" align=\"char\">73.176</td><td align=\"left\">632</td><td align=\"left\">426</td><td char=\".\" align=\"char\">76.7</td><td align=\"left\">73</td><td char=\".\" align=\"char\">67.5</td><td char=\".\" align=\"char\">663.29</td><td char=\".\" align=\"char\">458.12</td><td char=\".\" align=\"char\">80.85</td><td char=\".\" align=\"char\">75.40</td><td char=\".\" align=\"char\">70.39</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Analysed bioactive ingredients from optimized extract of graph seeds through GC<bold>–</bold>MS chromatogram<italic>.</italic></p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Retention time (min)</th><th align=\"left\">% Area of peak</th><th align=\"left\">Compound identified</th><th align=\"left\">Molecular formula</th><th align=\"left\">Molecular weight (g/mol)</th></tr></thead><tbody><tr><td align=\"left\">6.996</td><td char=\".\" align=\"char\">0.36</td><td align=\"left\">3-Hexenoic acid</td><td align=\"left\">C₆H₁₀O₂</td><td align=\"left\">114.14</td></tr><tr><td align=\"left\">9.697</td><td char=\".\" align=\"char\">7.14</td><td align=\"left\">5-Hydroxymethylfurfural</td><td align=\"left\">C₆H₆O₃</td><td align=\"left\">126.11</td></tr><tr><td align=\"left\">11.467</td><td char=\".\" align=\"char\">0.43</td><td align=\"left\">2-Amino-5,6-dimethyl-3H-pyrimidine</td><td align=\"left\">C₆H₉N₃O</td><td align=\"left\">139.16</td></tr><tr><td align=\"left\">11.702</td><td char=\".\" align=\"char\">0.52</td><td align=\"left\">Spiro[4.4]nonane-1,6-dione</td><td align=\"left\">C₉H₁₂O₂</td><td align=\"left\">152.19</td></tr><tr><td align=\"left\">12.692</td><td char=\".\" align=\"char\">9.22</td><td align=\"left\">8-Methylnonanoic acid</td><td align=\"left\">C₁₀H₂₀O₂</td><td align=\"left\">172.26</td></tr><tr><td align=\"left\">13.338</td><td char=\".\" align=\"char\">8.22</td><td align=\"left\">3,4-Altrosan</td><td align=\"left\">C₆H₁₀O₅</td><td align=\"left\">162.14</td></tr><tr><td align=\"left\">14.588</td><td char=\".\" align=\"char\">8.29</td><td align=\"left\">1,5-Anhydro-d-mannitol</td><td align=\"left\">C₆H₁₂O₅</td><td align=\"left\">164.16</td></tr><tr><td align=\"left\">16.366</td><td char=\".\" align=\"char\">0.38</td><td align=\"left\">9-Eicosenoic acid</td><td align=\"left\">C₂₀H₃₈O₂</td><td align=\"left\">310.5</td></tr><tr><td align=\"left\">18.245</td><td char=\".\" align=\"char\">1.00</td><td align=\"left\"><italic>cis</italic>-Vaccenic acid</td><td align=\"left\">C₁₈H₃₄O₂</td><td align=\"left\">282.5</td></tr><tr><td align=\"left\">22.909</td><td char=\".\" align=\"char\">0.68</td><td align=\"left\">1,37-Octatriacontadiene</td><td align=\"left\">C₃₈H₇₄</td><td align=\"left\">531</td></tr><tr><td align=\"left\">24.235</td><td char=\".\" align=\"char\">1.91</td><td align=\"left\">1,3-Benzenedicarboxylic acid</td><td align=\"left\">C₈H₆O₄</td><td align=\"left\">166.13</td></tr><tr><td align=\"left\">24.973</td><td char=\".\" align=\"char\">0.56</td><td align=\"left\">2-Methyl-7-phenylindole</td><td align=\"left\">C₁₅H₁₃N</td><td align=\"left\">207.27</td></tr></tbody></table></table-wrap>" ]

[ "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\% {\\text{ DPPH radical scavenging activity }} = \\, \\left( {\\left( {{\\text{A}}_{0} - {\\text{A}}_{{1}} } \\right) \\, \\times {1}00} \\right)/{\\text{A}}_{0} ,$$\\end{document}</tex-math><mml:math id=\"M2\" display=\"block\"><mml:mrow><mml:mo>%</mml:mo><mml:mrow><mml:mspace width=\"0.333333em\"/><mml:mtext>DPPH radical scavenging activity</mml:mtext><mml:mspace width=\"0.333333em\"/></mml:mrow><mml:mo>=</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mtext>A</mml:mtext><mml:mn>0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mtext>A</mml:mtext><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced><mml:mspace width=\"0.166667em\"/><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:mfenced><mml:mo stretchy=\"false\">/</mml:mo><mml:msub><mml:mtext>A</mml:mtext><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\% {\\text{ ABTS radical inhibition activity }} = \\, \\left( {\\left( {{\\text{A}}0 - {\\text{A1}}} \\right) \\, \\times {1}00} \\right)/{\\text{A}}0,$$\\end{document}</tex-math><mml:math id=\"M4\" display=\"block\"><mml:mrow><mml:mo>%</mml:mo><mml:mrow><mml:mspace width=\"0.333333em\"/><mml:mtext>ABTS radical inhibition activity</mml:mtext><mml:mspace width=\"0.333333em\"/></mml:mrow><mml:mo>=</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mtext>A</mml:mtext><mml:mn>0</mml:mn><mml:mo>-</mml:mo><mml:mtext>A1</mml:mtext></mml:mrow></mml:mfenced><mml:mspace width=\"0.166667em\"/><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:mfenced><mml:mo stretchy=\"false\">/</mml:mo><mml:mtext>A</mml:mtext><mml:mn>0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x_{i} = \\frac{{X_{i} - X_{Z} }}{{\\Delta X_{i} }}\\quad i = 1,2,3,...K,$$\\end{document}</tex-math><mml:math id=\"M6\" display=\"block\"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mspace width=\"1em\"/><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\text{N }} = { 2}^{{\\text{k}}} \\left( {\\text{factorial points}} \\right) \\, + {\\text{ 2k }}\\left( {\\text{axial points}} \\right) \\, + {\\text{ n}}_{0} \\left( {\\text{central points}} \\right),$$\\end{document}</tex-math><mml:math id=\"M8\" display=\"block\"><mml:mrow><mml:mrow><mml:mtext>N</mml:mtext><mml:mspace width=\"0.333333em\"/></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mtext>k</mml:mtext></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mtext>factorial points</mml:mtext></mml:mrow></mml:mfenced><mml:mspace width=\"0.166667em\"/><mml:mo>+</mml:mo><mml:mrow><mml:mspace width=\"0.333333em\"/><mml:mtext>2k</mml:mtext><mml:mspace width=\"0.333333em\"/></mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mtext>axial points</mml:mtext></mml:mrow></mml:mfenced><mml:mspace width=\"0.166667em\"/><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mspace width=\"0.333333em\"/><mml:mtext>n</mml:mtext></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mtext>central points</mml:mtext></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Y = \\alpha_{0} + \\sum\\limits_{i = 1}^{3} {\\alpha_{i} X_{i} } + \\sum\\limits_{i = 1}^{3} {\\alpha_{ii} X_{i}^{2} } + \\sum\\limits_{i = 1}^{2} {\\sum\\limits_{j = i + 1}^{3} {\\alpha_{ij} X_{i} X_{j} } } + \\varepsilon .$$\\end{document}</tex-math><mml:math id=\"M10\" display=\"block\"><mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:munderover><mml:mo movablelimits=\"false\">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>3</mml:mn></mml:munderover><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:munderover><mml:mo movablelimits=\"false\">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>3</mml:mn></mml:munderover><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ii</mml:mi></mml:mrow></mml:msub><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:munderover><mml:mo movablelimits=\"false\">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:munderover><mml:mrow><mml:munderover><mml:mo movablelimits=\"false\">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>3</mml:mn></mml:munderover><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ij</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:mi>ε</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equa\"><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\text{Y}} = \\alpha_{0} + \\alpha_{{1}} {\\text{X}}_{{1}} + \\alpha_{{2}} {\\text{X}}_{{2}} + \\alpha_{{3}} {\\text{X}}_{{3}} + \\alpha_{{4}} {\\text{X}}_{{4}} + \\alpha_{{5}} {\\text{X}}_{{{5} + }} \\alpha_{{{12}}} {\\text{X}}_{{1}} {\\text{X}}_{{2}} + \\alpha_{{{13}}} {\\text{X}}_{{1}} {\\text{X}}_{{3}} + \\alpha_{{{14}}} {\\text{X}}_{{1}} {\\text{X}}_{{4}} + \\alpha_{{{15}}} {\\text{X}}_{{1}} {\\text{X}}_{{5}} + \\alpha_{{{23}}} {\\text{X}}_{{2}} {\\text{X}}_{{3}} + \\alpha_{{{24}}} {\\text{X}}_{{2}} {\\text{X}}_{{4}} + \\alpha_{{{25}}} {\\text{X}}_{{2}} {\\text{X}}_{{5}} + \\alpha_{{{34}}} {\\text{X}}_{{3}} {\\text{X}}_{{4}} + \\, \\alpha_{{{35}}} {\\text{X}}_{{3}} {\\text{X}}_{{5}} + \\alpha_{{{45}}} {\\text{X}}_{{4}} {\\text{X}}_{{5}} + \\alpha_{{{11}}} {\\text{X}}_{{1}}^{{2}} + \\alpha_{{{22}}} {\\text{X}}_{{2}}^{{2}} + \\, \\alpha_{{{33}}} {\\text{X}}_{{3}}^{{2}} + \\alpha_{{{44}}} {\\text{X}}_{{4}}^{{2}} + \\alpha_{55} X_{5}^{2} ,$$\\end{document}</tex-math><mml:math id=\"M12\" display=\"block\"><mml:mrow><mml:mtext>Y</mml:mtext><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mrow><mml:mn>5</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msub><mml:msub><mml:mi>α</mml:mi><mml:mn>12</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>13</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>14</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>15</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>23</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>24</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>25</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>34</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>α</mml:mi><mml:mn>35</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>45</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>11</mml:mn></mml:msub><mml:msubsup><mml:mtext>X</mml:mtext><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>22</mml:mn></mml:msub><mml:msubsup><mml:mtext>X</mml:mtext><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>α</mml:mi><mml:mn>33</mml:mn></mml:msub><mml:msubsup><mml:mtext>X</mml:mtext><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>44</mml:mn></mml:msub><mml:msubsup><mml:mtext>X</mml:mtext><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mn>55</mml:mn></mml:msub><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\text{TPC }}\\left( {{\\text{y}}_{{1}} } \\right) \\, &amp; = { 483}.{67} - {95}.{59}X_{{1}} + {2}.{5}X_{{2}} + {3}.{19}X_{{3}} + {12}.{2}X_{{4}} + {3}.{36}X_{{5}} + {9}.{4}X_{{1}} X_{{2}} - {2}.{64}X_{{1}} X3 + {3}.0{1}X_{{1}} X_{{4}} \\\\ &amp;\\quad + { 8}.{29}X_{{1}} X_{{5}} + {4}.{13}X_{{2}} X_{{3}} + {5}.{91}X_{{2}} X_{{4}} + {4}.{71}X_{{2}} X_{{5}} - {1}.0{3}X_{{3}} X_{{4}} + {9}.{69}X_{{3}} X_{{5}} + {1}0.{72}X_{{4}} X_{{5}} \\\\ &amp;\\quad + {5}.0{7}X_{{1}}^{{2}} + {11}.{14}X_{{2}}^{{2}} + {12}.{22}X_{{3}}^{{2}} + {7}.{16}X_{{4}}^{{2}} + {14}.{44}X_{{5}}^{{2}} . \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M14\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mtext>TPC</mml:mtext><mml:mspace width=\"0.333333em\"/></mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mtext>y</mml:mtext><mml:mn>1</mml:mn></mml:msub></mml:mfenced><mml:mspace width=\"0.166667em\"/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>483.67</mml:mn><mml:mo>-</mml:mo><mml:mn>95.59</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>2.5</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>3.19</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>12.2</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>3.36</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>9.4</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>2.64</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>3.01</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mn>8.29</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>4.13</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>5.91</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>4.71</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>1.03</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>9.69</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>10.72</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mn>5.07</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>11.14</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>12.22</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>7.16</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>14.44</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\text{TFC}}\\left( {{\\text{y}}_{{2}} } \\right) \\, &amp; = { 324}.{5} - {51}.{6659}X_{{1}} + {3}.{96}X_{{2}} + {2}.{26}X_{{3}} + {7}.{99}X_{{4}} + {4}.{13}X_{{5}} + {2}.{58}X_{{1}} X_{{2}} - {5}.{63}X_{{1}} X3\\\\ &amp;\\quad + {2}.{76}X_{{1}} X_{{4}} + { 4}.{75}X_{{1}} X_{{5}} + {1}.{34}X_{{2}} X_{{3}} + {3}.{94}X_{{2}} X_{{4}} + {1}.0{1}X_{{2}} X_{{5}} + 0.00{81}X_{{3}} X_{{4}} + {5}.{61}X_{{3}} X_{{5}} \\\\ &amp;\\quad + {3}.{15}X_{{4}} X_{{5}} + {3}.{45}X_{{1}}^{{2}} + {5}.{36}X_{{2}}^{{2}} + {5}.{32}X_{{3}}^{{2}} + {4}.0{1}X_{{4}}^{{2}} + {7}.{93}X_{{5}}^{{2}} . \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M16\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mtext>TFC</mml:mtext><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mtext>y</mml:mtext><mml:mn>2</mml:mn></mml:msub></mml:mfenced><mml:mspace width=\"0.166667em\"/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>324.5</mml:mn><mml:mo>-</mml:mo><mml:mn>51.6659</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>3.96</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>2.26</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>7.99</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>4.13</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>2.58</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>5.63</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mn>2.76</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>4.75</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.34</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>3.94</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.01</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.0081</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>5.61</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mn>3.15</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>3.45</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>5.36</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>5.32</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>4.01</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mn>7.93</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\% {\\text{DPPH}}*{\\text{sc}}\\left( {{\\text{y}}_{{3}} } \\right) \\, &amp; = { 72}.{28} - {7}.{81}X_{{1}} + 0.{8766}X_{{2}} - 0.{4147}X_{{3}} + {1}.0{7}X_{{4}} + 0.{3561}X_{{5}} - 0.0{6}0{3}X_{{1}} X_{{2}} \\\\ &amp;\\quad- 0.{3}0{91}X_{{1}} X3 + {1}.{45}X_{{1}} X_{{4}} - 0.{4197}X_{{1}} X_{{5}} + 0.{9}0{91}X_{{2}} X_{{3}} + {1}.{46}X_{{2}} X_{{4}} \\\\ &amp;\\quad+ 0.0{584}X_{{2}} X_{{5}} - 0.{8547}X_{{3}} X_{{4}} + {1}.{47}X_{{3}} X_{{5}} + { 1}.{68}X_{{4}} X_{{5}} - {1}.{38}X_{{1}}^{{2}} - {1}.{41}X_{{2}}^{{2}} \\\\ &amp;\\quad- 0.{8231}X_{{3}}^{{2}} - 0.{8726}X_{{4}}^{{2}} - 0.{6}0{3}0X_{{5}}^{{2}} , \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M18\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mo>%</mml:mo><mml:mtext>DPPH</mml:mtext><mml:mrow/><mml:mo>∗</mml:mo><mml:mtext>sc</mml:mtext><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mtext>y</mml:mtext><mml:mn>3</mml:mn></mml:msub></mml:mfenced><mml:mspace width=\"0.166667em\"/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>72.28</mml:mn><mml:mo>-</mml:mo><mml:mn>7.81</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.8766</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.4147</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.07</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.3561</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.0603</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>0.3091</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1.45</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.4197</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.9091</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.46</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mn>0.0584</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.8547</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.47</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.68</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>1.38</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>1.41</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>0.8231</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>0.8726</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>0.6030</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\% {\\text{ABTS}}*{\\text{sc}}\\left( {{\\text{y}}_{{4}} } \\right) \\, &amp; = {67}.{22} - {7}.{66}X_{{1}} + {1}.{16}X_{{2}} - 0.{3762}X_{{3}} + {1}.{19}X_{{4}} + 0.{3226}X_{{5}} - 0.{2753}X_{{1}} X_{{2}} \\\\ &amp;\\quad- 0.{5772}X_{{1}} X3 + {1}.{52}X_{{1}} X_{{4}} - 0.{1147}X_{{1}} X_{{5}} + 0.{7822}X_{{2}} X_{{3}} + {1}.{33}X_{{2}} X_{{4}} \\\\ &amp;\\quad+ 0.{1359}X_{{2}} X_{{5}} - {1}.{1}0X_{{3}} X_{{4}} + {1}.{72}X_{{3}} X_{{5}} + {1}.{28}X_{{4}} X_{{5}} - { 1}.{33}X_{{1}}^{{2}} - { 1}.{16}X_{{2}}^{{2}} \\\\ &amp;\\quad- 0.{5714}X_{{3}}^{{2}} - 0.{7968}X_{{4}}^{{2}} - 0.{51}0{4}X_{{5}}^{{2}} , \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M20\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mo>%</mml:mo><mml:mtext>ABTS</mml:mtext><mml:mrow/><mml:mo>∗</mml:mo><mml:mtext>sc</mml:mtext><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mtext>y</mml:mtext><mml:mn>4</mml:mn></mml:msub></mml:mfenced><mml:mspace width=\"0.166667em\"/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>67.22</mml:mn><mml:mo>-</mml:mo><mml:mn>7.66</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.16</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.3762</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.19</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.3226</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.2753</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>0.5772</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1.52</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.1147</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.7822</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.33</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mn>0.1359</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>1.10</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.72</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.28</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>1.33</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>1.16</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>0.5714</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>0.7968</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>0.5104</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ10\"><label>10</label><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\text{FRAP}}\\left( {{\\text{y}}_{{5}} } \\right) \\, &amp; = { 62}.{85} - {7}.{69}X_{{1}} + {1}.{33}X_{{2}} - 0.{4159}X_{{3}} + {1}.{25}X_{{4}} + 0.{2843}X_{{5}} - 0.{2784}X_{{1}} X_{{2}} \\\\ &amp;\\quad- 0.{6759}X_{{1}} X_{{3}} + {1}.{45}X_{{1}} X_{{4}} - 0.{2834}X_{{1}} X_{{5}} + 0.{7691}X_{{2}} X_{{3}} + {1}.{37}X_{{2}} X_{{4}} \\\\ &amp;\\quad- 0.0{184}X_{{2}} X_{{5}} - 0.{9}0{97}X_{{3}} X_{{4}} + {1}.{82}X_{{3}} X_{{5}} + {1}.{36}X_{{4}} X_{{5}} - { 1}.{47}X_{{1}}^{{2}} - {1}.{2}0X_{{2}}^{{2}}\\\\ &amp;\\quad - 0.{672}0X_{{3}}^{{2}} - 0.{93}0{1}X_{{4}}^{{2}} - 0.{4652}X_{{5}}^{{2}} . \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M22\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mtext>FRAP</mml:mtext><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mtext>y</mml:mtext><mml:mn>5</mml:mn></mml:msub></mml:mfenced><mml:mspace width=\"0.166667em\"/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>62.85</mml:mn><mml:mo>-</mml:mo><mml:mn>7.69</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.33</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.4159</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.25</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.2843</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.2784</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>0.6759</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.45</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.2834</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>0.7691</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.37</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>0.0184</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>0.9097</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.82</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mn>1.36</mml:mn><mml:msub><mml:mi>X</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn>1.47</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>1.20</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>0.6720</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>0.9301</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:mn>0.4652</mml:mn><mml:msubsup><mml:mi>X</mml:mi><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p>*All the experiments were repeated three times and values are expressed as mean ± standard deviation.</p></table-wrap-foot>", "<table-wrap-foot><p>*All the experiments repeated three times.</p></table-wrap-foot>", "<table-wrap-foot><p>^aDegrees of freedom.</p><p>^bTest for comparing model variance with residual (error) variance.</p><p>^cProbability of seeing the observed F value if the null hypothesis is true.</p><p>^dStd Dev: 34.48; Mean: 526.91; R² = 0.9273; R² predicted = 0.6930; R² adjusted = 0.8772.</p><p>^eStd Dev: 18.04; Mean: 347.09; R² = 0.9323; adjusted R² = 0.8856; predicted R² = 0.7567.</p><p>^fStd Dev: 3.47; Mean: 67.88; R² = 0.9045; adjusted R² = 0.8386; predicted R² = 0.6661.</p><p>^gStd Dev: 4.0; Mean: 63.43; R² = 0.8730; adjusted R² = 0.7855; predicted R² = 0.5611.</p><p>^hStd Dev: 3.93; Mean: 58.74; R² = 0.8800; adjusted R² = 0.7973; predicted R² = 0.5789.</p></table-wrap-foot>", "<table-wrap-foot><p>*All the experiments repeated three times.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41598_2023_49839_MOESM1_ESM.doc\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par3\">Only a small portion of the proteome is considered druggable with traditional approaches^{##REF##27910877##1##,##REF##17139284##2##}. Specifically, monoclonal antibodies are restricted to the extracellular space and high-affinity engagement with small molecules is generally limited to deep hydrophobic pockets such as those found at enzymatic active sites. Thus, target classes such as transcription factors and intracellular protein-protein interactions (PPIs), remain largely out-of-reach. Stapled α-helical peptides (stapled peptides) represent a potential corresponding solution^{##REF##25798993##3##}. Indeed, these molecules can bind with high affinity to these targets’ flat surfaces to result in modulation of protein function^{##REF##22230563##4##}. Stapled peptides contain one or more specialized macrocycles that promote the α-helical conformation. Olefin staples, the most common staple type, typically incorporate two α-methylated amino acids at either i –&gt; i + 4 or i –&gt; i + 7 positions, linked via ring closing metathesis (RCM)^{##REF##22230563##4##,##REF##21637196##5##}. Drug-like properties result, including enhanced binding, stabilized helical structure, enhanced proteolytic stability, and in some cases, cell permeability^{##UREF##0##6##}. However, achieving sufficient cell permeability to engage the target while avoiding off-target effects has proven to be a central challenge. Accordingly, we sought to uncover stapled peptide ‘design rules’ by studying an existing class of cell-active peptides that disrupt the p53/Mdm2(X) interaction.</p>", "<p id=\"Par4\">p53, the “guardian of the genome” is a transcription factor that regulates a variety of anti-oncogenic processes such as DNA damage repair, cell cycle arrest, apoptosis, and prevention of angiogenesis^{##REF##19935675##7##}. The importance of these functions is cemented by the observation that p53 is the most mutated protein in human cancers^{##REF##29099487##8##}. As well, Mdm2 and MdmX (also known as Mdm4), critical negative regulators of p53 function, are commonly upregulated in a variety of human lesions^{##REF##16543935##9##}. Both proteins inhibit p53 function through a sequestrating interaction involving the p53 N-terminal α-helix. Mdm2, but not MdmX, also acts as an E3 ligase to further suppress p53 activity by tagging it with polyubiquitin, leading to p53 destruction in the proteasome^{##UREF##1##10##}.</p>", "<p id=\"Par5\">The p53/Mdm2 PPI represents a valuable opportunity to make cross-modality comparisons since both small molecule and stapled peptide antagonists have been developed^{##REF##19935675##7##}. Stapled peptides consisting of either L- or D-amino acids have been discovered with both classes of molecules binding to Mdm2 and MdmX to displace the p53 N-terminal helix^{##UREF##0##6##,##REF##22148351##11##–##REF##17284038##14##}. The L-peptides include the clinical compound ALRN-6924 and its well-characterized progenitor ATSP-7041^{##UREF##0##6##,##REF##23946421##13##,##UREF##2##15##}. Several small molecule inhibitors have also advanced to the clinic^{##REF##28673313##16##}. These bind to the same Mdm2 pocket as the stapled peptides but lack the capacity to strongly bind to and inhibit MdmX, thus the Mdm2/X dual-inhibitory nature typical of stapled peptides such as ATSP-7041 may represent a differentiating advantage^{##REF##23946421##13##}. Understanding this and how the drug-like properties of these two distinct modalities impact therapeutic potential could play an important role in strategic drug discovery investments.</p>", "<p id=\"Par6\">Despite their promise, the discovery of on-target, cellularly active stapled peptides has been challenging. Specifically, compounds that appear to show cellular activity are frequently confounded by off-target toxicities, most notably the induction of membrane lysis which can lead to false positives^{##REF##33062184##17##} and pose safety liabilities^{##REF##21971370##18##–##REF##35024121##20##}.</p>", "<p id=\"Par7\">Here, we gain key understandings for the design-rules for a well-behaved, cell permeable/active stapled peptide. Specifically, we synthesize a library consisting of &gt;350 individual ATSP-7041 analogs and test these for target binding, cellular activity, cellular permeability, membrane disruption, and counter-screen activity. We reveal insights including a correlation between lipophilicity and cell permeability, a tendency for cationic residues to cause off-target toxicities, while anionic residues are well-tolerated. Optimization of staple type and peptide length/sequence composition result in peptides with improved cellular activity, decreased off-target effects, and improved in vivo activities. Combining favorable attributes leads to a lead peptide with low-nanomolar cell proliferation inhibitory activity with no off-target cell proliferation effects. Application of these lessons culminates in a distinct Mdm2 antagonist stapled peptide series with no observable off-target toxicities and a cellular activity that is improved by &gt;150-fold.</p>" ]

[ "<title>Methods</title>", "<p id=\"Par36\">Biological assays were run in at least duplicates (biological replicates). Duplicate values were typically within 1.5x of each other. If the duplicates were &gt;3x different, a third replicate was run. At this point, if all collected values were within 3x of the geometric mean, no further measurements were typically taken. Otherwise, further measurements were taken until this requirement was met. Values were reported as geometric means.</p>", "<title>Mdm2 protein production</title>", "<p id=\"Par37\">For use in the peptide binding assay, a human Mdm2 1–125 sequence was cloned into a pNIC-GST vector. The TEV (tobacco etch virus) cleavage site was changed from ENLYFQS to ENLYFQG to give a fusion protein with the following sequence:</p>", "<p id=\"Par38\">MSDKIIHSPILGYWKIKGLVQPTRLLLEYLEEKYEEHLYERDEGDKWRNKKFELGLEFPNLPYYIDGDVKLTQSMAIIRYIADKHNMLGGCPKERAEISMLEGAVLDIRYGVSRIAYSKDFETLKVDFLSKLPEMLKMFEDRLCHKTYLNGDHVTHPDFMLYDALDVVLYMDPMCLDAFPKLVCFKKRIEAIPQIDKYLKSSKYIAWPLQGWQATFGGGDHPPKLEVLFQGHMHHHHHHSSGVDLGTENLYFQGMCNTNMSVPTDGAVTTSQIPASEQETLVRPKPLLLKLLKSVGAQKDTYTMKEVLFYLGQYIMTKRLYDEKQQHIVYCSNDLLGDLFGVPSFSVKEHRKIYTMIYRNLVVVNQQESSDSGTSVSEN-.</p>", "<p id=\"Par39\">The corresponding plasmid was transformed into BL21 (DE3) Rosetta T1R Escherichia coli cells and grown under kanamycin selection. Bottles of 750 mL Terrific Broth, supplemented with appropriate antibiotics and 100 μL of antifoam 204 (Sigma-Aldrich, St. Louis, MO, USA, were inoculated with 20 mL seed cultures grown overnight. The cultures were incubated at 37 °C in the LEX system (Harbinger Biotech, Toronto, Canada) with aeration and agitation through the bubbling of filtered air through the cultures. The LEX system temperature was reduced to 18 °C when culture OD600 reached 2, and the cultures were induced after 60 min with 0.5 mM IPTG. Protein expression was allowed to continue overnight. Cells were harvested by centrifugation at 4000× g, at 15 °C for 10 min. The supernatants were discarded and the cell pellets were resuspended in a lysis buffer (1.5 mL per gram of cell pellet). The cell suspensions were stored at −80 °C before purification work.</p>", "<p id=\"Par40\">The re-suspended cell pellet suspensions were thawed and sonicated (Sonics Vibra-Cell, Newtown, CO, USA) at 70% amplitude, 3 s on/off for 3 min, on ice. The lysate was clarified by centrifugation at 47,000× g, 4 °C for 25 min. The supernatants were filtered through 1.2 μm syringe filters and loaded onto the AKTA Xpress system (GE Healthcare, Fairfield, CO, USA). The purification regime is briefly described as follows. The lysates were loaded onto a 1 mL Ni-NTA Superflow column (Qiagen, Valencia, CA, USA) that had been equilibrated with 10 column volumes of wash 1 buffer. Overall buffer conditions were as follows: Immobilized metal affinity chromatography (IMAC) wash 1 buffer—20 mM HEPES ((4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid), 500 mM NaCl, 10 mM Imidazole, 10% (v/v) glycerol, 0.5 mM TCEP (Tris(2-carboxyethyl)phosphine), pH 7.5; IMAC wash 2 buffer—20 mM HEPES, 500 mM NaCl, 25 mM Imidazole, 10% (v/v) glycerol, 0.5 mM TCEP, pH 7.5; IMAC Elution buffer—20 mM HEPES, 500 mM NaCl, 500 mM Imidazole, 10% (v/v) glycerol, 0.5 mM TCEP, pH 7.5. The sample was loaded until air was detected by the air sensor, 0.8 mL/min. The column was then washed with wash 1 buffer for 20 column volumes, followed by 20 column volumes of wash 2 buffer. The protein was eluted with five column volumes of elution buffer. The eluted proteins were collected and stored in sample loops on the system and then injected into gel filtration (GF) columns. Elution peaks were collected in 2 mL fractions and analyzed on SDS-PAGE gels. The entire purification was performed at 4 °C. Relevant peaks were pooled, TCEP was added to a total concentration of 2 mM. The protein sample was concentrated in Vivaspin 20 filter concentrators (VivaScience, Littleton, MA, USA) at 15 °C to approximately 15 mg/mL. ( &lt; 18 kDa—5 K MWCO, 19–49 kDa—10 K MWCO, &gt;50 kDa—30 K MWCO). The final protein concentration was assessed by measuring absorbance at 280 nm on Nanodrop ND-1000 (Thermo Fisher, Waltham, MA, USA). The final protein purity was assessed on SDS-PAGE gel. The final protein batch was then aliquoted into smaller fractions, frozen in liquid nitrogen and stored at −80 °C.</p>", "<title>Mdm2 binding by competitive fluorescence anisotropy assay</title>", "<p id=\"Par41\">Purified Mdm2 (1-125) protein was titrated against 50 nM carboxyfluorescein (FAM)-labeled 12/1 peptide (FAM-RFMDYWEGL-NH2). The dissociation constants for titrations of Mdm2 against FAM-labeled 12/1 peptide were determined by fitting the experimental data to a 1:1 binding model equation shown below:</p>", "<p id=\"Par42\">[P] is the protein concentration (Mdm2), [L] is the labeled peptide concentration, r is the anisotropy measured, r₀ is the anisotropy of the free peptide, r_b is the anisotropy of the Mdm2–FAM-labeled peptide complex, K_d is the dissociation constant, [L]_t is the total FAM labeled peptide concentration, and [P]_t is the total Mdm2 concentration. The apparent K_d value for FAM-labeled 12/1 peptide against Mdm2 was determined to be 13.0 nM respectively. This value was then used to determine apparent K_d values of the respective competing ligands in subsequent competition assays in fluorescence anisotropy experiments.</p>", "<p id=\"Par43\">Mdm2 competition experiments were performed with their respective concentrations held constant at 250 nM in the presence of 50 nM of FAM-labeled 12/1. The competing molecules were then titrated against the complex of the FAM-labeled peptide and protein. Apparent Kd values were determined by fitting the experimental data to equations shown below:</p>", "<p id=\"Par44\">[L]_st and [L]_t denote labeled ligand and total unlabeled ligand input concentrations, respectively. K_d2 is the dissociation constant of the interaction between the unlabeled ligand and the protein. In all competition experiments, it is assumed that [P]t &gt; [L]_st, otherwise considerable amounts of free labeled ligand would always be present and would interfere with measurements. K_d1 is the apparent K_d for the labeled peptide used and has been experimentally determined as described in the previous paragraph. The FAM-labeled peptide was dissolved in dimethyl sulfoxide (DMSO) at 1 mM and diluted into experimental buffer. Readings were carried out with an Envision Multilabel Reader (PerkinElmer). Experiments were carried out in PBS (2.7 mM KCl, 137 mM NaCl, 10 mM Na2HPO4 and 2 mM KH2PO4 (pH 7.4)) and 0.001% Tween-20 buffer. Curve-fitting was carried out using Prism 4.0 (GraphPad). To validate the fitting of a 1:1 binding model we carefully ensured that the anisotropy value at the beginning of the direct titrations between Mdm2 and the FAM-labeled peptide did not differ significantly from the anisotropy value observed for the free fluorescently labeled peptide. Negative control titrations of the ligands under investigation were also carried out with the fluorescently labeled peptide (in the absence of Mdm2) to ensure no interactions were occurring between the ligands and the FAM-labeled peptide. In addition, we ensured that the final baseline in the competitive titrations did not fall below the anisotropy value for the free FAM-labeled peptide, which would otherwise indicate an unintended interaction between the ligand and the FAM-labeled peptide to be displaced from the Mdm2 binding site. Measurements were taken a minimum of three times (biological replicates) and values are reported as geometric means of the replicates.</p>", "<title>Solubility assay</title>", "<p id=\"Par45\">Kinetic solubility was determined by diluting 10 mM stock solution of the peptides in DMSO in PBS buffer at pH 7 to make test solutions. The standard reference solutions were prepared by diluting the 10 mM stock in 10:80:10 solution of acetonitrile:methanol:DMSO to 100 µM. Standard solution and test solutions were analyzed using Agilent 1290 UPLC/DAD system after filtering the test solutions through a 0.45 μm polypropylene filter.</p>", "<p id=\"Par46\">The solubility value is calculated by the following equation:</p>", "<p id=\"Par47\">Solubility [µM] = (Peak area of sample/ Peak area of standard) (Standard concentration)</p>", "<title>Whole cell homogenate stability</title>", "<p id=\"Par48\">Peptides at a concentration of 1 μM were incubated at 37 °C with HCT116 whole cell homogenates prepared from 1 million lyzed cells/mL. The reaction was stopped at 0, 1, 2, and 4 hours and 22 hours with an organic solvent followed by centrifugation. The resulting supernatant was injected to LC/MS for the detection of tested peptide. The remaining percentage of each compound was normalized to the 0 hour amount and reported.</p>", "<title>Plasma stability</title>", "<p id=\"Par49\">Peptide was incubated with human plasma at the concentration of 1 mM at 37 C for 1, 2, 3, and 4 hours. The incubation was stopped at indicated time points by addition of organic solvent followed by centrifugation. Parent compound in supernatant was analyzed by LC/MS. Percent remaining of peptide was calculated against the amount of compound at time 0.</p>", "<title>p53 beta-lactamase reporter gene cellular functional assay</title>", "<p id=\"Par50\">HCT116 cells were stably transfected with a p53 responsive β-lactamase reporter and expanded in McCoy’s 5 A Medium with 10% fetal bovine serum (FBS), Blasticidin, and Penicillin/Streptomycin and then transferred to 1.5 ml freezing vials and stored under liquid nitrogen in growth media containing 5% DMSO. One day prior the assay, a vial of banked cells was recovered in a cell culture flask and incubated for 24 hours, followed by removal of cell growth media and replacement with Opti-MEM containing 2% FBS. The cells were then seeded into a 384-well plate at a density of 8000 cells per well. Peptides were then dispensed to each well using a liquid handler, ECHO 555, and incubated 16 h. The final working concentration of DMSO was 0.5%. β-lactamase activity was detected using the ToxBLAzer Dual Screen (Invitrogen), as per the manufacturer’s instructions. Measurements were made using the Envision multiplate reader (Perkin–Elmer). Maximum p53 activity was defined as the amount of β-lactamase activity induced by 50 µM azide-ATSP-7041. This was determined as the highest amount of p53 activity induced by azide-ATSP-7041 from titrations on HCT116 cells. Measurements were taken a minimum of three times (biological replicates) and values are reported as geometric means of the replicates.</p>", "<title>Lactate dehydrogenase (LDH) release assay</title>", "<p id=\"Par51\">HCT116 cells were stably transfected with a p53 responsive β-lactamase reporter and expanded in McCoy’s 5 A Medium with 10% fetal bovine serum (FBS), Blasticidin, and Penicillin/Streptomycin and then transferred to 1.5 ml freezing vials and stored under liquid nitrogen in growth media containing 5% DMSO. One day prior the assay, a vial of banked cells was recovered in a cell culture flask and incubated for 24 hours, followed by removal of cell growth media and replacement with Opti-MEM containing 2% FBS. The cells were then seeded into a 384-well plate at a density of 8000 cells per well. Peptides were then dispensed to each well using a liquid handler, ECHO 555, and incubated 16 h. The final working concentration of DMSO was 0.5%. Lactate dehydrogenase release was detected using the CytoTox-ONE Homogenous Membrane Integrity Assay Kit (Promega), as per the manufacturer’s instructions. Measurements were carried out using the Tecan plate reader. Maximum LDH release was defined as the amount of LDH released as induced by the lytic peptide (iDNA79) and used to normalize the results. Measurements were taken a minimum of three times (biological replicates) and values are reported as geometric means of the replicates.</p>", "<title>Tetracycline beta-lactamase reporter gene cellular assay (counterscreen)</title>", "<p id=\"Par52\">This assay was based on Jump-In™ T-REx™ CHO-K1 BLA cells containing a stably integrated β-lactamase under the control of an inducible cytomegalovirus (CMV) promoter. Cells were maintained in Dulbecco’s Minimal Eagle Medium (DMEM) with 10% fetal bovine serum (FBS), Blasticidin, and Penicillin/Streptomycin and then transferred to 1.5 ml freezing vials and stored under liquid nitrogen in growth media containing 5% DMSO. One day prior the assay, a vial of banked cells was recovered in a cell culture flask and incubated for 24 hours, followed by removal of cell growth media and replacement with Opti-MEM containing 2% FBS. Cells were seeded into a 384-well plate at a density of 4000 cells per well. Peptides were then dispensed to each well using a liquid handler, ECHO 555 and incubated for 16 h. The final working concentration of DMSO was 0.5%. β-lactamase activity was detected using the ToxBLAzer Dual Screen (Invitrogen), as per the manufacturer’s instructions. Measurements were carried out using the Envision multiplate reader (Perkin–Elmer). Counterscreen activity was defined as the amount of β-lactamase activity induced by tetracycline. Measurements were taken a minimum of three times (biological replicates) and values are reported as geometric means of the replicates.</p>", "<title>Circular dichroism (CD)</title>", "<p id=\"Par53\">A total of 5 µL of the 10 mM stock peptide was mixed with 45 µL of 100% methanol, and dried for 2 h in the SpeedVac concentrator (Thermo Scientific). The dried peptide was reconstituted in a buffer (1 mM Hepes pH 7.4 and 5% methanol) to a concentration of 1 mM. The peptide sample was placed in a quartz cuvette with a path length of 0.2 cm. The peptide concentration was determined by the absorbance of the peptide at 280 nM. The CD spectrum was recorded from 300 to 190 nm using the Chirascan-plus qCD machine (Applied Photophysics, Surrey, UK), at 25 °C. All experiments were done in duplicates. The CD spectrum was converted to mean residue ellipticity before deconvolution and estimation of the secondary structure components of the peptide using the CDNN software (distributed by Applied Photophysics). Measurements were taken at least twice and were reported as arithmetic means.</p>", "<title>Cell proliferation studies</title>", "<p id=\"Par54\">Routine CellTiter-Glo®Cell Proliferation Assays: CellSensor™ p53RE-bla HCT-116 Cell Line was obtained from Invitrogen (K1640) and the Ca Ski cell line was obtained from American Type Culture Collection (CRM-CRL-1550). The medium for CellSensor™ p53RE-bla HCT-116 cells was McCoy’s 5 A Medium (GIBCO16600-002) supplied with 10% FBS (Hyclone, SH30406.05), 100 U/100ug/ml of Pen/Strep (SolarBio, P1400) and 5 μg/ml of blasticidin (GIBCO, A11139). The medium for Ca Ski cells was RPMI1640 (Hyclone, SH3080901B) supplied with 10% FBS and 100 U/100ug/ml of Pen/Strep. All cells were kept in humidified incubators with 5% CO2 at 37 °C. Culture media was changed after one day of subculturing and cells were passed again when there was 70–80% confluence. One day before the assay, the cells were trypsinized, collected, counted and viability was determined. The cells were seeded into a 384-well plate (Corning, 3570). The seeding density of CellSensor™ p53RE-bla HCT-116 was 750 cells/well/40 uL and the seeding density of Ca Ski was 600 cells/well/40 uL. The plates were kept in humidified incubators with 5% CO2 at 37 °C overnight. Compounds were prepared as a 10 point, 3x serial dilution in 100% DMSO, starting from a top concentration of 10 mM. Compounds were added to the assay plate by an Echo 550(Labcyte) and incubated with the cells for 72 hours in humidified incubators with 5% CO2 at 37 °C. At the end of the incubation the assay plate was equilibrated at room temperature for approximately 30 minutes prior to the addition of 25 uL of CellTiter-Glo® 2.0 Reagent. The assay plate was mixed for 2 minutes on an orbital shaker to induce cell lysis. Next, the plate was incubated at room temperature for 10 minutes to stabilize the luminescent signal prior to recording the luminescence on a plate reader.</p>", "<p id=\"Par55\">Extend CellTiter-Glo® Cell Proliferation Panel: Cell proliferation inhibition of compounds were performed on extended cell panels at fee-for-service at Shanghai ChemPartner Co., Ltd. Cell lines were procured form ATCC and included HCT116 (CCL-247), Ca Ski (CRL-1550), SJSA-1 (CRL-2098), A549(CCL-185), Hep G2 (HB-8065), MCF-7 (HTB-22), LoVo (CCL-229), SW48 (CCL-231), SW480(CCL-228), AsPC-1(CRL-1682), HL-60 (CCL-240), LS123 (CCL-255), MDA-MB-361 (HTB-27), MIA PaCa-2 (CRL-1420), HeLa (CCL-2), MS571 (HTB-34), SiHa (HTB-35), NCI-H1299 (CRL-5803), and Saos-2 (HTB-85). Amongst the cell lines used, the following lines are amongst those listed as frequently misidentified by the International Cell Line Authentication Committee: HeLa, A549, HepG2, MCF-7,LoVo, SW48,.AsPC-1,HL-60, and MIA PaCa-2. These latter lines were used in order to employ a variety of lines represented diverse cancer types and that represented different p53 status (wild-type, mutant, null, and HPV infected). Imporantly, assay ready cells were used for these experiments and PCR analysis of target short tandem repeat (STR) markers was used to authenticate cell lines prior to cell banking. Cell viabilities were determined using the CellTiter-Glo® assay kit (Promega G7558). Cells were cultured and seeded onto 384-well assay plate (Corning 3765) using the Thermo Scientific Multidrop. Assay plates were incubated at 37 °C, 5% CO2 overnight to allow cell attachment. Following day, compounds were dispensed into the assay plate using the Tecan HPD300 system and incubated at 37 °C, 5% CO2 for 120 h. At 120 h post dose, CellTiter-Glo assay was performed according to the manufacturer’s protocol. Assay plates were read on a Envision Reader with luminescence at an integration time of 0.1 second per well. Staurosporine (Selleckchem S1421) was used as a positive control for the assay.</p>", "<title>Nanoclick permeability assay</title>", "<p id=\"Par56\">This assay was previously described in detail^{##REF##33539064##22##}. The assay was performed in 384-well white assay plates (PerkinElmer CUSG03874) using assay-ready frozen cells that had been transiently transfected with the NanoLuc-HaloTag vector that were thawed at plated in complete media at a density of 6000 cells/ well and incubated at 37 °C 5% CO2 overnight. DIBAC-CA was diluted in assay buffer (OptiMem without phenol red + 1% FBS) and added to cells at a final concentration of 3 μM and incubated at 37 °C 5% CO2 for 1 h. Cells were subsequently centrifuged using a BlueWasher instrument (Blue Cat Bio) to remove the DIBAC-CA solution and washed two times with HBSS (Ca2 + , Mg2 + ). A volume of 30 μL of assay buffer was added back to cell plates. Peptides were serially diluted 4-fold in DMSO with a Hamilton Star apparatus and then delivered into assay plates with an acoustic liquid handler Labcyte ECHO (300 nl, 1% DMSO in-well concentration). After incubating cells with peptide for the desired time (4 or 18 h), the HaloTag ligand, NanoBret618-azide, was added to each well at a final concentration of 10 μM. After 1 h incubation at 37 °C, 5% CO2, a solution of NanoBRET Nano-Glo Substrate and extracellular NanoLuc Inhibitor was diluted in OptiMem to yield a final in-well concentration of 1× Nano-Glo Substrate and 20 μM of NanoLuc inhibitor and read on the Envision instrument immediately. Following addition of NanoBRET Nano-Glo Substrate, donor emission (450 nm) and acceptor emission (610 nm) were measured using an Envision instrument (PerkinElmer).</p>", "<title>In vivo xenograft models</title>", "<p id=\"Par57\">Human osteosarcoma SJSA-1 cells were purchased from ATCC (Manassas, VA, USA) and cultured with RPMI 1640 medium (Sigma Aldrich, Merck, Germany), supplemented with 10% fetal bovine serum (FBS), 1% l-glutamine, and 1% penicillin/streptomycin. Cells were cultured for less than 3 months after purchase.</p>", "<p id=\"Par58\">Female immunocompromised BALB/c nu/nu mice (<italic>N</italic> = 32, age = 5–8 weeks) were housed in individual ventilated cages and maintained in a 12-hour light-dark cycle (6 am to 6 pm), at a temperature of 19–24 °C with relative humidity of 45–58% and fed ad libitum. 2.5 ×106 SJSA-1 cells were injected subcutaneously in the right lower flank using a 1:1 mix of matrigel and PBS. Tumor size was measured using a digimatic caliper (Mitutoyo, Sweden) and volume was calculated as 4πabc/3 where a, b, and c were measured diameters in all dimensions.</p>", "<p id=\"Par59\">For the comparison of the efficacy and mechanism of action of the drugs used in the present study, we do not expect any difference based on the sex of the animals. However, we are aware that some xenografts may grow at different rates in males and females. The choice of females in this study serves to minimize variability (reduce biological variation) and increase the quality of the study while respecting the three R’s by not extending it to double the number of animals where males are also used.</p>", "<p id=\"Par60\">Animals were randomized into four treatment groups with 8 animals/group. Peptides were dissolved in DMSO at 30 mg/ml and administered i.v. in 30% (2-Hydroxypropyl)-β-cyclodextrin (HPβCD) or Sulfobutylether-β-Cyclodextrin (SBEβCD) (Sigma Aldrich, Merck, Germany). When tumors reached a size of 60–100 mm³, mice received at total of seven doses of ATSP-7041, ALRN-6924, MP-616 (alkyne staple) or vehicle twice a week with 30 mg/kg for twenty-five days. The vehicle group was treated with the same volume of DMSO and HPβCD. Tumor measurements were performed in connection with injections for the treatment (not blinded). Mouse weight and tumor growth were monitored every other day. All experiments complied with Swedish law and were performed with permission from the Uppsala Committee of Animal Research Ethics, permit #10966/2020.</p>", "<title>Peptide synthesis</title>", "<p id=\"Par61\">All peptides were sourced from CPC Scientific or made in-house at A*STAR. The purity and identity of the peptides was confirmed by analytic HPLC and mass spectrometry. All the final peptides have ≥90% purity. All peptides were dissolved in neat DMSO as 10 mM stock solution and diluted thereof for subsequent experiments. HATU is hexafluorophosphate azabenzotriazole tetramethyl uronium, HBTU is 2-(1H-benzotriazole-1-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate, DIC is N,N′-diisopropylcarbodiimide, HOBt is 1-hydroxybenzotriazole, NMM is N-methylmorpholine, PyAOP is (7-azabenzotriazol-1-yloxy)tripyrrolidinophosphonium hexafluorophosphate, RCM is ring closing metathesis.</p>", "<p id=\"Par62\">Peptides were synthesized using Knorr Amide MBHA Resin and Fmoc-protected amino acids, and coupled sequentially with HATU/NMM, HBTU/NMM, or DIC/HOBt, activating agents, depending on the peptide and residue being coupled. Amino acid (AA) and couple agent ratios were as follows: AA/HATU/NMM = 3/2.85/6, AA/HBTU/NMM = 3/2.85/6, and AA/HOBT/DIC = 3/3/3. The resin was first swelled in dimethylformamide (DMF) for 2.0 hours followed by addition of 20% piperidine in DMF. The mixture was kept at room temperature for 0.5 hour while a stream of nitrogen was bubbled through it. The mixture was filtered, and the peptidyl resin was washed five times with DMF. For couplings, the Fmoc-protected amino acid, DMF, NMM and HBTU or HATU were added into the resin sequentially. The suspension was kept at room temperature for 1 hour while a stream of nitrogen was bubbled through it. After the ninhydrin test had indicated complete coupling, the mixture was filtered, and the peptidyl resin was washed three times with DMF. 20% Piperidine in DMF was added into the resin to remove the Fmoc group. Subsequent amino acids were coupled to the resin bound peptide sequentially with reaction times between 0.5 and 1.5 hours, depending on the residues being coupled. After assembly of the linear peptide, the resin was washed twice with MeOH, twice with DCM, and twice and twice with MeOH. The resin was dried under vacuum overnight.</p>", "<p id=\"Par63\">For peptides with olefin staples, RCM was performed on-resin. The peptidyl resin was washed twice with 1,2-dichloroethane (DCE), followed by the addition of Grubbs(I) Catalyst dissolved in DCE (e.g. 150 mg of catalyst in 6 ml of DCE). The mixture was kept at 35 °C for 3 hours while a stream of nitrogen was bubbled through it. The mixture was filtered, and the peptidyl resin was washed three times with DMF (e.g., 3 × 20 mL). After the RCM was complete, a test cleavage was performed to ensure adequate yield.</p>", "<p id=\"Par64\">For peptides with lactam staples, Fmoc-Lys(Mtt)-OH was used and selectively deprotected by washing the resin twice with DCM, followed by addition of a 2%TFA/4%TIS/94%DCM solution. The mixture was kept at room temperature for 5 min while a stream of nitrogen was bubbled through it. The resin was then washed with DCM twice. This procedure was repeated 5 times before proceeding. 5 mL DMF, HOBT (10eq), DIPEA (10eq) and PyAOP (3eq) were added into the resin sequentially. The mixture was shaken at room temperature overnight and mass spectrometry had indicated a complete reaction. The resin was then washed with DMF twice.</p>", "<p id=\"Par65\">For peptide containing the dialkyne staple, stapling was performed on resin. The peptidyl resin was dried by washing three times with DCM, and then transferred to a glass vial. THF (10 mL), DIPEA (5 mL), Pd(PPh₃)₂Cl₂ (0.05 mmol 35 mg) and Cu(I) (0.1 mmol 20 mg) were and the mixture was put on a table concentrator rotated at ~30 °C under air for 16 hours. A test cleavage was then performed to ensure adequate yield and the solution was transferred to the reactor and filtered, and then washed six times with DMF.</p>", "<p id=\"Par66\">For peptides with acetylated N-termini, an acetic anhydride/NMM capping solution was applied for 30 minutes after the final coupling reaction. Peptides were cleaved and then purified as a mixture of cis-trans isomers by RP-HPLC.</p>", "<title>Computational methods</title>", "<p id=\"Par67\">Peptide design and molecular dynamics simulations were carried out using the AMBER18 package^{##UREF##11##47##} following a protocol used earlier^{##REF##32874502##30##} and are discussed below. The models of the peptides used in this study were based on the structural models of Mdm2: ATSP-7041, Mdm2: ^dPMI-δ (6-10 staple) and Mdm2: ^dPMI-δ (5-12 staple) published earlier^{##UREF##0##6##,##REF##32874502##30##}.</p>", "<p id=\"Par68\">All the structural models built were subjected to Molecular Dynamics (MD) simulations for further refinement. MD simulations were carried out on the free peptides and peptide – Mdm2 complexes. The Xleap module of AMBER18^{##UREF##12##48##} was used to prepare the system for the MD simulations. Hydrogen atoms were added and the N- and C- termini of the peptides were capped with ACE and NHE moieties respectively. The parameters for the staple linkers were taken from our previous studies^{##UREF##0##6##,##REF##32874502##30##}. All the simulation systems were neutralized with appropriate numbers of counter ions and solvated in an octahedral box with TIP3P^{##UREF##13##49##} water molecules, leaving at least 10 Ǻ between the solute atoms and the borders of the box. MD simulations were carried out with the pmemded module of the AMBER 18 package in combination with the ff14SB force field^{##REF##26574453##50##}. We have found that the combination of ff14SB and TIP3P and the parameters listed below have been successful in simulating the Mdm2-peptide systems^{##REF##26574453##50##,##UREF##14##51##}. All MD simulations were carried out in explicit solvent at 300 K. During the simulations, the long-range electrostatic interactions were treated with the particle mesh Ewald^{##UREF##14##51##} method using a real space cut off distance of 9 Ǻ. The settle^{##UREF##15##52##} algorithm was used to constrain bond vibrations involving hydrogen atoms, which allowed a time step of 2 fs during the simulations. Solvent molecules and counter ions were initially relaxed using energy minimization with restraints on the protein and peptide atoms. This was followed by unrestrained energy minimization to remove any steric clashes. Subsequently the system was gradually heated from 0 to 300 K using MD simulations with positional restraints (force constant: 50 kcal mol^-1 Å^-2) on protein and peptides over a period of 0.25 ns allowing water molecules and ions to move freely followed by gradual removal of the positional restraints and a 2 ns unrestrained equilibration at 300 K. The resulting systems were used as starting structures for the respective production phases of the MD simulations. For each case, three independent (using different initial random velocities) MD simulations were carried out starting from the well equilibrated structures. Each MD simulation was carried out for 250 ns and conformations were recorded every 4 ps. To enhance the conformational sampling, each peptide was subjected to Biasing Potential Replica Exchange MD (BP-REMD) simulations^{##REF##17120231##53##}; the BP-REMD technique is a type of Hamiltonian-REMD method but includes an additional biasing potential to promote dihedral transitions along the replicas^{##REF##17120231##53##}. For each system, BP-REMD was carried out with eight replicas including a reference replica without any bias. BP-REMD was carried out for 50 ns with exchange between the neighbouring replicas attempted every 2 ps and accepted or rejected according to the metropolis criteria^{##REF##24318649##54##}. Conformations sampled at the reference replica (no bias) were used for further analysis. Simulation trajectories were visualized using VMD^{##REF##8744570##55##} and figures were generated using Pymol^{##UREF##16##56##}.</p>", "<title>Reporting summary</title>", "<p id=\"Par69\">Further information on research design is available in the ##SUPPL##4##Nature Portfolio Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<title>ATSP-7041 shows on-target activity but with a narrow on-target window</title>", "<p id=\"Par8\">Therapeutic advancement of stapled peptides are often confounded by cellular toxicity^{##REF##33062184##17##}. We leveraged ATSP-7041 and analogs (such as the previously studied azido-version, MP-081^{##UREF##0##6##}, Fig. ##FIG##0##1a, b##), as these had been previously validated to be high-affinity Mdm2(X) binders with bona fide cellular activity^{##UREF##0##6##,##REF##27721413##21##}. However, these peptides did not represent fully optimized stapled peptides as they exhibited off-target effects in multi-day cell proliferation studies (Fig. ##FIG##0##1c##). Specifically, although these peptides showed measurable proliferation potencies against cell lines harboring wild-type (WT) p53, they had a narrow on-target index, with activities against control lines (p53 null, p53 mutant or p53-depleted through HPV infection) that were only ~10-fold weaker (Fig. ##FIG##0##1c##). This poly-pharmacology was not observed with the cell impermeable control peptide (MP-950, Fig. ##FIG##0##1c##) but was seen with a cell permeable non-binding control peptide (MP-202, ATSP-7041 with a F3 to D-Phe substitution, Fig. ##FIG##0##1c##), confirming the effects to be independent from Mdm2/X binding. These results suggested that further study of this peptide series might provide insights for optimizing the cellular activity while removing the off-target toxicities.</p>", "<title>Lipophilicity correlates with cell permeability</title>", "<p id=\"Par9\">To gain insights as to how to design well-behaved, cell-active stapled peptides against an intracellular target, we made &gt;350 ATSP-7041 analogs. These represented single and multiple amino acid substitutions and were characterized with a spectrum of metrics including binding, cellular activity, activity in a p53 independent counter-screen, circular dichroism spectroscopy, experimental LogD, calculated ALogP, solubility, NanoClick permeability^{##REF##33539064##22##}, and membrane disruption (as measured by lactate dehydrogenase (LDH) cytoplasmic release), (Supplementary Data ##SUPPL##3##1##). As the NanoClick cell permeability assay relies on intracellular click-chemistry, most peptides used the previously-studied^{##UREF##0##6##} azide-ATSP-7041 (MP-081) as a template (Fig. ##FIG##0##1a, b##). Other library members were based on the parent peptide, ATSP-7041^{##REF##23946421##13##} or PM2^{##REF##23214419##12##}, a related sequence (Fig. ##FIG##0##1b##).</p>", "<p id=\"Par10\">Peptides included those with single or multiple amino acid substitutions at various positions. To leverage cell activity as an important metric, we generally preserved amino acid residues critical for the Mdm2 binding interface (F3, W7, Cba10), as defined in Fig. ##FIG##0##1b## (Cba corresponds to cyclobutyl alanine, a non-natural leucine analog). To avoid having time and serum binding components confound permeability measurements, we used 0% serum and a 4-hour peptide incubation time as our standard assay condition. 16-hour time-points and 10% serum conditions were also collected for a subset of peptides (Supplementary Data ##SUPPL##3##1##). The library represented peptides with diverse properties as shown by a wide range of values in biochemical and cellular assays as well as calculated attributes (Fig. S##SUPPL##0##1##). Significantly, this structurally-diverse ATSP-7041 library represents a valuable public resource for a collective understanding of α-helical peptide design. Our initial analysis focused on variants of azide-ATSP-7041 (MP-081, Fig. ##FIG##0##1a, b##) and led to the following key observations:<list list-type=\"order\"><list-item><p id=\"Par11\">As expected, mutations to the three key binding residues (F3, W7, Cba10) generally had large decreases in binding affinity to shift the K_D by &gt;50x (Fig. ##FIG##1##2a## and Supplementary Table ##SUPPL##0##1##, parent K_D = 5 nM). The only exceptions were substitution of W7 with tryptophan analogues (within 2x of the parent affinity) and substitution of Cba with Leu (K_D = 56 nM) or Ala (K_D = 115 nM). Outside of the Mdm2 binding motif, ~70% (47 out of 66) of the single substitutions maintained low nanomolar-affinity binding ( &lt; 50 nM) and all but one maintained affinities of &lt;250 nM (Fig. ##FIG##1##2a##, Supplementary Table ##SUPPL##0##1##). The exception to the latter was E5P (K_D = 7.8 µM), (Fig. ##FIG##1##2a##, Supplementary Table ##SUPPL##0##1##), attributable to proline-induced helical structure loss as circular dichroism spectroscopy measured helicity of this peptide at 22%, compared to 50% for MP-081 (Supplementary Data ##SUPPL##3##1##). A preponderance (8 out of 10) of substitutions at Thr2 led to weaker binding (Fig. ##FIG##1##2a##), which is consistent with a known structural role of the threonine sidechain at this position^{##UREF##0##6##}. In addition, peptides with poor solubilities tended to have shifted binding constants (Supplementary Table ##SUPPL##0##1##), values that are likely artifactual due to the molecules being sequestered into soluble aggregates. Overall, these results indicate that if the binding motif and staple are held constant, there is a large sequence space that could be explored to optimize other peptide properties while maintaining high affinity. Indeed, exemplary peptides with multi-site substitutions to a single amino acid had K_Ds that were within 3-fold of the parent peptide; for example, azide-ATSP-7041 (L1D, E5D, A8D) and azide-ATSP-7041 (L1N, E5N, A8N, S12N, A13N, A14N), had K_D values of 5 and 15 nM, respectively (Supplementary Table ##SUPPL##0##1##, MP-495 and MP-359, respectively).</p></list-item><list-item><p id=\"Par12\">At non-binding positions, single substitutions to charged residues (K, R, hR (homo-Arg), H, E) usually resulted in decreased cellular activity (Fig. ##FIG##1##2b##, 22 of 31 substitutions), an observation that was slightly more common with basic substitutions (20 of 26, 77%) versus substitutions to acidic residues (5 of 8, 63%). We noted that single substitutions to basic residues almost universally led to poor solubility ( ≤ 10 µM, Supplementary Table ##SUPPL##0##1##), an observation likely due to the generation of peptides with a net charge of zero (except for substitutions at the E5 position). Furthermore, substitution to histidine often led to counterscreen efficacies that were greater than the tetracycline control, with the T2H peptide as the worst offender (277% efficacy at 50 μM, EC50 = 5.9 μM, Supplementary Table ##SUPPL##0##2##). As well, peptides containing multiple positive charges (e.g. MP-537, MP-538, MP-539, MP-879, MP-880) frequently resulted in LDH release and/or counterscreen activity (Supplementary Table ##SUPPL##0##1##). Further, there have been several literature reports^{##REF##21971370##18##–##REF##35024121##20##} that highlight that the combination of hydrophobic character and positive charge can result in mast cell degranulation (MCD), a potentially fatal condition^{##REF##21971370##18##–##REF##35024121##20##}. Overall, the results indicate that caution must be taken when introducing cationic residues.</p></list-item><list-item><p id=\"Par13\">Conversely, a full glutamic acid scan of MP-081 generated peptides with universally excellent solubility ( &gt; 90 µM, Supplementary Table ##SUPPL##0##1##). Although introduction of Glu at most positions led to decreased cellular activity, peptides with an A8E, S12E, or A14E substitution had cellular potencies that were equipotent (within 2x) to the parent peptide (Fig. ##FIG##1##2b##). Importantly, none of the peptides with additional acidic residues showed off-target effects, even when peptides contained two (e.g., the peptides in Fig. ##FIG##2##3a##), three (MP-496), four (MP-3684) or even up to seven (MP-950) glutamic acid residues, although these peptides were generally cellularly inactive (Supplementary Table ##SUPPL##0##1##). The NanoClick assay^{##REF##33539064##22##} determines permeability of azide-labeled peptides by combining intracellular copper-free click chemistry with NanoBRET technology. Specifically, if an azido-peptide achieves cytosolic exposure, it will react with a cyclooctyne-decorated Halotag construct that is fused with nanoluciferase. This reaction blocks the click labelling of a subsequently added azido-labeled acceptor dye, thus decreasing the NanoBRET signal in a manner that is target-binding agnostic. By applying this assay, we were able to study the permeability effects of the Glu scan, even at positions where target binding was abolished. We noted that the parent ATSP-7041 sequence is amphipathic, possessing a target-binding hydrophobic face (the hydrophobic staple and the apolar residues colored in black in Fig. ##FIG##2##3a##) and a solvent-exposed hydrophilic face (residues colored in blue or green, Fig. ##FIG##2##3a##). Introduction of a Glu on the hydrophilic side tended to maintain NanoClick permeabilities. In contrast, placing a Glu residue in the hydrophobic face tended to reduce NanoClick permeabilities, with the W7E peptide showing the most dramatic effects ( ~ 34x shift). Overall, these results suggest that charge and polar separation can be incorporated into a-helical stapled peptide design to balance the dual needs for permeability and solubility.</p></list-item><list-item><p id=\"Par14\">A weak correlation between peptide helicity and cellular permeability was observed. Specifically, when permeability (as measured by the cell ratio, defined as the cellular EC₅₀ / Mdm2 K_D), was plotted versus peptide helicity, we noted that peptides with poor cell ratios (400 or greater) also had low helicity values (&lt;31%, Fig. S##SUPPL##0##2A##). This observation suggests enhancing helicity may contribute to improved cellular permeability, as has been suggested by a previous study^{##REF##27547919##23##}.</p></list-item><list-item><p id=\"Par15\">A stronger correlation was observed between peptide polarity and permeability. Indeed, polar to apolar substitutions tended to enhance cellular activity in our standard assay (0% serum, 4 hours). When we analyzed the entire library of ATSP-7041 analogs, we found that peptide lipophilicity (experimental LogD) correlated with both permeability (as measured by the cell ratio, Fig. ##FIG##2##3b## or Nanoclick, Fig. S##SUPPL##0##3B##) and cellular activity (Fig. S##SUPPL##0##2C##). The most potent peptides were those rendered net-neutral charge (Fig. ##FIG##1##2d##, peptides highlighted in blue) through a substitution at residue E5 to an apolar residue (Fig. ##FIG##2##3b##) and represented a significant increase in cellular potency, up to 10x (e.g., 0.044 μM for MP-965, AZIDE-ATSP-7041 (E5A, S12A), Supplementary Table ##SUPPL##0##3##). However, we judged that designing peptides which were increasingly hydrophobic (LogD &gt; 3) was not a practical path to the clinic as these molecules also displayed poor solubilities (often &lt;1 μM, Supplementary Table ##SUPPL##0##3##). In addition, peptides with either measurable poor solubilities ( &lt; 10 μM) or those with poor behavior in our solubility assay (i.e., gave multiple peaks), showed &gt;10x loss in cellular potency when tested in the presence of 10% FBS (Supplementary Table ##SUPPL##0##3##). Furthermore, we tested one such highly hydrophobic peptide (MP-350, LogD = 3.37) in a cell proliferation panel and it showed off-target proliferation effects in control lines that overlapped with the on-target effects (Fig. S##SUPPL##0##3##). Although increasing hydrophobicity may seem an attractive option at the in vitro stage, poor solution behavior would pose a considerable challenge during formulation and testing in vivo.</p></list-item></list></p>", "<p id=\"Par16\">Next, we sought to improve solubility and reduce the observed off-target effects (Figs. ##FIG##0##1c## and S##SUPPL##0##3##). In addition to aiding in cell permeability (Fig S##SUPPL##0##2A##), we speculated that enhancing helicity would improve solubility by preventing β-sheet based peptide aggregation. Enhanced helicity might also limit alternative peptide conformations to mitigate toxicities related to promiscuous binding to off-target proteins. Accordingly, we sought to stabilize peptide helicity by I) extending the peptide with sequences of high helical propensity and II) optimizing both the number and nature of the peptide staples. To assess these effects, we shifted our primary focus to cellular activity in the presence of serum and measured at a later time point (16 hours) as it represented a more physiological condition.</p>", "<title>C-termini with high helical propensity enhance cellular activity</title>", "<p id=\"Par17\">Inspection of the patent literature suggested that increasing the number of residues on the C-terminus of the peptide leads to improved solubility^{##UREF##3##24##}. Specifically, Ala-rich C-terminal extensions (referred to here as C-terminal tails) were reported to increase peptide solubility. The most common patent sequences C-terminal to the staple were Ala-Ala-Ala-Ala-Ala-Ala-NH₂ (A₆-NH₂) and Ala-Ala-Ala-Ala-Ala-(D-Ala)-NH₂ (A₅-dA-NH₂). In our hands, when we replaced the MP-081’s SAA-NH₂ tail with the A₅-dA-NH₂ tail (MP-464), we observed a modest improvement in solubility (Table ##TAB##0##1##), and cellular activity was improved by ~3x (290 vs 880 nM, 10% serum, 16-hour assay, Table ##TAB##0##1##). A similar improvement in cellular activity was observed with the A₆-NH₂ tail (MP-464, Table ##TAB##0##1##), although this peptide did not behave well in our solubility assay. Interestingly, tails with six Ala residues appeared to be a ‘sweet spot’ as peptides containing a A₅-NH₂ (MP-685) or an A₇-NH₂ (MP-470 and MP-471) motif had slightly worse cellular activities in the presence of serum (Table ##TAB##0##1##). Notably, compared to the 6-residue tail peptides, those with additional Ala extensions (A₇-NH₂, MP-470 and MP-471; A₉-NH₂ motif, MP-759) had better cell potency (as low as 0.06 µM) in the 0%, 4-hour assay but had greatly right-shifted (up to 40x for MP-470) cellular potency in the 10% serum, 16-hour assay, presumably due to serum binding. Interestingly, when we studied the proteolytic stability of a subset of peptides in a protease-rich matrix (whole cell homogenate), we observed that both the A₅-dA-NH₂ and A_6-NH₂ peptides had short half-lives (t_1/2 values of 30 and 92 min for MP-032 (A₆-NH₂ tail) and MP-464 (A₅-dA-NH₂ tail), respectively), values that compare poorly to the parent peptide (t_1/2 &gt; 24 hours). Metabolic profiling identified the A14/A15 peptide bond to be the proteolytic site, liberating an active metabolite with an additional negative charge at the C-terminus. Interestingly, a peptide representing a pre-cleaved tail (Ala₃-COOH, MP-684) had a cellular potency that was right-shifted by &gt;5x in the presence of serum (Table ##TAB##0##1##), suggesting that the polyalanine tails are cleaved intracellularly. Indeed, this idea was supported by the fact that MP-464 (A₅-dA-NH₂ tail) was highly stable in serum plasma (Fig S##SUPPL##0##4##). We speculate that the intracellular generation of an uncapped C-terminus and its associated negative charge results in the peptide being better retained in the intracellular space, thus potentially contributing to the enhanced cellular activity. During the preparation of this manuscript, the sequence of the clinical molecule, ALRN-6924 (Sulanemadlin, MP-4897), was disclosed as Ac-LTF(R8)EYWAQL(S5)AAAAA(dA)-NH₂ (staple between R8 and S5)^{##UREF##4##25##}. A detailed account of the discovery and characterization of this molecule was subsequently published^{##UREF##2##15##}. We prepared this molecule and found that it behaved similarly to our azido-analogs (MP-032 and MP-464, Table ##TAB##0##1##). We also prepared a peptide similar to ALRN-6924 but with the (Ala)₆-NH₂ tail (MP-688) and found that it gave an equivalent potency in the 0% serum assay but a right-shifted potency in the 10% serum assay (1.3 µM, Table ##TAB##0##1##). The reason for the disconnect in potency between this peptide and our azido analog (MP-032) is not clear.</p>", "<p id=\"Par18\">We hypothesized that the enhanced cellular activities of peptides with polyAla tails were related to the helical propensity of these segments. It is important to remember that peptides with diverse sequences—including those containing residues of low helical propensity—usually adopt a very high degree of helicity in low dielectric constant environments^{##REF##9726967##26##}, such as the lipid bilayer and the membrane/water interface. Thus, stabilizing helicity in the aqueous phase might enhance permeability by decreasing the entropic penalty related to the transition to a highly helical membrane-inserted state. To challenge this hypothesis, we made a series of peptides with C-terminal tails that had either high or low predicted helical propensities in the aqueous environment (Table ##TAB##0##1##). Compared to MP-032 (-A₆-NH₂tail), all peptides containing tails with low helical propensity showed dramatic decreases in cellular activity (6.5x to &gt;172x), despite maintaining high affinity for Mdm2. Except for the (AA-dA)₂-NH2 tail peptide, all molecules containing tails with low predicted helical propensity, had poor experimental aqueous helicity, as determined by circular dichroism spectroscopy (Table ##TAB##0##1##). In contrast, sequences containing tails with high helical propensity had cellular potencies similar to those observed with the polyalanine tail peptides. However, we noted that although these peptides generally had higher solution-based helicities compared to the low propensity group, experimental aqueous helicity values were not enhanced compared to MP-081. Thus, further studies will be required to fully understand how these tails lead to improved cellular activities.</p>", "<title>A variety of C-terminal tails give sub-micromolar cellular potencies</title>", "<p id=\"Par19\">We sought to further enhance cell potency while avoiding off-target effects by optimizing the C-terminal tail sequence. Our multi-pronged approach involved optimization strategies, including: 1) solubility and solution state behavior through enhanced amphipathicity to balance the hydrophobic character; 2) enhancement of Mdm2 binding through productive interactions via the C-terminal tail, 3) tail stability through sequence optimization, residue a-methylation (addition of a methyl group to the amino acid’s alpha-carbon, a modification that is known to inhibit protease cleavage^{##UREF##5##27##}), and/or additional staples; and 4) increased cellular permeability, through enhanced interactions with the membrane.</p>", "<p id=\"Par20\">To improve peptide behavior, we probed for amino acid positions that would tolerate polar residues without compromising cellular activity. Accordingly, we scanned the C-terminal tail (positions 12 to 17), of MP-464 (-A₅-dA-NH₂ tail) with substitutions of glutamic acid, a residue with high helical propensity (Table ##TAB##1##2##). Like the Glu-scan on the shorter MP-081 peptide, introduction of Glu residues generally decreased cellular activity, this included the A12E substitution (MP-834), which contrasts with what we observed with the shorter peptide. Interestingly, placement of a gamma-carboxyglutamic acid residue (Gla, a residue containing two acidic groups in the side-chain) at position 12 (MP-897), gave cellular activities that were within 2-fold of the parent peptide (Table ##TAB##1##2##). Similarly, a peptide with an A14E substitution (MP-833) gave a slightly enhanced cellular potency in the presence of serum (0.19 μM). In addition, a peptide with three additional Glu residues (MP-3685, AZIDE-ATSP-7041 (A8E, EEAAAA TAIL), Supplementary Data ##SUPPL##3##1##) had good cell reporter activity under serum conditions (0.66 μM, Supplementary Data ##SUPPL##3##1##) and a strong HCT116 cell proliferation potency (0.64 μM, Supplementary Data ##SUPPL##3##1##), despite its overall -4 charge. These latter observations demonstrate that multiple negative charges can be accommodated in a cell-permeable stapled peptide. Most importantly, although peptides with the original A₆-NH₂ or A₅-dA-NH₂ tails tended to show some off-target proliferation effects in a counterscreen line that is devoid of cellular p53 protein (Ca Ski, Table ##TAB##1##2##), peptides with the additional Glu residues were largely devoid of proliferation effects in this line (Table ##TAB##1##2##). In addition, many of the peptides with Glu-containing tails had HCT-116 proliferation effects that approximated—or improved on—those of MP-464 or ARLN-6924. Overall, although the extra negative charge did not appear to markedly enhance peptide equilibrium solubility compared to MP-464 (Table ##TAB##1##2##), the increased anionic nature of these peptides may be assisting with peptide solution behavior in more subtle ways (i.e., solution micro-aggregation (oligomerization) state and/or dissolution kinetics) to result in potent molecules with very good on-target profiles.</p>", "<p id=\"Par21\">Examination of the helical wheel (Fig. ##FIG##3##4a##) revealed that placement of apolar residues at positions 14 and 17 might enhance both Mdm2 binding and promote interactions with the membrane by lengthening the apolar helical face. Molecular modeling suggested that phenylalanine might be an ideal residue at these positions (Fig. ##FIG##3##4b##). Accordingly, we made a series of peptides with Phe residues at one or both positions (Table ##TAB##1##2##). A peptide (MP-040) with Phe at both positions (14 and 17) showed enhanced cellular activity (EC₅₀ = 36 nM) in the 0% FBS, 4-hour assay but was right-shifted by &gt;20x in the 10% serum, 16- hour assay (MP-040 in Table ##TAB##1##2##), likely due to serum binding. The peptides with the extra Phe residues were either poorly soluble (12 µM or less) or poorly behaved in our solubility assay (Table ##TAB##1##2##), suggesting that they have very poor solubility. Notably, MP-220, a peptide with the di-Phe motif and an introduced single anionic residue (α-methyl Glu) had complete rescue of the shifted activity (0.20 and 0.21 µM in the 0% and 10% serum assays, respectively) and gave excellent solubility (157 μM, Table ##TAB##1##2##). However, it should be noted that this peptide had a narrow on-target index with an off-target EC₅₀ value in the Ca Ski proliferation assay of 19.9 μM, suggesting that further optimization is required for this sequence. In contrast to the improvements in peptide behavior imparted by the introduction of a single anionic residue, the addition of multiple copies of a polar—but non-ionic—residue (homoSer) failed to rescue solubility and serum shift (the -((hS)₂F)₂-NH₂ peptides_, Table ##TAB##1##2##). This highlights the charge requirement for enhancing solution behavior. Overall, these results suggest that it is possible to introduce additional apolar residues into the tail to improve interactions with Mdm2 and/or the cell membrane but that these need to be balanced with negative charge to maintain drug-like properties.</p>", "<title>Optimizing staple type and number significantly mitigates off-target activity</title>", "<p id=\"Par22\">To explore the effect of staple number and type on peptide properties, we made a series of peptides with alternative crosslinks. Within the context of MP-081 (-SAA tail), replacing the olefin staple with a triazole crosslink (Fig. ##FIG##4##5a##, MP-707) resulted in high affinity binding (1.1 nM) but gave poorer cellular potency, especially in the presence of 10% serum (13.6 μM, Fig. ##FIG##4##5a##). On the other hand, adding a second staple at the N-terminus through a K1 to E5 lactam bridge (Fig. ##FIG##4##5a##, MP-002) gave moderate cellular potency (2.2 μM, 10% serum, Fig. ##FIG##4##5a##) but also gave poor behavior in our solubility assay, presumably due to the removal of the negative charge. We also examined an MP-464 (polyAla) analog containing a patent-derived di-alkyne staple^{##UREF##3##24##}. This cross-link should be very rigid due to the conjugated triple bonds (see molecular structure in Fig. ##FIG##4##5a##). The resulting peptide (MP-616), containing both the rigid staple and the A₅-dA-NH₂ tail, had very good solubility (128 μM) and good cellular activities: 480 nM in the 10% serum, 16-hour p53 assay and 124 nM in the HCT116 cell proliferation assay (Fig. ##FIG##4##5a##). Importantly, both the lactam peptide and the di-alkyne stapled peptide proved to be remarkably devoid of off-target toxicity across our cell proliferation panel (Fig. ##FIG##4##5b##), which differentiated them from other stapled peptides examined (Figs. ##FIG##1##2c## and S##SUPPL##0##3##), as well as advanced Mdm2 small molecule antagonists, MK-4688^{##REF##34714078##28##} and AMG 232^{##REF##24456472##29##} (Fig. ##FIG##4##5b##). The way the double-stapled and di-alkyne stapled peptides avoid off-target toxicities is not clear. However, this result may be related to reduced promiscuous binding by restricting conformational freedoms – either of the staples themselves or of the peptide backbone.</p>", "<title>Peptides with polyAla tails have improved in vivo activity versus ATSP-7041</title>", "<p id=\"Par23\">To understand whether improvements in in vitro peptide activity translated to the in vivo setting, we compared ATSP-7041 head-to-head with two polyAla containing peptides in a mouse SJSA-1 xenograft model. As one candidate, we selected ALRN-6924 since it was of interest to explore the in vivo performance of the clinical molecule. For the other molecule, we chose the di-alkyne stapled peptide, MP-616 since it had a different macrocycle and a very clean off-target profile. ATSP-7041 had clear tumor growth inhibition ( ~ 33% tumor growth inhibition) when dosed intravenously every third day at 30 mg/kg but was outperformed by both ALRN-6924 and MP-616, which had large and significant improvements ( ~ 66% tumor growth inhibition, Fig. ##FIG##5##6##). Although not examined here, it would be interesting to understand if the clean off-target profile for MP-616 translates into fewer side-effects in vivo, especially considering the poly-pharmacology observed with ALRN-6924 at higher doses in the counterscreen line, Ca Ski (Table ##TAB##1##2##).</p>", "<title>Combining favorable attributes resulted in a peptide with low-nanomolar potency</title>", "<p id=\"Par24\">In addition to improvements from appending the polyalanine tails, judicious placement of negative charge, and the di-alkyne staple, we also noted that an L1 to azido-lysine substitution resulted in improved cellular potency in an ALRN-6924 analog (MP-062, 117 nM in 10% serum, 16 hours, Supplementary Data ##SUPPL##3##1##). Accordingly, we combined this improvement with the di-alkyne staple and an optimized C-terminal tail to arrive at MP-444: Ac-K(N3)-TF(X)EYWAQ(Cba)(X)EAFAAF-NH₂ (where X = the di-alkyne stapling positions), which had good solubility (167 µM), a binding K_D of 1.5 nM, cellular EC₅₀s of 51 and 153 nM (4 hours, 0% serum and 16 hours, 10% serum, respectively) and a cell proliferation EC₅₀ of 60 nM against HCT116 (Supplementary Data ##SUPPL##3##1##). This peptide also had some slight off-target effects, although the on-target index was ~1000x compared to the Ca Ski proliferation (EC₅₀ &gt; 50 μM but with 39.5% growth inhibition at 50 µM). Dramatic improvements were also seen with a di-alkyne stapled peptide with an a-methyl glutamic acid in the polyAla tail. Specifically, MP-467 (Ac-K(N3)-(betaAla)-LTF(X)EYWAQ(Cba)(X)AA(a-methly-Glu)AA(DAla)-NH2, Supplementary Data ##SUPPL##3##1##) showed a potency of 30 nM in the serum-containing cell reporter assay and an EC₅₀ = 13 nM in the HCT116 cell proliferation assay (Supplementary Data ##SUPPL##3##1##). Remarkably, this peptide was completely devoid of proliferation effects in the Ca Ski control line (Fig. ##FIG##6##7##, EC₅₀ ≫ 50,000 nM; no measurable inhibition at 50,000 nM). Overall, this peptide was the most potent molecule observed to date in our HCT116 cell proliferation assay and with an on-target index of &gt;3800x. Furthermore, in terms of cell proliferation potency, this peptide represents a 292x improvement over our starting point (azide-ATSP-7041) and an 80x improvement over ALRN-6924 (Fig. ##FIG##6##7##). Finally, MP-467 also greatly outperformed the advanced Mdm2 small molecule antagonists MK-4688 and AMG 232, both in terms of their on-target profiles (Fig. ##FIG##3##4b## vs Fig. ##FIG##5##6##) and 16-hour 10% serum p53 activities ( &gt; 10x superior potency, Supplementary Data ##SUPPL##3##1##).</p>", "<title>Application of peptide design insights to a stapled D-peptide improves its cellular potency by 100-fold and removes off-target activity</title>", "<p id=\"Par25\">Next, we sought to understand whether the lessons learned from the ATSP-7041 library could be used to improve peptides from an independent series. We focused on the ^dPMI-d(6-10 staple) molecule (MP-769), a previously described^{##REF##32874502##30##} all-D stapled peptide with Mdm2 antagonistic activity. This molecule was an ideal test case since it had innate hyper-stability (due to its all-D nature) and verified binding but exhibited poor cellular activity (e.g., inactive in 10% serum at 16 hr, Fig. ##FIG##7##8##) and suffered from LDH release and counterscreen liabilities, likely due to its multi-cationic nature (free N-terminus, K9 and R12, Fig. ##FIG##7##8##). It also had an amphipathic character (Fig S##SUPPL##0##5##) which we judged would be beneficial for maintaining peptide solubility. We first sought to remove the positive charges (<italic>vide supra</italic>). Using ATSP-7041 as an amphipathic template with good cell permeability and activity, we noted the presence of an acetylated N-terminus and Ser and Gln residues on its polar helical face (Fig S##SUPPL##0##5##). To mimic this topology, we acetylated the N-terminus of MP-769 and introduced the K9Q and R12S substitutions, changes that produced an improved peptide (MP-797) that was inactive in the LDH-release and counterscreen assays (EC₅₀s &gt; 50 µM, Fig. ##FIG##7##8##b). We noted that this peptide had good solubility (167 µM, Fig. ##FIG##7##8b##), a value that was dependent on the molecule having a net negative (-1) charge since a peptide with the same sequence, but with a net-neutral charge due to its free N-terminus, had poor solubility (1 µM, MP-795, Supplementary Data ##SUPPL##3##1##). The cellular activity of MP-797 was also improved by 3-fold (EC₅₀ = 3.6 µM, Fig. ##FIG##7##8b##) in the 0% serum, 4-hour assay. However, the compound still had weak cellular efficacy (EC₅₀ &gt; 50 µM) under 10% serum conditions and displayed a poor on-target cell proliferation profile (Fig. ##FIG##7##8b##). We then appended poly-d-alanine tails of different lengths. Consistent with the ATSP-7041 series, the (D-Ala)₆ C-terminal tail provided the best profile for the all-D series (Supplementary Data ##SUPPL##3##1##). Specifically, MP-042 had excellent solubility (150 µM) and a cellular activity of 0.28 µM in the 10% serum, 16-hour p53 assay, representing an overall improvement of &gt;178-fold compared to the initial parent peptide (Fig. ##FIG##7##8b##). However, despite being devoid of LDH and counterscreen activity, this peptide showed a narrow therapeutic index ( ~ 20-fold) with proliferation potencies of 1.5 and 31 µM in HCT116 and Ca Ski, respectively (Fig. ##FIG##7##8b##). This may result from the significant conformational freedom available to an i to i + 4 stapled peptide, which may allow for promiscuous binding to a variety of targets. Finally, decreasing (3x D-Ala, MP-230) or further increasing (9x D-Ala, MP-1230) the length of the tail led to compounds with poorer cellular efficacy, and for the 9x D-Ala tail peptide, poorer solubility (Supplementary Data ##SUPPL##3##1##), similar to observations in the ATSP-7041 series (Table ##TAB##1##2##).</p>", "<p id=\"Par26\">To address the off-target effects observed with the i to i + 4 stapled all-D peptide (MP-042), we explored whether switching a longer (i to i + 7) and more rigid (di-alkyne) linkage could mitigate these effects. Accordingly, we elected to apply our emerging design rules to ^dPMI-d(5-12 staple) (MP-770), a previously reported stapled all-D peptide with an i to i + 7 olefin staple^{##REF##32874502##30##}, with modest cellular potency that overlapped with its counterscreen activity (Fig. ##FIG##7##8b##). To address these deficiencies, we i) introduced a K9Q substitution along with N-terminal acetylation to remove the positive charges; ii) introduce the (D-Ala)₆ polyalanine C-terminal tail to optimize solubility and helicity; iii) replaced the i, i + 7 olefin macrocycle with the di-alkyne staple. These changes resulted in MP-793 which had ultra-tight binding (K_D &lt; 1 nM, Fig. ##FIG##7##8b##) and a &gt; 102x higher potency (0.3 μM, Fig. ##FIG##7##8b##) in the 10% serum, 16-hour assay (versus MP-770, the i to i + 7 olefin parent). Notably, compared to the optimized 6-10 stapled peptide (MP-042), MP-793 had a &gt; 2x improved cell proliferation potency and a greatly improved on-target index with proliferation EC₅₀s of 0.65 and &gt;50 μM against HCT116 and Ca Ski, respectively (HCT116 % inhibition at 50 μM = 0.5% Fig. ##FIG##7##8b##). This result is consistent with the excellent on-target profiles achieved with the di-alkyne stapled L-peptides (e.g., MP-467 and MP-616).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par27\">Although stapled peptides hold therapeutic promise to tackle highly validated but historically intractable targets, a corresponding approved therapeutic has yet to be realized. This is not surprising since it is a relatively new class of molecules, and its discovery and developmental challenges are still being defined. The work described herein is the most exhaustive report to-date to explore structure-activity relationships of a large library ( &gt; 400) of staple peptides. These studies have resulted in an improved understanding for how to generate a lead stapled peptide against an intracellular target. Learnings from the ATSP-7041 library resulted in molecules that had improved binding, cellular activity (up to 292x improvement), and, in some cases, undetectable off-target toxicity. Critically, a select lead compound also gave improved in vivo activity compared to ATSP-7041, a molecule that had already been extensively optimized^{##REF##23946421##13##}. Using the same target protein (Mdm2), these emerging ‘design rules’ were then validated in a second chemically distinct series, resulting in removal of off-target toxicities and an improvement in cellular activity of &gt;100x.</p>", "<p id=\"Par28\">To summarize the knowledge gained, we outline our general workflow for designing a lead stapled peptide against an intracellular target. In practice, the order of steps proposed is unlikely to be entirely linear as drug discovery often follows a meandering path where the improvements to one property often results in the worsening of another. As such, certain steps may need to be revisited before arriving at a lead molecule. Nevertheless, the stepwise protocol listed below should serve as a general framework:<list list-type=\"order\"><list-item><p id=\"Par29\"><bold>Identification of high-affinity binders:</bold> Lead identification initiates with the discovery of a high-affinity a-helical binder against a target of interest. Phage and mRNA display are mature technologies that allow for the selection of high affinity sequences with high probability^{##REF##33771353##31##–##UREF##6##33##}. Some systems^{##REF##26929989##32##,##REF##33038548##34##,##REF##36534810##35##} enable the use of staples within the primary screen, which can aid in the discovery of helical binders. Starting points can also be discovered through rational-design by leveraging a-helices that naturally mediate PPIs^{##REF##23071338##36##,##REF##21075307##37##}. Post-screening, affinity maturation may be achieved through substitution of interfacial residues with both natural and non-natural amino acids. At this stage, we recommend removing all cationic residues that are non-critical to binding. This is important as peptides that are rich in both apolar residues and have a net positive charge often promote cell toxicity and false-positive readouts in cellular assays, as shown by previous work^{##REF##33062184##17##} and this study (e.g. the net positively charged peptides in Supplementary Table ##SUPPL##0##1##).</p></list-item><list-item><p id=\"Par30\"><bold>Selection of staple position:</bold> With a high affinity helical binder in-hand, the next task is to identify the optimal stapling position. To be exhaustive, a staple-scan is preferred where all possible positions are surveyed. Although many staple types exist, our suggestion is to limit the initial analogs to a single chemistry: olefin staples resulting from ring closing metathesis of (S)-2-(4’-pentenyl)alanine and (R)-2-(7’-octenyl)alanine at the i and i + 7 positions, respectively. This initial chemistry is suggested as i, i -&gt; 7 staples give better helical stabilization and superior proteolytic resistance versus i, i -&gt; 4 staples. In addition, cost-effective commercial building blocks are readily available and the reaction results in high yields. With an initial library of stapled peptides in-hand, routine screening of binding, solubility, cellular activity, and stability should begin (although this latter property is not of concern if employing an all-D peptide). These criteria should be considered in aggregate for selecting the final stapling position. The position of the staple will also influence the peptide’s initial and potential amphipathicity^{##REF##27547919##23##}, a property that may be important for peptide solubility and aqueous behavior. For example, the binding interface of the ATSP-7041 peptide consists of three spatially contiguous apolar residues (F, W, and Cba) and is flanked by the apolar staple. This presentation makes it straightforward to engineer an amphipathic helix by placing hydrophilic residues on the solvent facing side, an arrangement that balances the dual needs for membrane interaction (for permeability) with good aqueous behavior.</p></list-item><list-item><p id=\"Par31\"><bold>Optimization of peptide length:</bold> Next, we recommend optimizing peptide length. Although this work provides examples where extending peptide length gives improved cellular activities, examinations of shorter peptides may also be fruitful. To lengthen a peptide, we recommend starting with a series of N- and C-terminal extensions by appending varying numbers of alanines, a slightly apolar residue with high helical propensity.</p></list-item><list-item><p id=\"Par32\"><bold>Optimization of staple type and number:</bold> Optimization of staple type and number may give improved peptide performance in a few ways. First, target affinity may be improved by stabilizing the peptide in its binding conformation. Peptide stability may also be improved by preventing proteases from engaging with exposed peptide bonds. In addition, peptides that are better locked into the a-helical conformation will make fewer hydrogen bonds with water as their backbone amide and carbonyl moieties will be engaged with each other, as part of the a-helical architecture. As a result, improved membrane permeabilities may result from a smaller desolvation penalty associated with traversing the membrane bilayer. As shown by this work, optimization of peptide type (e.g., the di-alkyne staple in MP-616) or number (e.g., the double-stapled MP-002) may also decrease non-specific toxicities, perhaps due to restricted conformational sampling of the peptide leading to decreased interactions with off-target biomolecules. A simple approach for restricting conformational heterogeneity is through the introduction of a rigid staple such as the dialkyne linkage reported by Aileron^{##UREF##3##24##} and used here. Another strategy is to employ multiple staples. Options include a variety of chemistries including but not limited to hydrocarbon staples via RCM, lactam bridges (e.g. MP-002), proline-locked peptides^{##UREF##7##38##}, hydrogen bond surrogates^{##REF##34325784##39##}, and a variety of other staple types^{##UREF##8##40##} including, crosslinked cysteine residue, and triazole linkers. Possibilities also encompass a variety of residue spanning topologies (e.g., i -&gt; i + 3, i -&gt; i + 4, i -&gt; i + 7, etc.)^{##REF##21637196##5##}. In addition peptides with multiple staples may have double^{##REF##20660316##41##}, stitched^{##REF##32874502##30##,##REF##25105213##42##} and cross-stitched arrangements^{##REF##29725689##43##}. It may be of interest to explore whether macrocyclic strategies that lock the entire peptide length into the helical conformation through a network of crosslinks from termini to termini would be optimal. Finally, although not macrocyclic in nature, conformational restriction can also be achieved through the introduction of residues with high helical propensity, including a-methylated residues. This latter strategy may also confer additional protease resistance.</p></list-item><list-item><p id=\"Par33\"><bold>Final sequence optimization:</bold> once peptide length and stapling strategies are finalized, peptide properties may be further optimized through sequence exploration. First, if the helix has been lengthened, there may be opportunities to improve binding affinity by introduction of sidechains within the extended region that productively engage the target surface (e.g., the introduction of the Phe residues in MP-040 and analogs such as MP-444). As observed here, once the target binding interface is optimized, stapled peptides can have extensive flexibility for sidechain identity at the solvent-facing positions. Sidechain exploration in this region is critical for optimizing peptide permeability while maintaining peptide solubility. We suggest aiming for a helix with both apolar and polar helical faces. In such amphipathic peptides, the apolar side is required to promote peptide permeability through productive membrane interactions. However, as seen from our library analysis, sequences should not be made too hydrophobic as they can result in cell toxicity, poor solubilities, and shifts in cellular activity in the presence of serum. Overtly hydrophobic sequences can potentially be rescued by judicious placement of hydrophilic residues. Specifically, placement of an acidic residue is preferred as basic residues have liabilities (<italic>vide supra)</italic> and non-charged side chains had minimal effects on peptide solubility, although these latter residues may be required as part of the hydrophilic face. Examples reported here show how a single Glu residue can enhance solubility (e.g., MP-444) and reduce off-target toxicities (e.g., the peptides with multiple anionic charges in Table ##TAB##1##2##). An extensive library of analogs, including non-natural amino acids, may be required to arrive at a peptide with the optimal balance of the nature, number, and arrangement of apolar and polar residues.</p></list-item></list></p>", "<p id=\"Par34\">Although the current work has provided valuable insights, we would like to underscore some limitations. First, although the application of lessons gained from the ATSP-7041 library resulted in significant improvements in a distinct chemical series (the ^dPMI-d peptides), it is important to highlight that both series are directed towards the same target(s) (Mdm2/X). Thus, future studies should aim to understand if the design rules uncovered here can make similar impacts to stapled peptides against distinct targets. Indeed, the workflow we propose here is likely to be most applicable to targets that - like Mdm2/X - have a hydrophobic PPI interface that is addressable with a helical motif. Indeed, we expect that not all targets will have geometries that will accommodate or otherwise be suitable for high-affinity binding to a helical segment. For targets where the PPI interface is hydrophilic, it will be interesting to explore whether our generalized workflow can be altered in a corresponding manner. In particular, one might focus on optimizing the polar surface for binding affinity while installing hydrophobic residues on the opposing side of the helix to gain cell permeability. In addition, it will be interesting to see if judicious placement of anionic residues and optimization of staple type/number is a generalizable approach for removing stapled peptide toxicities. Another limitation of our study is that although some of the peptides reported here appear to be devoid of off-target effects, those observations come from a narrow set of experiments. Conducting proteome-wide surveys (using MS-CETSA or related techniques) would be of interest to understand the extent to which these molecules can engage with off-targets. In addition, although we have increased our understanding for identifying lead peptides, drug hunters will appreciate that converting these leads to clinical candidates may require further exploration of the chemical space. In particular, in-depth studies of stapled peptide formulation and pharmacokinetic properties were not explored here and have yet to be reported elsewhere. Optimizing these properties may require extensive efforts. Furthermore, understanding the ways in which these molecules are similar to—and distinct from—small molecules will help inform on dosing regimens and routes of administration. Achieving oral bioavailability through sequence and/or formulation optimization would expand the disease-states stapled peptides can be applied to.</p>", "<p id=\"Par35\">Finally, the specific molecules identified here may represent interesting therapeutic candidates. For example, a di-alkyne stapled peptide appeared to give equivalent in vivo performance to ARLN-6924, a molecule that is currently undergoing clinical trials. Indeed, the optimized di-alkyne staple peptide (MP-467) may be a preferred clinical molecule given its greatly improved cellular potency (80x vs ALRN-6924) and superior on-target profile, which may translate to fewer adverse effects in humans. The all-D lead peptide (MP-793) would be interesting to explore as well given its inherent hyperstability. However, stoichiometric inhibitors engaging with the Mdm2 protein have only enjoyed limited clinical success so far, perhaps due to the built-in feedback mechanism that upregulates Mdm2 protein levels to limit therapeutic efficacy, including that of ARLN-6924. Accordingly, successfully addressing Mdm2 may require a targeted protein degradation approach. In fact, application of this paradigm to Mdm2 small molecules appears to bring improved efficacy^{##REF##30525597##44##,##UREF##9##45##} and an Mdm2 degrader has advanced to the clinic^{##UREF##10##46##}. Dual degrading of Mdm2/X may be therapeutically differentiated, especially in cancers that are MdmX upregulated. Thus, converting optimized Mdm2/X stapled peptide antagonists into degraders is worth pursuing, especially since dual degradation will likely be challenging with a small molecule ligand. Design ideas for such peptide-based degraders could include hybrid heterobifunctional molecules consisting of a stapled peptide fused to an E3 ligase small molecule ligand. On the other hand, insights from this manuscript suggest that Mdm2/X-directed stapled peptides could also be converted into Mdm2-degrading molecular glues. Specifically, given the tolerability for substitutions outside of the binding interface, researchers could explore substitutions on the solvent exposed side of the peptide to recruit an E3 ligase to degrade Mdm2/X. Of course, the same paradigm could also be applied to use Mdm2 as the recruited E3 ligase towards neosubstrates of therapeutic value.</p>" ]

[]

[ "<p id=\"Par1\">Although stapled α-helical peptides can address challenging targets, their advancement is impeded by poor understandings for making them cell permeable while avoiding off-target toxicities. By synthesizing &gt;350 molecules, we present workflows for identifying stapled peptides against Mdm2(X) with in vivo activity and no off-target effects. Key insights include a clear correlation between lipophilicity and permeability, removal of positive charge to avoid off-target toxicities, judicious anionic residue placement to enhance solubility/behavior, optimization of C-terminal length/helicity to enhance potency, and optimization of staple type/number to avoid polypharmacology. Workflow application gives peptides with &gt;292x improved cell proliferation potencies and no off-target cell proliferation effects ( &gt; 3800x on-target index). Application of these ‘design rules’ to a distinct Mdm2(X) peptide series improves ( &gt; 150x) cellular potencies and removes off-target toxicities. The outlined workflow should facilitate therapeutic impacts, especially for those targets such as Mdm2(X) that have hydrophobic interfaces and are targetable with a helical motif.</p>", "<p id=\"Par2\">Stapled α-helical peptides are promising for targeting challenging targets such as transcription factors, but achieving sufficient cell permeability while avoiding off-target cleavage is difficult. Here, the authors present workflows for identifying stapled peptides against Mdm2(X) with in vivo activity and no off-target effects based on comprehensive investigations of their properties.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41467-023-43346-4.</p>", "<title>Acknowledgements</title>", "<p>We thank Evans (Chen) Ge, Mike (Dixin) Xue, and Simon (Junhua) Li at Chinese Peptide Company (CPC) for peptide synthesis support. We thank Xin Dong, Jingxi Zhang, and Jie Wang at Pharmaron for biochemical and cellular assay support. Funding support from the Agency for Science, Technology and Research (A*STAR), Singapore Industry Alignment Fund-Pre-Positioning (IAF-PP) grant (H1701a0010) and Singapore Industry Alignment Fund-Industry Collaboration Project (IAF-ICP) grant (I1901E0039) were gratefully acknowledged.</p>", "<title>Author contributions</title>", "<p>Conceptualization, A.C., H.J., J.H., B.H., C.S.V., T.K.S., D.P.L., R.G., S.K., C.J.B., C.W.J., A.W.P.; methodology, A.C., H.J., T.Y.Y., S.K., C.J.B., A.W.P.; investigation, A.C., H.J., T.Y.Y., R.D., D.S., L.Y., Y.C.A.J., L.G., P.A., H.Y.K.K., Y.H.L., S.K., C.J.B., A.W.P., formal analysis, A.C., H.J., L.Y., B.S., J.H., S.K., C.J.B., A.W.P.; writing—original draft, A.C., R.D., JH., T.KS., S.K., C.J.B., C.W.J., A.W.P. Writing—review and editing, A.C., C.W.J., A.W.P. Resources, K.B., B.H., M.N., C.S.V., T.KS., D.P.L., C.J.B., C.W.J., A.W.P. Project administration, A.C., H.J., Y.H.L., B.H., C.S.V., T.KS., D.P.L., R.G., S.K., C.J.B., C.W.J., A.W.P.; supervision, Y.H.L., A.P., J.H., S.L., B.H., M.N., C.S.V., T.KS., D.P.L., R.G., S.K., C.J.B., C.W.J., A.W.P.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par70\"><italic>Nature Communications</italic> thanks Alison Hulme and the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.</p>", "<title>Data availability</title>", "<p>The full processed data set generated in this study is available as Supplementary Data. Raw data is available by request from the corresponding author Brian Henry at MSD Singapore.</p>", "<title>Competing interests</title>", "<p id=\"Par71\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Prototypic Mdm2/X dual antagonist stapled peptides show on-target cellular activity but with a narrow therapeutic index.</title><p><bold>a</bold> Structure of azide-ATSP-7041 (MP-081), <bold>b</bold> Peptide sequences for the p53 N-terminus, library template molecules (PM2, ATSP-7041, MP-081, a non-binding control peptide (MP-202), and a high-affinity but impermeable control (MP-950). Residues highlighted in grey correspond to the critical binding positions whereas the residues highlighted in blue are the stapling positions. R8 and S5 refer to (R)−2-(7’-octenyl)alanine and (S)−2-(4’-pentenyl)alanine (respectively) used in the ring closing metathesis reaction to form the olefin staple. <bold>c</bold> Proliferation profiles of ATSP-7041, its azido-analog (azide-ATSP-7041, MP-081), and the non-binding (MP-202) and cell impermeant (MP-950) controls against a panel of cancer cell lines that are either p53 WT (green) or p53 deficient (i.e., p53 null, mutant, or p53-depleted through HPV infection, red). Compounds were tested in duplicate.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>A library of ATSP-7041 analogs uncovers design trends.</title><p>For clarity, the N-terminal azido-lysine and beta-alanine residues are not shown in the helical wheel diagrams. Compounds coloured in blue represent acidic residues, those in red represent basic residues, and those in black represent apolar residues. Compounds were tested in duplicate. <bold>a</bold> Aside from the critical contact residues (F3, W7, &amp; Cba10), substitutions with a variety of amino acids tend to maintain high affinity binding ( &lt; 250 nM). <bold>b</bold> Single substitutions to charged residues (K, R, hR (homo-Arg), H, E) at non-binding positions, tend to result in decreased cellular activity while substitutions to other types of residues had varying affects.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Membrane permeability correlates with peptide lipophilicity, but acidic residues can be accommodated at select positions.</title><p><bold>a</bold> The ATSP-7041 core sequence is amphipathic as demonstrated by a helical wheel depiction where residues are coloured according to polarity; residues in black are apolar, those in blue are acidic, and those in green are uncharged polar. Application of a full glutamic acid scan of this amphipathic sequence demonstrates that placement of a Glu residue on the apolar helical face tended to decrease NanoClick permeability whereas placement on the polar face was generally tolerated. <bold>b</bold> Library analysis reveals that permeability (cell ratio = cellular EC₅₀ / binding K_D) is correlated with lipophilicity (LogD). To avoid the confounding effects of polypharmacology, peptides included were restricted to those that had a Mdm2 K_D value &lt; 10uM and had cell activities that were at least 10x greater than the potencies in the counterscreen and LDH assays.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Molecular modeling suggests that substitution of A14 and A17 with phenylalanine can increase binding affinity to Mdm2.</title><p><bold>a</bold> A helical wheel representation of MP-040 sequence with introduced Phe (F14 and F17) residues highlighted with an asterisk. Black circles represent positions with apolar residues whereas those with blue circles are negatively charged positions and those with green circles are uncharged polar positions. Stapling residues are indicated with an X. <bold>b</bold> Structural representation of MD snapshot of MP-040 / Mdm2 complex. Mdm2 is shown as surface (grey) and bound peptide (green) is shown as cartoon with interacting residues and the two Phe residues (magenta) highlighted in sticks. The hydrocarbon linker is highlighted in salmon.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Optimizing staple type and number significantly mitigates off-target activity.</title><p><bold>a</bold> Structure and profile of peptides with alternative cross-linking strategies with ARLN-6924 shown as a comparator. <bold>b</bold> Proliferation profiling against a panel of cancer cell lines that are either p53 WT (green) and p53 defective (i.e., p53 null, mutant, or p53-depleted through HPV infection, red) reveals that peptides with alternative crosslinking strategies (double stapled or di-alkyne stapled) produces molecules that were devoid of off-target proliferation effects whereas advanced small molecules (MK-4688 and AMG 232) showed significant off-target toxicities. Compounds were tested in duplicate.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Peptides with polyAla tails have improved in vivo activity versus ATSP-7041 in a SJSA-1 xenograft model.</title><p>Peptides were injected intravenously twice a week with vehicle control or peptide at 30 mg/kg for twenty-five days (ten mice per group). Mean values are plotted with error bars representing standard error of the mean.</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><title>Combining favorable attributes resulted in a peptide with low-nanomolar potency.</title><p>Appending MP-081 with a C-terminal polyAla tail, judicious placement of an additional anionic residue and replacement of the conventional olefin staple with a di-alkyne staple resulted in an optimized peptide (MP-467) whose cell proliferation profile greatly outperformed both MP-081 and ALRN-6924, both in terms of on-target (HCT116) potency and off-target (Ca Ski) toxicity. Compounds were tested in duplicate.</p></caption></fig>", "<fig id=\"Fig8\"><label>Fig. 8</label><caption><title>Application of peptide design insights to a stapled D-peptide improves its cellular potency by 100-fold and removes off-target activity.</title><p><bold>a</bold> helical wheel representations illustrating how the application of design rules derived from the ATSP-7041 series to an distinct all-D series transformed a cellularly inactive peptide with off-target toxicity (^dPMI-δ(6-10), also known as MP-769) to a peptide that is devoid of off-target toxicity and with &gt; 100x improvement in cellular activity. <bold>b</bold> Linear sequence representation of the step-wise improvements made to MP-769 resulting in MP-793. Black arrows highlight the peptide changes. Residues colored in black are apolar, those in red are cationic, those in blue are anionic, and those in green are uncharged polar. Values in the right hand table are in micromolar. Bind = binding affinity, Cell 0% = EC₅₀ value in the cellular assay (4 hour incubation, 0% serum), Cell 10% = EC₅₀ value in the cellular assay (16 hour incubation, 10% serum), LDH = EC₅₀ value in the LDH assay (4 hour incubation, 0% serum), Counter = EC₅₀ value in the cellular counterscreen assay (4 hour incubation, 0% serum), Sol = solubility, HCT116 = EC₅₀ value in the on-target cell proliferation assay, Ca Ski = EC₅₀ value in the off-target cell proliferation assay. Compounds were tested in duplicate.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Azide-ATSP-7041 analogs with different C-terminal tails</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Peptide</th><th>C-terminus (1st position is residue 14)</th><th>Series class</th><th>Binding K_D (nM)</th><th>Cell EC₅₀ (4 hr, 0% FBS) (µM)</th><th>Cell EC₅₀ (16 hr, 10% FBS) (µM)</th><th>Predicted tail helical propensity (aqueous)</th><th>Aqueous solution helicity (%)</th><th>Solubility (μM)</th></tr></thead><tbody><tr><td>MP-081</td><td>-SAA-NH₂</td><td>Template</td><td>5.0</td><td>0.47</td><td>0.88</td><td>High</td><td>48.35</td><td>105.3</td></tr><tr><td>MP-685</td><td>-A₅-NH₂</td><td>PolyA</td><td>8.2</td><td>0.11</td><td>0.32</td><td>High</td><td>28.3</td><td>N.D.</td></tr><tr><td>MP-032</td><td>-A₆-NH₂</td><td>PolyA</td><td>5.0</td><td>0.15</td><td>0.29</td><td>High</td><td>34.6</td><td>P.B.</td></tr><tr><td>MP-464</td><td>-A₅-dA-NH₂</td><td>PolyA</td><td>31</td><td>0.49</td><td>0.29</td><td>High</td><td>32</td><td>157</td></tr><tr><td>MP-470</td><td>-A₇-NH₂ (Early isomer)</td><td>PolyA</td><td>3.3</td><td>0.06</td><td>0.53</td><td>High</td><td>44</td><td>N.D.</td></tr><tr><td>MP-471</td><td>-A₇-NH₂ (Late isomer)</td><td>PolyA</td><td>6.7</td><td>0.10</td><td>0.60</td><td>High</td><td>40</td><td>N.D</td></tr><tr><td>MP-759</td><td>-A₉-NH₂</td><td>PolyA</td><td>6.1</td><td>0.10</td><td>4.2</td><td>High</td><td>27.55</td><td>15</td></tr><tr><td>MP-684</td><td>-AAA-COOH</td><td>Cleaved tail</td><td>11.5</td><td>0.25</td><td>1.7</td><td>High</td><td>32.6</td><td>N.D.</td></tr><tr><td>MP-688*</td><td>-A₆-NH₂</td><td>PolyA</td><td>30</td><td>0.16</td><td>1.3</td><td>High</td><td>49.8</td><td>N.D.</td></tr><tr><td>ALRN-6924*</td><td>-A₅-dA-NH₂</td><td>PolyA</td><td>2.5</td><td>0.14</td><td>0.32</td><td>High</td><td>51.25</td><td>P.B.</td></tr><tr><td>MP-413</td><td>-A-(Aib)₅-NH₂</td><td>Helical tail</td><td>1.7</td><td>0.45</td><td>0.71</td><td>High</td><td>N.D.</td><td>N.D.</td></tr><tr><td>MP-966</td><td>-AQA₃-dA-NH₂</td><td>Helical tail</td><td>45.9</td><td>0.39</td><td>1.0</td><td>High</td><td>N.D.</td><td>160</td></tr><tr><td>MP-425</td><td>-(AA-dA)₂-NH₂</td><td>Non-helical tail</td><td>4.2</td><td>1.0</td><td>2.6</td><td>Low</td><td>42.3</td><td>185</td></tr><tr><td>MP-056</td><td>-(A-dA)₃- NH₂</td><td>Non-helical tail</td><td>1.5</td><td>2.7</td><td>6.0</td><td>Low</td><td>22.23</td><td>157</td></tr><tr><td>MP-443</td><td>-A-Sar₅- NH₂</td><td>Non-helical tail</td><td>1.5</td><td>5.4</td><td>10</td><td>Low</td><td>30.45</td><td>180</td></tr><tr><td>MP-289</td><td>-G₆-NH₂</td><td>Non-helical tail</td><td>9.0</td><td>3.6</td><td>16</td><td>Low</td><td>24.33</td><td>142</td></tr><tr><td>MP-093</td><td>-P₆-NH₂ (Early isomer)</td><td>Non-helical tail</td><td>132</td><td>15</td><td>&gt;50</td><td>Low</td><td>16.5</td><td>156</td></tr><tr><td>MP-094</td><td>-P₆-NH₂ (Late isomer)</td><td>Non-helical tail</td><td>3.9</td><td>5.9</td><td>1.9</td><td>Low</td><td>18.7</td><td>158</td></tr><tr><td>MP-896</td><td>-dP₆-NH₂</td><td>Non-helical tail</td><td>11</td><td>&gt;50</td><td>&gt;50</td><td>Low</td><td>19.15</td><td>P.B.</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Strategic placement of charged residues in the C-terminal tail can enhance cellular activity and mitigate off-target effects</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"3\">Peptide</th><th rowspan=\"3\">C-terminus (1st position is residue 14)</th><th>Binding</th><th>Solubility</th><th>Cell EC50 (4 hr, 0% FBS) (µM)</th><th>Cell EC50 (16 hr, 10% FBS) (µM)</th><th>Proliferation EC₅₀</th><th>Proliferation EC₅₀</th><th>Proliferation % inhibition at 50 µM</th></tr><tr><th>K_D (nM)</th><th>(µM)</th><th/><th/><th>HCT116</th><th>Ca Ski</th><th>Ca Ski</th></tr><tr><th/><th/><th/><th/><th>(On-target) (µM)</th><th>(Off-target) (µM)</th><th>%</th></tr></thead><tbody><tr><td>MP-081</td><td>-SA₂-NH₂</td><td>5.0</td><td>105</td><td>0.49</td><td>0.86</td><td>2.3</td><td>32.8</td><td>85.5</td></tr><tr><td>MP-688*</td><td>-A₆-NH₂</td><td>21.5</td><td>N.D.</td><td>0.16</td><td>1.3</td><td>12.0</td><td>45.1</td><td>53.4</td></tr><tr><td>ALRN-6924*</td><td>-A₅-dA-NH₂</td><td>2.46</td><td>P.B.</td><td>0.14</td><td>0.32</td><td>0.87</td><td>47.5</td><td>48.7</td></tr><tr><td>MP-032</td><td>-A₆-NH₂</td><td>9.45</td><td>P.B.</td><td>0.14</td><td>0.24</td><td>0.96</td><td>26.6</td><td>47.5</td></tr><tr><td>MP-464</td><td>-A₅-dA-NH₂</td><td>30.9</td><td>157</td><td>0.43</td><td>0.29</td><td>0.42</td><td>&gt;49.75</td><td>9.9</td></tr><tr><td>MP-8834</td><td>-EA₄-dA-NH₂</td><td>1.1</td><td>167</td><td>1.0</td><td>3.4</td><td>1.4</td><td>&gt;49.75</td><td>-3.2</td></tr><tr><td>MP-965</td><td>-AEA₃-dA-NH₂</td><td>5.7</td><td>161</td><td>1.1</td><td>2.2</td><td>2.7</td><td>&gt;49.75</td><td>16.2</td></tr><tr><td>MP-833</td><td>-A₂EA₂-dA-NH₂</td><td>3.1</td><td>154</td><td>0.96</td><td>0.19</td><td>0.14</td><td>&gt;49.75</td><td>-11.1</td></tr><tr><td>MP-835</td><td>-A₃EA-dA-NH₂</td><td>&lt;1</td><td>162</td><td>0.65</td><td>0.82</td><td>0.55</td><td>&gt;49.75</td><td>-10.3</td></tr><tr><td>MP-837</td><td>-A₄E-dA-NH₂</td><td>5.7</td><td>160</td><td>0.76</td><td>1.67</td><td>0.66</td><td>&gt;49.75</td><td>8.6</td></tr><tr><td>MP-836</td><td>-A₅E-NH₂</td><td>&lt;1</td><td>164</td><td>0.55</td><td>1.06</td><td>1.05</td><td>&gt;49.75</td><td>13.2</td></tr><tr><td>MP-897</td><td>-(Gla)A₄-dA-NH₂</td><td>&lt;1</td><td>163</td><td>0.79</td><td>0.52</td><td>0.79</td><td>&gt;49.75</td><td>-19.1</td></tr><tr><td>MP-060</td><td>-A₅F-NH₂</td><td>2.1</td><td>P.B.</td><td>0.17</td><td>2.7</td><td>0.46</td><td>&gt;49.75</td><td>18.6</td></tr><tr><td>MP-228</td><td>-A₂FA₂-dA-NH₂</td><td>4.2</td><td>2</td><td>0.21</td><td>0.69</td><td>2.7</td><td>30.7</td><td>68.7</td></tr><tr><td>MP-040</td><td>-(A₂F)₂-NH₂</td><td>27.1</td><td>P.B.</td><td>0.036</td><td>0.75</td><td>1.22</td><td>&gt;49.75</td><td>4.4</td></tr><tr><td>MP-063</td><td>-A₂FA₂-dF-NH₂</td><td>56.0</td><td>9</td><td>0.11</td><td>2.13</td><td>2.78</td><td>&gt;49.75</td><td>24.0</td></tr><tr><td>MP-288</td><td>-A₂FA₂-(aMe-F)-NH₂</td><td>23.7</td><td>12</td><td>0.10</td><td>2.68</td><td>2.74</td><td>&gt;49.75</td><td>5.3</td></tr><tr><td>MP-229</td><td>-A₂FA-(aMe-E)-F-NH₂</td><td>4.8</td><td>153</td><td>0.20</td><td>0.21</td><td>2.32</td><td>19.9</td><td>102.7</td></tr><tr><td>MP-802</td><td>-((hS)₂F)₂-NH₂ (early isomer)</td><td>7.4</td><td>P.B.</td><td>0.23</td><td>0.75</td><td>4.58</td><td>19.1</td><td>95.2</td></tr><tr><td>MP-803</td><td>-((hS)₂F)₂-NH₂ (late isomer)</td><td>121.3</td><td>1</td><td>0.45</td><td>2.49</td><td>2.03</td><td>27.0</td><td>84.5</td></tr></tbody></table></table-wrap>" ]

[ "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r={r}_{o}+({r}_{b}-{r}_{o})\\times \\frac{\\left({K}_{d}+{\\left[L\\right]}_{t}+{\\left[P\\right]}_{t}\\right)-\\sqrt{{({K}_{d}+{\\left[L\\right]}_{t}+{\\left[P\\right]}_{t})}^{2}-4{[L]}_{t}{[P]}_{t}}}{2{[L]}_{t}}$$\\end{document}</tex-math><mml:math id=\"M2\"><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>o</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>o</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>×</mml:mo><mml:mfrac><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>−</mml:mo><mml:msqrt><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>4</mml:mn><mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msqrt></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r={r}_{o}+({r}_{b}-{r}_{o})\\times \\frac{2\\sqrt{({d}^{2}-3e)\\cos (\\theta /3)-9}}{3{K}_{d1}+2\\sqrt{({d}^{2}-3e)\\cos (\\theta /3)-d}}$$\\end{document}</tex-math><mml:math id=\"M4\"><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>o</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>o</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>×</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:msqrt><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>3</mml:mn><mml:mi>e</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>θ</mml:mi><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mn>9</mml:mn></mml:mrow></mml:msqrt></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msqrt><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>3</mml:mn><mml:mi>e</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>θ</mml:mi><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d={K}_{d1}+{K}_{d2}+{[L]}_{{st}}+{[L]}_{t}-{\\left[P\\right]}_{t}$$\\end{document}</tex-math><mml:math id=\"M6\"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$e=\\left({\\left[L\\right]}_{t}-{\\left[P\\right]}_{t}\\right){K}_{d1}+\\left({\\left[L\\right]}_{{st}}+{\\left[P\\right]}_{t}\\right){K}_{d2}+{K}_{d1}{K}_{d2}$$\\end{document}</tex-math><mml:math id=\"M8\"><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f=-{K}_{d1}{K}_{d2}{[P]}_{t}$$\\end{document}</tex-math><mml:math id=\"M10\"><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\theta={{{{{\\rm{ar}}}}}}\\,\\cos \\left[\\frac{-2{d}^{3}+9{de}-27f}{2\\sqrt{{({d}^{2}-3e)}^{3}}}\\right]$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mi>θ</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"normal\">ar</mml:mi><mml:mspace width=\"0.25em\"/><mml:mi>cos</mml:mi><mml:mfenced close=\"]\" 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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM5\"></supplementary-material>" ]

[ "<table-wrap-foot><p>Constant N-terminal sequence of Ac-K(N3)-βA-LTF(R8)EYWAQ(Cba)(S5)-, except for peptides marked with an asterisk which instead have an N-terminal sequence of Ac-LTF(R8)EYWAQL(S5)-. N.D.: Data not collected, P.B.: Poorly behaved; result inconclusive. Compounds were tested in duplicate.</p></table-wrap-foot>", "<table-wrap-foot><p>Constant N-terminal sequence of Ac-K(N3)-βA-LTF(R8)EYWAQ(Cba)(S5)-, except for peptides marked with a asterisk which instead have an N-terminal sequence of Ac-LTF(R8)EYWAQL(S5)-. N.D.: Data not collected, P.B.: Poorly behaved; result inconclusive. Compounds were tested in duplicate.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41467_2023_43346_MOESM1_ESM.pdf\"><caption><p>Supplementary Information</p></caption></media>", "<media xlink:href=\"41467_2023_43346_MOESM2_ESM.pdf\"><caption><p>Peer Review File</p></caption></media>", "<media xlink:href=\"41467_2023_43346_MOESM3_ESM.pdf\"><caption><p>Description of Additional Supplementary files</p></caption></media>", "<media xlink:href=\"41467_2023_43346_MOESM4_ESM.xlsx\"><caption><p>Supplementary dataset 1</p></caption></media>", "<media xlink:href=\"41467_2023_43346_MOESM5_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Memory and learning are fundamental cognitive processes, in which both the stimulatory glutamate^{##UREF##0##1##,##REF##10485705##2##} and the inhibitory gamma-aminobutyric acid (GABA)^{##REF##23727647##3##,##REF##8946426##4##} neurotransmitters play a pivotal role. The role of glutamate is somewhat better known^{##REF##12663083##5##}, but it has also been shown that systemic post-training injections of GABAergic compounds (such as the antagonist picrotoxin or the agonist muscimol) can also modulate memory^{##REF##10415392##6##}. Other studies revealed the effect of bicuculline (another antagonist of GABA) in memory facilitation during post-training administration into the hippocampus, entorhinal cortex and parietal cortex of rats^{##REF##15183170##7##}, and in memory consolidation in an invertebrate model^{##REF##19015009##8##}. Dysregulation of GABAergic activity in the prefrontal cortex of elderly rats negatively influenced their working memory performance^{##REF##24599447##9##}. Moreover, in humans, low GABA levels of the prefrontal cortex went along with worser working memory after an increased workload^{##REF##27852785##10##}. It is important to note that published studies have suggested a general effect, but a complete understanding of the contribution of different brain areas to these processes is still evolving.</p>", "<p id=\"Par3\">We focused on the median raphe region (MRR), which is located in the midbrain, and is implicated in the regulation of several cognitive and behavioral functions, among others in fear behavior^{##REF##28708877##11##}, memory consolidation^{##REF##25867120##12##} and reward-related behavior^{##REF##17328772##13##}. Although the MRR is widely known as a serotoninergic area, there is growing evidence pointing to the presence of non-serotoninergic neurons^{##REF##12097496##14##,##REF##18925658##15##}. In fact, it has been quantified that the majority of the neurons in the MRR are GABAergic^{##REF##27044051##16##}. However, it is yet to be elucidate the role of this neuron population in the MRR.</p>", "<p id=\"Par4\">Chemogenetic technique (designer receptors exclusively activated by designer drugs (DREADD) alongside with its artificial ligand, clozapine-N-oxide (CNO)) allows accurate manipulation of desired neurons on a well-defined brain area. Thus, it seems to be a suitable technique for testing the present hypothesis that the stimulation or inhibition of GABAergic neurons of the MRR influences learning and memory formation. Initially, we manipulated the whole MRR. A significant portion of the infected cells were found to be GABAergic, however, glutamatergic cells were labeled similarly. Thus, the simultaneous manipulation of stimulatory and inhibitory neurons might have counteracted each other. Therefore, as the next step, we used a mice line containing Cre recombinase enzyme under the vesicular GABA transporter (VGAT) promoter to investigate possible effects that MRR GABAergic neurons might have. With regard to behavioral measures, we focused on operant conditioning and active avoidance tests (consecutively) due to their sensitivity to cognitive changes and the fact that among others they assess behavioral functions known to be under the control of the MRR^{##REF##28708877##11##–##REF##17328772##13##}. These two reinforcement-based cognitive tests are different in nature, one is a reward driven (operant conditioning), while the other is a punishment avoiding (active avoidance) paradigm, what rationalizes the use of both.</p>" ]

[ "<title>Methods</title>", "<title>Animals</title>", "<p id=\"Par24\">All mice (C57BL/6J background) were obtained from the local colonies of the Institute of Experimental Medicine, Budapest, Hungary. VGAT-Cre mice (origin: The Jackson Laboratory, #016962) were bred in homozygous mating pairs. During the test battery performance adult male mice (14–15-week-old) were housed in groups of 2–3 in Macrolon cages (40 cm × 25 cm × 26 cm) under a 12-h light–dark cycle (lights on at 7 p.m., 21 ± 1 °C, 50–60% humidity), with food (standard mice chow, Charles River, Hungary) and tap-water available ad libitum if not stated otherwise. The tests were conducted during the early dark, active phase.</p>", "<p id=\"Par25\">All experiments were approved by the Workplace Animal Welfare Committee of Institute of Experimental Medicine and National Scientific Ethical Committee on Animal Experimentation of Hungary (PEI/001/33-4/2013, PE/EA/254-7/2019) and performed according to the European Communities Council Directive recommendations for the care and use of laboratory animals (2010/63/EU). The authors complied with the ARRIVE guidelines.</p>", "<title>Experimental design</title>", "<p id=\"Par26\">The C57BL/6J and VGAT-Cre animals were tested in separate series with minor differences in the protocol.</p>", "<title>Experiment 1: Whole MRR manipulation</title>", "<p id=\"Par27\">C57BL/6J control (N = 6) and MRR-stimulated (N = 9) animals were used. All animals were injected with an AAV containing stimulatory DREADD^{##REF##19607790##31##} and RFP sequences into their MRR^{##REF##34637795##26##}. The animals had 4 weeks to recover from the surgery, during which they were accustomed to the reversed light–dark cycle (min 2 weeks). Then an operant conditioning experiment with 4 days habituation to reduced food accessibility (to maintain their body weight on 80% of their initial weight), 14 days learning and 7 days reversed learning phases (Fig. ##FIG##1##2##a) was conducted followed by 4 days recovery and 5 days learning and 5 days reversed learning in an active avoidance paradigm (Fig. ##FIG##2##3##a) as we described earlier^{##REF##31622610##32##}. On each test day, 30 min before the animals were put into the testing box an intraperitoneal (i.p.) injection of either saline (control) or CNO (1 mg/10 ml saline/kg) was delivered. At the termination of the experiment the anesthetized animals were transcardially perfused 2 h after the CNO injection and their brains were checked by RFP immunohistochemistry for correctness of the injection as well as for detailed determination of the infected cell-types. We already successfully confirmed that the cells of the MRR express the RFP suggesting that they also express the DREADD receptor^{##REF##34637795##26##}. Only mice with correct hits were included in further analysis. The results of mice having out of target labelling in their dorsal raphe were not different from exclusively MRR-targeted animals, therefore their data were merged (Suppl. Tables ##SUPPL##0##1## and ##SUPPL##1##2##, Suppl. Figs. ##SUPPL##4##1## and ##SUPPL##5##2##).</p>", "<title>Experiment 2: MRR-GABA manipulation</title>", "<p id=\"Par28\">As Experiment 1 showed that most of the infected cells were GABAergic, we conducted a further experiment using VGAT-Cre mice. We followed the steps of Experiment 1 (Figs. ##FIG##3##4##a and ##FIG##4##5##a) using different viruses containing control (n = 11), stimulatory (n = 15) and inhibitory (n = 13) sequences^{##REF##31780530##18##}. In this experiment all animals got CNO injections. It was confirmed previously that this technique sufficiently manipulates MRR-GABA cells^{##REF##34896160##25##}.</p>", "<title>Delivering AAVs into the MRR</title>", "<p id=\"Par29\">Mice were anaesthetized (0.1 ml/10 g mixture of 0.5 ml ketamine [Produlab Pharma B.V.], 0.1 ml xylazine [Produlab Pharma B.V.] and 2.4 ml saline [KabiPac]) and with the help of a stereotaxic frame (David Kopf Instruments, Tujunga, CA, USA) and nanoinjector AAVs (10 nl; Addgene) were injected into the MRR (AP: − 4.1 mm; L: 0 mm; DV: 4.6 mm from Bregma) with the help of a glass micropipette as described earlier,^{##REF##31780530##18##,##REF##34637795##26##}. During Experiment 1, all animals got the same virus (AAV2-hSyn-hM3Dq-mCherry, 3.0e12 GC/ml titer, #50474). For Experiment 2, three subgroups were formed based on the injected Cre-dependent AAVs containing different DREADD sequences: control (no DREADD sequence, only RFP, AAV8-hSyn::DIO-mCherry, 4.1e12 GC/ml titer, #50459), stimulatory (AAV8-hSyn::DIO-hM3Dq-mCherry, 4.0e12 GC/ml titer, #44361) and inhibitory (AAV8-hSyn::DIO-hM4Di-mCherry, 1.9e13 GC/ml titer, #44362).</p>", "<title>Behavioral testing</title>", "<p id=\"Par30\">Tests were carried out between 9 and 13 h (early dark phase) in a separate room under similar lighting condition as in the animal facility and measured automatically by the equipments for operant chamber or active avoidance (Med Associates, St. Albans, VT, USA). The chambers were placed inside sound-attenuating cubicles and were interfaced with a computer running Med-PC IV software. Six animals were tested in one run containing animals from each group. Each test apparatus was cleaned with 20% ethanol and water and dried prior the next animal was introduced. The test battery included two types of reinforcement-based learning paradigms. In both tests reversal learning was also assessed, which was evaluated during the reversal learning phase.</p>", "<title>Operant conditioning</title>", "<p id=\"Par31\">To increase motivation the mice were kept on restricted diet started 72 h before testing^{##REF##31622610##32##}. The test was performed in an automated operant chamber using 45 mg food pellets (Bio-Serv Dustless Precision Rodent Pellet, Bilaney Consultants GmbH, Germany) as reward^{##REF##25117459##33##}. Animals were placed inside a test chamber for 30 min and were allowed to freely explore the environment. One of the nose pokes was immediately associated with a reward followed by a 25 s long timeout with the chamber light switched on. During the timeout period, responses were not rewarded, but were registered and used as a marker of impulsivity^{##REF##14739701##34##}.</p>", "<p id=\"Par32\">There were small differences between the experiment 1 and experiment 2. In the experiment 1, the test was divided into two phases, namely learning (day 1–14) and reversal learning (reversed learning, day 15–21) (Fig. ##FIG##1##2##a). In the experiment 2, the learning phase lasted 10 days and that of reversal learning 7 days (Fig. ##FIG##3##4##a). The position of the baited nose poke was changed between the phases in both experiments.</p>", "<p id=\"Par33\">Reward preference (ratio of responses on the rewarded nose poke) was calculated as follows:and the total number of responses (correct + incorrect) was also recorded.</p>", "<title>Active avoidance (shuttle-box) test</title>", "<p id=\"Par34\">Classical automated shuttle-box apparatus consisted of two identical compartments with photobeam sensors, stimulus light, tone generator, stainless steel grid floor and a guillotiner door^{##REF##28633291##35##}.</p>", "<p id=\"Par35\">Mice were placed in the left or right compartment of the apparatus for 10 days. After 1 min of habituation the 40 trials (each 30 s long) started. In each trial, 20 s after the start the light turned on and a tone was played, meanwhile the guillotine door opened (conditioning stimuli). During the last 5 s of each trial an electric footshock (0.15 mA) was applied to the grid floor (unconditioned stimulus) of one of the compartments. At the end of the trial all stimuli were switched off, the guillotine door closed and 5 s intertrial interval (ITI) started, then the subsequent trial was conducted. The 5 (Experiment 1, Fig. ##FIG##2##3##a) or 7 (Experiment 2, Fig. ##FIG##4##5##a) days learning phase was immediately followed by 5 days (day 6–10 in Experiment 1) or 3 days (day 8–10 in Experiment 2) of reversal learning phase, in which the shocks were applied to the opposite compartment.</p>", "<p id=\"Par36\">An avoidance response was recorded when the animal avoided the electric shock by entering (or during the reversed phase: not entering) the other compartment during the conditioned stimuli (escape during stimulus—EDST) or during the footshock (escape during footshock—EDFS). Escape failure (ESFL) was recorded when the animals remained in the chamber and got footshock (or during reversal phase: jumped into the other compartment). Average escape latencies were also calculated as possible sign of impulsivity. Due to missing data we present only the first 5 days of learning for both experiment.</p>", "<title>Immunohistochemistry and microscopy</title>", "<p id=\"Par37\">To check the correctness of the AAV injection, a nickel-3,3′-diaminobenzidine (Ni-DAB) staining against RFP was conducted^{##REF##27664119##36##}. The slices were washed with phosphate buffered saline (PBS) for 3 × 10 min. Membranes were permeabilized by adding 0.5% Triton X-100 (TXT) and 0.3% H₂O₂, followed by 2 × 10 min PBS washing. Blocking was done by 2% bovine serum albumin (BSA) diluted in PBS for 1 h. The slices were incubated in anti-RFP primer solution (1:4000, rabbit; 600-401-379, 2% BSA; 0.1% TXT diluted in PBS) for 2 nights on 4 °C. After 3 × 10 min of PBS washing they were incubated in biotinylated (biotin-SP) anti-rabbit secondary antibody solution (1:100. donkey; 2% BSA diluted in PBS). After 10 min PBS, then 10 min TRIS washing the slices were kept in avidin–biotin complex (ABC) diluted in TRIS for 1 h. They were pre-incubated in the dilution of TRIS, DAB (10 mg/ml) and 1% NiNH₄SO₄ for 10 min. After adding 0.003% H₂O₂ and waiting for precipitation the slices were washed with TRIS for 10 min. They were mounted with gelatin, dehydrated in xylol and covered with DPX (Sigma-Aldrich).</p>", "<p id=\"Par38\">The Ni-DAB-stained slices were evaluated with Olympus DP70 light microscope (4× objective). The virus expression was examined from − 4.04 to − 4.96 mm from Bregma. If there was no staining, or it was unilateral, or other brain regions were also stained, then the test animal and the data belonging to it was excluded from the statistical analysis. In cases where both the MRR and dorsal raphe were hit, statistical analysis was done to verify if the hits on dorsal raphe affected the behavior.</p>", "<p id=\"Par39\">To verify which cell-types were infected in Experiment 1, double immunofluorescent staining was done. The slices were washed with PBS for 3 × 10 min. Blocking was done with 5% normal goat serum (NGS, #31873, Thermo Fisher Scientific, Waltham, MA, US) and 0.2% TXT diluted in PBS for 30 min. For 2 nights they were incubated in anti-RFP (1:1000, rabbit), anti-GABA (1:500, rabbit, A2052, GABAergic marker) or anti-tryptophan hydroxylase (1:500, mouse, T0678, TPH, enzyme in serotoninergic cells) or anti-vesicular glutamate transporter 3 (1:500, rabbit, 135203, VGluT3, a major glutamatergic marker^{##REF##27044051##16##}), 5% NGS and 0.2% TXT primer solution diluted in PBS on 4 °C. After 3 × 10 min of PBS washing they were incubated in a seconder solution of anti-rabbit conjugated with Alexa-488 (1:500, goat) and anti-rat conjugated with Alexa-594 (1:1000, goat) diluted in PBS. After 3 × 10 min of PBS washing the slices were mounted with gelatin and covered with Mowiol. The double immunofluorescent staining was evaluated with C2 confocal laser-scanning microscope (Nikon Europe; 20× objective).</p>", "<p id=\"Par40\">c-Fos immunohistochemistry was applied to assess possible chemogenetic manipulation-induced neuronal activity in MRR. After 3 × 10 min PBS washing and 30 min incubation in 10% NGS fluorescent immunolabeling was used against c-Fos and RFP (1:2000 guinea-pig polyclonal anti-c-Fos IgG, #226004, Synaptic Systems with monoclonal rabbit anti-RFP IgG 1:4000, #600-401-379, Rockland) diluted in 2% NGS with 0.1% TXT in PBS overnight at 4 °C. Primary antibodies were detected by fluorescent-conjugated antibodies (1:500 Alexa-488 conjugated donkey anti-guinea-pig, #S32354, ThermoFisher Scientific, Waltham, MA, USA, and 1:500 A-594 conjugated goat anti-rabbit, #ab150160, Abcam plc, Cambridge, UK). c-Fos-RFP immunohistochemistry was imaged by C2 Confocal Laser-Scanning Microscope (Nikon CFI Plan Apo VC20X/N.A. 0.75, xy:0.62 μm/pixel, Nikon Europe, Amsterdam, The Netherlands). Quantitative analysis of the colocalizations was done with the NIS Elements software (Nikon Europe, Amsterdam, Netherlands).</p>", "<title>Statistical analysis</title>", "<p id=\"Par41\">Data were analyzed by Statistica 13.0 (StatSoft Inc., Tulsa, USA) utilizing single sample t-test (operant conditioning in comparison to 50%), one-way analysis of variance (ANOVA) (operant conditioning), repeated measure ANOVA (operant conditioning, active avoidance) followed by Bonferroni posthoc comparison where appropriate. Data are expressed as mean ± SEM and p &lt; 0.05 was considered statistically significant.</p>" ]

[ "<title>Results</title>", "<title>Experiment 1</title>", "<p id=\"Par5\">The immunohistochemical analyses revealed 47.9% of cells infected by the virus carrier were stained neither for the GABAergic marker nor for the vesicular glutamate transporter 3 (VGluT3) or tryptophan hydroxylase (TPH). The majority of stained neurons were GABAergic as shown by the co-localization of anti-RFP (red fluorescent protein) and GABA labeling (43.1%) (Fig. ##FIG##0##1##a,b). Much less prevalent were the serotonergic (TPH-expressing) (1.89%) and glutamatergic (VGluT3-expressing, highly abundant in MRR^{##REF##27044051##16##}) cells (8.31%) (Fig. ##FIG##0##1##c,d). As expected, intraperitoneal CNO injection increased the share of c-Fos positive cells (Fig. ##FIG##0##1##e,f).</p>", "<title>Operant conditioning</title>", "<p id=\"Par6\">Total number of responses increased across the days of learning, indicating that the animals learned the paradigm (significant time effect; see Table ##TAB##0##1##; Fig. ##FIG##1##2##). There was no significant difference between the two groups (control and MRR stimulation) during the learning phase (no treatment effect or interaction with time). Moreover, no consistent difference was found in the single sample t-test when analyzing the preference of baited nose hole in comparison to the chance level of 50% (p &gt; 0.05, Suppl. Table ##SUPPL##0##1##).</p>", "<p id=\"Par7\">On day 15, at the beginning of the reversal learning phase, the successful responses dropped for both groups, as expected (Fig. ##FIG##1##2##). On days 15–21 the performance of the MRR-stimulated mice measured by total responses was marginally worse than that of the control mice (Table ##TAB##0##1##. treatment x time interaction: p = 0.061), however, there were no significant differences between the two groups for the reward preference. Additionally, there was no significant difference in reward preference (t(13) = 0.651, p = 0.526) and total responses (t(13) = 1.221, p = 0.244) between the groups during the last day of learning and the first day of reversal learning (i.e. during \"switch\", calculated as Day15/Day14*100) (Fig. ##FIG##1##2##d). Moreover, for both parameters (reward preference and total responses) only the time effect was significant for the whole 21 days observation period either, with significant change during the first day of reversal learning phase compared to other days during Bonferroni posthoc analysis (Table ##TAB##0##1##).</p>", "<title>Active avoidance</title>", "<p id=\"Par8\">During learning (days 1–5, Fig. ##FIG##2##3##a, Table ##TAB##0##1##) the number of escapes during stimulus (EDST) increased in both groups suggesting successful learning (Fig. ##FIG##2##3##b). Complementary to this, escape during footshock (EDFS) decreased gradually (data not shown). The escape failure was rather low and did not improve significantly during learning (Fig. ##FIG##2##3##c). There were no differences between the groups in the above mentioned parameters as well as in the impulsivity marker average escape latencies (Fig. ##FIG##2##3##d).</p>", "<p id=\"Par9\">When the animals had to learn not to escape (during the reversal learning phase; days 6–10), there was a significant drop in their escape (EDST Fig. ##FIG##2##3##b), which remained low during the subsequent days, suggesting a rather fast adaptation. No significant difference was observed between the groups (Fig. ##FIG##2##3##). Moreover, the number of escape failures (in fact during this phase it was a correct behavioral answer) increased in both groups throughout the days, with a marginal group x time interaction effect (p = 0.07; Table ##TAB##0##1##). In addition, when we expressed the changes between the last day of learning and the first day of reversal learning there was no significant difference between the groups (Fig. ##FIG##2##3##e,f).</p>", "<title>Experiment 2</title>", "<title>Operant conditioning</title>", "<p id=\"Par10\">In chemogenetically MRR-GABA manipulated mice the successful learning of the paradigm was reflected by a gradual increase of the total number of responses across the days of learning (Fig. ##FIG##3##4##b, Table ##TAB##1##2##).</p>", "<p id=\"Par11\">The subgroups of mice bearing no DREADD sequence (Control), GABA stimulatory sequence (Stim group) and GABA inhibitory sequence (Inhib group) needed different time to learn the task (preference of baited nose hole exceeded the chance level of 50% by single sample t-test) (Fig. ##FIG##3##4##c, Suppl. Table ##SUPPL##1##2##). The mice of the Control group learned the paradigm by the 4th day of the experiment, those of the Stim group by the 10th day, and the mice of the Inhib group by the 5th day. There were no significant differences between the groups during the learning phase and the group × time interaction did not reach the level of significance either (Table ##TAB##1##2##).</p>", "<p id=\"Par12\">On days 11–17, during the reversal learning phase, there were significant differences in total responses between the Stim group and the other groups, as the responses dropped for the Control and Inhib groups, while they remained unchanged for the Stim group (p = 0.027; Fig. ##FIG##3##4##b, Table ##TAB##1##2##). Moreover, during this phase the mice in the Stim group showed higher preference for the rewarded nose hole, and this was the only group that consistently exceed the chance level of 50% after the 12th day. When we expressed the changes between the last day of learning and first day of reversal learning, there were no significant difference in reward preference and total responses between the groups (Fig. ##FIG##3##4##d, Table ##TAB##1##2##).</p>", "<p id=\"Par13\">For assessment of impulsivity, we analyzed timeout responses as well, which showed treatment effect during the reversal learning phase with significantly higher levels in stimulatory as both the control and inhibitory groups (p &lt; 0.05) (Fig. ##FIG##3##4##e, Table ##TAB##1##2##). The number of all rewarded or non-rewarded responses (either baited or timeout) showed only time effect both during the learning and reversal learning phases (data not shown).</p>", "<title>Active avoidance</title>", "<p id=\"Par14\">During the 7 days of learning the number of EDST increased in all groups (Fig. ##FIG##4##5##b, Table ##TAB##1##2##). The Stim group showed higher total responses than the other two groups (p &lt; 0.05). Complementary to this, EDFS (data not shown) and the number of the escape failures (Fig. ##FIG##4##5##c) decreased gradually during the learning.</p>", "<p id=\"Par15\">During the reversal learning phase (days 8–10) the number of EDST decreased across the days (Fig. ##FIG##4##5##b, Table ##TAB##1##2##). Similar to the results observed in experiment 1, the number of escape failures increased in all groups throughout the reversal training days. Take into consideration the whole observation period the ADST difference was even more pronounced being highly different in Stim than in Control and Inhib groups (p &lt; 0.01) (Fig. ##FIG##4##5##b, Table ##TAB##1##2##). No significant differences were found between the groups in the changes when the last day of learning was compared with the first day of reversal learning (Fig. ##FIG##4##5##d, Table ##TAB##1##2##).</p>", "<p id=\"Par16\">As a possible sign of impulsivity, the average latency to escape was also analyzed without any significant difference between the treatment groups (Fig. ##FIG##4##5##e, Table ##TAB##1##2##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par17\">Despite extensive research on the MRR^{##REF##28708877##11##,##REF##25867120##12##,##REF##32414785##17##} a consensual understanding of its involvement in learning has remained elusive. The present study shows that manipulating the whole MRR had no influence on operant and active avoidance learning nor reversal learning, while the stimulation of the MRR GABAergic neurons increased learning in the active avoidance paradigm and enhanced total responses in the operant conditioning task (Table ##TAB##2##3##).</p>", "<p id=\"Par18\">In the present experiment using an adenoassociated virus vector (AAV) containing only synapsin promoter without the Cre-loxP system, theoretically all neurons should have been labelled by RFP in proportion of their prevalence. Indeed, the vast majority of observed infected cells, 43.1% were GABAergic. This is in accordance with the previously reported predominance of GABAergic neurons (65.7 ± 4.38%)^{##REF##27044051##16##}. However, much less serotoninergic (only 1.89% TPH positive in contrast to previously reported 9.6%) and VGluT3 positive (8.31% in contrast previously reported 11.4%; partly overlapping with TPH) cells were co-labelled with RFP^{##REF##27044051##16##}. As AAVs were expressed differently in different cell-types not completely overlapping with their previously reported prevalence, we might conclude that AAVs might have some tropism and even when we intended to use non-cell-type specific manipulation, we might selectively influence special cell populations.</p>", "<p id=\"Par19\">As in Experiment 1. the share of serotonergic and glutamatergic neurons was very small; stimulation affected the MRR primarily via the GABAergic system. However, the major differences in the behavioral consequences of non-specific (Experiment 1) and GABA-specific (Experiment 2) stimulation suggest that either the few glutamatergic and serotonergic neurons were able to counteract the effects of the large number of GABAergic neurons, or that the latter was achieved by the stimulation of unidentified neurons. Indeed, a subsequent study by an overlapping set of authors suggested the presence of a large, VGLUT2 positive glutamatergic neuron population in the MRR^{##REF##31780530##18##}. Based on these earlier studies, the total share of glutamatergic neurons expressing either VGLUT3 or VGLUT2 is close to the share of GABAergic neurons in the MRR. As such, we hypothesize that the effects of GABAergic stimulation were counteracted in Experiment 1 by the concurrent stimulation of glutamatergic neurons. By contrast, the effects of GABAergic stimulation became conspicuous in Experiment 2, where the stimulation was specific.</p>", "<p id=\"Par20\">Indeed, the specific stimulation of MRR-GABA cells induced significant changes in both learning paradigms used. In the operant conditioning test, mice bearing GABA stimulatory sequence showed a high response rate even after the start of the reversal learning phase. This suggests a proclivity to impulsive behavior^{##REF##22134477##19##}. In support the number of timeout responses was also increased after stimulation, however, long time treatment was necessary (from 11th days on) and the unaffected escape latency during active avoidance test did not suggest a general increase in impulsivity, either. Additional, more specific studies is required to assess impulsivity. Our major question was the effect on memory formation, which we found to be negligible. Operant conditioning is based on reward, and the reward response is commonly associated with the mesolimbic dopaminergic system^{##REF##33257725##20##}. Over the past years, it was demonstrated that the ventral tegmental area (VTA)—one of the components of the mesolimbic dopaminergic system—does not contain only dopaminergic neurons, but also GABAergic cells^{##REF##24478655##21##}. Additionally, in recent retrograde tracing studies it has been documented that GABAergic neurons originating in the MRR have modest projections to the VTA^{##REF##24715505##22##}, silencing not only local interneurons but also other brain regions^{##REF##31866835##23##}. By doing so, they may act—among others—as a gate of dopaminergic activity, mediating the response to reward and aversion, and—in our case—impulsivity, in which dopaminergic VTA neurons are also implicated^{##REF##33559379##24##}.</p>", "<p id=\"Par21\">In the active avoidance test, mice bearing GABA stimulatory sequence displayed a high escape rate during the stimulus, resulting in a maladaptive and excessive avoidance coping response. These results indicate an increased formation of aversive memory during the stimulation of the GABAergic cells. This corroborates with the suggestion that MRR actively participates in the regulation of negative memories^{##REF##31780530##18##}. Such behavior was not observed during the reversal learning phase, in which all mice performed similarly. However, the footshock is a rather excessive motivation, and the response during the reversal learning phase is passive (the animals do not have to leave the chamber). It is therefore might have been difficult to detect any differences.</p>", "<p id=\"Par22\">We confirmed previous results that chemogenetics is an effective method to manipulate the neuron populations of the MRR, as we observed CNO-induced elevation in the c-Fos expression^{##REF##34896160##25##,##REF##34637795##26##}. It was important as previous studies questioned whether CNO reached the brain in functionally relevant concentration^{##REF##34637795##26##}. As original description considered CNO as inert drug^{##REF##17360345##27##,##REF##19893765##28##}<bold>,</bold> we used saline as control for Experiment 1. Although subsequent studies suggested possible back-metabolism of CNO to clozapine^{##REF##34637795##26##}, methodological issues could hardly influence the ineffectiveness of whole MRR manipulation. Moreover, we would have expected that the excitatory and inhibitory groups in Experiment 2. would have opposite effects, but our findings did not support this idea. The explanation could be that the two kinds of DREADD sequences activate different cellular pathways (Gq and Gi). Also, stimulation is a more active process, while inhibition mainly reduces the impact of other stimulatory signals. A further limitation of our technique was that it is hard to target MRR without going through the DR, thereby in many cases cells of both regions were infected. Although there were no statistically significant difference between the behavior of exclusively MRR targeted and MRR + DR co-targeted animals (Supplementary Table ##SUPPL##0##1##), we should be aware of the important role of serotonin and especially DR in reversal learning^{##REF##38168380##29##,##REF##37961492##30##}.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par23\">We have demonstrated that the stimulation of the MRR-GABA neurons in VGAT-Cre mice reduced reversal learning without an effect on memory formation during the operant conditioning test. Moreover, the same chemogenetic manipulation increased the formation of negative memory during the active avoidance test. The ineffectiveness of the whole MRR stimulation might be partially due to the limitation of the chemogenetic techniques, but underlines the importance of cell-type specific manipulation. Further studies addressing GABAergic subpopulations in the MRR may provide additional insights into the formation of reward- and punishment related memories.</p>" ]

[ "<p id=\"Par1\">Learning and memory are important in everyday life as well as in pathological conditions. The median raphe region (MRR) contributes to memory formation; however, its precise role and the neurotransmitters involved have yet to be elucidated. To address this issue, we stimulated the MRR neurons of mice by chemogenetic technique and studied them in the operant conditioning and active avoidance tests. The virus carrier infected a variety of neuron types including both GABAergic and glutamatergic ones. Behavior was not influenced by stimulation. We hypothesize that the lack of effect was due to opposing effects exerted via GABAergic and glutamatergic neurons. Therefore, next we used VGAT-Cre mice that allowed the specific manipulation of MRR-GABAergic neurons. The stimulation did not affect behavior in the learning phase of the operant conditioning task, but increased reward preference and total responses when operant contingencies were reversed. The enhanced responsiveness might be a proclivity to impulsive behavior. Stimulation facilitated learning in the active avoidance test but did not affect reversal learning in this paradigm. Our findings suggest that MRR-GABAergic neurons are involved in both learning and reversal learning, but the type of learning that is affected depends on the task.</p>", "<title>Subject terms</title>", "<p>Open access funding provided by University of Pécs.</p>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51743-y.</p>", "<title>Author contributions</title>", "<p>Conceptualization: J.H.; D.J.; D.Z.; methodology: T.C.; B.T.; Cs.L.F.; P.C.; P.K.; O.H.; E.S.; L.B.; formal analysis: T.C.; Cs.L.F.; L.B.; J.H.; investigation: T.C.; B.T.; Cs.L.F.; P.C.; P.K.; O.H.; E.S.; L.B.; writing—original draft: T.C.; B.T.; D.J.; D.Z; writing—review and editing: Cs.L.F.; P.C.; P.K.; O.H.; E.S.; L.B.; J.H.; visualization: T.C:; B.T.; supervision: J.H.; D.J.; D.Z.; funding acquisition: J.H.; D.J.; D.Z.</p>", "<title>Funding</title>", "<p>Open access funding provided by University of Pécs. This work was supported by the Thematic Excellence Program 2021 Health Sub-program of the Ministry for Innovation and Technology in Hungary, within the framework of the TKP2021-EGA-16 project of Pécs of University and by the National Brain Research Program (NAP 3.0) of the Hungarian Academy of Sciences, the National Research Development and Innovation Office of Hungary (grant numbers K141934, K138763, K120311, K134221). We declare that there is no conflict of interest in the conduct and reporting of research. The agencies had no further role in study design, in the collection, analysis or interpretation of the data.</p>", "<title>Data availability</title>", "<p>The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par42\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Colocalization of GABAergic and viral infection (RFP) markers. (<bold>a</bold>) Representative picture of the MRR cells infected by AAV containing RFP (A594) as a reporter protein. Majority of the neurons are GABA positive (A488) as well (×40 magnification) (<bold>b</bold>) Almost half of all AAV infected (RFP positive) cells were also GABAergic. (<bold>c</bold>) Representative picture of the RFP positive (A594), vGLUT3 positive (A488) and TPH positive (A633) neurons of the MRR (×40 magnification). (<bold>d</bold>) Ratio (%) of different neuron types based on their expressed neurotransmitter markers in the MRR. Only minority of the cells were serotonergic (TPH positive) and/or glutamatergic (VGluT3 positive) compared to all AAV infected (RFP positive) cells. (<bold>e</bold>) Representative picture of neuronal activation of marked cells studied by RFP and c-Fos colocalization. (<bold>f</bold>) The excitation of the whole MRR in C57BL/6J mice via excitatory DREADD resulted in a marked increase of c-Fos positive neuron nuclei compared to saline injected control animals. Data are expressed as mean ± SEM. Data were compared to each other with t-test. **p &lt; 0.01 vs control. AAV: adenoassociated viral vector; CNO: clozapine-N-oxide; DREADD: designer receptor exclusively activated by designer drugs; MRR: median raphe region; RFP: red fluorescent protein; TPH: tryptophan hydroxylase VGluT3: vesicular glutamate transporter type 3.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Operant conditioning test after whole MRR stimulation (Experiment 1). (<bold>a</bold>) Schematic timeline of the operant conditioning test. The learning phase consisted of 14 days while the reversal learning phase lasted for 7 days, each with 30-min-long training sessions per day. (<bold>b</bold>) Total numbers of responses (correct + incorrect) during learning phase increased across the days, without any difference between the groups. During reversal learning phase (indicated by the red dashed line) the total number of responses was marginally lower for the stimulated group. (<bold>c</bold>) Reward preference (percentage of correct nose pokes vs total nose pokes) did not differ throughout the whole experiment and did not reach the random chance 50%. (<bold>d</bold>) Percentage of change between the first day of reversal learning and last day of learning phase for total responses and reward preference, respectively. There were no differences between the groups. Data are expressed as mean ± SEM. Data were compared to each other with repeated-measures ANOVA (total responses, reward preference), single sample t-test (vs random chance 50%) and t-test (change between last and first). CNO: clozapine-N-oxide, MRR: median raphe region.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Active avoidance after whole MRR stimulation (Experiment 1). (<bold>a</bold>) Schematic timeline of the active avoidance test. The experiment lasted for a total of 10 days, 5 days of learning and 5 days of reversal learning phase. Each day there were 40 × 30 s long trials, with 1 min habituation before the start and 5 s intertrial interval. Learning was helped with sound and light cues. (<bold>b</bold>) During learning, the number of successful escapes increased without differences between the groups. Similarly, successful learning during reversal learning phase (indicated by red dashed line) was indicated by the rapid drop in the number of escapes, without an effect of treatment. (<bold>c</bold>) The number of escapes failures increased during reversal learning, without differences between the groups. (<bold>d</bold>) Average escape latency during learning as a possible measure of impulsivity. (<bold>e</bold>) Percentage of change between last day of learning phase and first day of reversal learning for EDST and EDFS did not differ between the groups. (<bold>f</bold>) Percentage of change between last day of learning phase and first day of reversal learning for escape failures did not differ between the groups. Data are expressed as mean ± SEM. Data were compared to each other with repeated-measures ANOVA (EDST, EDFS, escape failures) and t-test (change between last and first). CNO: clozapine-N-oxide; EDFS: escapes during footshock; EDST: escapes during stimulus; MRR: median raphe region.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Operant conditioning test after manipulation of the GABAergic cells of the median raphe region (Experiment 2). (<bold>a</bold>) Schematic timeline of the operant conditioning test carried out similarly as during Experiment 1. In this case, the learning phase lasted for 10 days, while the reversal learning phase lasted for 7 days. (<bold>b</bold>) The number of total responses (correct + incorrect) increased throughout the days, without any effect of treatment. However, during reversal learning (indicated by red dashed lines) the stimulatory grouped had higher number of total nose pokes compared to the other two groups. (<bold>c</bold>) Reward preference (percentage of correct nose pokes vs total nose pokes) did not differ between the groups, but the control and inhibitory group reached random chance 50% (indicated by blue dashed lines) sooner (4th and 5th day, respectively) than the stimulatory group (10th day). During reversal learning phase (indicated by red dashed lines), only the stimulatory group kept their performance above random chance 50% (indicated by blue dashed lines). (<bold>d</bold>) Percentage of changes between last day of learning phase and first day of reversal learning for total number of responses and reward preference showed no differences between the groups. (<bold>e</bold>) Number of timeout responses as possible sign of impulsivity. Data are expressed as mean ± SEM. Data were compared to each other with repeated-measures ANOVA (total responses, reward preference) and single sample t-test (vs random chance 50%). *p &lt; 0.01 vs random chance 50%. ^#p &lt; 0.01 main treatment effect during Bonferroni posthoc comparison, stimulatory group vs. control as well as inhibitory groups. Inhib: inhibitory receptor sequence containing virus vector, MRR: median raphe region, Stim: stimulatory receptor sequence containing virus vector. </p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Active avoidance after manipulation of the GABAergic cells of the median raphe region (Experiment 2). (<bold>a</bold>) Schematic timeline of the active avoidance test, carried out similarly as during Experiment 1. The learning phase lasted for 7 days, while the reversal learning phase was 3-day-long. (<bold>b</bold>) The number of escapes during stimulus increased throughout the learning phase and the stimulatory group had higher total responses. During reversal learning phase (indicated by red dashed lines), there were no differences between the groups. (<bold>c</bold>) There were no significant differences in the number of escape failures between the groups. (<bold>d</bold>) Percentage of change between last day of learning phase and first day of reversal learning did not differ across the groups in the case of escape stimulus. (<bold>e</bold>) Average escape latency during learning as a possible measure of impulsivity. Data are expressed as mean ± SEM. Data were compared to each other with repeated-measures ANOVA (escapes during stimulus, escapes during footshock, escape failures) and t-test (change between last and first). ^#p &lt; 0.01 main treatment effect during Bonferroni posthoc comparison, stimulatory group vs. control as well as inhibitory groups. Inhib: inhibitory receptor sequence containing virus vector, MRR: median raphe region, Stim: stimulatory receptor sequence containing virus vector. </p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Statistical details for the whole median raphe stimulation (Experiment 1) analyzed by repeated measures ANOVA.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"2\">Experiment</th><th align=\"left\">Parameters</th><th align=\"left\">Effect</th><th align=\"left\">Degree of freedom</th><th align=\"left\">F</th><th align=\"left\">p</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"18\">Operant conditioning</td><td align=\"left\" rowspan=\"6\">Learning</td><td align=\"left\" rowspan=\"3\">Total responses</td><td align=\"left\">Treatment</td><td align=\"left\">1,13</td><td char=\".\" align=\"char\">1.620</td><td char=\".\" align=\"char\">0.225</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">13,169</td><td char=\".\" align=\"char\">4.657</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">13,169</td><td char=\".\" align=\"char\">0.399</td><td char=\".\" align=\"char\">0.968</td></tr><tr><td align=\"left\" rowspan=\"3\">Reward preference</td><td align=\"left\">Treatment</td><td align=\"left\">1,13</td><td char=\".\" align=\"char\">0.022</td><td char=\".\" align=\"char\">0.882</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">13,169</td><td char=\".\" align=\"char\">2.591</td><td char=\".\" align=\"char\">0.002</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">13,169</td><td char=\".\" align=\"char\">0.666</td><td char=\".\" align=\"char\">0.793</td></tr><tr><td align=\"left\" rowspan=\"6\">Reversal learning</td><td align=\"left\" rowspan=\"3\">Total responses</td><td align=\"left\">Treatment</td><td align=\"left\">1,12</td><td char=\".\" align=\"char\">2.614</td><td char=\".\" align=\"char\">0.131</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">6,72</td><td char=\".\" align=\"char\">3.300</td><td char=\".\" align=\"char\">0.006</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">6,72</td><td char=\".\" align=\"char\">2.117</td><td char=\".\" align=\"char\">0.061</td></tr><tr><td align=\"left\" rowspan=\"3\">Reward preference</td><td align=\"left\">Treatment</td><td align=\"left\">1,12</td><td char=\".\" align=\"char\">0.144</td><td char=\".\" align=\"char\">0.710</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">6,72</td><td char=\".\" align=\"char\">11.431</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">6,72</td><td char=\".\" align=\"char\">0.418</td><td char=\".\" align=\"char\">0.864</td></tr><tr><td align=\"left\" rowspan=\"6\">Learning + reversal learning</td><td align=\"left\" rowspan=\"3\">Total responses</td><td align=\"left\">Treatment</td><td align=\"left\">1,12</td><td char=\".\" align=\"char\">3.521</td><td char=\".\" align=\"char\">0.085</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">20,240</td><td char=\".\" align=\"char\">4.080</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">20,240</td><td char=\".\" align=\"char\">0.960</td><td char=\".\" align=\"char\">0.511</td></tr><tr><td align=\"left\" rowspan=\"3\">Reward preference</td><td align=\"left\">Treatment</td><td align=\"left\">1,12</td><td char=\".\" align=\"char\">0.133</td><td char=\".\" align=\"char\">0.722</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">20,240</td><td char=\".\" align=\"char\">4.503</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">20,240</td><td char=\".\" align=\"char\">0.494</td><td char=\".\" align=\"char\">0.967</td></tr><tr><td align=\"left\" rowspan=\"30\">Active avoidance</td><td align=\"left\" rowspan=\"12\">Learning</td><td align=\"left\" rowspan=\"3\">N# of EDST</td><td align=\"left\">Treatment</td><td align=\"left\">1,7</td><td char=\".\" align=\"char\">0.007</td><td char=\".\" align=\"char\">0.933</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">16.205</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">1.954</td><td char=\".\" align=\"char\">0.115</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of EDFS</td><td align=\"left\">Treatment</td><td align=\"left\">1,7</td><td char=\".\" align=\"char\">0.250</td><td char=\".\" align=\"char\">0.625</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">8.000</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">0.388</td><td char=\".\" align=\"char\">0.815</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of ESFL</td><td align=\"left\">Treatment</td><td align=\"left\">1,7</td><td char=\".\" align=\"char\">0.386</td><td char=\".\" align=\"char\">0.544</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">0.810</td><td char=\".\" align=\"char\">0.524</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">0.759</td><td char=\".\" align=\"char\">0.556</td></tr><tr><td align=\"left\" rowspan=\"3\">Average latency to escape</td><td align=\"left\">Treatment</td><td align=\"left\">1,12</td><td char=\".\" align=\"char\">0.023</td><td char=\".\" align=\"char\">0.883</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">13.190</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × Treatment</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">0.634</td><td char=\".\" align=\"char\">0.641</td></tr><tr><td align=\"left\" rowspan=\"9\">Reversal learning</td><td align=\"left\" rowspan=\"3\">N# of EDST</td><td align=\"left\">Treatment</td><td align=\"left\">1,7</td><td char=\".\" align=\"char\">1.053</td><td char=\".\" align=\"char\">0.323</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">16.419</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">0.709</td><td char=\".\" align=\"char\">0.589</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of EDFS</td><td align=\"left\">Treatment</td><td align=\"left\">1,7</td><td char=\".\" align=\"char\">1.862</td><td char=\".\" align=\"char\">0.195</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">0.923</td><td char=\".\" align=\"char\">0.457</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">1.478</td><td char=\".\" align=\"char\">0.222</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of ESFL</td><td align=\"left\">Treatment</td><td align=\"left\">1,7</td><td char=\".\" align=\"char\">1.372</td><td char=\".\" align=\"char\">0.262</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">7.288</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">4,28</td><td char=\".\" align=\"char\">2.270</td><td char=\".\" align=\"char\">0.074</td></tr><tr><td align=\"left\" rowspan=\"9\">Learning + reversal learning</td><td align=\"left\" rowspan=\"3\">N# of EDST</td><td align=\"left\">Treatment</td><td align=\"left\">1,13</td><td char=\".\" align=\"char\">0.000</td><td char=\".\" align=\"char\">0.982</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">9,117</td><td char=\".\" align=\"char\">22.157</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">9,117</td><td char=\".\" align=\"char\">0.838</td><td char=\".\" align=\"char\">0.582</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of EDFS</td><td align=\"left\">Treatment</td><td align=\"left\">1,13</td><td char=\".\" align=\"char\">1.474</td><td char=\".\" align=\"char\">0.246</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">9,117</td><td char=\".\" align=\"char\">32.055</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">9,117</td><td char=\".\" align=\"char\">0.335</td><td char=\".\" align=\"char\">0.962</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of ESFL</td><td align=\"left\">Treatment</td><td align=\"left\">1,13</td><td char=\".\" align=\"char\">1.478</td><td char=\".\" align=\"char\">0.246</td></tr><tr><td align=\"left\">Time</td><td align=\"left\">9,117</td><td char=\".\" align=\"char\">111.291</td><td char=\".\" align=\"char\">0.000</td></tr><tr><td align=\"left\">Time × treatment</td><td align=\"left\">9,117</td><td char=\".\" align=\"char\">0.933</td><td char=\".\" align=\"char\">0.499</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Statistical details for manipulation of the GABAergic cells of the median raphe region (Experiment 2) analyzed by repeated measures ANOVA.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Experiment</th><th align=\"left\"/><th align=\"left\">Parameters</th><th align=\"left\">Effect</th><th align=\"left\">Degree of freedom</th><th align=\"left\">F</th><th align=\"left\">p</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"27\">Operant conditioning</td><td align=\"left\" rowspan=\"9\">Learning</td><td align=\"left\" rowspan=\"3\">Total responses</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">1.410</td><td char=\".\" align=\"char\">0.257</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">9,315</td><td char=\".\" align=\"char\">13.772</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">18,315</td><td char=\".\" align=\"char\">1.094</td><td char=\".\" align=\"char\">0.356</td></tr><tr><td align=\"left\" rowspan=\"3\">Reward preference</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">1.163</td><td char=\".\" align=\"char\">0.324</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">9,315</td><td char=\".\" align=\"char\">16.807</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">18,315</td><td char=\".\" align=\"char\">0.909</td><td char=\".\" align=\"char\">0.567</td></tr><tr><td align=\"left\" rowspan=\"3\">Timeout response</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">0.539</td><td char=\".\" align=\"char\">0.588</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">9,315</td><td char=\".\" align=\"char\">16.883</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">18,315</td><td char=\".\" align=\"char\">1.146</td><td char=\".\" align=\"char\">0.307</td></tr><tr><td align=\"left\" rowspan=\"9\">Reversal learning</td><td align=\"left\" rowspan=\"3\">Total responses</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">4.031</td><td char=\".\" align=\"char\"><bold>0.027</bold></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">6,210</td><td char=\".\" align=\"char\">2.941</td><td char=\".\" align=\"char\"><bold>0.009</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">12,210</td><td char=\".\" align=\"char\">0.567</td><td char=\".\" align=\"char\">0.866</td></tr><tr><td align=\"left\" rowspan=\"3\">Reward preference</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">3.721</td><td char=\".\" align=\"char\"><bold>0.035</bold></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">6,210</td><td char=\".\" align=\"char\">7.652</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">12,210</td><td char=\".\" align=\"char\">0.932</td><td char=\".\" align=\"char\">0.515</td></tr><tr><td align=\"left\" rowspan=\"3\">Timeout response</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">3.822</td><td char=\".\" align=\"char\"><bold>0.031</bold></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">6,210</td><td char=\".\" align=\"char\">0.461</td><td char=\".\" align=\"char\">0.837</td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">12,210</td><td char=\".\" align=\"char\">0.512</td><td char=\".\" align=\"char\">0.906</td></tr><tr><td align=\"left\" rowspan=\"9\">Learning + reversal learning</td><td align=\"left\" rowspan=\"3\">Total responses</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,32</td><td char=\".\" align=\"char\">2.566</td><td char=\".\" align=\"char\"><italic>0.092</italic></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">16,512</td><td char=\".\" align=\"char\">9.561</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">32,512</td><td char=\".\" align=\"char\">0.974</td><td char=\".\" align=\"char\">0.511</td></tr><tr><td align=\"left\" rowspan=\"3\">Reward preference</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">1.153</td><td char=\".\" align=\"char\">0.328</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">16,560</td><td char=\".\" align=\"char\">9.748</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">32,560</td><td char=\".\" align=\"char\">1.584</td><td char=\".\" align=\"char\"><bold>0.024</bold></td></tr><tr><td align=\"left\" rowspan=\"3\">Timeout response</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">1.753</td><td char=\".\" align=\"char\">0.188</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">16,560</td><td char=\".\" align=\"char\">9.174</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">32,560</td><td char=\".\" align=\"char\">1.417</td><td char=\".\" align=\"char\"><italic>0.066</italic></td></tr><tr><td align=\"left\" rowspan=\"24\">Active avoidance</td><td align=\"left\" rowspan=\"12\">Learning</td><td align=\"left\" rowspan=\"3\">N# of EDST</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,27</td><td char=\".\" align=\"char\">4.570</td><td char=\".\" align=\"char\"><bold>0.019</bold></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">6,162</td><td char=\".\" align=\"char\">24.146</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">12,162</td><td char=\".\" align=\"char\">1.099</td><td char=\".\" align=\"char\">0.363</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of EDFS</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,27</td><td char=\".\" align=\"char\">1.070</td><td char=\".\" align=\"char\">0.356</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">6,162</td><td char=\".\" align=\"char\">7.706</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">12,162</td><td char=\".\" align=\"char\">1.255</td><td char=\".\" align=\"char\">0.250</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of ESFL</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,27</td><td char=\".\" align=\"char\">2.325</td><td char=\".\" align=\"char\">0.116</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">6,162</td><td char=\".\" align=\"char\">3.054</td><td char=\".\" align=\"char\"><bold>0.007</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">12,162</td><td char=\".\" align=\"char\">0.879</td><td char=\".\" align=\"char\">0.568</td></tr><tr><td align=\"left\" rowspan=\"3\">Average latency to escape</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,36</td><td char=\".\" align=\"char\">2.545</td><td char=\".\" align=\"char\"><italic>0.092</italic></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">4,144</td><td char=\".\" align=\"char\">3.009</td><td char=\".\" align=\"char\"><bold>0.020</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">8,144</td><td char=\".\" align=\"char\">0.406</td><td char=\".\" align=\"char\">0.916</td></tr><tr><td align=\"left\" rowspan=\"6\">Reversal learning</td><td align=\"left\" rowspan=\"3\">N# of EDST</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,36</td><td char=\".\" align=\"char\">0.330</td><td char=\".\" align=\"char\">0.720</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">2,72</td><td char=\".\" align=\"char\">10.168</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">4,72</td><td char=\".\" align=\"char\">0.713</td><td char=\".\" align=\"char\">0.585</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of ESFL</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,36</td><td char=\".\" align=\"char\">0.320</td><td char=\".\" align=\"char\">0.727</td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">2,72</td><td char=\".\" align=\"char\">10.593</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">4,72</td><td char=\".\" align=\"char\">0.741</td><td char=\".\" align=\"char\">0.566</td></tr><tr><td align=\"left\" rowspan=\"6\">Learning + reversal learning</td><td align=\"left\" rowspan=\"3\">N# of EDST</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,27</td><td char=\".\" align=\"char\">7.555</td><td char=\".\" align=\"char\"><bold>0.002</bold></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">9,243</td><td char=\".\" align=\"char\">16.859</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">18,243</td><td char=\".\" align=\"char\">0.818</td><td char=\".\" align=\"char\">0.678</td></tr><tr><td align=\"left\" rowspan=\"3\">N# of ESFL</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,27</td><td char=\".\" align=\"char\">3.124</td><td char=\".\" align=\"char\"><italic>0.060</italic></td></tr><tr><td align=\"left\">Time</td><td char=\",\" align=\"char\">9,243</td><td char=\".\" align=\"char\">49.196</td><td char=\".\" align=\"char\"><bold>0.000</bold></td></tr><tr><td align=\"left\">Time × treatment</td><td char=\",\" align=\"char\">18,243</td><td char=\".\" align=\"char\">1.066</td><td char=\".\" align=\"char\">0.388</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"7\">Changes between last learning day and first reversed learning day analyzed by one way ANOVA</th></tr><tr><th align=\"left\">Experiment</th><th align=\"left\">Parameters</th><th align=\"left\">Effect</th><th align=\"left\">Degree of freedom</th><th align=\"left\">F</th><th align=\"left\">p</th><th align=\"left\"/></tr></thead><tbody><tr><td align=\"left\" rowspan=\"2\">Operant conditioning</td><td align=\"left\">Total responses</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">0.882</td><td char=\".\" align=\"char\">0.422</td><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\">Reward preference</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,35</td><td char=\".\" align=\"char\">0.364</td><td char=\".\" align=\"char\">0.697</td><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" rowspan=\"2\">Active avoidance</td><td align=\"left\">N# of EDST</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,23</td><td char=\".\" align=\"char\">0.540</td><td char=\".\" align=\"char\">0.589</td><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\">N# of ESFL</td><td align=\"left\">Treatment</td><td char=\",\" align=\"char\">2,13</td><td char=\".\" align=\"char\">0.575</td><td char=\".\" align=\"char\">0.576</td><td char=\".\" align=\"char\"/></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Summary of the results.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"5\">Experiment 1. Whole median raphe stimulation</th></tr><tr><th align=\"left\">Experiment</th><th align=\"left\">Phase</th><th align=\"left\">Parameters</th><th align=\"left\">Excitatory</th><th align=\"left\"/></tr></thead><tbody><tr><td align=\"left\" rowspan=\"4\">Operant conditioning</td><td align=\"left\" rowspan=\"2\">Learning</td><td align=\"left\">Reward preference</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\">Total response</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\" rowspan=\"2\">Reversal learning</td><td align=\"left\">Reward preference</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\">Total response</td><td align=\"left\">Marginally decreased</td><td align=\"left\"/></tr><tr><td align=\"left\" rowspan=\"6\">Active avoidance</td><td align=\"left\" rowspan=\"3\">Learning</td><td align=\"left\">N# of EDST</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\">N# of EDFS</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\">N# of ESFL</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\" rowspan=\"3\">Reversal learning</td><td align=\"left\">N# of EDST</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\">N# of EDFS</td><td align=\"left\">Ø</td><td align=\"left\"/></tr><tr><td align=\"left\">N# of ESFL</td><td align=\"left\">Marginally increased</td><td align=\"left\"/></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"5\">Experiment 2. Manipulation of the VGAT positive cells of the median raphe region</th></tr><tr><th align=\"left\">Experiment</th><th align=\"left\">Phase</th><th align=\"left\">Parameters</th><th align=\"left\">Excitatory</th><th align=\"left\">Inhibitory</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"4\">Operant conditioning</td><td align=\"left\" rowspan=\"2\">Learning</td><td align=\"left\">Reward preference</td><td align=\"left\">Ø</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\">Total response</td><td align=\"left\">Ø</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\" rowspan=\"2\">Reversal learning</td><td align=\"left\">Reward preference</td><td align=\"left\">Increased</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\">Total response</td><td align=\"left\">Increased</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\" rowspan=\"6\">Active avoidance</td><td align=\"left\" rowspan=\"3\">Learning</td><td align=\"left\">N# of EDST</td><td align=\"left\">Increased</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\">N# of EDFS</td><td align=\"left\">Ø</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\">N# of ESFL</td><td align=\"left\">Ø</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\" rowspan=\"3\">Reversal learning</td><td align=\"left\">N# of EDST</td><td align=\"left\">Ø</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\">N# of EDFS</td><td align=\"left\">Ø</td><td align=\"left\">Ø</td></tr><tr><td align=\"left\">N# of ESFL</td><td align=\"left\">Ø</td><td align=\"left\">Ø</td></tr></tbody></table></table-wrap>" ]

[ "<disp-formula id=\"Equa\"><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Reward \\; preference= \\frac{correct \\; nose \\; poke}{incorrect+correct \\; nose\\; pokes}\\times 100$$\\end{document}</tex-math><mml:math id=\"M2\" display=\"block\"><mml:mrow><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>d</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>f</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>p</mml:mi><mml:mi>o</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:mfrac><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM5\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM6\"></supplementary-material>" ]

[ "<table-wrap-foot><p>EDST: escape during stimulus; EDFS: escape during footshock; ESFL: escape failure.</p></table-wrap-foot>", "<table-wrap-foot><p>EDST: escape during stimulus; EDFS: escape during footshock; ESFL: escape failure; N.A. not applicable.</p></table-wrap-foot>", "<table-wrap-foot><p>Ø no difference compared to control; EDST: escape during stimulus; EDFS: escape during footshock; ESFL: escape failure.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41598_2024_51743_MOESM1_ESM.docx\"><caption><p>Supplementary Table 1.</p></caption></media>", "<media xlink:href=\"41598_2024_51743_MOESM2_ESM.docx\"><caption><p>Supplementary Table 2.</p></caption></media>", "<media xlink:href=\"41598_2024_51743_MOESM3_ESM.docx\"><caption><p>Supplementary Table 3.</p></caption></media>", "<media xlink:href=\"41598_2024_51743_MOESM4_ESM.docx\"><caption><p>Supplementary Table 4.</p></caption></media>", "<media xlink:href=\"41598_2024_51743_MOESM5_ESM.tif\"><caption><p>Supplementary Figure 1.</p></caption></media>", "<media xlink:href=\"41598_2024_51743_MOESM6_ESM.tif\"><caption><p>Supplementary Figure 2.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Boron is an interesting and complex element, many aspects of which are still to be explored. The properties of boron are found between metals and insulators. While boron has only three valence electrons, which would favor metallicity, they are localized enough to produce insulating states. However, pressure, temperature, and impurities can easily shift this subtle balance between metallic and insulating states. Pure boron is one of the best alternatives to carbon fullerenes (CFs) and nanotubes (CNTs), which exhibit superior properties, in the form of novel solids and nanostructures, such as quasiplanar clusters, quasi-crystals, nanosheets, nanoribbons, nano chains, and nanotubes^{##UREF##0##1##}. Besides being the only non-metal element in Group III, boron is unique in its structural complexity and has exceptional chemical and physical properties, including low densities, high melting points, and high hardness^{##UREF##1##2##}. Initially, Boron exists in three crystalline forms, , and ^{##UREF##2##3##}. Later different forms of boron crystalline have been synthesized, such as - rhombohedral, -rhombohedral, tetragonal, -orthorhombic, and -Ga type. In addition, there are amorphous phases and nanosized structures^{##UREF##3##4##}. One of them is the icosahedral that is linked together by “inter-icosahedral covalent units” or “chains”^{##UREF##4##5##}. The boron-rich ceramics based on icosahedral are second only to diamonds as hard materials. When compared to diamond-based materials, this class of ceramics offer low density, better thermal and chemical resistance, and ease of mass production.</p>", "<p id=\"Par3\">In boron -icosahedral nanosheet, each crystal contains an icosahedron molecule of , which is linked to form a three-dimensional network^{##UREF##0##1##} as shown in Fig. ##FIG##0##1##. A regular icosahedron has 12 vertices, 30 edges and 20 faces. The icosahedral boron sheet, and have been proposed in recent years with special properties. Kah et al.^{##REF##26523799##6##} proposed many icosahedral nanosheets based on clusters, and Zhou et al.^{##UREF##5##7##} presented an antiferromagnetic metallic sheet. Higashi et al.^{##UREF##6##8##} investigated the first 2D icosahedral networks. The icosahedral nanosheet bonding is complex and was well explained by Emin^{##REF##28743020##9##}. The boron allotropes attract major material researchers since they exhibit properties like thermal conductivity, hardness, and neutron scattering length^{##UREF##7##10##}. The novel icosahedral structures exhibit interesting chemical bonding and electronic properties and are structurally and energetically stable. Additionally, these -icosahedral nanosheets, which are a gapless system, exhibit semiconducting properties, suggesting an application in nanoelectronics and computer chips. is a good choice, In industrial semiconductor applications like solar cells with high solar light conversion efficiency, the icosahedal boron nanosheet is a prominent component^{##UREF##8##11##}.</p>", "<p id=\"Par4\">In a molecular graph, each edge of a molecule corresponds to a chemical bond between atoms, while each vertex and degree denotes an atom and valence of the atom. In order to characterize the structural features of these molecules, several theoretical tools are employed. A topological index can be used to model relationships between chemical structures and their corresponding biochemical and physicochemical activities^{##UREF##9##12##,##UREF##10##13##}. Large combinatorial chemical libraries are required to compute the physicochemical properties of a structure. These include novel development methods such as topological structural descriptors, combinatorial quantum chemistry tools for functional group analysis, shape-activity relations, and topological attributes of electron densities, etc. The degree-based topological indexes are used extensively in network science for investigating networks, in which the indexes are calculated based on the degrees of the graph. A breakthrough was made in degree-based indices by Deutsch and Klavar^{##UREF##11##14##}, introducing the M-polynomial. Readers can refer to^{##UREF##12##15##–##UREF##15##18##} for recent work in M-polynomial and topological indices.</p>", "<p id=\"Par5\">Boron -icosahedral nanosheets are grabbing immense attention due to their numerous applications in emerging technologies. Thus, understanding the properties of these structures is imperative for industrial applications. In this paper, the degree-based structure analysis of -icosahedral nanosheet is performed using M-polynomial. The analytical expressions for some prominent indices are evaluated and their graphical representations are plotted using the numerical values of these indices and compared. The shear modulus and Young’s modulus of the icosahedral nanosheet are compared against its structural parameters, which helps to predict the properties of numerous additional boron allotropes.</p>" ]

[]

[ "<title>Main results and discussion</title>", "<title>M-polynomial of boron -icosahedral nanosheet</title>", "<title>Theorem 1</title>", "<p id=\"Par11\">If represents a boron -icosahedral nanosheet, then -polynomial is</p>", "<p>\n\n</p>", "<title>Proof</title>", "<p id=\"Par13\">The boron -icosahedral nanosheet, contains vertices and edges. icosahedral nanosheets are categorized into edge sets based on the degree of the vertex, . The edge partition of based on the vertex degree is depicted in Fig. ##FIG##2##3##. The edge sets, is classified into three types and the parameter value, is characterized by the following value,By the Definition (##FORMU##36##1##), -polynomial of boron -icosahedral nanosheet, is defined asFigure ##FIG##3##4## shows the graphical illustration of the -polynomial function of . Thus, can be formulated as,</p>", "<p>\n\n</p>", "<title>Results for boron -icosahedral nanosheet</title>", "<p id=\"Par15\">Using Theorem 1 and -polynomial formula in Table ##TAB##0##1##, vertex degree-based topological indices such as of boron -icosahedral nanosheet, are computed. Here, . The numerical value of the derived analytical expression is compared with each index is depicted in Tables ##TAB##1##2##, ##TAB##2##3##, ##TAB##3##4## and ##TAB##4##5##. And the graphical comparison is illustrated in Figs. ##FIG##4##5##, ##FIG##5##6## and ##FIG##6##7##.</p>", "<title>Theorem 2</title>", "<p id=\"Par16\">Let be a boron -icosahedral nanosheet then <list list-type=\"order\"><list-item><p id=\"Par17\"></p></list-item><list-item><p id=\"Par18\"></p></list-item><list-item><p id=\"Par19\"></p></list-item><list-item><p id=\"Par20\"></p></list-item></list></p>", "<title>Proof</title>", "<p id=\"Par21\">\n<list list-type=\"order\"><list-item><p id=\"Par22\">\n\n\n</p></list-item><list-item><p id=\"Par23\">\n\n\n</p></list-item><list-item><p id=\"Par24\">\n\n\n</p></list-item><list-item><p id=\"Par25\">\n\n\n</p></list-item></list>\n</p>", "<p>\n\n</p>", "<p>\n\n</p>", "<title>Theorem 3</title>", "<p id=\"Par28\">Let be a boron -icosahedral nanosheet then <list list-type=\"order\"><list-item><p id=\"Par29\"></p></list-item><list-item><p id=\"Par30\"></p></list-item><list-item><p id=\"Par31\"></p></list-item><list-item><p id=\"Par32\"></p></list-item></list></p>", "<title>Proof</title>", "<p id=\"Par33\">\n<list list-type=\"order\"><list-item><p id=\"Par34\">\n\n\n</p></list-item><list-item><p id=\"Par35\">\n\n\n</p></list-item><list-item><p id=\"Par36\">\n\n\n</p></list-item><list-item><p id=\"Par37\">\n\n\n</p></list-item></list>\n</p>", "<p>\n\n</p>", "<p>\n\n</p>", "<title>Theorem 4</title>", "<p id=\"Par40\">Let be a boron -icosahedral nanosheet then <list list-type=\"order\"><list-item><p id=\"Par41\"></p></list-item><list-item><p id=\"Par42\"></p></list-item><list-item><p id=\"Par43\"></p></list-item><list-item><p id=\"Par44\"></p></list-item></list></p>", "<title>Proof</title>", "<p id=\"Par45\">\n<list list-type=\"order\"><list-item><p id=\"Par46\">\n\n\n</p></list-item><list-item><p id=\"Par47\">\n\n\n</p></list-item><list-item><p id=\"Par48\">\n\n\n</p></list-item><list-item><p id=\"Par49\">\n\n\n</p></list-item></list>\n</p>", "<p>\n\n</p>", "<p>\n\n</p>" ]

[ "<title>Main results and discussion</title>", "<title>M-polynomial of boron -icosahedral nanosheet</title>", "<title>Theorem 1</title>", "<p id=\"Par11\">If represents a boron -icosahedral nanosheet, then -polynomial is</p>", "<p>\n\n</p>", "<title>Proof</title>", "<p id=\"Par13\">The boron -icosahedral nanosheet, contains vertices and edges. icosahedral nanosheets are categorized into edge sets based on the degree of the vertex, . The edge partition of based on the vertex degree is depicted in Fig. ##FIG##2##3##. The edge sets, is classified into three types and the parameter value, is characterized by the following value,By the Definition (##FORMU##36##1##), -polynomial of boron -icosahedral nanosheet, is defined asFigure ##FIG##3##4## shows the graphical illustration of the -polynomial function of . Thus, can be formulated as,</p>", "<p>\n\n</p>", "<title>Results for boron -icosahedral nanosheet</title>", "<p id=\"Par15\">Using Theorem 1 and -polynomial formula in Table ##TAB##0##1##, vertex degree-based topological indices such as of boron -icosahedral nanosheet, are computed. Here, . The numerical value of the derived analytical expression is compared with each index is depicted in Tables ##TAB##1##2##, ##TAB##2##3##, ##TAB##3##4## and ##TAB##4##5##. And the graphical comparison is illustrated in Figs. ##FIG##4##5##, ##FIG##5##6## and ##FIG##6##7##.</p>", "<title>Theorem 2</title>", "<p id=\"Par16\">Let be a boron -icosahedral nanosheet then <list list-type=\"order\"><list-item><p id=\"Par17\"></p></list-item><list-item><p id=\"Par18\"></p></list-item><list-item><p id=\"Par19\"></p></list-item><list-item><p id=\"Par20\"></p></list-item></list></p>", "<title>Proof</title>", "<p id=\"Par21\">\n<list list-type=\"order\"><list-item><p id=\"Par22\">\n\n\n</p></list-item><list-item><p id=\"Par23\">\n\n\n</p></list-item><list-item><p id=\"Par24\">\n\n\n</p></list-item><list-item><p id=\"Par25\">\n\n\n</p></list-item></list>\n</p>", "<p>\n\n</p>", "<p>\n\n</p>", "<title>Theorem 3</title>", "<p id=\"Par28\">Let be a boron -icosahedral nanosheet then <list list-type=\"order\"><list-item><p id=\"Par29\"></p></list-item><list-item><p id=\"Par30\"></p></list-item><list-item><p id=\"Par31\"></p></list-item><list-item><p id=\"Par32\"></p></list-item></list></p>", "<title>Proof</title>", "<p id=\"Par33\">\n<list list-type=\"order\"><list-item><p id=\"Par34\">\n\n\n</p></list-item><list-item><p id=\"Par35\">\n\n\n</p></list-item><list-item><p id=\"Par36\">\n\n\n</p></list-item><list-item><p id=\"Par37\">\n\n\n</p></list-item></list>\n</p>", "<p>\n\n</p>", "<p>\n\n</p>", "<title>Theorem 4</title>", "<p id=\"Par40\">Let be a boron -icosahedral nanosheet then <list list-type=\"order\"><list-item><p id=\"Par41\"></p></list-item><list-item><p id=\"Par42\"></p></list-item><list-item><p id=\"Par43\"></p></list-item><list-item><p id=\"Par44\"></p></list-item></list></p>", "<title>Proof</title>", "<p id=\"Par45\">\n<list list-type=\"order\"><list-item><p id=\"Par46\">\n\n\n</p></list-item><list-item><p id=\"Par47\">\n\n\n</p></list-item><list-item><p id=\"Par48\">\n\n\n</p></list-item><list-item><p id=\"Par49\">\n\n\n</p></list-item></list>\n</p>", "<p>\n\n</p>", "<p>\n\n</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par61\">Using a degree-vertex M-polynomial graph technique, the topological indices of the boron -icosahedral nanosheet are determined. The structural characterization is used to analyse the topological connectivity properties of boron -icosahedral nanosheet, by combining quantum chemical descriptors with nanosheet results. This research could provide a crucial tool for determining the significance of nanosheets in many areas, such as material science, drug discovery, and predictive toxicology. Furthermore, the topological indices are used in the study of boron -icosahedral nanosheets and provide QSAR expressions that predict several molecular properties such as band gap, optical and electronic stability, molecular density, enthalpies, conductivity, and so on. In this research, we correlate our theoretical results with the shear modulus and Young’s modulus original data synthesized in recent years, which showed a high correlation of 0.9835 and 0.9932 with hyper Zagreb. This type of research has not been explored earlier. So, it has a significant contribution to research by finding a correlation between topological indices and properties of boron allotropes. This allows us to explore other nanosheets, it is left as an open problem for future research.</p>" ]

[ "<p id=\"Par1\">Nanosheets with boron elements have excellent characteristics which makes the boron polymorphs unique and super hard. A boron -icosahedral nanosheet in crystalline form has superconductivity and thermal electronic properties. In theoretical chemistry and QSPR/QSAR study, a topological descriptor is an important analytical tool. It helps to analyse the structure and its properties and also correlates the with numerical expressions. The valence-based M-polynomial provides quantitative measures of molecular properties based on their geometric, electrostatic, and quantum chemical characteristics. In this article, the QSPR/QSAR analysis is performed for this nanosheet and the analytical expressions are validated with original synthesized data, and received excellent correlation values of 0.9835 and 0.9932. The mathematical expression of the structure is analysed and the indices are compared graphically and numerically.</p>", "<title>Subject terms</title>" ]

[ "<title>Computational techniques</title>", "<p id=\"Par6\">A chemical compound can be modeled as a simple graph, with vertex and edge sets, and respectively. The valency of an atom is denoted by of the vertex , whereas the maximum degree over all the vertices of is denoted by . The degree of the vertex of boron -icosahedral nanosheet is illustrated in Fig. ##FIG##1##2##. The set are consider, . We denote and . The -polynomial^{##UREF##11##14##} for simple connected graph, is defined bywhere be the total number of edges such that . The bond additive is the function from into specified as real numbers , induced by . The degree-based structural descriptors for , where is the function of degree based indices is depicted as</p>", "<p id=\"Par7\">A brief discussion of bond additive degree-based indices is given below regarding the above-specified real numbers, . First degree-based structure descriptors were studied^{##UREF##16##19##} and developed^{##UREF##17##20##} with the Zagreb index, defined by based on the square root of the vertex degrees to analyze the influence of total electron energy on structure. The next analogous of Zagreb index is <italic>second Zagreb index</italic>, represented as . These indices help in analyzing the complexity of the molecular system and increase with extent branching of the carbon skeleton. The other analogous of Zagreb index are <italic>augumented Zagreb index</italic> , ^{##UREF##18##21##} and <italic>hyper Zagreb index</italic>, ^{##UREF##19##22##} is defined by and respectively. These indices are used to analyze new drugs’ molecular structures and to understand their biological and chemical properties. Based on the inverse value of vertex degree, the other invariant of Zagreb index, <italic>modified Zagreb</italic>, ^{##UREF##20##23##} defined by is evolved. Several studies have demonstrated that the augmented Zagreb index can predict the temperature at which octanes and heptanes form. These variants of Zagreb indices can be used for determining the isomerism of ZE, chirality, heat formation, and heterogeneity of hetero systems.</p>", "<p id=\"Par8\">Based on the degrees of the end vertices of , several methods have been proposed to examine the branching properties of alkanes. In 1975 Milan Randić^{##UREF##21##24##} developed the topological index of graph, under the label “molecular connectivity index” in the description and . A <italic>general Randić index</italic>, latterly developed by Bollobas and Erdos^{##UREF##22##25##} by substituting and with a real integer is defined as . The other variant of randić index are <italic> reciprocal randić</italic>, ^{##UREF##23##26##} and <italic>harmonic index</italic>, ^{##UREF##24##27##} are represented as and . Graph eigenvalues were analyzed by Favaron et al.^{##UREF##25##28##} in relation to harmonic indices. A correlation has been demonstrated between these variants of randic index and various physicochemical properties of alkanes, including the formation of enthalpies, surface areas, vapor pressure, boiling points, Kovats constants, and so on^{##UREF##26##29##}.</p>", "<p id=\"Par9\"><italic>Symmetric division degree index</italic>, ^{##UREF##27##30##} is a great tool for predicting polychlorobiphenyl surfaces is defined by or . <italic>Forgotten index</italic>, ^{##UREF##28##31##}, which greatly enhances the physicochemical prediction of the First Zagreb index, and it is defined as . An important tool for estimating octane isomer surface area is the <italic>inverse sum index</italic>\n^{##UREF##29##32##} defined as . And <italic>sigma index</italic>, is given by . By analyzing the above discussion, it is evident that the bond additive degree is a significant aspect to investigate the physicochemical properties of molecular structures. Table ##TAB##0##1## outlines the formulations for the M-polynomial method.</p>", "<p id=\"Par10\">The operators are required which relate the degree-based topological descriptors with the -polynomial,</p>", "<title>Properties prediction of boron crystal sheet</title>", "<p id=\"Par52\">By emphasizing topological descriptors’ importance in QSAR/QSPR research and illustrating their predictive and assessment factors for boron sheets, a key focus of this study is described in this section. Using regression analysis, an equation has been formulated to relate the topological descriptors and the significant properties of boron sheets. With the aid of these formulations, one may further predict the characteristics of boron sheets, independent of their dimensions.</p>", "<title>Significance of molecular descriptors</title>", "<p id=\"Par53\">In quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR), the topological descriptors, ’describes’ the molecular structure’s properties or activities in mathematical terminologies. QSAR/QSPR mathematically correlates the physicochemical properties or biological activity of chemical compounds with molecular descriptors. The base for this idea, QSAR/QSPR modelling is many chemical compounds have been implicitly equated with the overall risks which cause acute effects on human health. Some of the pesticide compounds are highly toxic and few may cause cancer.</p>", "<p id=\"Par54\">The toxicological testing of an active ingredient is usually limited. To estimate and rank the potentially hazardous chemicals, it is essential to develop an accurate and simple method^{##REF##6403090##33##}. Thus, it is a critical need to analyze and understand the structural properties of molecular compounds. Linear regression, multiple linear regression, logistic regression^{##UREF##30##34##}, efficient linear method^{##UREF##31##35##}, principal component analysis^{##UREF##32##36##}, partial least square regression^{##UREF##33##37##}, decision tree^{##UREF##34##38##} and random forest^{##UREF##35##39##} are the modelling techniques or methods that are used to analyze or predict the molecular compounds. In our study, linear regression method is deployed for statistical analysis of boron -icosahedral nanosheet. The graphica flowchart insisting on the topological descriptors and their potential uses is exhibited in Fig. ##FIG##7##8##.</p>", "<title>Variant of boron sheets and its descriptors</title>", "<p id=\"Par55\">Boron has recently received a lot of attention due to its diverse chemical properties and similarities to carbon. Due to the large number of allotropes and complex bonding nature of boron, many are interested to study its crystal structures and stability^{##REF##19182772##40##}. Icosahedra exhibit electrical and structural stability as well as interesting chemical bonding characteristics. A few of the two-dimensional boron sheets such as boron -icosahedral nanosheet, -^{##UREF##1##2##}, borophene nanosheet^{##UREF##36##41##}, borophene nanosheet^{##UREF##37##42##}, -borphene nanosheet^{##REF##28050875##43##} were analyzed through regression analysis. The above-mentioned boron sheet is illustrated in Fig. ##FIG##8##9##. The degree-vertex value of the base structure of boron sheets is listed in Table ##TAB##4##5##.</p>", "<p id=\"Par56\">\n\n</p>", "<p id=\"Par57\">In our study, we investigate the elastic, geometric, thermodynamic, and mechanical properties of the boron sheets. An elastic constant is used to determine the mechanical properties of a material and describe its ability to resist deformation by external forces. With elastic constant, some mechanical properties such as Young’s modulus <italic>E</italic>, bulk modulus <italic>B</italic> and Shear modulus <italic>G</italic> can be determined. The elastic properties are closely related to the thermodynamic properties like melting point, heat capacity, vacancy defect, and temperature. The Young’s modulus, <italic>E</italic>, and Shear modulus, <italic>G</italic> data of various boron nanosheets are summarized in Table ##TAB##5##6##^{##UREF##38##44##–##UREF##40##46##}. The Young’s modulus (N/m) indicates a material’s ability to withstand changes in length when brought under tension or compression and shear modulus (GPa) is a measure of elastic shear material’s stiffness that reflects body rigidity.</p>", "<title>Properties analysis and theoretical prediction</title>", "<p id=\"Par58\">The mechanical properties, Young’s modulus and shear modulus of the above-mentioned boron sheets are analyzed with topological descriptors by a regression model. Legendre^{##UREF##41##47##} and Gauss^{##UREF##42##48##} introduced the least squares approach to linear regression in 1805 and 1809 respectively. Regression analysis is a statistical technique that determines the correlation between two or more variables. The correlation coefficient ranges from 1 to -1. The perfect positive and negative correlation is 1 and -1 where near 0 indicates weak correlation. A correlation coefficient and regression analysis are used to derive the equation connecting the descriptors and properties. The linear regression model,where M is the mechanical properties of the boron nanosheets, and TD is topological descriptors. Using SPSS software^{##UREF##43##49##,##UREF##44##50##}, the invariant, <italic>i</italic> and regression coefficient, <italic>j</italic> can be calculated. The correlation coefficients between dependent variables, physical properties of boron sheets and independent variables, topological descriptors of nanosheets are listed in Table ##TAB##6##7##. For recent work on QSPR analysis by linear regression method, readers can refer^{##UREF##45##51##,##UREF##46##52##}.</p>", "<p id=\"Par59\">The correlation table indicates that these boron derivatives have strong correlations within themselves for both chemical attributes. In comparison to other indices, the hyper Zagreb index has a strong correlation for Young’s modulus and shear modulus. The linear regression model for shear modulus is shown below,where G is shear modulus and HM is hyper Zagreb index. Similarly, the linear regression equation for Young’s modulus is determined as followswhere E is Young’s modulus. The molecular characteristics with a greater dimension can be predicted with an appropriate regression model. In Fig. ##FIG##9##10##, the scatter plots for the highest correlated properties and descriptors are shown.</p>", "<p id=\"Par60\">\n\n</p>" ]

[ "<title>Author contributions</title>", "<p>Conceptualization, A.A.; Methodology, A.S.; Software, A.S.; Formal analysis, K.J.; Investigation, K.J., and A.A.; Resources, A.A.; Writing—original draft, A.A. and K.J., A.S.; Supervision, A.A. and D.A.X.</p>", "<title>Funding</title>", "<p>This work is not funded by government or any private agency.</p>", "<title>Data availability </title>", "<p>The datasets generated and/or analyz during the current study are available in this current article.</p>", "<title>Competing interests</title>", "<p id=\"Par62\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Crystal structure of boron -icosahedral nanosheet.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Degree of boron -icosahedral nanosheet.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Edge partition of boron -icosahedral nanosheet, .</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>-polynomial of boron -icosahedral nanosheet, .</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Visualization of \n\n\n.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Graphical representation of \n\n\n.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Graphical illustration of \n\n\n.</p></caption></fig>", "<fig id=\"Fig8\"><label>Figure 8</label><caption><p>Graphical flowchart indicating the topological descriptors significance.</p></caption></fig>", "<fig id=\"Fig9\"><label>Figure 9</label><caption><p>Boron nanosheet and its allotropes; (<bold>a</bold>) -icosahedral, - (<bold>b</bold>) borophene (<bold>c</bold>) borophene (<bold>d</bold>) borphene.</p></caption></fig>", "<fig id=\"Fig10\"><label>Figure 10</label><caption><p>Scatter visualisation for the properties and indices.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>The derivation of vertex-degree -polynomials.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Topological indices</th><th align=\"left\"></th><th align=\"left\">Derivation from </th></tr></thead><tbody><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Numerical value of \n\n\n.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th></tr></thead><tbody><tr><td align=\"left\">(1, 1)</td><td align=\"left\">300</td><td align=\"left\">750</td><td align=\"left\">75</td><td align=\"left\">1.2</td></tr><tr><td align=\"left\">(1, 2)</td><td align=\"left\">622</td><td align=\"left\">1586</td><td align=\"left\">155.2727</td><td align=\"left\">2.3611</td></tr><tr><td align=\"left\">(2, 2)</td><td align=\"left\">1332</td><td align=\"left\">3528</td><td align=\"left\">332.1818</td><td align=\"left\">4.58</td></tr><tr><td align=\"left\">(3, 3)</td><td align=\"left\">3140</td><td align=\"left\">8522</td><td align=\"left\">782.8182</td><td align=\"left\">10.08</td></tr><tr><td align=\"left\">(4, 3)</td><td align=\"left\">4238</td><td align=\"left\">11572</td><td align=\"left\">1056.4545</td><td align=\"left\">13.3589</td></tr><tr><td align=\"left\">(5, 5)</td><td align=\"left\">9084</td><td align=\"left\">25158</td><td align=\"left\">2264.4545</td><td align=\"left\">27.44</td></tr><tr><td align=\"left\">(5, 6)</td><td align=\"left\">10958</td><td align=\"left\">30426</td><td align=\"left\">2731.6364</td><td align=\"left\">32.8411</td></tr><tr><td align=\"left\">(6, 6)</td><td align=\"left\">13220</td><td align=\"left\">36800</td><td align=\"left\">3295.4545</td><td align=\"left\">39.3</td></tr><tr><td align=\"left\">(6, 7)</td><td align=\"left\">15482</td><td align=\"left\">43176</td><td align=\"left\">3859.3636</td><td align=\"left\">45.7611</td></tr><tr><td align=\"left\">(7, 8)</td><td align=\"left\">20782</td><td align=\"left\">58142</td><td align=\"left\">5180.5454</td><td align=\"left\">60.8011</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Numerical value of \n\n\n.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th></tr></thead><tbody><tr><td align=\"left\">(1, 1)</td><td align=\"left\">750</td><td align=\"left\">1500</td><td align=\"left\">915.5273</td><td align=\"left\">3000</td></tr><tr><td align=\"left\">(1, 2)</td><td align=\"left\">1586</td><td align=\"left\">3182</td><td align=\"left\">1942.9053</td><td align=\"left\">6354</td></tr><tr><td align=\"left\">(2, 2)</td><td align=\"left\">3528</td><td align=\"left\">7092</td><td align=\"left\">4370.407</td><td align=\"left\">14148</td></tr><tr><td align=\"left\">(3, 3)</td><td align=\"left\">8522</td><td align=\"left\">17140</td><td align=\"left\">10637.9321</td><td align=\"left\">34184</td></tr><tr><td align=\"left\">(4, 3)</td><td align=\"left\">11572</td><td align=\"left\">23278</td><td align=\"left\">14471.7565</td><td align=\"left\">46422</td></tr><tr><td align=\"left\">(5, 5)</td><td align=\"left\">25158</td><td align=\"left\">50604</td><td align=\"left\">31610.9189</td><td align=\"left\">100920</td></tr><tr><td align=\"left\">(5, 6)</td><td align=\"left\">30426</td><td align=\"left\">61198</td><td align=\"left\">38263.5878</td><td align=\"left\">122050</td></tr><tr><td align=\"left\">(6, 6)</td><td align=\"left\">36800</td><td align=\"left\">74020</td><td align=\"left\">46316.3806</td><td align=\"left\">147620</td></tr><tr><td align=\"left\">(6, 7)</td><td align=\"left\">43176</td><td align=\"left\">86842</td><td align=\"left\">54375.3723</td><td align=\"left\">173194</td></tr><tr><td align=\"left\">(7, 8)</td><td align=\"left\">58142</td><td align=\"left\">116942</td><td align=\"left\">73299.8022</td><td align=\"left\">233226</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Numerical value of \n\n\n.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th><th align=\"left\">\n\n</th></tr></thead><tbody><tr><td align=\"left\">(1, 1)</td><td align=\"left\">1.2</td><td align=\"left\">60</td><td align=\"left\">6</td><td align=\"left\">0</td></tr><tr><td align=\"left\">(1, 2)</td><td align=\"left\">2.3611</td><td align=\"left\">122.3333</td><td align=\"left\">11.9848</td><td align=\"left\">10</td></tr><tr><td align=\"left\">(2, 2)</td><td align=\"left\">4.58</td><td align=\"left\">253.2</td><td align=\"left\">23.9455</td><td align=\"left\">36</td></tr><tr><td align=\"left\">(3, 3)</td><td align=\"left\">10.08</td><td align=\"left\">583.2</td><td align=\"left\">53.8545</td><td align=\"left\">96</td></tr><tr><td align=\"left\">(4, 3)</td><td align=\"left\">13.3589</td><td align=\"left\">782.4667</td><td align=\"left\">71.797</td><td align=\"left\">134</td></tr><tr><td align=\"left\">(5, 5)</td><td align=\"left\">27.44</td><td align=\"left\">1653.6</td><td align=\"left\">149.5636</td><td align=\"left\">288</td></tr><tr><td align=\"left\">(5, 6)</td><td align=\"left\">32.8411</td><td align=\"left\">1989.5333</td><td align=\"left\">179.4758</td><td align=\"left\">346</td></tr><tr><td align=\"left\">(6, 6)</td><td align=\"left\">39.3</td><td align=\"left\">2394</td><td align=\"left\">215.3637</td><td align=\"left\">420</td></tr><tr><td align=\"left\">(6, 7)</td><td align=\"left\">45.7611</td><td align=\"left\">2798.3333</td><td align=\"left\">251.2576</td><td align=\"left\">490</td></tr><tr><td align=\"left\">(7, 8)</td><td align=\"left\">60.8011</td><td align=\"left\">3743.9333</td><td align=\"left\">335.003</td><td align=\"left\">658</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Experimental data for Young’s modulus and shear modulus of boron nanosheets.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">SI. no</th><th align=\"left\">Boron nanosheets</th><th align=\"left\">Shear modulus, <italic>G</italic></th><th align=\"left\">Young’s modulus, <italic>E</italic></th></tr></thead><tbody><tr><td align=\"left\">1</td><td align=\"left\">-icosahedral, -</td><td align=\"left\">210 GPa</td><td align=\"left\">480 N/m</td></tr><tr><td align=\"left\">2</td><td align=\"left\"> borophene</td><td align=\"left\">88 GPa</td><td align=\"left\">210 N/m</td></tr><tr><td align=\"left\">3</td><td align=\"left\"> borophene</td><td align=\"left\">108 GPa</td><td align=\"left\">241 N/m</td></tr><tr><td align=\"left\">4</td><td align=\"left\">borphene</td><td align=\"left\">68.5 GPa</td><td align=\"left\">179 N/m</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab6\"><label>Table 6</label><caption><p>Degree-vertex value of boron nanosheets.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Indices</th><th align=\"left\">-icosahedral</th><th align=\"left\">-borophene</th><th align=\"left\"></th><th align=\"left\">-borophene</th></tr></thead><tbody><tr><td align=\"left\"></td><td align=\"left\">3140</td><td align=\"left\">1222</td><td align=\"left\">1364</td><td align=\"left\">1318</td></tr><tr><td align=\"left\"></td><td align=\"left\">8522</td><td align=\"left\">2968</td><td align=\"left\">3441</td><td align=\"left\">3023</td></tr><tr><td align=\"left\"></td><td align=\"left\">10.08</td><td align=\"left\">6.1511</td><td align=\"left\">6.0986</td><td align=\"left\">7.6156</td></tr><tr><td align=\"left\"><italic>A</italic></td><td align=\"left\">10637.932</td><td align=\"left\">3520.5917</td><td align=\"left\">3910.979</td><td align=\"left\">3508.5186</td></tr><tr><td align=\"left\"><italic>R</italic></td><td align=\"left\">8522</td><td align=\"left\">2968</td><td align=\"left\">3441</td><td align=\"left\">3028</td></tr><tr><td align=\"left\"><italic>RR</italic></td><td align=\"left\">10.08</td><td align=\"left\">6.1511</td><td align=\"left\">6.0986</td><td align=\"left\">7.6156</td></tr><tr><td align=\"left\"><italic>H</italic></td><td align=\"left\">53.8545</td><td align=\"left\">26.849</td><td align=\"left\">26.1612</td><td align=\"left\">31.9423</td></tr><tr><td align=\"left\"><italic>HM</italic></td><td align=\"left\">34184</td><td align=\"left\">12148</td><td align=\"left\">14714</td><td align=\"left\">12452</td></tr><tr><td align=\"left\"><italic>F</italic></td><td align=\"left\">17140</td><td align=\"left\">6212</td><td align=\"left\">7832</td><td align=\"left\">6814</td></tr><tr><td align=\"left\"></td><td align=\"left\">96</td><td align=\"left\">276</td><td align=\"left\">950</td><td align=\"left\">360</td></tr><tr><td align=\"left\"><italic>SDD</italic></td><td align=\"left\">583.2</td><td align=\"left\">266.667</td><td align=\"left\">313.9048</td><td align=\"left\">304.9333</td></tr><tr><td align=\"left\"><italic>I</italic></td><td align=\"left\">782.8182</td><td align=\"left\">297.9432</td><td align=\"left\">316.349</td><td align=\"left\">319.6294</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab7\"><label>Table 7</label><caption><p>Correlation coefficient between properties and descriptors.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Indices</th><th align=\"left\">Shear modulus, <italic>G</italic></th><th align=\"left\">Young’s modulus, <italic>E</italic></th></tr></thead><tbody><tr><td align=\"left\"></td><td align=\"left\">0.9701</td><td align=\"left\">0.981</td></tr><tr><td align=\"left\"></td><td align=\"left\">0.98</td><td align=\"left\">0.9915</td></tr><tr><td align=\"left\"></td><td align=\"left\">0.8109</td><td align=\"left\">0.8494</td></tr><tr><td align=\"left\"><italic>A</italic></td><td align=\"left\">0.9774</td><td align=\"left\">0.9901</td></tr><tr><td align=\"left\"><italic>R</italic></td><td align=\"left\">0.9798</td><td align=\"left\">0.9914</td></tr><tr><td align=\"left\"><italic>RR</italic></td><td align=\"left\">0.8109</td><td align=\"left\">0.8494</td></tr><tr><td align=\"left\"><italic>H</italic></td><td align=\"left\">0.9013</td><td align=\"left\">0.93005</td></tr><tr><td align=\"left\"><italic>HM</italic></td><td align=\"left\">0.9835</td><td align=\"left\">0.9932</td></tr><tr><td align=\"left\"><italic>F</italic></td><td align=\"left\">0.9794</td><td align=\"left\">0.989</td></tr><tr><td align=\"left\"></td><td align=\"left\">0.39799</td><td align=\"left\">0.45497</td></tr><tr><td align=\"left\"><italic>SDD</italic></td><td align=\"left\">0.9636</td><td align=\"left\">0.9777</td></tr><tr><td align=\"left\"><italic>I</italic></td><td align=\"left\">0.9645</td><td align=\"left\">0.98102</td></tr></tbody></table></table-wrap>" ]

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mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq5\"><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M6\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq6\"><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha -B_{12}$$\\end{document}</tex-math><mml:math id=\"M8\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq7\"><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta -B_{106}$$\\end{document}</tex-math><mml:math id=\"M10\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mn>106</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq8\"><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma -B_{28}$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mrow><mml:mi>γ</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mn>28</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq9\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:mi>β</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq18\"><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{20}$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:msub><mml:mi>B</mml:mi><mml:mn>20</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq19\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq20\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{20}$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:msub><mml:mi>B</mml:mi><mml:mn>20</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq21\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq22\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq23\"><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\breve{z}$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mover accent=\"true\"><mml:mi>z</mml:mi><mml:mo>˘</mml:mo></mml:mover></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq24\"><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M44\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq25\"><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M46\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq26\"><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:mi>χ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq27\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathcal {V}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:mrow><mml:mi mathvariant=\"script\">V</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq28\"><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathcal {E}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M52\"><mml:mrow><mml:mi mathvariant=\"script\">E</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq29\"><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{d}_\\mu$$\\end{document}</tex-math><mml:math id=\"M54\"><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq30\"><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mu \\in {\\mathcal {V}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M56\"><mml:mrow><mml:mi>μ</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=\"script\">V</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq31\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:mi>χ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq32\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Psi$$\\end{document}</tex-math><mml:math id=\"M60\"><mml:mi mathvariant=\"normal\">Ψ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq33\"><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M62\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq34\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{\\mathfrak {D}}}= \\{({\\mathfrak {k,h}} \\in \\mathbb {N\\times N})| 1\\le {{\\mathfrak {k}}}\\le {{\\mathfrak {h}}}\\le \\Psi \\}$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:mrow><mml:mi mathvariant=\"fraktur\">D</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow><mml:mo>∈</mml:mo><mml:mrow><mml:mi mathvariant=\"double-struck\">N</mml:mi><mml:mo>×</mml:mo><mml:mi mathvariant=\"double-struck\">N</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>≤</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi><mml:mo>≤</mml:mo><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq35\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{d}_{{\\mathfrak {k,h}}}=|\\{\\mu \\eta \\in {\\mathcal {E}}(\\chi )|\\texttt{d}_\\mu ={{\\mathfrak {k}}}$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:mrow><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mi>μ</mml:mi><mml:mi>η</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=\"script\">E</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">k</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq36\"><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{d}_\\eta ={{\\mathfrak {h}}}\\}|$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:mrow><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>η</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi><mml:mrow><mml:mo stretchy=\"false\">}</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq37\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq38\"><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi$$\\end{document}</tex-math><mml:math id=\"M72\"><mml:mi>χ</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\mathbb {M}}(\\chi ;{\\mathfrak {y,z}})=\\sum _{{{\\mathfrak {k}}}\\le {{\\mathfrak {h}}}}\\texttt{m}_{{\\mathfrak {kh}}}(\\chi ){{\\mathfrak {y}}}^{{\\mathfrak {k}}}{\\mathfrak {z}}^{{\\mathfrak {h}}} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M74\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>≤</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi mathvariant=\"monospace\">m</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq39\"><alternatives><tex-math id=\"M75\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{m}_{\\mathfrak {kh}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M76\"><mml:mrow><mml:msub><mml:mi mathvariant=\"monospace\">m</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M77\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mu \\eta \\in {\\mathcal {E}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M78\"><mml:mrow><mml:mi>μ</mml:mi><mml:mi>η</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=\"script\">E</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M79\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{\\texttt{d}_\\mu ,\\texttt{d}_\\eta \\}=\\{{\\mathfrak {k,h}}\\}$$\\end{document}</tex-math><mml:math id=\"M80\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>η</mml:mi></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq42\"><alternatives><tex-math id=\"M81\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi$$\\end{document}</tex-math><mml:math id=\"M82\"><mml:mi>χ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq43\"><alternatives><tex-math id=\"M83\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {R}}$$\\end{document}</tex-math><mml:math id=\"M84\"><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq44\"><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {k,h}}}$$\\end{document}</tex-math><mml:math id=\"M86\"><mml:msub><mml:mi>β</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq45\"><alternatives><tex-math id=\"M87\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({\\mathfrak {k,h}})\\in {{\\mathfrak {D}}}$$\\end{document}</tex-math><mml:math id=\"M88\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>∈</mml:mo><mml:mi mathvariant=\"fraktur\">D</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq46\"><alternatives><tex-math id=\"M89\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta (\\chi )= \\sum _{({\\mathfrak {k,h}})\\in {{\\mathfrak {D}}}}\\texttt{d}_{{\\mathfrak {kh}}}\\beta _{{\\mathfrak {kh}}}$$\\end{document}</tex-math><mml:math id=\"M90\"><mml:mrow><mml:mi>β</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mo>∑</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>∈</mml:mo><mml:mi mathvariant=\"fraktur\">D</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq47\"><alternatives><tex-math id=\"M91\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi$$\\end{document}</tex-math><mml:math id=\"M92\"><mml:mi>χ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq48\"><alternatives><tex-math id=\"M93\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{f}(\\texttt{d}_\\mu , \\texttt{d}_\\eta )$$\\end{document}</tex-math><mml:math id=\"M94\"><mml:mrow><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>η</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><alternatives><tex-math id=\"M95\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\Lambda (\\chi )=\\displaystyle \\sum _{\\mu \\eta \\in {{\\mathfrak {D}}}}\\texttt{f}(\\texttt{d}_\\mu , \\texttt{d}_\\eta ) \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M96\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"><mml:mrow><mml:mi mathvariant=\"normal\">Λ</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mi>η</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=\"fraktur\">D</mml:mi></mml:mrow></mml:munder><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>η</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq49\"><alternatives><tex-math id=\"M97\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M98\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq50\"><alternatives><tex-math id=\"M99\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}$$\\end{document}</tex-math><mml:math id=\"M100\"><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq51\"><alternatives><tex-math id=\"M101\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1(\\chi )$$\\end{document}</tex-math><mml:math id=\"M102\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq52\"><alternatives><tex-math id=\"M103\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= {\\mathfrak {k+h}}$$\\end{document}</tex-math><mml:math id=\"M104\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq53\"><alternatives><tex-math id=\"M105\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2(\\chi )$$\\end{document}</tex-math><mml:math id=\"M106\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq54\"><alternatives><tex-math id=\"M107\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= {\\mathfrak {kh}}$$\\end{document}</tex-math><mml:math id=\"M108\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq55\"><alternatives><tex-math id=\"M109\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$AZ(\\chi )$$\\end{document}</tex-math><mml:math id=\"M110\"><mml:mrow><mml:mi>A</mml:mi><mml:mi>Z</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq56\"><alternatives><tex-math id=\"M111\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$HM(\\chi )$$\\end{document}</tex-math><mml:math id=\"M112\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq57\"><alternatives><tex-math id=\"M113\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= \\big (\\frac{{\\mathfrak {kh}}}{{\\mathfrak {k+h}}-2}\\big )^3$$\\end{document}</tex-math><mml:math id=\"M114\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mi mathvariant=\"fraktur\">kh</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:msup><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq58\"><alternatives><tex-math id=\"M115\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= ({\\mathfrak {k+h}})^2$$\\end{document}</tex-math><mml:math id=\"M116\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq59\"><alternatives><tex-math id=\"M117\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m(\\chi )$$\\end{document}</tex-math><mml:math id=\"M118\"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq60\"><alternatives><tex-math id=\"M119\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= \\frac{1}{{\\mathfrak {kh}}}$$\\end{document}</tex-math><mml:math id=\"M120\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq61\"><alternatives><tex-math id=\"M121\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi$$\\end{document}</tex-math><mml:math id=\"M122\"><mml:mi>χ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq62\"><alternatives><tex-math id=\"M123\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi$$\\end{document}</tex-math><mml:math id=\"M124\"><mml:mi>χ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq63\"><alternatives><tex-math id=\"M125\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{-1}$$\\end{document}</tex-math><mml:math id=\"M126\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq64\"><alternatives><tex-math id=\"M127\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{-1/2}$$\\end{document}</tex-math><mml:math id=\"M128\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq65\"><alternatives><tex-math id=\"M129\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{{\\mathfrak {d}}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M130\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq66\"><alternatives><tex-math id=\"M131\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{-1}$$\\end{document}</tex-math><mml:math id=\"M132\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq67\"><alternatives><tex-math id=\"M133\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{-1/2}$$\\end{document}</tex-math><mml:math id=\"M134\"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq68\"><alternatives><tex-math id=\"M135\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{\\mathfrak {d}}}$$\\end{document}</tex-math><mml:math id=\"M136\"><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq69\"><alternatives><tex-math id=\"M137\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= ({\\mathfrak {kh}})^{{\\mathfrak {d}}}$$\\end{document}</tex-math><mml:math id=\"M138\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"fraktur\">kh</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq70\"><alternatives><tex-math id=\"M139\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RR_{{\\mathfrak {d}}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M140\"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq71\"><alternatives><tex-math id=\"M141\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H(\\chi )$$\\end{document}</tex-math><mml:math id=\"M142\"><mml:mrow><mml:mi>H</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq72\"><alternatives><tex-math id=\"M143\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= \\frac{1}{({\\mathfrak {kh}})^{{\\mathfrak {d}}}}$$\\end{document}</tex-math><mml:math id=\"M144\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"fraktur\">kh</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msup></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq73\"><alternatives><tex-math id=\"M145\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= \\frac{2}{{\\mathfrak {k+h}}}$$\\end{document}</tex-math><mml:math id=\"M146\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq74\"><alternatives><tex-math id=\"M147\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SSD(\\chi )$$\\end{document}</tex-math><mml:math id=\"M148\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq75\"><alternatives><tex-math id=\"M149\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= \\frac{{{\\mathfrak {k}}}}{{{\\mathfrak {h}}}}+\\frac{{{\\mathfrak {h}}}}{{{\\mathfrak {k}}}}$$\\end{document}</tex-math><mml:math id=\"M150\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">h</mml:mi><mml:mi mathvariant=\"fraktur\">k</mml:mi></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq76\"><alternatives><tex-math id=\"M151\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= \\frac{{\\mathfrak {k^2+h^2}}}{{\\mathfrak {kh}}}$$\\end{document}</tex-math><mml:math id=\"M152\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant=\"fraktur\">h</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup></mml:mrow><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq77\"><alternatives><tex-math id=\"M153\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F(\\chi )$$\\end{document}</tex-math><mml:math id=\"M154\"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq78\"><alternatives><tex-math id=\"M155\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= {\\mathfrak {k^2+h^2}}$$\\end{document}</tex-math><mml:math id=\"M156\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant=\"fraktur\">h</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq79\"><alternatives><tex-math id=\"M157\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I(\\chi )$$\\end{document}</tex-math><mml:math id=\"M158\"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq80\"><alternatives><tex-math id=\"M159\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= \\frac{{\\mathfrak {kh}}}{{\\mathfrak {k+h}}}$$\\end{document}</tex-math><mml:math id=\"M160\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">kh</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq81\"><alternatives><tex-math id=\"M161\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma (\\chi )$$\\end{document}</tex-math><mml:math id=\"M162\"><mml:mrow><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq82\"><alternatives><tex-math id=\"M163\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{{\\mathfrak {kh}}}= ({\\mathfrak {k-h}})^2$$\\end{document}</tex-math><mml:math id=\"M164\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq83\"><alternatives><tex-math id=\"M165\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M166\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq84\"><alternatives><tex-math id=\"M167\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{f}({\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M168\"><mml:mrow><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq85\"><alternatives><tex-math id=\"M169\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M170\"><mml:mrow><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq86\"><alternatives><tex-math id=\"M171\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1(\\chi )$$\\end{document}</tex-math><mml:math id=\"M172\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq87\"><alternatives><tex-math id=\"M173\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathfrak {y+z}}$$\\end{document}</tex-math><mml:math id=\"M174\"><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq88\"><alternatives><tex-math id=\"M175\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M176\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq89\"><alternatives><tex-math id=\"M177\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2(\\chi )$$\\end{document}</tex-math><mml:math id=\"M178\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq90\"><alternatives><tex-math id=\"M179\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathfrak {yz}}$$\\end{document}</tex-math><mml:math id=\"M180\"><mml:mi mathvariant=\"fraktur\">yz</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq91\"><alternatives><tex-math id=\"M181\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(D_{{\\mathfrak {y}}}D_{{\\mathfrak {z}}})({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M182\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq92\"><alternatives><tex-math id=\"M183\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m(\\chi )$$\\end{document}</tex-math><mml:math id=\"M184\"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq93\"><alternatives><tex-math id=\"M185\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{1}{{\\mathfrak {yz}}}$$\\end{document}</tex-math><mml:math id=\"M186\"><mml:mfrac><mml:mn>1</mml:mn><mml:mi mathvariant=\"fraktur\">yz</mml:mi></mml:mfrac></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq94\"><alternatives><tex-math id=\"M187\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(S_{{\\mathfrak {y}}}S_{{\\mathfrak {z}}})({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M188\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq95\"><alternatives><tex-math id=\"M189\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$A(\\chi )$$\\end{document}</tex-math><mml:math id=\"M190\"><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq96\"><alternatives><tex-math id=\"M191\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\frac{{\\mathfrak {yz}}}{{\\mathfrak {y+z-2}}})^3$$\\end{document}</tex-math><mml:math id=\"M192\"><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">yz</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:mrow></mml:mfrac><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq97\"><alternatives><tex-math id=\"M193\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(S_{{\\mathfrak {y}}}^3Q_{-2}D_{{\\mathfrak {y}}}^3D_{{\\mathfrak {z}}}^3)({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M194\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq98\"><alternatives><tex-math id=\"M195\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{{\\mathfrak {d}}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M196\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq99\"><alternatives><tex-math id=\"M197\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({\\mathfrak {yz}})^{{\\mathfrak {d}}}$$\\end{document}</tex-math><mml:math id=\"M198\"><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"fraktur\">yz</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq100\"><alternatives><tex-math id=\"M199\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(D_{{\\mathfrak {y}}}^{{\\mathfrak {d}}}+D_{{\\mathfrak {z}}}^{{\\mathfrak {d}}})({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M200\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq101\"><alternatives><tex-math id=\"M201\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RR_{{\\mathfrak {d}}}(\\chi )$$\\end{document}</tex-math><mml:math id=\"M202\"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq102\"><alternatives><tex-math id=\"M203\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\big (\\frac{1}{{\\mathfrak {yz}}}\\big )^{{\\mathfrak {d}}}$$\\end{document}</tex-math><mml:math id=\"M204\"><mml:mrow><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi mathvariant=\"fraktur\">yz</mml:mi></mml:mfrac><mml:msup><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq103\"><alternatives><tex-math id=\"M205\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$S_{{\\mathfrak {y}}}^{{\\mathfrak {d}}} S_{{\\mathfrak {z}}}^{{\\mathfrak {d}}}(D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M206\"><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq104\"><alternatives><tex-math id=\"M207\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H(\\chi )$$\\end{document}</tex-math><mml:math id=\"M208\"><mml:mrow><mml:mi>H</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq105\"><alternatives><tex-math id=\"M209\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{2}{{\\mathfrak {y+z}}}$$\\end{document}</tex-math><mml:math id=\"M210\"><mml:mfrac><mml:mn>2</mml:mn><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow></mml:mfrac></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq106\"><alternatives><tex-math id=\"M211\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2S_{{\\mathfrak {y}}}J({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M212\"><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mi>J</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq107\"><alternatives><tex-math id=\"M213\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$HM(\\chi )$$\\end{document}</tex-math><mml:math id=\"M214\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq108\"><alternatives><tex-math id=\"M215\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({\\mathfrak {y+z}})^2$$\\end{document}</tex-math><mml:math id=\"M216\"><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq109\"><alternatives><tex-math id=\"M217\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})^2({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M218\"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq110\"><alternatives><tex-math id=\"M219\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F(\\chi )$$\\end{document}</tex-math><mml:math id=\"M220\"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq111\"><alternatives><tex-math id=\"M221\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathfrak {y^2+z^2}}$$\\end{document}</tex-math><mml:math id=\"M222\"><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq112\"><alternatives><tex-math id=\"M223\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(D_{{\\mathfrak {y}}}^2+D_{{\\mathfrak {z}}}^2)({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M224\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq113\"><alternatives><tex-math id=\"M225\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma (\\chi )$$\\end{document}</tex-math><mml:math id=\"M226\"><mml:mrow><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq114\"><alternatives><tex-math id=\"M227\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({\\mathfrak {y-z}})^2$$\\end{document}</tex-math><mml:math id=\"M228\"><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq115\"><alternatives><tex-math id=\"M229\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(D_{{\\mathfrak {y}}}-D_{{\\mathfrak {z}}})^2({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M230\"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq116\"><alternatives><tex-math id=\"M231\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SDD(\\chi )$$\\end{document}</tex-math><mml:math id=\"M232\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq117\"><alternatives><tex-math id=\"M233\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{\\mathfrak {y^2+z^2}}}{{\\mathfrak {yz}}}$$\\end{document}</tex-math><mml:math id=\"M234\"><mml:mfrac><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">2</mml:mn></mml:msup></mml:mrow><mml:mi mathvariant=\"fraktur\">yz</mml:mi></mml:mfrac></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq118\"><alternatives><tex-math id=\"M235\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(D_{{\\mathfrak {y}}}S_{{\\mathfrak {z}}}+D_{{\\mathfrak {z}}}S_{{\\mathfrak {y}}})({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M236\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq119\"><alternatives><tex-math id=\"M237\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I(\\chi )$$\\end{document}</tex-math><mml:math id=\"M238\"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq120\"><alternatives><tex-math id=\"M239\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{\\mathfrak {yz}}}{{\\mathfrak {y+z}}}$$\\end{document}</tex-math><mml:math id=\"M240\"><mml:mfrac><mml:mi mathvariant=\"fraktur\">yz</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow></mml:mfrac></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq121\"><alternatives><tex-math id=\"M241\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(S_{{\\mathfrak {y}}}JD_{{\\mathfrak {y}}}D_{{\\mathfrak {z}}})({\\mathbb {M}}(\\chi ); {\\mathfrak {y,z}})|_{{\\mathfrak {y=1}}}$$\\end{document}</tex-math><mml:math id=\"M242\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mi>J</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>χ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq122\"><alternatives><tex-math id=\"M243\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M244\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ3\"><alternatives><tex-math id=\"M245\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} D_{{\\mathfrak {y}}}(\\texttt{f}({\\mathfrak {y,z}}))= &amp; {} {{\\mathfrak {y}}}\\frac{\\partial (\\texttt{f}({\\mathfrak {y,z}}))}{\\partial {{\\mathfrak {y}}}}, D_{{\\mathfrak {z}}}(\\texttt{f}({\\mathfrak {y,z}}))={{\\mathfrak {z}}}\\frac{\\partial (\\texttt{f}({\\mathfrak {y,z}}))}{\\partial {{\\mathfrak {z}}}}, S_{{\\mathfrak {y}}}(\\texttt{f}({\\mathfrak {y,z}}))= \\int _{0}^{{{\\mathfrak {y}}}} \\frac{\\texttt{f}({\\mathfrak {q,z}})}{{{\\mathfrak {q}}}}d{{\\mathfrak {q}}} \\\\ S_{{\\mathfrak {z}}}(\\texttt{f}({\\mathfrak {y,z}}))= &amp; {} \\int _{0}^{{{\\mathfrak {z}}}} \\frac{\\texttt{f}({\\mathfrak {y,q}})}{{{\\mathfrak {q}}}}d{{\\mathfrak {q}}}, J(\\texttt{f}({\\mathfrak {y,z}}))= \\texttt{f}({\\mathfrak {y,y}}), Q_\\kappa (\\texttt{f}({\\mathfrak {y,z}}))= {{\\mathfrak {y}}}^\\kappa \\texttt{f}({\\mathfrak {y,z}}); \\kappa \\ne 0. \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M246\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mrow/><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∫</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msubsup><mml:mfrac><mml:mrow><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">q</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi mathvariant=\"fraktur\">q</mml:mi></mml:mfrac><mml:mi>d</mml:mi><mml:mi mathvariant=\"fraktur\">q</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mrow/><mml:msubsup><mml:mo>∫</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msubsup><mml:mfrac><mml:mrow><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">q</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mi mathvariant=\"fraktur\">q</mml:mi></mml:mfrac><mml:mi>d</mml:mi><mml:mi mathvariant=\"fraktur\">q</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi>κ</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi>κ</mml:mi></mml:msup><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mi>κ</mml:mi><mml:mo>≠</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq123\"><alternatives><tex-math id=\"M247\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M248\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq124\"><alternatives><tex-math id=\"M249\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\chi = I_\\alpha ({\\mathfrak {s,p}})|{\\mathfrak {s,p}}\\ge 1$$\\end{document}</tex-math><mml:math id=\"M250\"><mml:mrow><mml:mi>χ</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq125\"><alternatives><tex-math id=\"M251\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M252\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq126\"><alternatives><tex-math id=\"M253\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M254\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><alternatives><tex-math id=\"M255\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}});{\\mathfrak {y,z}})&amp;=(4{\\mathfrak {sp}}+14{{\\mathfrak {s}}}+16{{\\mathfrak {p}}}-4){\\mathfrak {y^5z^5}} +(12{\\mathfrak {sp}}-2{{\\mathfrak {p}}}+2{{\\mathfrak {s}}}-12) {\\mathfrak {y^5z^6}}\\\\&amp;\\quad +(18{\\mathfrak {sp}}-17{{\\mathfrak {p}}}-19{{\\mathfrak {s}}}+18) {\\mathfrak {y^6z^6}} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M256\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>+</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>18</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq127\"><alternatives><tex-math id=\"M257\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M258\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq128\"><alternatives><tex-math id=\"M259\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {4,4}})$$\\end{document}</tex-math><mml:math id=\"M260\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mn mathvariant=\"fraktur\">4</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant=\"fraktur\">4</mml:mn></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq129\"><alternatives><tex-math id=\"M261\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M262\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq130\"><alternatives><tex-math id=\"M263\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})|{\\mathfrak {s,p}}\\ge 1$$\\end{document}</tex-math><mml:math id=\"M264\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq131\"><alternatives><tex-math id=\"M265\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$12{\\mathfrak {sp}}$$\\end{document}</tex-math><mml:math id=\"M266\"><mml:mrow><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq132\"><alternatives><tex-math id=\"M267\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$34{\\mathfrak {sp}}-3{{\\mathfrak {s}}}-3{{\\mathfrak {p}}}+2$$\\end{document}</tex-math><mml:math id=\"M268\"><mml:mrow><mml:mn>34</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>3</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>3</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq133\"><alternatives><tex-math id=\"M269\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{\\mathfrak {D}}}=\\{(5,5), (5,6), (6,6)\\}$$\\end{document}</tex-math><mml:math id=\"M270\"><mml:mrow><mml:mi mathvariant=\"fraktur\">D</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>5</mml:mn><mml:mo>,</mml:mo><mml:mn>5</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>5</mml:mn><mml:mo>,</mml:mo><mml:mn>6</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>6</mml:mn><mml:mo>,</mml:mo><mml:mn>6</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq134\"><alternatives><tex-math id=\"M271\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})$$\\end{document}</tex-math><mml:math id=\"M272\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq135\"><alternatives><tex-math id=\"M273\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathcal {E}}(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M274\"><mml:mrow><mml:mi mathvariant=\"script\">E</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq136\"><alternatives><tex-math id=\"M275\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{d}_{{\\mathfrak {kh}}}$$\\end{document}</tex-math><mml:math id=\"M276\"><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ5\"><alternatives><tex-math id=\"M277\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\texttt{d}_{55}&amp;= |\\{\\mu \\eta \\in {\\mathcal {E}}(I_\\alpha ({\\mathfrak {s,p}})|\\texttt{d}_\\mu = 5 \\text { and } \\texttt{d}_\\eta = 5\\}|= 4{\\mathfrak {sp}}+14{{\\mathfrak {s}}}+16{{\\mathfrak {p}}}-4\\\\ \\texttt{d}_{56}&amp;= |\\{\\mu \\eta \\in {\\mathcal {E}}(I_\\alpha ({\\mathfrak {s,p}})|\\texttt{d}_\\mu = 5 \\text { and } \\texttt{d}_\\eta = 6\\}|= 12{\\mathfrak {sp}}+2{{\\mathfrak {s}}}-2{{\\mathfrak {p}}}-12\\\\ \\texttt{d}_{66}&amp;= |\\{\\mu \\eta \\in {\\mathcal {E}}(I_\\alpha ({\\mathfrak {s,p}})|\\texttt{d}_\\mu = 6 \\text { and } \\texttt{d}_\\eta = 6\\}|= 18{\\mathfrak {sp}}-19{{\\mathfrak {s}}}-17{{\\mathfrak {p}}}+18 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M278\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mn>55</mml:mn></mml:msub></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mi>μ</mml:mi><mml:mi>η</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=\"script\">E</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mspace width=\"0.333333em\"/><mml:mtext>and</mml:mtext><mml:mspace width=\"0.333333em\"/><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>η</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>+</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mn>56</mml:mn></mml:msub></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mi>μ</mml:mi><mml:mi>η</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=\"script\">E</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mspace width=\"0.333333em\"/><mml:mtext>and</mml:mtext><mml:mspace width=\"0.333333em\"/><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>η</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>6</mml:mn><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo>=</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mn>66</mml:mn></mml:msub></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mo stretchy=\"false\">{</mml:mo><mml:mi>μ</mml:mi><mml:mi>η</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=\"script\">E</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>6</mml:mn><mml:mspace width=\"0.333333em\"/><mml:mtext>and</mml:mtext><mml:mspace width=\"0.333333em\"/><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mi>η</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>6</mml:mn><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mo>=</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq137\"><alternatives><tex-math id=\"M279\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M280\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq138\"><alternatives><tex-math id=\"M281\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M282\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq139\"><alternatives><tex-math id=\"M283\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})|{\\mathfrak {s,p}}\\ge 1$$\\end{document}</tex-math><mml:math id=\"M284\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ6\"><alternatives><tex-math id=\"M285\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}});{\\mathfrak {y,z}})= \\sum _{{{\\mathfrak {k}}}\\le {{\\mathfrak {h}}}}\\texttt{m}_{{\\mathfrak {kh}}}(I_\\alpha ({\\mathfrak {s,p}})){{\\mathfrak {y}}}^{{{\\mathfrak {k}}}}{{\\mathfrak {z}}}^{{{\\mathfrak {h}}}} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M286\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi><mml:mo>≤</mml:mo><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi mathvariant=\"monospace\">m</mml:mi><mml:mi mathvariant=\"fraktur\">kh</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">k</mml:mi></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">h</mml:mi></mml:msup></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq140\"><alternatives><tex-math id=\"M287\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M288\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq141\"><alternatives><tex-math id=\"M289\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})|{{\\mathfrak {s}}}=4 \\text { and }{{\\mathfrak {p}}}=5$$\\end{document}</tex-math><mml:math id=\"M290\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mspace width=\"0.333333em\"/><mml:mtext>and</mml:mtext><mml:mspace width=\"0.333333em\"/><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq142\"><alternatives><tex-math id=\"M291\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}});{\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M292\"><mml:mrow><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ7\"><alternatives><tex-math id=\"M293\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} {\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}});{\\mathfrak {y,z}})&amp;= \\sum _{{{\\mathfrak {5}}}\\le {{\\mathfrak {5}}}}\\texttt{m}_{{\\mathfrak {55}}}(I_\\alpha ({\\mathfrak {s,p}})){{\\mathfrak {y}}}^{{{\\mathfrak {5}}}}{{\\mathfrak {z}}}^{{{\\mathfrak {5}}}}+ \\sum _{{{\\mathfrak {5}}}\\le {{\\mathfrak {6}}}}\\texttt{m}_{{\\mathfrak {56}}}(I_\\alpha ({\\mathfrak {s,p}})){{\\mathfrak {y}}}^{{{\\mathfrak {5}}}}{{\\mathfrak {z}}}^{{{\\mathfrak {6}}}}+ \\sum _{{{\\mathfrak {6}}}\\le {{\\mathfrak {6}}}}\\texttt{m}_{{\\mathfrak {66}}}(I_\\alpha ({\\mathfrak {s,p}})){{\\mathfrak {y}}}^{{{\\mathfrak {6}}}}{{\\mathfrak {z}}}^{{{\\mathfrak {6}}}}\\\\&amp;= \\texttt{d}_{55}{{\\mathfrak {y}}}^{{{\\mathfrak {5}}}}{{\\mathfrak {z}}}^{{{\\mathfrak {5}}}}+ \\texttt{d}_{56}{{\\mathfrak {y}}}^{{{\\mathfrak {5}}}}{{\\mathfrak {z}}}^{{{\\mathfrak {6}}}}+ \\texttt{d}_{66}{{\\mathfrak {y}}}^{{{\\mathfrak {6}}}}{{\\mathfrak {z}}}^{{{\\mathfrak {6}}}}\\\\&amp;=(4{\\mathfrak {sp}}+14{{\\mathfrak {s}}}+16{{\\mathfrak {p}}}-4){\\mathfrak {y^5z^5}} +(12{\\mathfrak {sp}}-2{{\\mathfrak {p}}}+2{{\\mathfrak {s}}}-12) {\\mathfrak {y^5z^6}}\\\\&amp;\\qquad +(18{\\mathfrak {sp}}-17{{\\mathfrak {p}}}-19{{\\mathfrak {s}}}+18) {\\mathfrak {y^6z^6}} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M294\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mn mathvariant=\"fraktur\">5</mml:mn><mml:mo>≤</mml:mo><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:mrow></mml:munder><mml:msub><mml:mi mathvariant=\"monospace\">m</mml:mi><mml:mn mathvariant=\"fraktur\">55</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mn mathvariant=\"fraktur\">5</mml:mn><mml:mo>≤</mml:mo><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:mrow></mml:munder><mml:msub><mml:mi mathvariant=\"monospace\">m</mml:mi><mml:mn mathvariant=\"fraktur\">56</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mn mathvariant=\"fraktur\">6</mml:mn><mml:mo>≤</mml:mo><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:mrow></mml:munder><mml:msub><mml:mi mathvariant=\"monospace\">m</mml:mi><mml:mn mathvariant=\"fraktur\">66</mml:mn></mml:msub><mml:mrow><mml:mo 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mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mn>56</mml:mn></mml:msub><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant=\"monospace\">d</mml:mi><mml:mn>66</mml:mn></mml:msub><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>+</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"2em\"/><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>18</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq143\"><alternatives><tex-math id=\"M295\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M296\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq144\"><alternatives><tex-math id=\"M297\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M298\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq145\"><alternatives><tex-math id=\"M299\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {4,5}})$$\\end{document}</tex-math><mml:math id=\"M300\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mn mathvariant=\"fraktur\">4</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq146\"><alternatives><tex-math id=\"M301\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M302\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq147\"><alternatives><tex-math id=\"M303\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mathbb {M}}$$\\end{document}</tex-math><mml:math id=\"M304\"><mml:mi mathvariant=\"double-struck\">M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq148\"><alternatives><tex-math id=\"M305\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1, M_2, M_2^m, A, R_{{\\mathfrak {d}}}, RR_{{\\mathfrak {d}}}, H, HM, F, \\sigma , SDD \\text { and } I$$\\end{document}</tex-math><mml:math id=\"M306\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mo>,</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mi>F</mml:mi><mml:mo>,</mml:mo><mml:mi>σ</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mspace width=\"0.333333em\"/><mml:mtext>and</mml:mtext><mml:mspace width=\"0.333333em\"/><mml:mi>I</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq149\"><alternatives><tex-math id=\"M307\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M308\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq150\"><alternatives><tex-math id=\"M309\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})|{\\mathfrak {s,p}}\\ge 1$$\\end{document}</tex-math><mml:math id=\"M310\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq151\"><alternatives><tex-math id=\"M311\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\texttt{f}({\\mathfrak {y,z}})= {\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}});{\\mathfrak {y,z}})=(4{\\mathfrak {sp}}+14{{\\mathfrak {s}}}+16{{\\mathfrak {p}}}-4){\\mathfrak {y^5z^5}} +(12{\\mathfrak {sp}}-2{{\\mathfrak {p}}}+2{{\\mathfrak {s}}}-12) {\\mathfrak {y^5z^6}}+(18{\\mathfrak {sp}}-17{{\\mathfrak {p}}}-19{{\\mathfrak {s}}}+18) {\\mathfrak {y^6z^6}}$$\\end{document}</tex-math><mml:math id=\"M312\"><mml:mrow><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>+</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>18</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq152\"><alternatives><tex-math id=\"M313\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})|{\\mathfrak {s,p}}\\ge 1$$\\end{document}</tex-math><mml:math id=\"M314\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq153\"><alternatives><tex-math id=\"M315\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M316\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq154\"><alternatives><tex-math id=\"M317\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1(I_\\alpha ({\\mathfrak {s,p}})) =388{{\\mathfrak {s}}}{{\\mathfrak {p}}}-66{{\\mathfrak {p}}}-66{{\\mathfrak {s}}}+44$$\\end{document}</tex-math><mml:math id=\"M318\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>388</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>66</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>66</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>44</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq155\"><alternatives><tex-math id=\"M319\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}})) = 1108{\\mathfrak {sp}}-272{{\\mathfrak {p}}}-274{{\\mathfrak {s}}}+188$$\\end{document}</tex-math><mml:math id=\"M320\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1108</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>272</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>274</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>188</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq156\"><alternatives><tex-math id=\"M321\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I(I_\\alpha ({\\mathfrak {s,p}})= \\displaystyle \\frac{1064{\\mathfrak {sp}}}{11}-\\frac{181{{\\mathfrak {p}}}}{11}-\\frac{182{{\\mathfrak {s}}}}{11}+\\frac{124}{11}$$\\end{document}</tex-math><mml:math id=\"M322\"><mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1064</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>181</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>182</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>124</mml:mn><mml:mn>11</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq157\"><alternatives><tex-math id=\"M323\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RR_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}}) = \\displaystyle \\frac{89{{\\mathfrak {s}}}}{900}+\\frac{91{{\\mathfrak {p}}}}{900}+\\frac{53{\\mathfrak {sp}}}{50}-\\frac{3}{50}$$\\end{document}</tex-math><mml:math id=\"M324\"><mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo></mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>89</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>91</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>53</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>50</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>3</mml:mn><mml:mn>50</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq158\"><alternatives><tex-math id=\"M325\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1(I_\\alpha ({\\mathfrak {s,p}})) = (D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}}));{\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M326\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ8\"><alternatives><tex-math id=\"M327\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})(\\texttt{f}({\\mathfrak {y,z}}))&amp;= 2{{\\mathfrak {y}}}^5{{\\mathfrak {z}}}^5(70{{\\mathfrak {s}}}+80{{\\mathfrak {p}}}-66{{\\mathfrak {z}}}+20{{\\mathfrak {s}}}{{\\mathfrak {p}}}+11{{\\mathfrak {s}}}{{\\mathfrak {z}}}-11{{\\mathfrak {p}}}{{\\mathfrak {z}}}+108{{\\mathfrak {y}}}{{\\mathfrak {z}}}+66{{\\mathfrak {s}}}{{\\mathfrak {p}}}{{\\mathfrak {z}}}\\\\ {}&amp;\\qquad -114{{\\mathfrak {s}}}{{\\mathfrak {y}}}{{\\mathfrak {z}}}-102{{\\mathfrak {p}}}{{\\mathfrak {y}}}{{\\mathfrak {z}}}+108{{\\mathfrak {s}}}{{\\mathfrak {p}}}{{\\mathfrak {y}}}{{\\mathfrak {z}}}-20)\\big |_{{\\mathfrak {y=z=1}}}\\\\&amp;= 388{{\\mathfrak {s}}}{{\\mathfrak {p}}}-66{{\\mathfrak {p}}}-66{{\\mathfrak {s}}}+44 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M328\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>70</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>80</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>66</mml:mn><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>20</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>11</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>-</mml:mo><mml:mn>11</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>108</mml:mn><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>66</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:mrow/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mrow><mml:mspace width=\"2em\"/><mml:mo>-</mml:mo><mml:mn>114</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>-</mml:mo><mml:mn>102</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>108</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>-</mml:mo><mml:mn>20</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>388</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>66</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>66</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>44</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq159\"><alternatives><tex-math id=\"M329\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}})) = (D_{{\\mathfrak {y}}}^{{\\mathfrak {d}}}+D_{{\\mathfrak {z}}}^{{\\mathfrak {d}}})({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})|_{{\\mathfrak {y=z=1}}}$$\\end{document}</tex-math><mml:math id=\"M330\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ9\"><alternatives><tex-math id=\"M331\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (D_{{\\mathfrak {y}}}^{{\\mathfrak {d}}}+D_{{\\mathfrak {z}}}^{{\\mathfrak {d}}})(\\texttt{f}({\\mathfrak {y,z}}))&amp;= 5^{2{{\\mathfrak {d}}}}(14{{\\mathfrak {s}}}+16{{\\mathfrak {p}}}+4{\\mathfrak {sp}}-4) -6^{2{{\\mathfrak {d}}}}(19{{\\mathfrak {s}}}+17{{\\mathfrak {p}}}-18{\\mathfrak {sp}}-18)\\\\&amp;\\quad +5^{{\\mathfrak {d}}}6^{{\\mathfrak {d}}}(2{{\\mathfrak {s}}}-2{{\\mathfrak {p}}}+12{\\mathfrak {sp}}-12)\\Big |_{{\\mathfrak {y=z=1}}; {{\\mathfrak {d}}}=1}\\\\&amp;= 1108{\\mathfrak {sp}}-272{{\\mathfrak {p}}}-274{{\\mathfrak {s}}}+188 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M332\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mn>5</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mn>6</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:msup><mml:mn>5</mml:mn><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msup><mml:msup><mml:mn>6</mml:mn><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow><mml:mo>;</mml:mo><mml:mi mathvariant=\"fraktur\">d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>1108</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>272</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>274</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>188</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq160\"><alternatives><tex-math id=\"M333\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I(I_\\alpha ({\\mathfrak {s,p}}))= (S_{{\\mathfrak {y}}}JD_{{\\mathfrak {y}}}D_{{\\mathfrak {z}}})({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M334\"><mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mi>J</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ10\"><alternatives><tex-math id=\"M335\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (S_{{\\mathfrak {y}}}JD_{{\\mathfrak {y}}}D_{{\\mathfrak {z}}})(\\texttt{f}({\\mathfrak {y,z}}))&amp;= {{\\mathfrak {y}}}^{12}(54{\\mathfrak {sp}}-51{{\\mathfrak {p}}}-57{{\\mathfrak {s}}}+54) +{{\\mathfrak {y}}}^{11}\\bigg (\\frac{60{{\\mathfrak {s}}}}{11}-\\frac{60{{\\mathfrak {p}}}}{11}\\\\&amp;\\quad +\\frac{360{\\mathfrak {sp}}}{11}-\\frac{360}{11}\\bigg )+{{\\mathfrak {y}}}^{10}(10{\\mathfrak {sp}}+35{{\\mathfrak {s}}}+40{{\\mathfrak {p}}}-10)\\Big |_{{\\mathfrak {y=1}}}\\\\&amp;= \\frac{1064{\\mathfrak {sp}}}{11}-\\frac{181{{\\mathfrak {p}}}}{11}-\\frac{182{{\\mathfrak {s}}}}{11}+\\frac{124}{11} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M336\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mi>J</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>12</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>54</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>51</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>57</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>54</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mn>60</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>60</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>360</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>360</mml:mn><mml:mn>11</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>10</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>10</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>+</mml:mo><mml:mn>35</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>40</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>10</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1064</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>181</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>182</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>124</mml:mn><mml:mn>11</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq161\"><alternatives><tex-math id=\"M337\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RR_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}}) = S_{{\\mathfrak {y}}}^{{\\mathfrak {d}}} S_{{\\mathfrak {z}}}^{{\\mathfrak {d}}}(D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M338\"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo></mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ11\"><alternatives><tex-math id=\"M339\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} S_{{\\mathfrak {y}}}^{{\\mathfrak {d}}} S_{{\\mathfrak {z}}}^{{\\mathfrak {d}}}(\\texttt{f}({\\mathfrak {y,z}}))&amp;= \\frac{1}{5^{2{{\\mathfrak {d}}}}}(14{{\\mathfrak {s}}}+16{{\\mathfrak {p}}}+4{\\mathfrak {sp}}-4)+\\frac{1}{30^{{\\mathfrak {d}}}}(2{{\\mathfrak {s}}}-2{{\\mathfrak {p}}}+12{\\mathfrak {sp}}-12)\\\\ {}&amp;\\qquad \\frac{-1}{6^{2{{\\mathfrak {d}}}}}(19{{\\mathfrak {s}}}+17{{\\mathfrak {p}}}-18{\\mathfrak {sp}}-18)\\Big |_{{\\mathfrak {y=z=1}}; {{\\mathfrak {d}}}=1} \\\\&amp;= \\frac{89{{\\mathfrak {s}}}}{900}+\\frac{91{{\\mathfrak {p}}}}{900}+\\frac{53{\\mathfrak {sp}}}{50}-\\frac{3}{50} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M340\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msup><mml:mn>5</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:mrow></mml:msup></mml:mfrac><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msup><mml:mn>30</mml:mn><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msup></mml:mfrac><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:mrow/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"2em\"/><mml:mfrac><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:msup><mml:mn>6</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:mrow></mml:msup></mml:mfrac><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow><mml:mo>;</mml:mo><mml:mi mathvariant=\"fraktur\">d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>89</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>91</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>53</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>50</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>3</mml:mn><mml:mn>50</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq162\"><alternatives><tex-math id=\"M341\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M342\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq163\"><alternatives><tex-math id=\"M343\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M344\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq164\"><alternatives><tex-math id=\"M345\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M346\"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq165\"><alternatives><tex-math id=\"M347\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RR_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M348\"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq166\"><alternatives><tex-math id=\"M349\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({\\mathfrak {s,p}})$$\\end{document}</tex-math><mml:math id=\"M350\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq167\"><alternatives><tex-math id=\"M351\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M352\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq168\"><alternatives><tex-math id=\"M353\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M354\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq169\"><alternatives><tex-math id=\"M355\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M356\"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq170\"><alternatives><tex-math id=\"M357\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RR_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M358\"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq171\"><alternatives><tex-math id=\"M359\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M360\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq172\"><alternatives><tex-math id=\"M361\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M362\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq173\"><alternatives><tex-math id=\"M363\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M364\"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq174\"><alternatives><tex-math id=\"M365\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RR_{{\\mathfrak {d}}}(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M366\"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant=\"fraktur\">d</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq175\"><alternatives><tex-math id=\"M367\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})|{\\mathfrak {s,p}}\\ge 1$$\\end{document}</tex-math><mml:math id=\"M368\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq176\"><alternatives><tex-math id=\"M369\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M370\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq177\"><alternatives><tex-math id=\"M371\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2(I_\\alpha ({\\mathfrak {s,p}}))= 1108{{\\mathfrak {s}}}{{\\mathfrak {p}}}-272{{\\mathfrak {p}}}-274{{\\mathfrak {s}}}+188$$\\end{document}</tex-math><mml:math id=\"M372\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1108</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>272</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>274</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>188</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq178\"><alternatives><tex-math id=\"M373\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F(I_\\alpha ({\\mathfrak {s,p}}))= 2228{\\mathfrak {sp}}-546{{\\mathfrak {p}}}-546{{\\mathfrak {s}}}+364$$\\end{document}</tex-math><mml:math id=\"M374\"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mn>2228</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>546</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>546</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>364</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq179\"><alternatives><tex-math id=\"M375\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$A(I_\\alpha ({\\mathfrak {s,p}})= \\displaystyle \\frac{202510477{\\mathfrak {sp}}}{144000}- \\frac{40926041{{\\mathfrak {p}}}}{108000} - \\frac{332764271{{\\mathfrak {s}}}}{864000}+ \\frac{39354227}{144000}$$\\end{document}</tex-math><mml:math id=\"M376\"><mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>202510477</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>144000</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>40926041</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>108000</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>332764271</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>864000</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>39354227</mml:mn><mml:mn>144000</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq180\"><alternatives><tex-math id=\"M377\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$HM(I_\\alpha ({\\mathfrak {s,p}}))= 4444{\\mathfrak {sp}}-1090{{\\mathfrak {p}}}-1094{{\\mathfrak {s}}}+740$$\\end{document}</tex-math><mml:math id=\"M378\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mn>4444</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>1090</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>1094</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>740</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq181\"><alternatives><tex-math id=\"M379\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2(I_\\alpha ({\\mathfrak {s,p}})) = D_{{\\mathfrak {y}}}D_{{\\mathfrak {z}}}({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}}));{\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M380\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ12\"><alternatives><tex-math id=\"M381\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} D_{{\\mathfrak {y}}}D_{{\\mathfrak {z}}}(\\texttt{f}({\\mathfrak {y,z}}))&amp;={{\\mathfrak {y}}}{{\\mathfrak {z}}} \\big (30{{\\mathfrak {y}}}^4{{\\mathfrak {z}}}^5(2{{\\mathfrak {s}}}-2{{\\mathfrak {p}}}+12{{\\mathfrak {s}}}{{\\mathfrak {p}}}-12) +25{{\\mathfrak {y}}}^4{{\\mathfrak {z}}}^4(14{{\\mathfrak {s}}}+16{{\\mathfrak {p}}}+4{{\\mathfrak {s}}}{{\\mathfrak {p}}}-4)\\\\&amp;\\quad -36{{\\mathfrak {y}}}^5{{\\mathfrak {z}}}^5(19{{\\mathfrak {s}}}+17{{\\mathfrak {p}}}-18{{\\mathfrak {s}}}{{\\mathfrak {p}}}-18)\\big )\\big |_{{\\mathfrak {y=z=1}}}\\\\&amp;= 1108{{\\mathfrak {s}}}{{\\mathfrak {p}}}-272{{\\mathfrak {p}}}-274{{\\mathfrak {s}}}+188 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M382\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mn>30</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>25</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mn>36</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>1108</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>272</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>274</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>188</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq182\"><alternatives><tex-math id=\"M383\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F(I_\\alpha ({\\mathfrak {s,p}}))= (D_{{\\mathfrak {y}}}^2+D_{{\\mathfrak {z}}}^2)({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M384\"><mml:mrow><mml:mi>F</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ13\"><alternatives><tex-math id=\"M385\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (D_{{\\mathfrak {y}}}^2+D_{{\\mathfrak {z}}}^2)(\\texttt{f}({\\mathfrak {y,z}}))&amp;= 2{{\\mathfrak {y}}}^5{{\\mathfrak {z}}}^5(350{{\\mathfrak {s}}}+400{{\\mathfrak {p}}}-366{{\\mathfrak {z}}}+100{{\\mathfrak {s}}}{{\\mathfrak {p}}}+61{{\\mathfrak {s}}}{{\\mathfrak {z}}}-61{{\\mathfrak {p}}}{{\\mathfrak {z}}}+648{\\mathfrak {yz}}\\\\ {}&amp;\\qquad +366{\\mathfrak {spz}}-684{\\mathfrak {syz}}-612{\\mathfrak {pyz}}+648{\\mathfrak {psyz}}-100)\\Big |_{{\\mathfrak {y=z=1}}} \\\\&amp;= 2228{\\mathfrak {sp}}-546{{\\mathfrak {p}}}-546{{\\mathfrak {s}}}+364 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M386\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>350</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>400</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>366</mml:mn><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>100</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>61</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>-</mml:mo><mml:mn>61</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>648</mml:mn><mml:mi mathvariant=\"fraktur\">yz</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:mrow/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mrow><mml:mspace width=\"2em\"/><mml:mo>+</mml:mo><mml:mn>366</mml:mn><mml:mi mathvariant=\"fraktur\">spz</mml:mi><mml:mo>-</mml:mo><mml:mn>684</mml:mn><mml:mi mathvariant=\"fraktur\">syz</mml:mi><mml:mo>-</mml:mo><mml:mn>612</mml:mn><mml:mi mathvariant=\"fraktur\">pyz</mml:mi><mml:mo>+</mml:mo><mml:mn>648</mml:mn><mml:mi mathvariant=\"fraktur\">psyz</mml:mi><mml:mo>-</mml:mo><mml:mn>100</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>2228</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>546</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>546</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>364</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq183\"><alternatives><tex-math id=\"M387\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$A(I_\\alpha ({\\mathfrak {s,p}}))= (S_{{\\mathfrak {y}}}^3Q_{-2}D_{{\\mathfrak {y}}}^3D_{{\\mathfrak {z}}}^3)({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M388\"><mml:mrow><mml:mi>A</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ14\"><alternatives><tex-math id=\"M389\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (S_{{\\mathfrak {y}}}^3Q_{-2}D_{{\\mathfrak {y}}}^3D_{{\\mathfrak {z}}}^3)(\\texttt{f}({\\mathfrak {y,z}}))&amp;= {{\\mathfrak {y}}}^{10}\\bigg (\\frac{104976{{\\mathfrak {s}}}{{\\mathfrak {p}}}}{125}-\\frac{99144{{\\mathfrak {p}}}}{125}-\\frac{110808{{\\mathfrak {s}}}}{125}+\\frac{104976}{125}\\bigg )\\\\ {}&amp;\\qquad +{{\\mathfrak {y}}}^9\\bigg (\\frac{2000{{\\mathfrak {s}}}}{27}-\\frac{2000{{\\mathfrak {p}}}}{27}+\\frac{4000{{\\mathfrak {s}}}{{\\mathfrak {p}}}}{9}-\\frac{4000}{9}\\bigg )\\\\ {}&amp;\\qquad +{{\\mathfrak {y}}}^8\\bigg (\\frac{109375{{\\mathfrak {s}}}}{256}+\\frac{15625{{\\mathfrak {p}}}}{32}+\\frac{15625{{\\mathfrak {s}}}{{\\mathfrak {p}}}}{128}-\\frac{15625}{128}\\bigg )\\Big |_{{\\mathfrak {y=1}}}\\\\&amp;= \\frac{202510477{\\mathfrak {sp}}}{144000}- \\frac{40926041{{\\mathfrak {p}}}}{108000} - \\frac{332764271{{\\mathfrak {s}}}}{864000}+\\frac{39354227}{144000} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M390\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>10</mml:mn></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mn>104976</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>125</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>99144</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>125</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>110808</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>125</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>104976</mml:mn><mml:mn>125</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:mrow/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"2em\"/><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>9</mml:mn></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mn>2000</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>27</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>2000</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>27</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>4000</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>9</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>4000</mml:mn><mml:mn>9</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:mrow/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"2em\"/><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>8</mml:mn></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mn>109375</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>256</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>15625</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>32</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>15625</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>128</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>15625</mml:mn><mml:mn>128</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>202510477</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>144000</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>40926041</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>108000</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>332764271</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>864000</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>39354227</mml:mn><mml:mn>144000</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq184\"><alternatives><tex-math id=\"M391\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$HM(I_\\alpha ({\\mathfrak {s,p}}))= (D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})^2({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M392\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ15\"><alternatives><tex-math id=\"M393\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (D_{{\\mathfrak {y}}}+D_{{\\mathfrak {z}}})^2(\\texttt{f}({\\mathfrak {y,z}}))&amp;= 2{{\\mathfrak {y}}}^5{{\\mathfrak {z}}}^5(700{{\\mathfrak {s}}}+800{{\\mathfrak {p}}}-726{{\\mathfrak {z}}}+200{{\\mathfrak {s}}}{{\\mathfrak {p}}}+121{{\\mathfrak {s}}}{{\\mathfrak {z}}}-121{{\\mathfrak {p}}}{{\\mathfrak {z}}}+1296{\\mathfrak {yz}}\\\\ {}&amp;\\qquad +726{\\mathfrak {spz}}-1368{\\mathfrak {syz}}-1224{\\mathfrak {pyz}}+1296{\\mathfrak {spyz}}-200)\\Big |_{{\\mathfrak {y=z=1}}}\\\\&amp;= 4444{\\mathfrak {sp}}-1090{{\\mathfrak {p}}}-1094{{\\mathfrak {s}}}+740 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M394\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>700</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>800</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>726</mml:mn><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>200</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>121</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>-</mml:mo><mml:mn>121</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>1296</mml:mn><mml:mi mathvariant=\"fraktur\">yz</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:mrow/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mrow><mml:mspace width=\"2em\"/><mml:mo>+</mml:mo><mml:mn>726</mml:mn><mml:mi mathvariant=\"fraktur\">spz</mml:mi><mml:mo>-</mml:mo><mml:mn>1368</mml:mn><mml:mi mathvariant=\"fraktur\">syz</mml:mi><mml:mo>-</mml:mo><mml:mn>1224</mml:mn><mml:mi mathvariant=\"fraktur\">pyz</mml:mi><mml:mo>+</mml:mo><mml:mn>1296</mml:mn><mml:mi mathvariant=\"fraktur\">spyz</mml:mi><mml:mo>-</mml:mo><mml:mn>200</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>4444</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>1090</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>1094</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>740</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq185\"><alternatives><tex-math id=\"M395\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M396\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq186\"><alternatives><tex-math id=\"M397\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M398\"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq187\"><alternatives><tex-math id=\"M399\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$A(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M400\"><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq188\"><alternatives><tex-math id=\"M401\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$HM(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M402\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq189\"><alternatives><tex-math id=\"M403\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({\\mathfrak {s,p}})$$\\end{document}</tex-math><mml:math id=\"M404\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq190\"><alternatives><tex-math id=\"M405\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M406\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq191\"><alternatives><tex-math id=\"M407\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M408\"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq192\"><alternatives><tex-math id=\"M409\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$A(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M410\"><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq193\"><alternatives><tex-math id=\"M411\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$HM(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M412\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq194\"><alternatives><tex-math id=\"M413\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M414\"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq195\"><alternatives><tex-math id=\"M415\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M416\"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq196\"><alternatives><tex-math id=\"M417\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$A(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M418\"><mml:mrow><mml:mi>A</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq197\"><alternatives><tex-math id=\"M419\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$HM(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M420\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq198\"><alternatives><tex-math id=\"M421\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_\\alpha ({\\mathfrak {s,p}})|{\\mathfrak {s,p}}\\ge 1$$\\end{document}</tex-math><mml:math id=\"M422\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq199\"><alternatives><tex-math id=\"M423\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M424\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq200\"><alternatives><tex-math id=\"M425\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m(I_\\alpha ({\\mathfrak {s,p}}))= \\displaystyle \\frac{89{{\\mathfrak {s}}}}{900}+\\frac{91{{\\mathfrak {p}}}}{900}+\\frac{53{\\mathfrak {sp}}}{50}-\\frac{3}{50}$$\\end{document}</tex-math><mml:math id=\"M426\"><mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>89</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>91</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>53</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>50</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>3</mml:mn><mml:mn>50</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq201\"><alternatives><tex-math id=\"M427\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SDD(I_\\alpha ({\\mathfrak {s,p}}))=\\displaystyle \\frac{342{\\mathfrak {sp}}}{5}-\\frac{91{{\\mathfrak {p}}}}{15}-\\frac{89{{\\mathfrak {s}}}}{15}+\\frac{18}{5}$$\\end{document}</tex-math><mml:math id=\"M428\"><mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>342</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>91</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>15</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>89</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>15</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>18</mml:mn><mml:mn>5</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq202\"><alternatives><tex-math id=\"M429\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H(I_\\alpha ({\\mathfrak {s,p}})) = \\displaystyle \\frac{{{\\mathfrak {p}}}}{330}-\\frac{{{\\mathfrak {s}}}}{330}+\\frac{329{\\mathfrak {sp}}}{55}+\\frac{1}{55}$$\\end{document}</tex-math><mml:math id=\"M430\"><mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"><mml:mrow><mml:mi>H</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mn>330</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mn>330</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>329</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>55</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>55</mml:mn></mml:mfrac></mml:mrow></mml:mstyle></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq203\"><alternatives><tex-math id=\"M431\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma (I_\\alpha ({\\mathfrak {s,p}}))= 2{{\\mathfrak {s}}}-2{{\\mathfrak {p}}}+12{\\mathfrak {sp}}-12$$\\end{document}</tex-math><mml:math id=\"M432\"><mml:mrow><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq204\"><alternatives><tex-math id=\"M433\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m(I_\\alpha ({\\mathfrak {s,p}})) = S_{{\\mathfrak {y}}}S_{{\\mathfrak {z}}}({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}}));{\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M434\"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ16\"><alternatives><tex-math id=\"M435\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} S_{{\\mathfrak {y}}}S_{{\\mathfrak {z}}}(\\texttt{f}({\\mathfrak {y,z}}))&amp;= \\frac{{{\\mathfrak {y}}}^5{{\\mathfrak {z}}}^6(2{{\\mathfrak {s}}} -2{{\\mathfrak {p}}}+12{{\\mathfrak {s}}}{{\\mathfrak {p}}}-12)}{30}+\\frac{{{\\mathfrak {y}}}^5{{\\mathfrak {z}}}^5(14{{\\mathfrak {s}}}+ 16{{\\mathfrak {p}}}+4{{\\mathfrak {s}}}{{\\mathfrak {p}}}-4)}{25}\\\\&amp;\\quad -\\frac{{{\\mathfrak {y}}}^6{{\\mathfrak {z}}}^6(19{{\\mathfrak {s}}}+17{{\\mathfrak {p}}}-18{{\\mathfrak {s}}}{{\\mathfrak {p}}}-18)}{36} \\Big |_{{\\mathfrak {y=z=1}}}\\\\&amp;= \\frac{89{{\\mathfrak {s}}}}{900}+\\frac{91{{\\mathfrak {p}}}}{900}+\\frac{53{\\mathfrak {sp}}}{50}-\\frac{3}{50} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M436\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>6</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mn>30</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>14</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>16</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mn>25</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>6</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mn>6</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>18</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mn>36</mml:mn></mml:mfrac><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>89</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>91</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>900</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>53</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>50</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>3</mml:mn><mml:mn>50</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq205\"><alternatives><tex-math id=\"M437\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SDD(I_\\alpha ({\\mathfrak {s,p}}))= (D_{{\\mathfrak {y}}}S_{{\\mathfrak {z}}}+D_{{\\mathfrak {z}}}S_{{\\mathfrak {y}}})({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M438\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ17\"><alternatives><tex-math id=\"M439\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (D_{{\\mathfrak {y}}}S_{{\\mathfrak {z}}}+D_{{\\mathfrak {z}}}S_{{\\mathfrak {y}}})(\\texttt{f}({\\mathfrak {y,z}}))&amp;= \\frac{{\\mathfrak {y^5z^5}}}{15}\\big (420{{\\mathfrak {s}}}+480{{\\mathfrak {p}}}-366{{\\mathfrak {z}}}+120{\\mathfrak {sp}}+61{\\mathfrak {sz}}-61{\\mathfrak {pz}}+540{\\mathfrak {yz}}\\\\ {}&amp;\\qquad +366{\\mathfrak {spz}}-570{\\mathfrak {syz}}-510{\\mathfrak {pyz}}+540{\\mathfrak {spyz}}-120\\big ) \\Big |_{{\\mathfrak {y=z=1}}}\\\\&amp;= \\frac{342{\\mathfrak {sp}}}{5}-\\frac{91{{\\mathfrak {p}}}}{15}-\\frac{89{{\\mathfrak {s}}}}{15}+\\frac{18}{5} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M440\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup></mml:mrow><mml:mn>15</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mn>420</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>+</mml:mo><mml:mn>480</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>-</mml:mo><mml:mn>366</mml:mn><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>+</mml:mo><mml:mn>120</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>+</mml:mo><mml:mn>61</mml:mn><mml:mi mathvariant=\"fraktur\">sz</mml:mi><mml:mo>-</mml:mo><mml:mn>61</mml:mn><mml:mi mathvariant=\"fraktur\">pz</mml:mi><mml:mo>+</mml:mo><mml:mn>540</mml:mn><mml:mi mathvariant=\"fraktur\">yz</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow/><mml:mrow/></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"2em\"/><mml:mo>+</mml:mo><mml:mn>366</mml:mn><mml:mi mathvariant=\"fraktur\">spz</mml:mi><mml:mo>-</mml:mo><mml:mn>570</mml:mn><mml:mi mathvariant=\"fraktur\">syz</mml:mi><mml:mo>-</mml:mo><mml:mn>510</mml:mn><mml:mi mathvariant=\"fraktur\">pyz</mml:mi><mml:mo>+</mml:mo><mml:mn>540</mml:mn><mml:mi mathvariant=\"fraktur\">spyz</mml:mi><mml:mo>-</mml:mo><mml:mn>120</mml:mn><mml:mrow><mml:mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>342</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>91</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>15</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>89</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>15</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>18</mml:mn><mml:mn>5</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq206\"><alternatives><tex-math id=\"M441\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H(I_\\alpha ({\\mathfrak {s,p}})) = 2S_{{\\mathfrak {y}}}J({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M442\"><mml:mrow><mml:mi>H</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ18\"><alternatives><tex-math id=\"M443\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} 2S_{{\\mathfrak {y}}}J(\\texttt{f}({\\mathfrak {y,z}}))&amp;= 2{{\\mathfrak {y}}}^{10}\\bigg (\\frac{7{{\\mathfrak {s}}}}{5} +\\frac{8{{\\mathfrak {p}}}}{5}+\\frac{2{\\mathfrak {sp}}}{5}-\\frac{2}{5}\\bigg )-2{{\\mathfrak {y}}}^{12} \\bigg (\\frac{19{{\\mathfrak {s}}}}{12}+\\frac{17{{\\mathfrak {p}}}}{12}-\\frac{3{\\mathfrak {sp}}}{2}-\\frac{3}{2}\\bigg )\\\\&amp;\\quad +2{{\\mathfrak {y}}}^{11}\\bigg (\\frac{2{{\\mathfrak {s}}}}{11}-\\frac{2{{\\mathfrak {p}}}}{11}+\\frac{12{\\mathfrak {sp}}}{11}-\\frac{12}{11}\\bigg ) \\Big |_{{\\mathfrak {y=1}}}\\\\&amp;= \\frac{{{\\mathfrak {p}}}}{330}-\\frac{{{\\mathfrak {s}}}}{330}+\\frac{329{\\mathfrak {sp}}}{55}+\\frac{1}{55} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M444\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>10</mml:mn></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mn>7</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>8</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>2</mml:mn><mml:mn>5</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>12</mml:mn></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mn>19</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>12</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>17</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>12</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>3</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:msup><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">(</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>11</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mn>12</mml:mn><mml:mn>11</mml:mn></mml:mfrac><mml:mrow><mml:mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mn>330</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mn>330</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>329</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi></mml:mrow><mml:mn>55</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>55</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq207\"><alternatives><tex-math id=\"M445\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma (I_\\alpha ({\\mathfrak {s,p}}))= (D_{{\\mathfrak {y}}}-D_{{\\mathfrak {z}}})^2({\\mathbb {M}}(I_\\alpha ({\\mathfrak {s,p}})); {\\mathfrak {y,z}})$$\\end{document}</tex-math><mml:math id=\"M446\"><mml:mrow><mml:mi>σ</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"double-struck\">M</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ19\"><alternatives><tex-math id=\"M447\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} (D_{{\\mathfrak {y}}}-D_{{\\mathfrak {z}}})^2(\\texttt{f}({\\mathfrak {y,z}}))&amp;= 2{\\mathfrak {y^5z^6}}({{\\mathfrak {s}}}-{{\\mathfrak {p}}}+6{\\mathfrak {sp}}-6)\\Big |_{{\\mathfrak {y=z=1}}}\\\\&amp;= 2{{\\mathfrak {s}}}-2{{\\mathfrak {p}}}+12{\\mathfrak {sp}}-12 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M448\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"monospace\">f</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mrow><mml:msup><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mn mathvariant=\"fraktur\">5</mml:mn></mml:msup><mml:msup><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mn mathvariant=\"fraktur\">6</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>6</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>6</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\">|</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant=\"fraktur\">y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant=\"fraktur\">z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=\"fraktur\">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi mathvariant=\"fraktur\">p</mml:mi><mml:mo>+</mml:mo><mml:mn>12</mml:mn><mml:mi mathvariant=\"fraktur\">sp</mml:mi><mml:mo>-</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq208\"><alternatives><tex-math id=\"M449\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M450\"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq209\"><alternatives><tex-math id=\"M451\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SDD(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M452\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq210\"><alternatives><tex-math id=\"M453\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M454\"><mml:mrow><mml:mi>H</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq211\"><alternatives><tex-math id=\"M455\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma (I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M456\"><mml:mrow><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq212\"><alternatives><tex-math id=\"M457\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({\\mathfrak {s,p}})$$\\end{document}</tex-math><mml:math id=\"M458\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq213\"><alternatives><tex-math id=\"M459\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M460\"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq214\"><alternatives><tex-math id=\"M461\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SDD(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M462\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq215\"><alternatives><tex-math id=\"M463\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H(I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M464\"><mml:mrow><mml:mi>H</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq216\"><alternatives><tex-math id=\"M465\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma (I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M466\"><mml:mrow><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq217\"><alternatives><tex-math id=\"M467\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M468\"><mml:mrow><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq218\"><alternatives><tex-math id=\"M469\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SDD(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M470\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq219\"><alternatives><tex-math id=\"M471\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H(I_\\alpha ({\\mathfrak {s,p}})),$$\\end{document}</tex-math><mml:math id=\"M472\"><mml:mrow><mml:mi>H</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq220\"><alternatives><tex-math id=\"M473\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma (I_\\alpha ({\\mathfrak {s,p}}))$$\\end{document}</tex-math><mml:math id=\"M474\"><mml:mrow><mml:mi>σ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>α</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"fraktur\">s</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"fraktur\">p</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq221\"><alternatives><tex-math id=\"M475\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M476\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq222\"><alternatives><tex-math id=\"M477\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M478\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq223\"><alternatives><tex-math id=\"M479\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M480\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq224\"><alternatives><tex-math id=\"M481\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M482\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq225\"><alternatives><tex-math id=\"M483\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M484\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq226\"><alternatives><tex-math id=\"M485\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8-Pmmn$$\\end{document}</tex-math><mml:math id=\"M486\"><mml:mrow><mml:mn>8</mml:mn><mml:mo>-</mml:mo><mml:mi>P</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq227\"><alternatives><tex-math id=\"M487\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{12}$$\\end{document}</tex-math><mml:math id=\"M488\"><mml:msub><mml:mi>β</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq228\"><alternatives><tex-math id=\"M489\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M490\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq229\"><alternatives><tex-math id=\"M491\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M492\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq230\"><alternatives><tex-math id=\"M493\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M494\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq231\"><alternatives><tex-math id=\"M495\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M496\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq232\"><alternatives><tex-math id=\"M497\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8-Pmmn$$\\end{document}</tex-math><mml:math id=\"M498\"><mml:mrow><mml:mn>8</mml:mn><mml:mo>-</mml:mo><mml:mi>P</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq233\"><alternatives><tex-math id=\"M499\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{12}-$$\\end{document}</tex-math><mml:math id=\"M500\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mn>12</mml:mn></mml:msub><mml:mo>-</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq234\"><alternatives><tex-math id=\"M501\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M502\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq235\"><alternatives><tex-math id=\"M503\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M504\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq236\"><alternatives><tex-math id=\"M505\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$B_{12}$$\\end{document}</tex-math><mml:math id=\"M506\"><mml:msub><mml:mi>B</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq237\"><alternatives><tex-math id=\"M507\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M508\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq238\"><alternatives><tex-math id=\"M509\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8-Pmmn$$\\end{document}</tex-math><mml:math id=\"M510\"><mml:mrow><mml:mn>8</mml:mn><mml:mo>-</mml:mo><mml:mi>P</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq239\"><alternatives><tex-math id=\"M511\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{12}-$$\\end{document}</tex-math><mml:math id=\"M512\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mn>12</mml:mn></mml:msub><mml:mo>-</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq240\"><alternatives><tex-math id=\"M513\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M514\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq241\"><alternatives><tex-math id=\"M515\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M516\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq242\"><alternatives><tex-math id=\"M517\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8-pmmn$$\\end{document}</tex-math><mml:math id=\"M518\"><mml:mrow><mml:mn>8</mml:mn><mml:mo>-</mml:mo><mml:mi>p</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq243\"><alternatives><tex-math id=\"M519\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _{12}$$\\end{document}</tex-math><mml:math id=\"M520\"><mml:msub><mml:mi>β</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq244\"><alternatives><tex-math id=\"M521\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1$$\\end{document}</tex-math><mml:math id=\"M522\"><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq245\"><alternatives><tex-math id=\"M523\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2$$\\end{document}</tex-math><mml:math id=\"M524\"><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq246\"><alternatives><tex-math id=\"M525\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m$$\\end{document}</tex-math><mml:math id=\"M526\"><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq247\"><alternatives><tex-math id=\"M527\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma$$\\end{document}</tex-math><mml:math id=\"M528\"><mml:mi>σ</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ20\"><alternatives><tex-math id=\"M529\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} M=i+j(TD) \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M530\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>T</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ21\"><alternatives><tex-math id=\"M531\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} G=165.46(HM)-1252.8 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M532\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mn>165.46</mml:mn><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>-</mml:mo><mml:mn>1252.8</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ22\"><alternatives><tex-math id=\"M533\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} E= 76.659 (HM)-2898.5 \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M534\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mn>76.659</mml:mn><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>H</mml:mi><mml:mi>M</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>-</mml:mo><mml:mn>2898.5</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq248\"><alternatives><tex-math id=\"M535\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_1$$\\end{document}</tex-math><mml:math id=\"M536\"><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq249\"><alternatives><tex-math id=\"M537\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2$$\\end{document}</tex-math><mml:math id=\"M538\"><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq250\"><alternatives><tex-math id=\"M539\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M_2^m$$\\end{document}</tex-math><mml:math id=\"M540\"><mml:msubsup><mml:mi>M</mml:mi><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq251\"><alternatives><tex-math id=\"M541\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma$$\\end{document}</tex-math><mml:math id=\"M542\"><mml:mi>σ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq252\"><alternatives><tex-math id=\"M543\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M544\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula 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[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">RNA epigenetic modifications exert important effects in myriad biological processes by regulating RNA export [##REF##35962235##1##–##REF##35141044##3##], stability [##REF##35210361##4##–##REF##35974338##6##], and translation [##REF##33283887##7##–##REF##33199375##9##]. The regulatory functions of certain eukaryotic RNA modifications, including N6-methyladenosine (m⁶A), 5-methylcytosine (m⁵C), and N4-acetylcytidine (ac4C), have been well characterized [##REF##30230927##10##, ##REF##27808276##11##]. In particular, m⁵C is formed via the addition of a methyl group from S-adenosylmethionine (SAM) to the carbon-5 position of cytosine in RNA; this process is catalyzed by NOL1/NOP2/Sun domain (NSUN) family members or DNA methyltransferase-2 (DNMT2) [##REF##27313037##12##]. In addition to ribosomal RNAs (rRNAs) and transfer RNAs (tRNAs), m⁵C is present in messenger RNAs (mRNAs) [##REF##33438329##13##]. NOP2/Sun RNA Methyltransferase 2 (NSUN2) functions as a major methyltransferase associated with m⁵C in mRNA. Meanwhile, Aly/REF export factor (ALYREF) and Y-box binding protein 1 (YBX1) serve as “reader” proteins that recognize m⁵C and promote mRNA export from the nucleus, or stabilize RNA, respectively [##REF##33438329##13##–##REF##34631286##16##]. However, the distribution of m⁵C in mRNA varies among cell types. That is, although m⁵C is distributed throughout the mRNA transcript, it may be enriched in specific regions, such as the coding sequence (CDS) [##REF##28965832##17##, ##REF##28062751##18##], 3′ untranslated region (UTR) [##REF##28062751##18##, ##REF##30009162##19##] or the region proximal to the start codon [##REF##32275888##20##–##REF##30704115##22##].</p>", "<p id=\"Par3\">Hepatitis B virus (HBV) infection is a common cause of cirrhosis and cancer. Although the HBV vaccine offers 98%–100% protection against infection, HBV infection remains a global health issue, with significant morbidity and mortality (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.who.int/news-room/fact-sheets/detail/hepatitis-b\">https://www.who.int/news-room/fact-sheets/detail/hepatitis-b</ext-link>). HBV contains a relaxed-circular DNA genome of approximately 3.2 kb that is transcribed into four HBV mRNA transcripts (3.5 kb, 2.4 kb, 2.1 kb, and 0.7 kb). Among them, the 3.5 kb mRNA encodes three viral proteins, core antigen (HBc), E antigen (HBe), and polymerase (Pol); the 2.4 and 2.1 kb mRNAs encode three S antigens, preS1, preS2, and HBs; whereas the 0.7 kb mRNA encodes X protein (HBx) [##REF##32866519##23##]. HBx is a multi-functional protein that promotes HBV transcription by interacting with damage specific DNA binding protein 1 (DDB1) and recruiting E3 ligase to degrade the structural maintenance of chromosome protein (Smc)5/6 complex [##REF##26983541##24##]. It also interferes with interferon (IFN) production and signaling by targeting mitochondrial antiviral signaling protein (MAVS) [##REF##21068253##25##, ##REF##20554965##26##], cytokine signaling 3 (SOCS3), and protein phosphatase 2 A (PP2A) [##REF##27459003##27##].</p>", "<p id=\"Par4\">Similar to other RNA modifications, m⁵C in viral RNA influences viral replication by regulating RNA splicing, stability, and translation [##REF##31415754##28##]. m⁵C in HIV-1 mRNA is modified by NSUN2, whereas the loss of NSUN2 perturbs HIV-1 alternative splicing and ribosomal recruitment [##REF##31415754##28##]. Meanwhile, m⁵C in the EBV-encoded non-coding RNA, Epstein-Barr virus-encoded protein 1 (EBER1) is essential for viral lytic replication and negatively impacts RNA stability [##REF##32354721##29##]. Despite these few viral studies emphasizing the importance of m⁵C modification during viral infection [##REF##31415754##28##–##REF##32321818##30##], it remains largely unclear how viruses hijack and manipulate the host m⁵C system to promote viral replication.</p>", "<p id=\"Par5\">RNA modification also significantly suppresses RNA-induced innate immune responses in mammalian cells [##REF##16111635##31##]. The most abundant internal RNA modification, m⁶A, serves as a molecular signature that assists viruses, including HBV, in evading the immune system [##REF##33961823##32##–##REF##32719095##34##]. Given that stimulator of IFN gene protein (STING)-mediated DNA sensing is deficient in hepatocytes [##REF##27312012##35##], HBV infection triggers an innate immune response through retinoic acid-inducible protein I (RIG-I)-mediated RNA sensing [##REF##25557055##36##]. RIG-I binds to the 5′ epsilon stem-loop of HBV pre-genomic RNA (pgRNA) to induce type III, not type I, interferon responses [##REF##25557055##36##]. However, Adenosine1907 in the 5’ epsilon stem-loop is typically m⁶A-modified, which reduces the interaction between pgRNA and RIG-I and inhibits IRF-3–mediated IFN production [##REF##32719095##34##]. Meanwhile, m⁵C-modified nucleotides do not trigger RIG-I-mediated immune signaling [##REF##27651356##37##]. However, the function of HBV m⁵C in virus-induced immune evasion has not been elucidated.</p>", "<p id=\"Par6\">In this study, we characterize the role of m⁵C and its methyltransferase NSUN2 in the HBV-induced innate immune response and demonstrate that the precise balance of NSUN2 expression is vital for the HBV life cycle. That is, reduced NSUN2 expression is sufficient for maintaining HBV m⁵C to facilitate efficient viral infection, however, does not increase IFN m⁵C abundance, preventing the induction of IFN expression. Our study reveals that HBV m⁵C and NSUN2 are important factors in HBV-induced innate immune responses.</p>" ]

[ "<title>Materials and methods</title>", "<title>Cell culture and transfection</title>", "<p id=\"Par28\">Huh7, HepG2, HepG2-NTCP, and HepG2.2.15 cells, which stably express HBV, were cultured in Dulbecco’s modified Eagle’s medium supplemented with 10% fetal bovine serum at 37 °C in a 5% CO₂ environment. Plasmid transfection was carried out using Lipofectamine 2000 reagent (Invitrogen, Carlsbad, CA, USA; catalog no. 11668-019) according to the manufacturer’s instructions.</p>", "<title>Nanopore direct RNA sequencing (DRS-seq)</title>", "<p id=\"Par29\">PolyA+ RNA was purified from 1 mg of total RNA from HepG2.2.15 cells or AAV-HBV transduced mouse liver [##REF##34242702##38##, ##REF##35718932##39##] using a GenEluteTM mRNA Miniprep Kit (Sigma-Aldrich). Independent experiments of DRS-seq were performed according to the manufacturer’s instructions (Oxford Nanopore DRS protocol; SQKRNA002). Briefly, the sequencing library prepared from PolyA+ RNA was loaded onto the FLO-MIN106D flow cell, followed by a 72 h sequencing run on a MinION device (Oxford Nanopore Technologies). Multi-fast5 reads were base called guppy (v3.1.5) and then converted to single-read fast5 using the command multi_to_single_fast5 in the Oxford Nanopore Technologies API, ont_fast5_api (v3.0.2). Single-fast5 data were mapped to the reference genome of HBV (NC_003977.2) using Tombo (v1.5.1). The specific modifications were detected by the Tombo detect_modifications command, and the all-context alternate model was used to identify 5-methylcytosine in any sequence by running “-alternate-bases 5mC.” Subsequently, the “text_output” command was applied to obtain the methylation score and coverage rate at each position.</p>", "<title>Bisulfite sequencing (BS-seq)</title>", "<p id=\"Par30\">Total RNA was extracted from Huh7 cells transfected with Poly I:C and HBV 1.1-mer at 18 h post-transfection using TRIzol™ Reagent (Thermo Fisher Scientific). PolyA+ RNA was then selected and the library was constructed using the EZ RNA Methylation™ Kit (ZYMO RESEARCH) and KC UMI RNA Library Kit (Wuhan SeqHealth Tech) according to the manufacturer’s instructions. Sequencing of three samples in each condition was performed using a MGISEQ-T7 sequencing system (BGI). Sequencing data was uploaded to the GEO repository (GSE246879). Raw reads were first processed using fastp (version 0.23.0) to remove residual adaptor sequences and low-quality reads [##REF##30423086##72##]. The clean reads were then mapped to the reference genome, and duplicated reads were removed using Bismark (version 0.22.3) [##REF##21493656##73##]. The chromosome depth and coverage were calculated using MosDepth (version 0.3.1) and RSeQC (version 4.0.0) [##REF##29096012##74##]. Methylation detection along the whole genome was conducted using Bismark, which calculates the proportion of methylated reads at each genomic site. DMRs between different groups were detected using methylene (version 0.2–8) [##REF##26631489##75##].</p>", "<title>Plasmid constructs</title>", "<p id=\"Par31\">NSUN2, DNMT2, ALYREF, HBx, HBsAg, and HBcAg expression plasmids were cloned into the PXJ40-Flag/HA vector. The Flag-C321A plasmid was constructed as described previously [##REF##31415754##28##]. shRNA-resistant cDNAs of NSUN2 plasmids were constructed by introducing four site mutations into the NSUN2 expression plasmids. C1204T, C705T, C1235G, C1291T, and M-ALL plasmids were generated by introducing site mutations into the pch9-3091 plasmid. The HBV 0.7 kb mRNA wt and mt plasmids were generated by inserting the 5′-UTR, CDS and 3′-UTR region of HBx from the pch9-3091 plasmid into the PXJ40-HA vector. The 5′-UTR-wt and 5′-UTR-mt plasmids were generated by inserting the HBx wt 5′-UTR and m5C mutant 5′-UTR into the PGL3-basic plasmid. The NSUN2 promoter luciferase reporter plasmid and truncated plasmids were constructed by inserting the −190 to +100, −1000 to +100, −500 to +100, −300 to +100, −200 to +100, and-100 to +100 promoter regions of the NSUN2 genome from huh7 cells into the vector PGL3-basic.</p>", "<title>Dot blot</title>", "<p id=\"Par32\">Ten micrograms of total RNA isolated from huh7 cells were denatured at 75 °C for 5 min and then added dropwise onto the Hybound N+ membrane (GE Healthcare). The membrane was then dried and exposed to UV light to crosslink the RNA samples. The membrane was blocked in 5% skimmed milk and incubated with primary antibody against m⁵C modification (cat. no. ab10805; Abcam, Cambridge, UK) overnight at 4 °C. After three washes, the membranes were incubated with secondary antibodies [horseradish peroxidase (HRP) goat anti-mouse IgG (H + L) 115-035-003] for 1 h at room temperature. Next, 1 mL of the prepared chemiluminescent reagent mix was added to the membrane after three washes. Immunoblot signals were detected using the Tanon-5200 ChemiDoc MP imaging system (Tanon Science &amp; Technology, Shanghai, China). Three independent experiments of Dot blots were performed, and one representative result was shown Fig. ##FIG##2##3B##.</p>", "<title>Western blotting</title>", "<p id=\"Par33\">Cells were lysed on ice for 30 min with lysis buffer (P0013, Beyotime), centrifuged at 14,000 rpm for 10 min, and denatured at 100 °C. Proteins were separated by SDS-PAGE and transferred to nitrocellulose membranes. The following steps were performed as described previously [##REF##35971620##51##]. The primary antibodies included Flag (cat. no. F1804-1 MG; Sigma-Aldrich), GAPDH (cat. no. 60004-1-lg; Proteintech, Rosemont, IL, USA), NSUN2 (cat. no. 20854-1-AP; Proteintech, Rosemont, IL, USA), DNMT2 (cat. no. 19221-1-AP; Proteintech, Rosemont, IL, USA), ALYREF (cat. no. 16690-1-AP; Proteintech, Rosemont, IL, USA), HA (cat. no. 51064-2-AP; Proteintech, Rosemont, IL, USA), and PreS2 (cat. No. sc-23944; Santa Cruz Biotechnology, Dallas, TX, USA). The anti-HBsAg antibody was gifted by Dr. Bing Yan from the Wuhan Institute of Virology, CAS. At least three independent experiments for each western blot were performed. Original western blots are shown in ##SUPPL##0##Supplementary Material##.</p>", "<title>Immunofluorescence</title>", "<p id=\"Par34\">Cells were seeded in microplates at 50% confluence and then transfected with the HBV 1.1-mer plasmid, pch9-3091, as described above. The following day, cells were fixed with 3.7% paraformaldehyde for 30 min at room temperature 72 h post-transfection and then permeabilized in 0.5% Triton-X100 on ice for 10 min. After blocking in 3% BSA for 1 h, the cells were incubated with primary antibodies at a dilution of 1:50 for 1 h at room temperature and then incubated with secondary antibodies (A-11001 or A-11011, Invitrogen) for 1 h at room temperature. Finally, the samples were stained with Hoechst for 5 min. Images were obtained using a VoX confocal microscope (PerkinElmer, Waltham, MA, USA).</p>", "<title>M⁵C-methylated RNA immunoprecipitation (m⁵C-RIP) and RT-qPCR</title>", "<p id=\"Par35\">Total RNA was extracted from HepG2.2.15 cells using TRIzol reagent (Invitrogen, Carlsbad, CA, USA). m⁵C-RIP was performed as previously described [##REF##30364964##55##]. Briefly, 300 μg of RNA were resuspend in immunoprecipitation (IP) buffer (150 mmol/L NaCl, 0.1% NP-40, 10 mmol/L Tris-HCl pH 7.4) and incubated with an anti-m⁵C antibody (ab10805, Abcam) or normal rabbit/mouse IgG antibody (Proteintech) overnight at 4 °C. The RNA and antibody mixture was then incubated with 35 μL of magnetic beads (New England Biolabs) for 2 h at 4 °C. Beads were washed with IP buffer six times and then incubated with 300 μL of elution buffer (5 mmol/L Tris-HCl pH 7.5, 1 mmol/L EDTA pH 8.0, 0.05% SDS, 4.2 μL 20 mg/mL proteinase K) at 50 °C for 1.5 h. Eluted RNA was purified using phenol/chloroform. Immunoprecipitated RNA was used for cDNA synthesis using the HiScript 1st Strand cDNA Synthesis Kit (Vazyme) according to the manufacturer’s protocol. The relative RNA level was measured by quantitative PCR (qPCR) using Hieff® qPCR SYBR® Green Master Mix (Yeasen Biotech Co., Shanghai, China) on a CFX Connect real-time system (Bio-Rad Laboratories, Hercules, CA, USA). The primers used for RT-qPCR were listed in Table ##SUPPL##0##S6##. At least three samples in each qPCR analysis were prepared, and three independent experiments were performed.</p>", "<title>Formaldehyde-crosslinked RNA-immunoprecipitation</title>", "<p id=\"Par36\">Cells (1 × 10⁷) seeded in 10-cm plates were cross-linked by 1% formaldehyde at 37 °C for 10 min. Next, 2.5 mol/L glycine was added to the plate at a final concentration of 0.125 mol/L to stop the cross-linking reaction. The cells were washed three times with phosphate-buffered saline (PBS) and scraped from the plate. After centrifugation at 800 ×g for 3 min at 4 °C, the cells were resuspended with 800 μL of RIP buffer (150 mmol/L KCl, 25 mmol/L Tris-HCl pH 7.4, 5 mmol/L EDTA, 0.5 mmol/L DTT, 0.5% NP40, 100 U/mL RNase inhibitor, 100 μmol/L PMSF, 1 μg/mL proteinase Inhibitors) and incubated on ice for 30 min. The cell lysates were centrifugated at 13000 ×g for 10 min; 100 μL of the supernatant were collected as an input control. The remaining lysates were divided into two aliquots and stored at −80 °C until further analysis.</p>", "<p id=\"Par37\">The lysates were incubated with anti-Flag antibody (Sigma-Aldrich) or IgG antibody (Proteintech) overnight at 4 °C. Protein-G agarose beads were washed three times with wash buffer (300 mmol/L KCl, 25 mmol/L Tris-HCl pH 7.4, 5 mmol/L EDTA, 0.5 mmol/L DTT, 0.5% NP40, 100 U/mL RNase inhibitor, 100 µmol/L PMSF, 1 μg/mL proteinase inhibitors) and added to the cell lysate and antibody mixture, and incubated at 4 °C for 2 h. The beads were washed three times with RIP buffer and three times with wash buffer. RNA was extracted using the TRIzol reagent (Invitrogen, Carlsbad, CA, USA) for qRT-PCR.</p>", "<title>Enzyme-linked immunosorbent assay (ELISA)</title>", "<p id=\"Par38\">Huh7 cells were transfected with the HBV 1.1-mer plasmid, pch9-3091, using Lipofectamine 2000 as described above. Cell culture supernatants were harvested 72 h post-transfection. HBsAg and HBeAg were detected using an enzyme-linked immunosorbent assay (ELISA) kit (Kehua Bio-Engineering, Shanghai, China) according to the manufacturer’s instructions. IFN-β was assayed at 24 h post-transfection with a human IFN-β/IFNB ELISA Kit (MM-1641H1, MEIMIAN) according to the manufacturer’s instructions.</p>", "<title>Southern blotting</title>", "<p id=\"Par39\">HBV DNA was extracted from huh7 cells 72 h post-transfection, as described previously [##REF##31204557##76##]. In brief, 5 × 10⁶ cells were lysed with 800 μL HBV DNA lysis buffer (50 mmol/L Tris-HCl pH7.4, 1 mmol/L EDTA, 1%NP-40) on ice for 10 min. The cells were scraped off and centrifugated at 14,000 rpm for 3 min. The supernatants were mixed with 8 μL DNaseI(10 mg/mL) and 8 μL 1 mol/L MgCl₂, and incubated at 37 °C for 30 min. Then, 40 μL of 0.5 mol/L EDTA was added to stop the reaction. HBV capsids were digested at 55 °C for 2 h after adding 20 μL of 20 mg/mL proteinase K and 80 μL of 10% SDS to cell lysates. Core-associated DNA was extracted using a phenol/chloroform mixture. The extracted DNA was separated on a 1% agarose gel for 4 h at 50 V, followed by denaturation and transfer to Hybound N+ membranes (GE Healthcare) in 20× SSC (3 mol/L NaCl, 0.3 mol/L sodium citrate). The membrane was UV-crosslinked and hybridized with a DIG-labeled probe (DIG HIGH PRIME Kit II). Viral DNA was detected as previously described [##REF##27881651##77##].</p>", "<title>Nuclear and cytoplasmic fractionation</title>", "<p id=\"Par40\">The cells (1 × 10⁶) were harvested 24 h post-transfection. The cytoplasmic and nuclear fractions were extracted using the Cytoplasmic and Nuclear RNA Purification Kit (21000, NORGEN), respectively, according to the manufacturer’s instructions. Purified RNA was reverse-transcribed for qPCR, as described above. U6 and GAPDH serve as internal controls in nucleus and cytoplasm respectively.</p>", "<title>Immuno-precipitation (IP)</title>", "<p id=\"Par41\">IP was performed as previously described [##REF##34225491##48##]. Briefly, cells were washed with cold PBS and then lysed with IP buffer (50 mmol/L Tris-HCl pH 7.5, 1 mmol/L EGTA, 1 mmol/L EDTA, 1% Triton X-100, 150 mmol/L NaCl, 2 mmol/L DTT, 100 μmol/L PMSF, 1 μg/mL proteinase inhibitors) on ice for 30 min. Next, 10% of the cell lysates were collected and used as input control after being centrifuged at 13,000 rpm and 4 °C for 10 min. The remaining lysates were incubated with primary or normal IgG antibodies overnight at 4 °C respectively. Protein-G agarose (catalog number) was added to the mixture and incubated for 1 h at 4, followed by six washes with IP buffer. Immunoprecipitated proteins were eluted in SDS loading buffer. All samples were heat-denatured before SDS-PAGE and western blotting was performed.</p>", "<title>Dual luciferase reporter assay</title>", "<p id=\"Par42\">Huh7 cells were seeded in a 12-well plate and transfected with luciferase vectors using Lipofectamine 2000 (Invitrogen) as described above. Dual-luciferase reporter assays (Promega #E1910) were performed according to the manufacturer’s instructions 24 h post-transfection. Briefly, 100 Μl Passive Lysis Buffer was added to each PBS-washed well. Then, 20 μL of cell lysates was transferred to an Optiplate-96 following a 15 min incubation at room temperature. Firefly and Rellina luciferase activities were assayed using a GloMax Luminometer (Promega). The relative luciferase activity of each sample was calculated as the ratio of firefly to Renilla luciferase activity.</p>", "<title>HBV virus production and infection</title>", "<p id=\"Par43\">HepG2.2.15 cells were cultured for more than three days. The culture supernatants were then harvested and centrifuged at 1000 × <italic>g</italic> and 4 °C for 15 min to remove cell debris. The clarified supernatants was mixed with 5% (w/v) PEG8000 and incubated at 4 °C overnight. The mixture was centrifuged at 4000 rpm and 4 °C for 30 min. The pellets were dissolved in culture medium containing 1% of the starting volume. HepG2-NTCP cells were seeded in 12-well plates prior to HBV infection. The cells were incubated with the collected virus in the presence of 4% PEG8000 and 2% DMSO at 37 °C for 24 h. The cells were washed twice and cultured in fresh medium containing 2% DMSO for more than seven days.</p>", "<title>Ribosome loading</title>", "<p id=\"Par44\">Huh7 cells were cultured and transfected as described above; 2 × 10⁷ cells were treated with 5 mg/mL cycloheximide at 37 °C for 10 min 24 h post-transfection. The cells were then washed three times with PBS and resuspended in 1 mL of ribosome lysis buffer (10 mmol/L Tris-HCl pH 7.4, 5 mmol/L MgCl₂, 100 mmol/L KCl, 1% Triton X, Protease inhibitor, 2 mmol/L DTT, 100 mg/mL cycloheximide, and RNase inhibitor). RNA was extracted from 10% of the cell lysates and used as the input control. The remaining lysates were loaded into a gradient sucrose solution ranging from 5% to 50% (5% increments) in an SW41 transparent ultracentrifuge tube. The sucrose solution was prepared and stored at 4 °C for 24 h to form a continuous gradient. Sucrose (1 mL) was collected by ultracentrifugation at 30,000 × <italic>g</italic> for 2 h at 4 °C. The OD 260/320 ratio of each fraction was measured using a NanoDrop One. RNA was extracted from the fraction with the highest OD 260/320 nm. The amount of HBV mRNA in this fraction was measured by qPCR.</p>", "<title>RNA oligo pull down</title>", "<p id=\"Par45\">huh7 cells (8 × 10⁷) were harvested and lysed in 2 mL of RIPA buffer (50 mM Tris-HCl, pH 8.0, 0.5 mM EDTA, 0.1% SDS, 1% NP-40, 150 mM NaCl). The cell lysates were centrifuged at 13000 rpm for 15 min at 4 °C. Then, the supernatant was collected as INPUT, and 50 μL of neutravidin beads (29200, Thermo) were washed twice with Tris-buffered saline (TBS). Next, 5 μg of m⁵C modified oligo RNA (Beijing Tsingke Biotech Co., Ltd) or control oligo RNA were added to the beads, the volume was adjusted to 500 μL and rotated at 4 °C for 2 h. The beads were washed three times, and 100 μL of huh7 cell lysate was added to the beads and rotated at 4 °C overnight. The beads were washed again with cold TBS three times, and 40 μL 2x LDS Laemmli buffer was added. Pull-down proteins were analyzed by western blotting.</p>", "<title>RNA stability assay</title>", "<p id=\"Par46\">huh7 cells (1 × 10⁴) were seeded into a 12-well plate. Cells were harvested at 0 h, 2 h, 4 h, 6 h, and 8 h following treatment with 4 μg/mL Actinomycin D (Sigma) at 24 h post-transfection. Total RNA was extracted from huh7 cells at different time points using TRIzol reagent. The same amount of RNA was reverse-transcribed for qPCR, as described above. The proportion of target gene expression relative to 0 h was calculated, and a one-step decay curve was drawn to calculate the half-life.</p>", "<title>Double-stranded DNA oligo pull down</title>", "<p id=\"Par47\">Five micrograms of sense and anti-sense biotin-labeled oligo DNA were incubated at 95 °C for 10 min, and cooled at room temperature. Next, 80 μL of NeutrAvidinTM Agarose (29200, thermo) was washed three times with wash buffer (20 mmol/L Tris-HCl pH 7.5, 100 mmol/L NaCl, 1 mmol/L MgCl2, 0.5 mmol/L EDTA, 0.5 mmol/L DTT). The beads were resuspended in 1 mL of wash buffer, annealed double-stranded oligonucleotide DNAs were added, and the beads were incubated for 2 h at room temperature. The beads were then washed three times with wash buffer and resuspended with 900 μL of pull down buffer (20 mmol/L Tris-HCl pH 7.5, 100 mmol/L NaCl, 1 mmol/L MgCl₂, 0.5 mmol/L EDTA, 0.5 mmol/L DTT, 4% Glycerol, 10 µg/mL Poly dI-Dc,1× Roche’s protease inhibitor cocktail). Subsequently, 100 μL of cell lysates in RIPA buffer were added to the bead and oligo mixture and incubated overnight at 4 °C. The beads were washed with wash buffer six times and resuspended in 40 μL 2× LDS Laemmli buffer. Proteins were analyzed by western blotting.</p>", "<title>Statistical analysis</title>", "<p id=\"Par48\">Comparisons between two groups were performed using students’ unpaired <italic>t</italic>-tests, while comparisons of the decay curves were performed using two-way ANOVA. <italic>P</italic> ≤ 0.05 is considered statistically significant. All statistical analyses were conducted in GraphPad prism software.</p>" ]

[ "<title>Results</title>", "<title>HBV m⁵Cs are essential for viral replication</title>", "<p id=\"Par7\">To explore whether m⁵C is present in HBV mRNA, the overall level of m⁵C was determined using m⁵C-methylated RNA immunoprecipitation (m⁵C-RIP) in HepG2.2.15 cells stably transfected with the HBV ayw strain. Approximately 70-fold more HBV mRNA was immunoprecipitated with an m⁵C specific antibody compared with the negative control IgG antibody (Fig. ##FIG##0##1A##), indicating that HBV mRNA contained m⁵C modifications. The precise m⁵C positions were then determined by nanopore direct RNA sequencing (DRS-seq) using poly (A) + RNAs purified from HepG2.2.15 cells. Four sites, m⁵C-705, m⁵C-1204, m⁵C-1235, and m⁵C-1291, were identified by applying two stringent criteria: (1) the m⁵C rate of each candidate site was at least 90%; (2) the candidate sites could be re-detected by independent DRS (Fig. ##FIG##0##1B## and Table ##SUPPL##1##S1##). Consistently, m⁵C-1204 and m⁵C-1291 with m⁵C rate more than 90% were also identified in DRS-seq of poly (A) + RNAs from AAV-HBV transduced mouse liver [##REF##34242702##38##, ##REF##35718932##39##] (Fig. ##FIG##0##1B## and Table ##SUPPL##1##S1##). To further confirm the identified HBV m⁵Cs, bisulfite sequencing (BS-seq) was performed on HBV 1.1-mer-transfected cells. Three sites, m⁵C-1204, m⁵C-1235, and m⁵C-1291, were detected using BS-seq (Table ##SUPPL##1##S1##), however, their detection rates were lower. Statistical m⁵C motif analysis using MEME [##REF##19458158##40##] showed no obvious base preference around the candidate m⁵C sites in either DRS-seq or BS-seq (Fig. ##FIG##0##1C##).</p>", "<p id=\"Par8\">To investigate the function of HBV m⁵C in the HBV life cycle, point mutations were introduced at four identified m⁵C positions in the HBV genome (Fig. ##FIG##0##1D##). Three non-synonymous mutations were generated due to limited mutagenesis options (Fig. ##FIG##0##1D##). The viral DNA replication of mutants was then examined by Southern blot. As shown in Fig. ##FIG##0##1E##, the synthesis of core-associated DNA including relaxed circular DNA, duplex-linear DNA, and single-stranded DNA was relatively eliminated in the C705T, C1291T, C1235G, and M-ALL mutants, and decreased in the C1204T mutant. In addition, compared to wild-type HBV, all mutants resulted in a significant reduction in HBeAg and HBsAg secretion which was quantified by ELISA in Huh7 cells, while the M-ALL mutant exhibited a synergistic inhibitory effect (Fig. ##FIG##0##1F, G##). These data indicate that the m⁵Cs are functional and facilitate HBV replication.</p>", "<title>HBV m⁵C-1291 promotes viral RNA export and translation and suppresses RIG-I recognition</title>", "<p id=\"Par9\">m⁵C has important roles in RNA export, stability, and translation [##REF##33438329##13##, ##REF##32303268##15##]. The HBV genome primarily encodes at least four mRNAs (Fig. ##FIG##0##1B##); among the four identified HBV m⁵Cs, only m⁵C-1291 was located in all four mRNAs and was in the 5’-UTR of the 0.7 kb mRNA. Therefore, m⁵C-1291 was selected for further functional analysis. ALYREF is an m⁵C reader that promotes mRNA export [##REF##32321818##30##]. HBV mRNA was co-immunoprecipitated with ALYREF in a formaldehyde-crosslinked RNA immunoprecipitation (RIP) assay, indicating ALYREF bound HBV mRNA (Fig. ##FIG##1##2A##). Fractionation experiments revealed that ALYREF overexpression significantly increased the export of nuclear HBV mRNA into the cytoplasm (Fig. ##FIG##1##2B##). The fractionation efficiency was verified by qPCR analysis of glyceraldehyde 3-phosphate dehydrogenase (<italic>GAPDH</italic>) and <italic>U6</italic> (Fig. ##SUPPL##0##S1A##). To further confirm this result, we constructed a cDNA reporter of 0.7 kb mRNA driven by the CMV promoter according to the reported HBV mRNA isoforms (Fig. ##FIG##1##2C##) [##REF##3009868##41##]. Notably, the m⁵C-1291 mutation did not affect the stability of the 0.7 kb mRNA after transcription inhibition by Actinomycin D (Fig. ##SUPPL##0##S1B##). Meanwhile, ALYREF overexpression significantly promoted the export of the wild-type 0.7 kb mRNA, but not that of the mutant 0.7 kb mRNA (Fig. ##FIG##1##2C##). The binding efficiency of ALYREF to the mutant 0.7 kb mRNA was lower than that of the wild-type 0.7 kb mRNA in the RIP assay (Fig. ##FIG##1##2D##). In summary, ALYREF binds m⁵C-1291 and promotes the export of HBV mRNA.</p>", "<p id=\"Par10\">The HBV 0.7 kb mRNA potentially encodes the HBx protein. To investigate whether m⁵C-1291 is important for HBx translation, a ribosome-loading assay was performed to determine the association between the HBV 0.7 kb mRNA and ribosomes. GAPDH was used as a negative control (Fig. ##FIG##1##2E##). Approximately 4-fold more ribosomes were loaded onto wild-type 0.7 kb mRNA compared to mutant 0.7 kb mRNA (Fig. ##FIG##1##2F##). Furthermore, we inserted the wild-type and mutant 5′-UTR of the 0.7 kb mRNA into a luciferase reporter and evaluated the luciferase activity via dual-luciferase assay (Fig. ##FIG##1##2G## bottom) [##REF##3009868##41##]. The wild type 5′-UTR exhibited 2-fold higher luciferase activity than the mutant (Fig. ##FIG##1##2G top##). Taken together, these data suggest that HBV m⁵C-1291 promotes 0.7 kb mRNA translation.</p>", "<p id=\"Par11\">RNA modifications suppress toll-like receptor (TLR) and RIG-I triggered innate immune signaling [##REF##16111635##31##, ##REF##27651356##37##]. Transfection with m⁵C mutants induced upregulation of IFN-β (Fig. ##FIG##1##2H## and Fig. ##SUPPL##0##S1C##) and certain ISG mRNAs (Fig. ##FIG##1##2I##) in poly I:C treated cells by qPCR assays. Similar results were obtained without poly I:C treatment (Fig. ##SUPPL##0##S1D, E##). RIG-I can be activated by double-stranded RNA in the absence of a 5′-triphosphate terminus [##REF##21947008##42##]; meanwhile, m⁵C-1291 was predicted to be located in the stem region of a folded 5′-UTR structure (nt 1250–1375 in the HBV genome) by RNA structure folding program (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.mfold.org/mfold/applications/rna-folding-form.php\">http://www.mfold.org/mfold/applications/rna-folding-form.php</ext-link>; ΔG = −36.40; Fig. ##SUPPL##0##S1F## and Table ##SUPPL##2##S2##). To explore whether m⁵C-1291 affects RIG-I recognition [##REF##25557055##36##], an RNA oligo pulldown assay with Huh7 cell extract containing endogenous RIG-I was performed using an RNA oligo (nt 1250–1329) derived from the 5′-UTR of the 0.7 kb mRNA. Unmodified RNA oligos exhibited a stronger interaction with RIG-I than m⁵C-modified RNA oligos (Fig. ##FIG##1##2J##). Collectively, these results indicate that m⁵C-1291 is important for viral RNA to escape RIG-I recognition.</p>", "<title>HBx interacts with EGR1 to downregulate NSUN2 promoter activity</title>", "<p id=\"Par12\">HBV does not encode methyltransferases. Thus, the expression of host m⁵C “writers,” NSUN2 and DNMT2, and “readers,” ALYREF and YBX1 were analyzed by Western blot [##REF##33438329##13##, ##REF##32303268##15##, ##REF##34631286##16##, ##REF##33461542##43##, ##REF##32210357##44##]. A decrease in NSUN2, DNMT2, and YBX1, and an increase in ALYREF were observed in HepG2.2.15 cells compared with parent HepG2 cells (Fig. ##FIG##2##3A##, left). The decrease in NSUN2 was not due to stable HBV expression from DNA integration in HepG2.2.15 cells, since this was also detected in HepG2-NTCP cells infected with HBV for 10 days (Fig. ##FIG##2##3A## middle and Fig. ##SUPPL##0##S2A##), and Huh7 cells transiently transfected with HBV 1.1-mer for 72 h (Fig. ##FIG##2##3A## right). The global m⁵C levels in Huh7 cells was also significantly reduced by HBV-1.1mer transfection. (Fig. ##FIG##2##3B##). Low NSUN2 expression was consistently observed in HBV patient samples with acute liver failure [##REF##23185381##45##] (Fig. ##SUPPL##0##S2B##), indicating that HBV infection reduces NSUN2 expression in both cell culture and clinical samples.</p>", "<p id=\"Par13\">To investigate which viral protein contributes NSUN2 downregulation, HBs HBc, and HBx were overexpressed in Huh7 cells, and endogenous NSUN2 expression was analyzed. HBx overexpression reduced NSUN2 mRNA (Fig. ##FIG##2##3C## and Fig. ##SUPPL##0##S2C, D##) and protein levels (Fig. ##FIG##2##3D##). Notably, HBx did not interact with NSUN2 in the co-immunoprecipitation (co-IP) assay (Fig. ##FIG##2##3E##) or affect the stability of NSUN2 mRNA in the RNA stability assay (Fig. ##SUPPL##0##S2E##).</p>", "<p id=\"Par14\">Considering that HBx is a well-studied transcriptional regulator of HBV infection [##REF##27084040##46##], we hypothesized that NSUN2 expression is transcriptionally regulated by HBx. To test this hypothesis, a ~2 kb DNA fragment containing the whole promoter of NSUN2 was inserted into luciferase reporter and the luciferase activities were evaluated using a dual-luciferase assay. Promoter activity was reduced by HBV 1.1-mer transfection or HBx expression (Fig. ##FIG##2##3F##). To explore the core promoter and cis-regulatory elements, promoter activities of the truncated sequence were tested. Although the −500 and −300 promoters exhibited similar activities (Fig. ##FIG##2##3G##), only the-500 promoter responded to HBx expression (Fig. ##FIG##2##3H##). Presumably, the promoter region between −500 nt and −300 nt contained HBx response elements. Moreover, based on our JASPAR database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://jaspar.genereg.net/\">https://jaspar.genereg.net/</ext-link>) analysis, EGR1, SP1, and ZNF148 may bind to two GC-enriched motifs (−476 to −463 and −350 to −333) in the NSUN2 promoter (Table ##SUPPL##3##S3##). EGR1, which interacts with HBx [##REF##8567959##47##], was identified as a transactivator of the NSUN2 promoter (Fig. ##FIG##2##3I##). EGR1 bound to the second GC-enriched motif via DNA oligo pulldown (Fig. ##FIG##3##4J##), while the expression and binding of EGR1 were decreased by HBx (Fig. ##FIG##3##4K##). Taken together, these data suggest that HBx suppresses NSUN2 promoter activity by interacting with EGR1 and preventing its binding to the NSUN2 promoter.</p>", "<title>NSUN2 functions as the methyltransferase of HBV m⁵C while suppressing HBV infection</title>", "<p id=\"Par15\">To explore which methyltransferase is responsible for the addition of m⁵C to HBV mRNAs, an RIP assay was performed to determine whether HBV mRNAs are associated with NSUN2 or DNMT2. HBV mRNAs co-immunoprecipitated with NSUN2, not DNMT2 (Fig. ##FIG##3##4A## and ##SUPPL##0##S3A##). The overall level of m⁵C in HBV mRNA was increased by <italic>NSUN2</italic> overexpression (Fig. ##FIG##3##4B##) and decreased by <italic>NSUN2</italic> knockdown in m⁵C-RIP assay (Fig. ##FIG##3##4C##). However, overexpression or knockdown of <italic>DNMT2</italic> did not impact m⁵C levels in HBV mRNA (Fig. ##SUPPL##0##S3B, C##). Moreover, the NSUN2 C321A mutant, which disrupts the transient covalent bond to cytosine [##REF##31415754##28##], failed to enhance HBV m⁵C levels compared with wild-type NSUN2 in m⁵C-RIP assay (Fig. ##FIG##3##4D##). In contrast to cytoplasmic replicating viruses [##REF##34225491##48##], nuclear localization of NSUN2 was not altered by transient HBV transfection (Fig. ##SUPPL##0##S3D##) or stable HBV ayw strain transfection (Fig. ##SUPPL##0##S3E##). Thus, NSUN2 directly binds to HBV mRNA to catalyze cytosine methylation in hepatocyte nuclei.</p>", "<p id=\"Par16\">Given that host RNA modification enzymes promote viral replication by modifying viral RNAs [##REF##31415754##28##, ##REF##27773535##49##–##REF##35971620##51##], the role of NSUN2 in the HBV life cycle was investigated. A significant reduction in HBeAg and HBsAg secretion was observed in cells overexpressing <italic>NSUN2</italic> (Fig. ##FIG##3##4E, F##). Core-associated DNA, including relaxed circular DNA, duplex-linear DNA, and single-stranded DNA, were suppressed by NSUN2 (Fig. ##FIG##3##4G##). Knockdown of endogenous NSUN2 using two shRNAs enhanced antigen secretion (Fig. ##FIG##3##4H, I##) and viral replication (Fig. ##FIG##3##4J##). Restoration of NSUN2 expression via transfection with shRNA-resistant cDNA reversed the enhanced antigen secretion (Fig. ##FIG##3##4K, L##) and viral replication (Fig. ##FIG##3##4M##). These data suggest that NSUN2 catalyzes HBV m⁵C addition, however, suppresses HBV replication.</p>", "<title>The delicate balance of NSUN2 expression inhibits IFN production</title>", "<p id=\"Par17\">To investigate the mechanism by which NSUN2 suppresses HBV replication, altered global m⁵C levels in host genes in HBV 1.1-mer-transfected cells were examined. We performed BS-Seq to analyze differentially methylated cellular RNAs. The sequencing data showed that the m⁵C modifications were primarily distributed in the 5′-UTR (Fig. ##FIG##4##5A##). Consistent with the globally reduced m⁵C levels (Fig. ##FIG##2##3B##), the average m⁵C density in CDS and 3′-UTR decreased following HBV 1.1-mer transfection (Fig. ##FIG##4##5A## and Table ##SUPPL##4##S4##). A total of 20,148 differentially methylated regions (DMRs) were identified (Table ##SUPPL##5##S5##), which were hierarchically clustered in a heat map (Fig. ##FIG##4##5B##). Moreover, the m⁵C levels were significantly altered in cellular RNA involved in innate immune responses, including those encoding IRF3, IFNB1, IFNAR1, IFNAR2, IFNGR2, and IFNGR1 (Table ##SUPPL##5##S5##).</p>", "<p id=\"Par18\">Given that the HBV-induced immune response correlates with RIG-I recognition [##REF##25557055##36##], we assessed the m⁵C densities of molecules related to RIG-I signaling, including RIG-I, MAVS, TRIM25, TBK1, IRF3, IFNA1, IFNA4, IFNB1, and IFNG. Notably, the m⁵C density in the 5′-UTR of IRF3 and the exon of IFNB1 was significantly decreased (Fig. ##FIG##4##5C##). Additionally, according to the m⁵C-RIP analysis, m⁵C levels were decreased in IFNA1 and IFNB1 RNAs (Fig. ##FIG##4##5D##). In addition, HBV 1.1-mer transfection inhibited poly I: C-induced IFNA1 and IFNB1 mRNA in qPCR assays (Fig.##FIG##4##5E##) and protein secretion in ELISA (Fig. ##FIG##4##5F##), which was associated with reduced RNA stability (Fig. ##FIG##4##5G, H##). These data imply that HBV transfection suppresses type I IFN production by reducing m⁵C levels and RNA stability.</p>", "<p id=\"Par19\">Negligible levels of type I IFN have been detected in patients with HBV; however, the mechanism associated with its downregulation is poorly understood [##REF##29445209##52##]. To explore the correlation between NSUN2 and inhibited IFN production, NSUN2 was depleted or overexpressed, followed by measurement of IFN production by ELISA and IFN expression by qPCR assay. As expected, NSUN2 knockdown decreased the poly I: C-induced IFN-α and IFN-α production (Fig. ##FIG##5##6A, B##). In contrast, overexpression of NSUN2 increased IFN-α and IFN-β production (Fig. ##FIG##5##6C, D##). NSUN2 depletion also significantly decreased virus-induced IFN production (Fig. ##FIG##5##6E##). Restoration of NSUN2 in HBV 1.1-mer-transfected cells rescued the inhibited IFN-α and IFN-β production (Fig. ##FIG##5##6F, G##), as well as the reduced ISGs (ISG20, TRIM14, CBFB, IFI6 and IFI27; Fig. ##FIG##5##6H##). Taken together, IFN-α and IFN-β production is closely correlated to the m⁵C levels of their mRNA and NSUN2 expression.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par20\">Host RNA modification enzymes are reportedly essential for viral replication and pathogenesis by modifying viral RNA [##REF##31415754##28##, ##REF##27773535##49##–##REF##35971620##51##]. In the present study, we found that NSUN2 plays an important role in the HBV life cycle (Fig. ##FIG##6##7##). NSUN2 expression is downregulated by HBx which decreases the binding of EGR1 to the NSUN2 promoter. NSUN2 catalyzes the addition of m⁵Cs in HBV mRNAs, and functional m⁵Cs promote HBV RNA export and translation while inhibiting the innate immune response by decreasing RIG-I binding. In contrast, decreased NUSN2 expression reduces m⁵Cs in IFN RNA, resulting in decreased IFN production. Thus, maintaining a delicate balance in NSUN2 expression during HBV infection is important for the viral life cycle.</p>", "<p id=\"Par21\">RNA modifications, including m⁶A, m⁵C, and ac4C, of viral RNA are indispensable for viral replication as they regulate viral RNA splicing, stability, and translation [##REF##31415754##28##, ##REF##35971620##51##]. Certain functional m⁵Cs were identified in HBV mRNA by DRS-seq and confirmed by BS-seq. These m⁵Cs have multiple roles in the HBV lifecycle. First, introducing mutations in HBV m⁵Cs abolishes viral replication and decreases antigen secretion. Second, HBV m⁵C modifications promote viral mRNA export by binding to ALYREF [##REF##32321818##53##]. Third, m⁵C-1291 in the 5′-UTR of the 0.7 kb mRNA promotes HBx translation, which further promotes HBV transcription and influences IFN production [##REF##26983541##24##–##REF##27459003##27##]. Finally, m⁵C-1291 attenuates the immune response by decreasing RIG-I binding to the 0.7 kb HBV mRNA. Owing to the importance of this single nucleotide in HBV infection, a specific targeting strategy combined with HBV therapy may improve the efficiency of HBV infection clearance.</p>", "<p id=\"Par22\">Host RNA modification enzymes are often elevated and hijacked by viral proteins to promote the infection [##REF##34225491##48##, ##REF##30104368##50##, ##REF##30463905##54##, ##REF##30364964##55##]. Depletion of the methyltransferase of m⁶A modification, METTL3, suppresses the production of EV71 [##REF##30364964##55##] and SARS-CoV-2 [##REF##34225491##48##] by disrupting viral RNA stability and translation. However, the expression of NSUN2 was downregulated in HBV-infected cell cultures and patient samples by HBx. To understand the cause of this discrepancy, genome-wide m⁵C levels in cellular RNAs were investigated in HBV DNA-transfected cells. HBV infection led to reduced m⁵C in IFN RNA and decreased IFN secretion, likely mediated by reduced NSUN2 expression. Thus, a balance in NSUN2 expression results in decreased m⁵C levels in IFN RNA, which appears necessary for the virus to complete its life cycle.</p>", "<p id=\"Par23\">NSUN2 expression was moderately downregulated by viral encoded HBx through inhibiting EGR1 binding to NSUN2 promoter. NSUN2 catalyzed the m⁵C addition to both HBV and IFN mRNAs. The repressed NSUN2 expression decreased m⁵C levels and RNA stabilities of IFN genes, which led to impair the immune responses; while the existing amount of NSUN2 was sufficient to catalyze the m⁵C addition in HBV mRNA, which promoted viral RNA exportation and translational efficiency but inhibited the RIG-I recognition of viral RNAs. Thus, we speculated the delicate balance in NSUN2 expression was important during HBV replication.</p>", "<p id=\"Par24\">In previous reports, increased methyltransferases were found to be post-translationally regulated by viral proteins [##REF##34225491##48##, ##REF##35971620##51##, ##REF##30364964##55##]. However, our data revealed a different mechanism of NSUN2 down-regulation during HBV infection, which was transcriptionally suppressed by HBx. We also identified an HBx response region in the NSUN2 promoter. Given that HBx is not a DNA-binding protein, interaction with other host factors or activation of signal transduction is necessary for HBx to target the NSUN2 promoter [##REF##35203390##56##]. In fact, DNA-binding proteins, including DDB1 [##REF##26983541##24##], CBFβ [##REF##33846566##57##], p53 [##REF##8134379##58##] and TFIIB [##REF##9488473##59##] interact with HBx. HBx also physically interacts with EGR1, EGR2, and EGR3, but only transactivates EGR2 and EGR3, not EGR1, by recruiting the coactivator CBP [##REF##15173177##60##]. In this study, we found that EGR1 transactivates the <italic>NUSN2</italic> promoter by binding to the second GC-rich motif while HBx interacts with EGR1 and inhibits its binding, resulting in suppressed <italic>NSUN2</italic> transcription.</p>", "<p id=\"Par25\">IFN production and signaling pathways are compromised by HBV infection [##REF##28665004##61##–##REF##16014900##64##], which may account for the failure of IFN-α therapy in many patients with chronic HBV infection [##REF##25034484##65##]. Here we demonstrated that NUSN2 positively regulates the expression of IFN-α and IFN-β production in HBV-infected cells. Thus, we hypothesize that HBV-mediated IFN inhibition occurs through the downregulation of NSUN2. In fact, restoring NSUN2 expression in HBV cell cultures rescued the inhibition of IFN production. However, the opposite function was recently reported for NSUN2; Zhang et.al. found that NSUN2 depletion transcriptionally upregulates polymerase (Pol) III-transcribed ncRNAs, which serve as RIG-I substrates to induce an IFN response in A549 cells. However, the mechanism of NSUN2-mediated transcriptional regulation is unclear [##REF##36240321##66##]. Considering that hepatocytes were used in the current study, we hypothesize that NUSN2-mediated innate immune responses differ in a cell context-dependent manner, however, this requires further confirmation.</p>", "<p id=\"Par26\">Although our data suggest that m⁵C is preferentially localized in the common region of the four HBV mRNAs, the sequencing reads in our current DRS were not sufficiently long to map all HBV transcripts. Accordingly, we were unable to distinguish transcript-specific m⁵Cs. Moreover, a previous report found that m⁵C modifications generated by NSUN2 are typically localized in GC-rich regions of mRNAs [##REF##28418038##14##], but no preferential sequences were identified around the m⁵C sites by our motif analysis. The motifs of NSUN2-mediated m⁵C modifications differ between ncRNAs and tRNA [##REF##23871666##67##, ##REF##17071714##68##]. Bohnsack et. al. reviewed the motif of NSUN2-mediated m⁵C modifications and proposed that NSUN2 targets the secondary structure of RNA substrates rather than a specific RNA sequence [##REF##30704115##22##]. This hypothesis is supported by the notion that NSUN2-mediated m⁵C₃₄ is dependent on the elongated anticodon stem structure of pre-tRNALeu [##REF##17071714##68##]. Although this study provides valuable insights into the role of m⁵C and NSUN2 in HBV pathogenesis, their precise functions require further investigation in animal models and clinical patient cases [##REF##34777385##69##–##REF##34896285##71##].</p>", "<p id=\"Par27\">In summary, m⁵Cs and the host methyltransferase NSUN2 are key factors in HBV-mediated IFN inhibition, indicating that they are promising targets for the development or improvement of HBV therapy.</p>" ]

[]

[ "<p id=\"Par1\">Eukaryotic five-methylcytosine (m⁵C) is an important regulator of viral RNA splicing, stability, and translation. However, its role in HBV replication remains largely unknown. In this study, functional m⁵C sites are identified in hepatitis B virus (HBV) mRNA. The m⁵C modification at nt 1291 is not only indispensable for Aly/REF export factor (ALYREF) recognition to promote viral mRNA export and HBx translation but also for the inhibition of RIG-I binding to suppress interferon-β (IFN-β) production. Moreover, NOP2/Sun RNA methyltransferase 2 (NSUN2) catalyzes the addition of m⁵C to HBV mRNA and is transcriptionally downregulated by the viral protein HBx, which suppresses the binding of EGR1 to the NSUN2 promoter. Additionally, NSUN2 expression correlates with m⁵C modification of type I IFN mRNA in host cells, thus, positively regulating IFN expression. Hence, the delicate regulation of NSUN2 expression induces m⁵C modification of HBV mRNA while decreasing the levels of m⁵C in host IFN mRNA, making it a vital component of the HBV life cycle. These findings provide new molecular insights into the mechanism of HBV-mediated IFN inhibition and may inform the development of new IFN-α based therapies.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41419-023-06412-9.</p>", "<title>Acknowledgements</title>", "<p>This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences [XDB0490000], National Natural Science Foundation of China [31970168], Key R&amp;D Program of Hubei Province [2021BCD004], Hubei Science and Technology Major Project [2021ACB004], Wuhan Knowledge Innovation Special Project [2023020201020303] and Emergency Key Project of Guangzhou Laboratory [EKPG21-30-2]. Total RNA isolated from HBV AAV-HBV transduced mouse liver was kindly provided by Dr. Yuchen Xia (TaiKang Medical School, Wuhan University).We thank the Core Facility and Technical Support in the Wuhan Institute of Virology (WIV), Chinese Academy of Sciences (CAS), especially Lei Zhang and Ding Gao, for their assistant with ultracentrifugation and confocal microscopy.</p>", "<title>Author contributions</title>", "<p>SD, HL, FZ, and WG designed research; SD, ZC, MZ, Lishi Liu, XZ, HH and Z performed research; SD, HL, Lijuan Liu, LM, FH, FZ, and WG analyzed data; and SD, HL, FZ, and WG wrote the paper. All authors commented on the manuscript.</p>", "<title>Data availability</title>", "<p>All data generated or analyzed during this study are included in this published article and its ##SUPPL##0##supplementary information## files.</p>", "<title>Competing interests</title>", "<p id=\"Par49\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Identification of m⁵C in HBV mRNA essential for viral replication.</title><p><bold>A</bold> Total level of HBV m⁵C quantified by m⁵C-RIP. HBV RNA transcripts were immunoprecipitated by m⁵C specific antibody in HepG2.2.15 cells stably transfected with HBV genomic DNA. The enriched HBV RNA was then measured by qPCR with primers targeting the 3′-UTR. <bold>B</bold> Top panel: rate of each m⁵C site, named according to HBV genomic position, quantified by Direct-RNA sequencing with purified polyA+ RNAs from HepG2.2.15 cells or AAV-HBV transduced mouse liver. Identified m⁵C sites with a rate &gt; 90% in two independent experiments with HepG2.2.15 cells are labeled in red, while those with a rate &gt; 90% in one experiment were labeled in green or blue. The m⁵C sites with a rate &gt; 90% identified in AAV-HBV transduced mouse liver were labeled in yellow. Bottom panel: distribution of four confident m⁵C locations (color dots) in HBV RNA transcripts. Four major transcripts from HBV genome with coding potentials are shown. <bold>C</bold> m⁵C motif predicted by MEME [##REF##19458158##40##]. <bold>D</bold>–<bold>G</bold> HBV m⁵Cs are essential for viral replication. The table shows point mutations introduced to each m⁵C and the altered amino acids in proteins. <bold>D</bold> M-ALL mutant containing all m⁵C mutations. Huh7 cells were transfected with HBV 1.1-mer wild-type or mutants. The core-associated DNA was detected by Southern blot using a probe spanning from nt 1 to nt 3182 at 72 h post-transfection. <bold>E</bold> RC relaxed circular DNA, DL duplex-linear DNA, SS single-stranded DNA. Secretion of HBeAg (<bold>F</bold>) and HBsAg (<bold>G</bold>) in cell culture supernatant quantified by ELISA at 72 h post-transfection.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>HBV m⁵C-1291 promotes viral RNA export and translation and prevents RIG-I recognition of viral RNA.</title><p><bold>A</bold> HBV transcripts are associated with ALYREF. Huh7 cells were transfected with Flag-ALYREF and then with HBV 1.1-mer at 24 h post-transfection. HBV transcripts were immunoprecipitated by anti-Flag antibody at 48 h post-transfection. The enriched HBV RNA was measured by qPCR (<bold>A</bold> top). Immunoprecipitated ALYREF examined by western blot. (<bold>A</bold> bottom). <bold>B</bold> ALYREF promotes HBV RNA export. Subcellular distribution of HBV transcripts in the cytoplasmic and nuclear fractions examined by qPCR after overexpression of ALYREF for 48 h (<bold>B</bold> top panel). ALYREF expression examined by western blot (B, bottom). <bold>C</bold>–<bold>E</bold> The m⁵C-1291 promotes 0.7 kb mRNA export. A point mutation of C1291T is shown, which was introduced to m⁵C-1291 in the cDNA reporter of HBV 0.7 kb mRNA (<bold>C</bold> bottom). Huh7 cells were co-transfected with Flag-ALYREF, and cDNA of 0.7 kb mRNA-wt or 0.7 kb mRNA-mt for 48 h, respectively. Subcellular distribution of 0.7 kb mRNA-wt or 0.7 kb mRNA-mt were examined as described in (<bold>B</bold>) (<bold>C</bold> top). HBV 0.7 kb mRNA wt or mt were then immunoprecipitated by anti-Flag antibody against Flag-ALYREF and measured by qPCR (<bold>D</bold>). <bold>E</bold>–<bold>G</bold> The m⁵C-1291 promotes 0.7 kb mRNA translation. Huh7 cells were transfected with cDNA of 0.7 kb mRNA-wt or 0.7 kb mRNA-mutant for 48 h. Cell lysates were hyper-centrifuged in a sucrose gradient after cycloheximide treatment, and RNA was extracted from the layer with maximum absorbance at OD260. Ribosome-associated HBV 0.7 kb mRNA was assessed by qPCR (<bold>F</bold>). GAPDH was used as a control (<bold>E</bold>). The 5′-UTR of 0.7 kb mRNA-wt or 0.7 kb mRNA-mt were fused to firefly luciferase (Fluc) reporter, respectively (<bold>G</bold> bottom). Huh7 cells were transfected with wild-type or mutant 5′-UTR Fluc reporter. The relative luciferase activities were calculated by dual luciferase assay at 24 h post-transfection (<bold>G</bold> top). Renilla luciferase (Rluc) served as an internal control. (<bold>H</bold>) HBV m⁵C mutants increase IFN-β mRNA expression. Huh7 cells were co-transfected with poly I:C and HBV 1.1-mer wild type or mutants. The expression of IFN-β was assessed by RT-qPCR at 18 h post-transfection. (<bold>I</bold>) Expression of five ISGs assessed by RT-qPCR at 18 h post-transfection. <bold>J</bold> The m⁵C-1291 blocks RIG-I recognition. RNA-oligo pulldown was performed with huh7 cell lysate using biotin-labeled oligos, which contained m⁵C-1291, m⁵C-1255, or non-m⁵C, respectively. The pulled-down proteins were immunoblotted by anti-RIG-I antibody. Pull down without oligos (Beads) served as the control. The bar represents the mean from three independent experiments. ***<italic>P</italic> &lt; 0.001; **<italic>P</italic> &lt; 0.01; *<italic>P</italic> &lt; 0.05.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>HBV infection downregulates NSUN2 expression through HBx, EGR1, and SP1.</title><p><bold>A</bold> HBV infection downregulates NSUN2 expression. The endogenous expression of NSUN2, DNMT2, ALYREF, and YBX1 quantified by western blot in HepG2.2.15 cells or HepG2 cells (<bold>A</bold> left), HepG2-NTCP cells with or without HBV infection for 7 days (A middle), and Huh7 cells transiently transfected with HBV 1.1-mer or control vector for 72 h (<bold>A</bold> right). <bold>B</bold> The global m⁵C levels in Huh7 cells transiently transfected with HBV 1.1-mer or control vector for 72 h were examined by m⁵C dot blot. Methylene blue staining served as the RNA loading control. <bold>C</bold>, <bold>D</bold> Viral protein, HBx is responsible for NSUN2 downregulation by HBV infection. Huh7 cells were transfected with Flag-HBx or flag vector, respectively. Transfection reagent served as the MOCK control. The endogenous RNA level of NSUN2 was quantified by qPCR at 24 h post-transfection. GAPDH was used as an internal control (<bold>C</bold>). The expression of NSUN2 protein and exogenous HBx protein were accessed by western blot, and GAPDH served as the loading control (<bold>D</bold>). <bold>E</bold> Huh7 cells were co-transfected with HA-HBx and Flag-NSUN2. Co-IP with an anti-Flag was performed 48 h post-transfection. HBx protein was immunoblotted with an anti-HA. <bold>F</bold> HBV transfection or HBx expression suppresses NSUN2 promoter activity. A 2-kb DNA fragment (−1900 to +100) of the NSUN2 promoter was fused to Firefly luciferase (Fluc) reporter. Fluc reporter was co-transfected with the control vector, HBV 1.1-mer, flag vector, or Flag-HBx in Huh7 cells. The promoter activity was determined by dual luciferase assay 24 h post-transfection. Renilla luciferase (Rluc) served as a promoter control. <bold>G</bold> Mapping of the core promoter by 5′-end deletions in the Fluc reporter. The Huh7 cells were transfected with truncated Fluc reporter. The promoter activity was determined by dual luciferase assay at 24 h post-transfection. (<bold>H</bold>) Identification of HBx response region in the NSUN2 promoter. Two truncated Fluc reporters, −500 or −300 were co-transfected with Flag-HBx or flag vector in Huh7 cells. The promoter activity was determined by dual luciferase assay as above. <bold>I</bold> Fluc reporter was co-transfected with Flag vector or Flag-EGR1 in Huh7 cells. The promoter activity was determined by dual luciferase assay 24 h post-transfection. <bold>J</bold> Biotinylated double-stranded WT or MT oligos contained EGR1 or mutated motif, respectively. The pulled-down EGR1 protein by WT or MT oligos was accessed by western blot. The oligo containing YY1 motif served as the positive control. <bold>K</bold> Oligo pulled down was performed using cell lysates from Huh7 cells transfected with Flag-HBx or flag vector, respectively. EGR1 protein was accessed by western blot. The bar represents the mean from three independent experiments. ***<italic>P</italic> &lt; 0.001; **<italic>P</italic> &lt; 0.01; *<italic>P</italic> &lt; 0.05.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>NSUN2 is the methyltransferase of HBV m⁵C and suppresses HBV infection.</title><p><bold>A</bold>–<bold>D</bold> NSUN2 serves as the methyltransferase of HBV m⁵C. <bold>A</bold> NSUN2 was associated with HBV mRNA. Huh7 cells were transfected with Flag-NSUN2 and HBV-1.1mer. HBV mRNA were then immunoprecipitated by Flag antibody and measured by qPCR at 48 h post-transfection (<bold>A</bold> top). The immunoprecipitated NSUN2 was examined by western blot (<bold>A</bold> bottom). Overexpression of NSUN2 enhanced the total level of HBV m⁵C determined by m⁵C-RIP (<bold>B</bold>). Knock-down of NSUN2 by two specific shRNAs decreased the total level of HBV m⁵C determined by m⁵C-RIP (<bold>C</bold>). Mutant NSUN2 (C321A) could not increase the level of HBV m⁵C modification compared to wild-type NSUN2 (D). <bold>E</bold>–<bold>G</bold> Overexpression of NSUN2 suppressed HBV antigen secretion and replication. Transfection with flag-NSUN2 and HBV 1.1-mer in Huh7 cells were performed as above. Secretion of viral proteins, HBeAg (<bold>E</bold>) and HBsAg (<bold>F</bold>), in cell culture supernatant were quantified by ELISA at 72 h post-transfection. The core-associated DNA was detected by Southern blot using a probe spanning nt 1 to nt 3182 at 72 h post-transfection (<bold>G</bold>). RC relaxed circular DNA; DL duplex-linear DNA; SS single-stranded DNA. <bold>H</bold>–<bold>J</bold> Knock-down of NSUN2 promotes HBV replication and antigen secretion. NSUN2 was knocked down by two shRNAs as described above. The secretion of HBeAg (<bold>H</bold>) and HBsAg (<bold>I</bold>), and the core-associated DNA (<bold>J</bold>), were examined. (<bold>K</bold>–<bold>M</bold>) Restoration of NSUN2 in NSUN2 knock-down cells reduces the enhanced HBV infection. Huh7 cells expressing NSUN2 shRNAs were transfected with shRNA-resistant NSUN2 cDNA by introducing mutations at shRNA seed regions. The secretion of HBeAg (K) and HBsAg (<bold>L</bold>), and the core-associated DNA (<bold>M</bold>), were examined as above. ***<italic>P</italic> &lt; 0.001; **<italic>P</italic> &lt; 0.01; *<italic>P</italic> &lt; 0.05.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>HBV infection decreases m⁵C level in IFN-related genes.</title><p><bold>A</bold>–<bold>C</bold> BS-seq was performed with total RNA isolated from Huh7 cells transfected with HBV 1.1-mer at 18 h post-transfection. The average m⁵C density in each gene structure, 5′-UTR, CDS and 3′-UTR was calculated in HBV 1.1-mer transfected or un-transfected cells (<bold>A</bold>). The heatmap shows the differentially methylated region identified in six samples (B). The line graph shows the m⁵C density in each gene structure, promoter, 5′-UTR, exon, intron, 3′-UTR and downstream of several genes related to RIG-I signaling (RIG-I, MAVS, TRIM25, IRF3, and IFNB1) (<bold>C</bold>). <bold>D</bold> validation of the m⁵C level of genes related to RIG-I signaling by m⁵C-RIP assay in HBV 1.1-mer transfected or un-transfected cells. <bold>E</bold>–<bold>H</bold> HBV 1.1-mer transfection inhibits poly I:C induced IFN-α and IFN-β production. Huh7 cells were transfected with poly I:C and HBV 1.1-mer, or poly I:C and control vector for 18 h, respectively. The production (<bold>E</bold>) and mRNA expression (<bold>F</bold>) of IFN-α and IFN-β were assessed by qPCR or ELISA, respectively. The RNA stability of IFNA1 (<bold>G</bold>) and IFNB1 (<bold>H</bold>) RNA was reduced by HBV-1.1 mer transfection. ***<italic>P</italic> &lt; 0.001; **<italic>P</italic> &lt; 0.01; *<italic>P</italic> &lt; 0.05.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>NSUN2 is a positive regulator in poly I:C-induced IFN-α and IFN-β production.</title><p><bold>A</bold>, <bold>B</bold> Knock-down of NSUN2 decreases poly I:C-induced IFN-α and IFN-β production. The NSNUN2 or NC shRNA stably expressing cells were treated with poly I:C for 18 h. The protein (<bold>A</bold>) and mRNA expression (<bold>B</bold>) of IFN-α and IFN-β were assessed by ELISA or qPCR, respectively. <bold>C</bold>, <bold>D</bold> Overexpression of NSUN2 increases poly I:C-induced IFN-α and IFN-β production. Huh7 cells were transfected with poly I:C and Flag-NSUN2, or poly I:C and flag vector for 18 h. The protein (<bold>C</bold>) and mRNA expression (<bold>D</bold>) of IFN-α and IFN-β were assessed. <bold>E</bold> NSUN2 positively regulates IFN-β expression in uninfected, EV71-infected, and VSV-infected cells. Huh7 cells were infected with EV71 or VSV, or without virus for 24 h, and IFN-β mRNA expression was assessed. <bold>F</bold>–<bold>H</bold> HBV-mediated IFN inhibition is dependent on NSUN2. Poly I:C was co-transfected with the control vector, HBV 1.1-mer, and flag vector, or HBV 1.1-mer and Flag-NSUN2 in Huh7 cells for 18 h. The protein (<bold>F</bold>) and mRNA expression (<bold>G</bold>) of IFN-α and IFN-β were assessed. The expression of several ISGs was accessed by qPCR (<bold>H</bold>). ***<italic>P</italic> &lt; 0.001; **<italic>P</italic> &lt; 0.01; *<italic>P</italic> &lt; 0.05.</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><title>Proposed model of how HBV regulates the host RNA methyltransferase NSUN2 to facilitate its replication.</title><p>During the HBV infection, NSUN2 is transcriptionally repressed by HBx through inhibition of EGR1 binding to its promoter in the nucleus. The reduced NSUN2 catalyzes m⁵C modifications in HBV mRNAs to promote viral RNA export. However, the m⁵C modifications in the RNAs of IFN-α and IFN-β were decreased due to the repressed level of NSUN2. After the viral and cellular mRNAs are delivered into cytosol, HBV m⁵Cs promote viral RNA translation and inhibit RIG-I recognition. The reduced m⁵Cs in IFN-α and IFN-β RNAs result in low expression of IFN-α and IFN-β, which ultimately leads to efficient HBV replication.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM5\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM6\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM7\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM8\"></supplementary-material>" ]

[ "<fn-group><fn><p>Edited by Professor Mauro Piacentini</p></fn><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Shuang Ding, Haibin Liu.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41419_2023_6412_Fig1_HTML\" id=\"d32e624\"/>", "<graphic xlink:href=\"41419_2023_6412_Fig2_HTML\" id=\"d32e812\"/>", "<graphic xlink:href=\"41419_2023_6412_Fig3_HTML\" id=\"d32e1000\"/>", "<graphic xlink:href=\"41419_2023_6412_Fig4_HTML\" id=\"d32e1150\"/>", "<graphic xlink:href=\"41419_2023_6412_Fig5_HTML\" id=\"d32e1346\"/>", "<graphic xlink:href=\"41419_2023_6412_Fig6_HTML\" id=\"d32e1461\"/>", "<graphic xlink:href=\"41419_2023_6412_Fig7_HTML\" id=\"d32e1501\"/>" ]

[ "<media xlink:href=\"41419_2023_6412_MOESM1_ESM.pdf\"><caption><p>Suplementary Imformation</p></caption></media>", "<media xlink:href=\"41419_2023_6412_MOESM2_ESM.xlsx\"><caption><p>Table S1</p></caption></media>", "<media xlink:href=\"41419_2023_6412_MOESM3_ESM.xlsx\"><caption><p>Table S2</p></caption></media>", "<media xlink:href=\"41419_2023_6412_MOESM4_ESM.xlsx\"><caption><p>Table S3</p></caption></media>", "<media xlink:href=\"41419_2023_6412_MOESM5_ESM.xlsx\"><caption><p>Table S4</p></caption></media>", "<media xlink:href=\"41419_2023_6412_MOESM6_ESM.xls\"><caption><p>Table S5</p></caption></media>", "<media xlink:href=\"41419_2023_6412_MOESM7_ESM.pdf\"><caption><p>Original Data File</p></caption></media>", "<media xlink:href=\"41419_2023_6412_MOESM8_ESM.pdf\"><caption><p>aj-checklist-CDDIS-23-3260-T</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Radioactivity Laboratory (RadioLab) is an Italian outreach project, carried on by the National Institute of Nuclear Physics (INFN) and designed to provide a tool that can be used at school level for scientific dissemination about environmental radioactivity^{##UREF##0##1##, ##UREF##1##2##}. The project was born, more than a decade ago, from the consideration and observation that the human subjective perception of risk almost always does not coincide with the real risk, since everything that is not well known generates stress and anxiety, and, hence, perception of risk and danger. This aspect is particularly evident with the radioactivity issue. Strengthened by these assumptions, the basic idea of RadioLab is to bring the new generations (young people attending school), and indirectly the rest of the population, closer to the theme of ionizing radiation and the effects on human health^{##UREF##2##3##}. This goal is achieved by several progressive activities, which include administration of surveys to assess the background knowledge, preparatory lessons on environmental radioactivity and its monitoring, laboratory sessions to carry out measurements, study sessions to handle the data with analysis and presentation of the results^{##UREF##3##4##}. By means of these activities, school students are offered the opportunity to approach the world of scientific research, and become familiar with the use of detectors for ionizing radiation. Scientific communication, teaching and scientific research are integrated through the implementation of orientation training actions in a process that follows the phases of a scientific research work^{##UREF##4##5##}. The activities carried out by the students within the project also promote the acquisition of transversal skills by developing their analytical skills, their ability to analyze and outline real situations, to manage information and to disseminate them^{##UREF##5##6##}. The INFN sections directly involved in the RadioLab project are: Napoli, Milano, Cagliari, Cosenza, Lecce, Padova, Pisa, Torino, Trieste, Catania (until 2019). These sections collaborate with the regional schools, performing the goal activities, and also involving the population. Furthermore, RadioLab aims to spread in the regions close to the ones where the involved INFN sections are present. RadioLab pursues the common objective in all INFN sections that, however, have their own autonomy in declining the various activities of the project, according to the instrumentation at disposal and/or the particular local skills.</p>", "<p id=\"Par3\">In the context of the RadioLab project, the issue of radioactive gas radon and its measurement is explored. Nowadays radon is highly topical, especially after the promulgation of the new Italian Legislative Decree 101/2020^{##UREF##6##7##} in the field of radioprotection, which is the transposition of the European Directive 2013/59/Euratom^{##UREF##7##8##}. Radon (²²²Rn) is a radioactive natural gas, arising from the decay chain of ²³⁸U, which is present throughout the Earth’s crust. This gas is by far the most important source of ionizing radiation among the sources of natural origin, and radon is well-known to be the main cause of lung cancer just after cigarette smoking. Although RadioLab has been implemented for more than a decade, only recently (since 2018) a systematic monitoring activity about the knowledge of the problems related to radon exposure in closed environments has been introduced. The first activity used to assess the awareness on the radon issue is the administration of the survey “do you know the radon gas?”, in which questions about radon knowledge are proposed to the interviewees. The survey is intended not only for school-age people but also for their relatives, the school workers and the public; hence, an online version and a printed version exist, which are administered during exhibitions or outreach events. The results of the survey performed nationwide in Italy, together with a deep statistical analysis, are reported in this paper.</p>" ]

[ "<title>Materials and methods</title>", "<title>Structure of the survey</title>", "<p id=\"Par4\">Surveys are effective tools for gathering and synthesizing information in a compact way that can be easily managed for successive appropriate analysis^{##UREF##8##9##}. On the other hand, surveys can be difficult to implement as a long time can be needed to get enough statistics. The survey “do you know the radon gas?” has been adopted to monitor the knowledge of radon gas in Italy, and its structure is reported in Table ##TAB##0##1##: the knowledge of radon and of its sources together with information on personal, cultural and territorial details of the interviewees are catched. In particular, the questions are: (1) ‘date of the survey’, used to obtain a trend on the radon knowledge over the years (from 2018 to 2022); (2) ‘scenario where the survey was done’, used to obtain information about the dissemination activity (event; online; school/university); (3) ‘home city of the interviewee’, used to map the data; (4) ‘gender of the of interviewee’, used to evaluate the distribution of the survey between males and females; (5) ‘age of the of interviewee’, used to evaluate the distribution of the survey among school population (&lt; 19), university age range (19–30), adulthood range (30–50), adult and senior population (&gt; 50); (6) ‘education level of the interviewee’, used to correlate the knowledge and background on the radon issue; (7) ‘do you know radon?’, i.e. the main question of the survey about the knowledge of radon gas; (8) ‘if you know radon, please add the knowledge source’, used to establish the way in which the knowledge of the radon issue is achieved and to evaluate the effectiveness of RadioLab; (9) ‘do you think a radon measurement in your city is urgent?’, used to evaluate the risk perception of radon. The survey is in dual form: online (web.infn.it/RadioLAB/) and printed. It is administered during exhibitions or outreach events, summer/spring workshops, dissemination events like the European Researchers' Night and the European Radon Day, and seminars in universities and schools^{##UREF##9##10##, ##UREF##10##11##}. These modalities are mainly addressed to school-age population, but the implementation of such methodology also leads to the spread of the survey even outside the school environment. In fact, students continue to administer the survey interviewing other peers, family members, friends, and acquaintances. In this regards, the online version of the survey is of great help, allowing to carry it out comfortably from home, at work or anywhere. A QR-code has also been generated, allowing the easy compilation of the survey on the smartphones. The administration of the survey is approved by the INFN and the informed consent was obtained from all involved subjects.</p>", "<title>Data management and analysis</title>", "<p id=\"Par5\">The total number of collected surveys are 29,106. About the 1.7% of the data (494) had anomalies linked to the incorrect filling of the survey by interviewees, for instance interviewees with age &lt; 19 stating to have university degree, or interviewees saying they do not know what radon is but add newspaper/tv/web as source of knowledge. These inconsistent 494 surveys have been excluded. The final analysed dataset consists of 28,612 entries, covering the five-year period 2018–2022 and involving all twenty Italian regions. On these data, both qualitative and quantitative statistical analyses have been performed. The qualitative description of the dataset reports: (i) the number of surveys per region; (ii) the amount of male and female involved, grouped by age and education level; (iii) the number of survey sorted by ‘scenario where the survey was done’; (iv) the number of surveys per year. The quantitative analysis of the dataset reports several bar graphs, combining together two and/or three questions of the survey. The first set shows bar graphs of the answers from the main question ‘do you know radon?’ matched with: (i) the gender and age of the interviewees; (ii) the education level of the interviewees; (iii) the age of the interviewees and the source of their knowledge if they know what radon gas is. The second set shows bar graphs of the answers from the question ‘do you think a radon measurement in your city is urgent?’ matched with: (i) the age of the interviewees; (ii) the education level of the interviewees. The quantitative statistical analysis is concluded by: (i) the bar graph of the answers from the main question ‘do you know radon?’ matched with the answers from the question ‘do you think a radon measurement in your city is urgent?’; (ii) the trend per age of the interviewees who know radon during the years of administration of the survey (2018–2022).</p>", "<title>Human ethics</title>", "<p id=\"Par6\">All experiments were performed in accordance with the current and relevant guidelines and regulations in in force; the administration of the survey was approved by the INFN; the informed consent was obtained from all involved subjects.</p>" ]

[ "<title>Results and discussion</title>", "<title>Qualitative analysis of the data</title>", "<p id=\"Par7\">The ten Italian regions in dark blue in Fig. ##FIG##0##1## (Campania, Lombardia, Sardegna, Calabria, Puglia, Veneto, Toscana, Piemonte, Friuli-Venezia Giulia, Sicilia), i.e. those with more than 150 surveys administered, correspond to the ten regions in which the INFN sections directly involved in the RadioLab project (Napoli, Milano, Cagliari, Cosenza, Lecce, Padova, Pisa, Torino, Trieste, Catania) are located. The regions in light blue in Fig. ##FIG##0##1## (Valle d’Aosta, Trentino-Alto Adige, Liguria, Marche, Emilia-Romagna, Umbria, Abruzzo, Molise), in which no INFN sections are directly involved, carried out the administration of less than 100 surveys. This aspect demonstrates the spread of RadioLab in dissemination of scientific culture on the theme of environmental radioactivity, in particular related to the knowledge of radon gas. It is interesting to note the case of the two regions in sky-blue in Fig. ##FIG##0##1##, which, with 144 (Basilicata) and 149 (Lazio) surveys administered, are affected by a greater influence due to the neighboring regions in which INFN sections are present. Campania region administered the highest number of surveys (14,972), followed at a considerable distance by Toscana (3373) and Calabria (3062).</p>", "<p id=\"Par8\">From Fig. ##FIG##1##2## is evident that an almost perfect gender balance is present, both among the various age groups and among the education level groups. The highest percentage of interviewees (49%) regards young people (&lt; 19), and it decreases as the age increases (Fig. ##FIG##1##2##a). This aspect is due to the fact that RadioLab is mainly designed for school-age interviewees, and it is confirmed, as can be seen in Fig. ##FIG##1##2##b, by the fact that primary/middle school diploma is the most frequent education level (59%). The amount of the interviewees decreases with the increase in the education level (Fig. ##FIG##1##2##b).</p>", "<p id=\"Par9\">The survey “do you know the radon gas?”, being the easiest way, has been carried out mostly in online mode (57%), then at scientific events (23%) and at schools/universities (20%) during seminars (Fig. ##FIG##2##3##a). In the time frame of the administration of the survey “do you know the radon gas?”, most of the entries (46%) have been gathered in the year 2020. Such high value is actually explicable by the promulgation in 2020 of the D.lgs 101^{##UREF##6##7##} implementation of the 2013/59/Euratom^{##UREF##7##8##}, which establishes the basic safety standards relating to protection against the risk arising from exposure to ionizing radiation. In particular, the radon exposure topic is addressed by proposing a national radon action plan and fixing a reference level of 300 Bq/m³. With the D.lgs 101/2020, a great attention of public opinion has been given to radon issue, and, thus, this fact explains the increase in filling up the survey “do you know the radon gas?” in 2020^{##REF##34201142##12##}. The early years 2018 (14%) and 2019 (27%) were also productive, testifying the growing interest in radon issue (Fig. ##FIG##2##3##b). The years 2021 (3%) and 2022 (10%) show a notable decrease in performing the survey, mainly due to the peak period of the COVID-19 pandemic^{##UREF##11##13##} (Fig. ##FIG##2##3##b).</p>", "<p id=\"Par10\">A more detailed analysis has been done in Fig. ##FIG##3##4## concerning the percentage per year of question ‘scenario where the survey was done’. Firstly, Fig. ##FIG##3##4## highlights the in-presence modalities (events and at schools/universities) for carrying out the survey as the main ways used in the initial years, before the COVID-19 disease: 2018 with 69%, increasing in the 2019 with 87%. From 2020 to 2022, due to COVID-19, the predominant mode for carrying out the survey is the online one, with about 83% in 2020 and 2021, up to 95% in 2022^{##UREF##11##13##}.</p>", "<p id=\"Par11\">Overall qualitative analysis denotes the statistically significance of the used sample.</p>", "<title>Quantitative analysis of the data</title>", "<p id=\"Par12\">A deep quantitative statistical analysis on the 28,612 data resulting from the survey “do you know the radon gas?” is presented in the following. In total, 39% of interviewees declare to know radon gas. Figure ##FIG##4##5## reports the percentage per gender of the interviewees who know or do not know the radon gas, combined with the age. This analysis underlines several aspects: (i) the male are more informed about radon (male 40% and 37% female, on average); (ii) the difference between male and female about the knowledge of radon is slight in the age groups of 19–30, 30–50, &gt; 50 (~ 3%), while it is more marked in the age &lt; 19 (7%); (iii) the knowledge of radon is nearly constant in the age groups of 19–30, 30–50, &gt; 50 (~ 45%), with a clear decrease in younger age &lt; 19 (~ 32%)^{##UREF##12##14##}.</p>", "<p id=\"Par13\">Figure ##FIG##5##6## reports the percentage per education level of the interviewees who know or do not know the radon gas. This analysis highlights the evident influence of the education level in the knowledge of radon issue: the interviewees who know radon grow with increasing education level^{##UREF##13##15##}. In particular: (i) the number of interviewees who know radon having high school diploma is slightly higher than the one of those having primary/middle school diploma (difference of 2%); (ii) most of interviewees having the highest level of education, i.e. university degree, know radon (56%), exceeding the two lower levels of education by more than 20%.</p>", "<p id=\"Par14\">Figure ##FIG##6##7## reports the percentage per source of radon knowledge for interviewees who declare to know the gas, combined with their age. This analysis reveals that interviewees who know radon gas: (i) from projects decrease with the age increase (from 31 to 17%); (ii) from newspapers/tv/web increase with the age increase (from 26 to 43%); (ii) from exhibitions or orientation events and other sources are costant (~ 5% event, ~ 37% other). Projects are mostly widespread in the school-age population (&lt; 19), indeed RadioLab is mainly designed for students and raised awareness in the theme of radon gas. Older people mention newspapers/tv/web as the most popular media source of knowledge of radon gas.</p>", "<p id=\"Par15\">Figure ##FIG##7##8## reports the percentage per age of the interviewees who consider the three options for a radon measurement in their city: urgent, not urgent, do not know. This analysis shows: (i) deeming it urgent, or not knowing whether it is urgent increases as respondents age; (ii) deeming a radon measurement in their city not urgent decreases as the age of interviewees increases. Awareness of radon issue increases in adulthood, being aware about the potential risk of radon^{##UREF##12##14##}.</p>", "<p id=\"Par16\">Figure ##FIG##8##9## reports the percentage per education level of the interviewees who consider the three options for a radon measurement in their city: urgent, not urgent, do not know. This analysis highlights: (i) deeming it urgent, or not knowing whether it is urgent increases as the education level of interviewees; (ii) deeming a radon measurement in their area not urgent decreases as the education level of interviewees increases. Similar considerations drawn from Fig. ##FIG##7##8## can be transposed to Fig. ##FIG##8##9##, showing that the awareness of radon issue increases with the education level. Joining together the results from Figs. ##FIG##7##8## and ##FIG##8##9##, it emerges that the knowledge of the problems related to radon exposure in environments is strongly linked to the education level of the people, and hence, to their age^{##UREF##12##14##, ##UREF##13##15##}. However, it is interesting to note that the percentage of people who do not consider urgent a radon measurement in their city is always less than a half of each group of interviewees by age and by education level.</p>", "<p id=\"Par17\">The last part of the quantitative statistical analysis is reported in the last two figures, i.e. Figures ##FIG##9##10## and ##FIG##10##11##. Figure ##FIG##9##10## represents the bar graph of the answers to the main question ‘do you know radon?’, matched with the answers from the question ‘do you think a radon measurement in your city is urgent?’. Most of the interviewees familiar with the topic of radon reply that gas measurement is urgently needed (51%), while the minority of the interviewees is divided almost equally between those who doubt and those who are not concerned about the radon measurement. The situation is completely different when the interviewees are those who are not familiar with the radon issue: (i) half of them is unsure whether or not a measure of radon in their city is urgent (50%); (ii) the other half is divided into 30% of people who do not want to measure radon in their city, and 20% who want to measure it. This is significant of the fact that the knowledge of a topic, whatever it may be (in this case radon), increases awareness of it and everything related to it (in the case of radon: risk perception), while ignorance on a topic tipically generates insecurity and uncertainty^{##UREF##14##16##}.</p>", "<p id=\"Par18\">Figure ##FIG##10##11## represents the trend by age of the interviewees about the knowledge of radon during the years of administration of the survey “do you know the radon gas?”, from 2018 to 2022. The knowledge of radon increases over the years, mainly in interviewees in school-age with a percentage gain of 30% in 2021. This figure demonstrates the real effectiveness of the scientific dissemination on the radon theme promoted by RadioLab, mainly for the students for which the project was designed. In the age group 19–30, and especially in adults 30–50 and &gt; 50, the increase in knowledge of radon can also be associated with the promulgation of D.lgs 101/2020^{##UREF##6##7##}, which establishes the basic safety standards related to protection against the dangers arising from exposure to ionizing radiation, and in particular to the radon exposure (“Qualitative analysis of the data” and Fig. ##FIG##3##4##).</p>" ]

[ "<title>Results and discussion</title>", "<title>Qualitative analysis of the data</title>", "<p id=\"Par7\">The ten Italian regions in dark blue in Fig. ##FIG##0##1## (Campania, Lombardia, Sardegna, Calabria, Puglia, Veneto, Toscana, Piemonte, Friuli-Venezia Giulia, Sicilia), i.e. those with more than 150 surveys administered, correspond to the ten regions in which the INFN sections directly involved in the RadioLab project (Napoli, Milano, Cagliari, Cosenza, Lecce, Padova, Pisa, Torino, Trieste, Catania) are located. The regions in light blue in Fig. ##FIG##0##1## (Valle d’Aosta, Trentino-Alto Adige, Liguria, Marche, Emilia-Romagna, Umbria, Abruzzo, Molise), in which no INFN sections are directly involved, carried out the administration of less than 100 surveys. This aspect demonstrates the spread of RadioLab in dissemination of scientific culture on the theme of environmental radioactivity, in particular related to the knowledge of radon gas. It is interesting to note the case of the two regions in sky-blue in Fig. ##FIG##0##1##, which, with 144 (Basilicata) and 149 (Lazio) surveys administered, are affected by a greater influence due to the neighboring regions in which INFN sections are present. Campania region administered the highest number of surveys (14,972), followed at a considerable distance by Toscana (3373) and Calabria (3062).</p>", "<p id=\"Par8\">From Fig. ##FIG##1##2## is evident that an almost perfect gender balance is present, both among the various age groups and among the education level groups. The highest percentage of interviewees (49%) regards young people (&lt; 19), and it decreases as the age increases (Fig. ##FIG##1##2##a). This aspect is due to the fact that RadioLab is mainly designed for school-age interviewees, and it is confirmed, as can be seen in Fig. ##FIG##1##2##b, by the fact that primary/middle school diploma is the most frequent education level (59%). The amount of the interviewees decreases with the increase in the education level (Fig. ##FIG##1##2##b).</p>", "<p id=\"Par9\">The survey “do you know the radon gas?”, being the easiest way, has been carried out mostly in online mode (57%), then at scientific events (23%) and at schools/universities (20%) during seminars (Fig. ##FIG##2##3##a). In the time frame of the administration of the survey “do you know the radon gas?”, most of the entries (46%) have been gathered in the year 2020. Such high value is actually explicable by the promulgation in 2020 of the D.lgs 101^{##UREF##6##7##} implementation of the 2013/59/Euratom^{##UREF##7##8##}, which establishes the basic safety standards relating to protection against the risk arising from exposure to ionizing radiation. In particular, the radon exposure topic is addressed by proposing a national radon action plan and fixing a reference level of 300 Bq/m³. With the D.lgs 101/2020, a great attention of public opinion has been given to radon issue, and, thus, this fact explains the increase in filling up the survey “do you know the radon gas?” in 2020^{##REF##34201142##12##}. The early years 2018 (14%) and 2019 (27%) were also productive, testifying the growing interest in radon issue (Fig. ##FIG##2##3##b). The years 2021 (3%) and 2022 (10%) show a notable decrease in performing the survey, mainly due to the peak period of the COVID-19 pandemic^{##UREF##11##13##} (Fig. ##FIG##2##3##b).</p>", "<p id=\"Par10\">A more detailed analysis has been done in Fig. ##FIG##3##4## concerning the percentage per year of question ‘scenario where the survey was done’. Firstly, Fig. ##FIG##3##4## highlights the in-presence modalities (events and at schools/universities) for carrying out the survey as the main ways used in the initial years, before the COVID-19 disease: 2018 with 69%, increasing in the 2019 with 87%. From 2020 to 2022, due to COVID-19, the predominant mode for carrying out the survey is the online one, with about 83% in 2020 and 2021, up to 95% in 2022^{##UREF##11##13##}.</p>", "<p id=\"Par11\">Overall qualitative analysis denotes the statistically significance of the used sample.</p>", "<title>Quantitative analysis of the data</title>", "<p id=\"Par12\">A deep quantitative statistical analysis on the 28,612 data resulting from the survey “do you know the radon gas?” is presented in the following. In total, 39% of interviewees declare to know radon gas. Figure ##FIG##4##5## reports the percentage per gender of the interviewees who know or do not know the radon gas, combined with the age. This analysis underlines several aspects: (i) the male are more informed about radon (male 40% and 37% female, on average); (ii) the difference between male and female about the knowledge of radon is slight in the age groups of 19–30, 30–50, &gt; 50 (~ 3%), while it is more marked in the age &lt; 19 (7%); (iii) the knowledge of radon is nearly constant in the age groups of 19–30, 30–50, &gt; 50 (~ 45%), with a clear decrease in younger age &lt; 19 (~ 32%)^{##UREF##12##14##}.</p>", "<p id=\"Par13\">Figure ##FIG##5##6## reports the percentage per education level of the interviewees who know or do not know the radon gas. This analysis highlights the evident influence of the education level in the knowledge of radon issue: the interviewees who know radon grow with increasing education level^{##UREF##13##15##}. In particular: (i) the number of interviewees who know radon having high school diploma is slightly higher than the one of those having primary/middle school diploma (difference of 2%); (ii) most of interviewees having the highest level of education, i.e. university degree, know radon (56%), exceeding the two lower levels of education by more than 20%.</p>", "<p id=\"Par14\">Figure ##FIG##6##7## reports the percentage per source of radon knowledge for interviewees who declare to know the gas, combined with their age. This analysis reveals that interviewees who know radon gas: (i) from projects decrease with the age increase (from 31 to 17%); (ii) from newspapers/tv/web increase with the age increase (from 26 to 43%); (ii) from exhibitions or orientation events and other sources are costant (~ 5% event, ~ 37% other). Projects are mostly widespread in the school-age population (&lt; 19), indeed RadioLab is mainly designed for students and raised awareness in the theme of radon gas. Older people mention newspapers/tv/web as the most popular media source of knowledge of radon gas.</p>", "<p id=\"Par15\">Figure ##FIG##7##8## reports the percentage per age of the interviewees who consider the three options for a radon measurement in their city: urgent, not urgent, do not know. This analysis shows: (i) deeming it urgent, or not knowing whether it is urgent increases as respondents age; (ii) deeming a radon measurement in their city not urgent decreases as the age of interviewees increases. Awareness of radon issue increases in adulthood, being aware about the potential risk of radon^{##UREF##12##14##}.</p>", "<p id=\"Par16\">Figure ##FIG##8##9## reports the percentage per education level of the interviewees who consider the three options for a radon measurement in their city: urgent, not urgent, do not know. This analysis highlights: (i) deeming it urgent, or not knowing whether it is urgent increases as the education level of interviewees; (ii) deeming a radon measurement in their area not urgent decreases as the education level of interviewees increases. Similar considerations drawn from Fig. ##FIG##7##8## can be transposed to Fig. ##FIG##8##9##, showing that the awareness of radon issue increases with the education level. Joining together the results from Figs. ##FIG##7##8## and ##FIG##8##9##, it emerges that the knowledge of the problems related to radon exposure in environments is strongly linked to the education level of the people, and hence, to their age^{##UREF##12##14##, ##UREF##13##15##}. However, it is interesting to note that the percentage of people who do not consider urgent a radon measurement in their city is always less than a half of each group of interviewees by age and by education level.</p>", "<p id=\"Par17\">The last part of the quantitative statistical analysis is reported in the last two figures, i.e. Figures ##FIG##9##10## and ##FIG##10##11##. Figure ##FIG##9##10## represents the bar graph of the answers to the main question ‘do you know radon?’, matched with the answers from the question ‘do you think a radon measurement in your city is urgent?’. Most of the interviewees familiar with the topic of radon reply that gas measurement is urgently needed (51%), while the minority of the interviewees is divided almost equally between those who doubt and those who are not concerned about the radon measurement. The situation is completely different when the interviewees are those who are not familiar with the radon issue: (i) half of them is unsure whether or not a measure of radon in their city is urgent (50%); (ii) the other half is divided into 30% of people who do not want to measure radon in their city, and 20% who want to measure it. This is significant of the fact that the knowledge of a topic, whatever it may be (in this case radon), increases awareness of it and everything related to it (in the case of radon: risk perception), while ignorance on a topic tipically generates insecurity and uncertainty^{##UREF##14##16##}.</p>", "<p id=\"Par18\">Figure ##FIG##10##11## represents the trend by age of the interviewees about the knowledge of radon during the years of administration of the survey “do you know the radon gas?”, from 2018 to 2022. The knowledge of radon increases over the years, mainly in interviewees in school-age with a percentage gain of 30% in 2021. This figure demonstrates the real effectiveness of the scientific dissemination on the radon theme promoted by RadioLab, mainly for the students for which the project was designed. In the age group 19–30, and especially in adults 30–50 and &gt; 50, the increase in knowledge of radon can also be associated with the promulgation of D.lgs 101/2020^{##UREF##6##7##}, which establishes the basic safety standards related to protection against the dangers arising from exposure to ionizing radiation, and in particular to the radon exposure (“Qualitative analysis of the data” and Fig. ##FIG##3##4##).</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par19\">As one of the most important tool for collecting and synthesizing information in a compact and easy way for data analysis, the survey is used in this paper to assess the awareness on radon gas. The survey “do you know the radon gas?” was administered to school students mainly, but also to the public, as part of the national RadioLab project (promoted by INFN), aimed at disseminating scientific culture with particular regard to the theme of radioactivity. This survey provides a state of the art on the radon gas knowledge in Italy since 2018, and how this knowledge has been changing over the years until 2022. The survey includes some questions about personal, cultural and territorial information of the interviewees, and the main questions about radon knowledge and the source of this knowledge, and, finally, a question about the need for radon measurements in the city of the interviewees. The survey has been administered both online and in printed version during scientific or orientation events, workshops and seminars held in universities and schools. The main results on a statistically significant sample of 28,612 interviewees, during the 2018–2022 period, highlight: (i) the knowledge of radon increases with the age and the education level of the interviewees, as does the awareness of considering the radon measurement in their city urgent; (ii) knowing radon also means knowing the risk it entails and, therefore, the need to monitor the gas; (iii) the real effectiveness of the RadioLab project in raising the knowledge of radon in the years investigated, especially among school students. These results are independent of gender since no particular differences are found between male and female answers. RadioLab is still ongoing, aiming to increase the number of surveys to be administered in the Italian regions with fewer numbers, in order to make familiar and raise awareness of more and more students, teachers, relatives and general public about the presence of environmental radioactivity of natural origin, in particular radon gas and its risks.</p>" ]

[ "<p id=\"Par1\">RadioLab is an Italian project, addressed to school-age people, and designed for the dissemination of scientific culture on the theme of environmental radioactivity, with particular regards to the importance of knowledge of radon gas exposure. The project is a nationwide initiative promoted by the National Institute of Nuclear Physics- INFN. First tool used by the project, and of immediate impact to assess the public awareness on radon, is the administration of the survey “do you know the radon gas?”. In the survey, together with the knowledge of radon and of its sources, information on personal, cultural and territorial details regarding the interviewees are also taken. Reasonably, the survey invests not only young people, but also their relatives, school workers and, gradually, the public. The survey is administrated during exhibitions or outreach events devoted to schools, but also open to the public. The survey is in dual form: printed and online. The online mode clearly leads RadioLab project even outside the school environment. Based on the results of the survey, several statistical analyses have been performed and many conclusions are drawn about the knowledge of the population on the radon risk. The RadioLab benefit and the requirement to carry on the project goals, spreading awareness of environmental radioactivity from radon, emerge. The dataset involves all twenty Italian regions and consists of 28,612 entries covering the 5-year period 2018–2022.</p>", "<title>Subject terms</title>" ]

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[ "<title>Author contributions</title>", "<p>M.P. and F.G. conceived the initial idea of the manuscript. F.A. wrote the manuscript and prepared all figures. F.A. and M.C. made the statistical analysis. F.A. and G.L.V. acquired the data from all surveys and reorganized them. G.L.V. administered the surveys in Campania region. M.C. and F.G. administered the surveys in Lombardia region. V.F. and D.B. administered the surveys in Sardegna region. A.C. and S.H. administered the surveys in Veneto region. M.L.D.G. and A.V. administered the surveys in Puglia region. J.I. and A.P. administered the surveys in Sicilia region. M.B. and M.V. administered the surveys in Friuli-Venezia Giulia region. V.M. administered the surveys in Toscana region. M.C. and R.T. administered the surveys in Calabria region. M.C. and L.V. administered the surveys in Piemonte region. M.P. and F.G. coordinated the activities of each group and administered the resources. All authors disseminated the survey online and in the Italian regions not directly involved in the Radiolab project. All authors reviewed the manuscript.</p>", "<title>Funding</title>", "<p>This work was supported by INFN’s RadioLab project.</p>", "<title>Data availability</title>", "<p>The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par20\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Number of surveys “do you know the radon gas?” carried out by region. The map was created by Microsoft Excel 2016 version number 16.78 (<ext-link ext-link-type=\"uri\" xlink:href=\"https://office.microsoft.com/excel\">https://office.microsoft.com/excel</ext-link>).</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Number and percentage of male (wood color) and female (jeans color) to which survey “do you know the radon gas?” was administered, assorted by: (<bold>a</bold>) age of the interviewees (&lt; 19; 19–30; 30–50; &gt; 50); (<bold>b</bold>) education level of the interviewees (primary/middle school diploma; high school diploma; university degree).</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Number and percentage of survey “do you know the radon gas?” slitted by: (<bold>a</bold>) scenario where the survey was done (event; online; school/university), (<bold>b</bold>) years (2018–2022).</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Percentage per year (2018–2022) of the question ‘scenario where the survey was done’ (event in blue; online in orange; school/university in gray), concerning the survey “do you know the radon gas?”.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Bar graph of the percentage per gender about the knowledge of radon gas (‘yes’ in green, ‘no’ in black) combined with the age of the interviewees (&lt; 19;19–30;30–50; &gt; 50).</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Bar graph of the percentage per education level (primary/middle school diploma; high school diploma; university degree) on the knowledge of radon (‘yes’ in green, ‘no’ in black).</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Bar graph of the percentage per source of radon knowledge (project in red; newspaper/tv/web in violet; event in ocher; other in brown) for interviewees, combined with their age (&lt; 19;19–30;30–50; &gt; 50).</p></caption></fig>", "<fig id=\"Fig8\"><label>Figure 8</label><caption><p>Bar graph of the percentage per age of the interviewees (&lt; 19;19–30;30–50; &gt; 50) answering the question ‘do you think a radon measurement in your city is urgent?’ (‘yes’ in lime; ‘I do not know’ in gold; ‘no’ in silver).</p></caption></fig>", "<fig id=\"Fig9\"><label>Figure 9</label><caption><p>Bar graph of the percentage per education level of the interviewees (primary/middle school diploma; high school diploma; university degree) answering the question ‘do you think a radon measurement in your city is urgent?’ (‘yes’ in lime; ‘I do not know’ in gold; ‘no’ in silver).</p></caption></fig>", "<fig id=\"Fig10\"><label>Figure 10</label><caption><p>Bar graph of the percentage per interviewees who know or do not know about the radon gas, answering the question ‘do you think a radon measurement in your city is urgent?’ (‘yes’ in lime; ‘I do not know’ in gold; ‘no’ in silver).</p></caption></fig>", "<fig id=\"Fig11\"><label>Figure 11</label><caption><p>Trend per age (&lt; 19 with gray line; 19–30 with yellow line; 30–50 with blue line; &gt; 50 with orange line) of the interviewees who answered ‘yes’ to the question ‘do you know radon?’, during 2018–2022.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Schematic view of the survey “do you know the radon gas?” within the RadioLab project.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Questions of the survey “do you know the radon gas?”</th><th align=\"left\">Possible answers</th></tr></thead><tbody><tr><td align=\"left\">Date of the survey</td><td align=\"left\">From 2018 to 2022</td></tr><tr><td align=\"left\">Scenario where the survey was done</td><td align=\"left\">Event; online; school/university</td></tr><tr><td align=\"left\">Home city of the interviewee</td><td align=\"left\">Italian locations</td></tr><tr><td align=\"left\">Gender of the of interviewee</td><td align=\"left\">Male; female</td></tr><tr><td align=\"left\">Age of the of interviewee</td><td align=\"left\"> &lt; 19; 19–30; 30–50; &gt; 50</td></tr><tr><td align=\"left\">Education level of the interviewee</td><td align=\"left\">Primary/middle school diploma; high school diploma; university degree</td></tr><tr><td align=\"left\">Do you know radon?</td><td align=\"left\">Yes; no</td></tr><tr><td align=\"left\">If you know radon, please add the knowledge source</td><td align=\"left\">Project; newspaper/tv/web; event; other</td></tr><tr><td align=\"left\">Do you think a radon measurement in your city is urgent?</td><td align=\"left\">Yes; no; I do not know</td></tr></tbody></table></table-wrap>" ]

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[ "<table-wrap-foot><p>All questions and the corresponding possible answers are reported. The questions are the same for the online and the printed versions of the survey.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: F. Groppi and M. Pugliese.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">The global trend of mobile devices, rapid advances in electric vehicles, and the deployment of smart grids that require millions of energy-saving sensors have put wireless technology back in the spotlight. Unlike Information and Communication Technology (ICT), which requires small amounts of energy to transmit useful data, the goal of WPT is to safely transmit large amounts of electrical energy over a given distance to a load. In recent decades, the use of battery-powered devices such as mobile phones, electric vehicles, and medical implants has increased significantly around the world, and WPT can find significant applications.</p>", "<p id=\"Par3\">WPT is used in a variety of industrial applications and robotics, such as transferring electrical energy through bent joints without physical contact^{##UREF##0##1##–##UREF##3##4##}, and robotic devices performing tasks such as disaster relief in inaccessible or hazardous locations. It can also be used for applications^{##UREF##4##5##–##UREF##7##8##}. For these reasons, there is a need to develop more efficient and secure designs for WPT technology. The purpose of this paper is to provide an up-to-date overview of current WPT topologies and highlight the limitations of the most commonly used technology, inductive power transfer systems, through simulations and hands-on analysis.</p>", "<p id=\"Par4\">It is common knowledge that in order to transfer actual power to the load side of an IPT system, the leakage inductors of a loosely coupled transformer (LCT) must be corrected. To compensate the primary side and/or secondary side, a number of compensation networks have been proposed. Their major objectives are to attain or enhance the good traits listed below^{##UREF##8##9##–##UREF##12##13##}: an output with a constant current and voltage that is unaffected by load resistance; zero voltage switching (ZVS), which can achieve great efficiency by soft switching, requires a weak inductive input impedance; Less sensitivity to the fluctuating coupling coefficient, which significantly broadens the range of applications.</p>", "<p id=\"Par5\">In an IPT system, it is generally challenging for a compensation circuit to satisfy all the requirements. Tolerance for IPT namely, serial-serial (SS), serial-parallel (SP), parallel-serial (PS), and parallel-parallel (PP), are widely used in many scenarios. The SS compensation architecture, which achieves zero voltage switching and nearly zero reactive power without experiencing bifurcation occurrences, has more desirable properties than the other three topologies. For SS topology, only two compensating capacitors are required, which leads to less power loss, smaller size, higher power density, and lower cost. The performance of the converter's transfer, however, is almost fixed after the transformer has been identified unless a new LTC is substituted. Low design freedom and high sensitivity to misalignment highly restrict the practical promotion of SS-compensated IPT system.</p>", "<p id=\"Par6\">Higher order compensation techniques, such LCL compensation topology, are suggested^{##UREF##13##14##–##UREF##15##16##} as a solution to the issue of ultra-large current in SS topology. Inverter and resonant tank power exchange is balanced by the additional compensating inductance. By using magnetic coupling, the primary coil current behaves as a current source and gives the secondary side a steady voltage. The LCC compensation topologies provide many desirable performances, such as (Zero Phase Angle) ZPA operations, high freedom of design, but more resonant elements, resulting in complex tune and the increase of system size and cost.</p>", "<p id=\"Par7\">Once the practical and/or commercial use is under consideration the cost, size efficiency and power performance are the main issues, which are defining the qualitative indicators of the system. It is therefore desirable to utilize trusted, reliable, and robust solutions. This paper focuses on the standard SS compensated WPT system, while the analysis is related to the properties investigation of the secondary side rectifier configurations. The common bridge diode rectifier is compared to alternative solutions. First it is discussed about the impedance matching requirement, so for this purpose the determination of the reflecting AC side resistance is provided. Consequently, the operational properties of certain rectifier types are evaluated through simulation analysis in time domain followed by the performance investigation through laboratory measurements. Individual rectifier configurations are evaluated from efficiency point of view, while the recommendations for the target application use are given at the end of the paper.</p>" ]

[ "<title>Materials and methods</title>", "<p id=\"Par8\">Wireless power transfer systems are being under development for more than a decade. Through the time, many configurations of compensation network have been analyzed, while various application purposes have been identified as well. This research is focused on the series-series (SS) compensated WPT system, which is well suited to the application area of high-power vehicle battery chargers due to their electrical and transfer properties. SS compensated WPT system, similarly to other configurations, has certain specifications which must be considered when designing a WPT system for defined parameters of target application. The correct system settings, or impedance matching considering the type of the load is crucial according to achieve optimal operating parameters, especially efficiency and performance. Here, one of the important issues, which is affecting this performance is the type of the used secondary side rectifier^{##UREF##16##17##–##UREF##20##21##}.</p>", "<p id=\"Par9\">The investigated system can be illustrated using Fig. ##FIG##0##1##, which shows the input WPT system supply source, the WPT inverter, the coupling elements in series-series topology and power electronics of the on-board part of the secondary side system. Because presented research is focused on the optimization of the WPT system performance using alternative configuration of secondary side rectifier, four topologies as a direct connection to the load (resistor or battery) are considered.<list list-type=\"bullet\"><list-item><p id=\"Par10\">Standard bridge diode rectifier,</p></list-item><list-item><p id=\"Par11\">Diode rectifier in combination with a DC-DC converter,</p></list-item><list-item><p id=\"Par12\">Diode rectifier with current output (I_type),</p></list-item><list-item><p id=\"Par13\">Diode rectifier with voltage output (U_type).</p></list-item></list></p>", "<p id=\"Par14\">The entire system control and data acquisition from measurements are supervised by the PC equipped by relevant control algorithm. The parameters of individual core components are listed in Table ##TAB##0##1##.</p>", "<title>Backround theory of the impedance matching for SS WPT system considering topology variations for secondary side rectifier</title>", "<p id=\"Par15\">Several key conclusions can be derived from the theory of coupling elements of a WPT system using series-series configuration of the compensation network (Fig. ##FIG##1##2##). First of all, it is about defining the basic circuit description (Eq. (##FORMU##0##1##)) and consequently identify the optimal value of the load resistance (Eqs. (##FORMU##1##2##), (##FORMU##2##3##)), i.e. targeting maximum system efficiency^{##UREF##21##22##,##UREF##22##23##}.</p>", "<p id=\"Par16\">Considering zero I2R losses (2) changes into (3).</p>", "<p id=\"Par17\">The Eq. (##FORMU##2##3##) identifies that once the ideal situation occurs, i.e., the parasitic resistances of the primary and secondary coils are zero, the optimal value of the load resistance is directly proportional to resonant frequency and the value of mutual inductance.</p>", "<p id=\"Par18\">Since it is a resonance coupling, then Eq. (##FORMU##3##4##) must be satisfied. It defines the resonant frequency as the operating frequency of the WPT system.</p>", "<p id=\"Par19\">The dependency of the load resistance on the optimal operation point regarding efficiency and output power of the WPT system is graphically interpreted on Fig. ##FIG##2##3##, which is valid for the 65 kW system power (the highest efficiency (97.5%) refers to the 50 kW of the output power). As it is clear from this figure, if the load of the coupling elements is not impedance-matched, then efficiency decrease would happen, which is an undesirable phenomenon that must be minimized.</p>", "<p id=\"Par20\">As follows from Eq. (##FORMU##1##2##), the optimal load resistance is dependent on the parasitic resistance of the circuit R (R₁ = R₂ = R), i.e. due to thermal changes of the ESRL and ESRC parameters. Apart from changes in R, RLηmax also depends on the operating parameter in the form of mutual inductance M, which is a function of the coupling factor between the coupling elements and thus on their relative position (alignment) and distance (transmission distance). A more detailed description regarding coupling elements influences can be found in the literature^{##UREF##0##1##}.</p>", "<title>Impedance matching of the standard bridge diode rectifier</title>", "<p id=\"Par21\">According to the terms of impedance matching for direct connection of the DC load using the bridge diode rectifier (Fig. ##FIG##3##4##), the situation can be described by Eq. (##FORMU##4##5##). Impedance conversion is independent of the circuit parameters and is defined only by a physical principle. For the real case, however, Eq. (##FORMU##4##5##) is incomplete, as it does not respect the static and dynamic resistance of individual diodes. Ultimately, the impedance conversion of the diode rectifier will be slightly dependent on the circuit parameters, which can be neglected with minimal error.</p>", "<p id=\"Par22\">Achieving the optimal operating condition of the WPT is therefore possible only by changing the design of the coupling elements, or by changing the resistance of the DC load in order to fulfill the condition of Eq. (##FORMU##2##3##).</p>", "<title>Impedance matching of the standard bridge diode rectifier with DC/DC converter</title>", "<p id=\"Par23\">Adding a buck DC-DC type of the converter to the diode bridge rectifier, it is possible to achieve an active and continuous impedance matching of the load and compensation element. The impedance conversion is then given by the combination of the rectifier conversion rate (Eq. (##FORMU##4##5##)) and the DC-DC converter (Eq. (##FORMU##5##6##)). The resistance on the DC side of the rectifier R_zDC is given by the magnitude of the equivalent resistance of the load R_{load eq}, which is given bz the by Ohm's law of the output terminals, by the actual ratio between voltage and absorbed current of the battery, and by the duty cycle value of the DC-DC converter.</p>", "<p id=\"Par24\">The resulting impedance matching function of this combination is given by Eq. (##FORMU##6##7##).</p>", "<p id=\"Par25\">According to proper operation of the system, the condition defined by Eq. (##FORMU##7##8##) must be met, i.e. the value of the resistance at the DC side of the rectifier (R_LDC) must be much higher than the value of the equivalent resistance. The second condition concerns the battery-type load, when the load current cannot exceed the maximum battery current, while the minimum current cannot be lower that the ripple's own value (Eqs. (##FORMU##8##9##), (##FORMU##9##10##)).where “n” is representing the transformation ratio of the L₁ and L₂ turns (Figs. ##FIG##0##1##, ##FIG##2##3##).</p>", "<title>Impedance matching of the current-doubler diode rectifier</title>", "<p id=\"Par26\">Equivalent schematic of the WPT system equipped by a special, current-type rectifier with is shown in Fig. ##FIG##4##5##. Its topology replaces the upper diodes of the standard H-bridge rectifier by inductors, while there is no mutual coupling between them. The value of the inductance to meet operational conditions characterized by the system´s best efficiency performance is given by Eq. (##FORMU##10##11##). So, as is clear, the size of the inductances of I_{type RECT} (current type rectifier) is dependent on the size of the load and thus the condition from Eq. (##FORMU##2##3##) is fulfilled only for one specific value of the load for which the L_{I_RECT} (11) and the coupling elements are designed.</p>", "<p id=\"Par27\">The impedance matching ratio for the I_type rectifier is defined by Eq. (##FORMU##11##12##), while it is seen that main specific according to the operation of this rectifier type is impedance increasing function.</p>", "<title>Impedance matching of the voltage-doubler diode rectifier</title>", "<p id=\"Par28\">The last alternative considers the second variant of a special type of rectifier with voltage output. The upper diodes of the H-bridge topology are replaced with magnetically coupled inductances in the \"common mode\" connection according to Fig. ##FIG##0##1##. Unlike I_type RECT, the size of the inductances can be designed for the wide range of values. L_{U_RECT} is limited by a minimum value so that discontinuous character do not occur during the operation with the lowest load current. The U_type RECT impedance conversion ratio is given by Eq. (##FORMU##12##13##), which results in a clear increasing impedance function, but approximately half that of the standard U_type H-bridge rectifier (##SUPPL##0##Supplementary Information##).</p>" ]

[ "<title>Results</title>", "<p id=\"Par29\">From Eqs. (##FORMU##4##5##), (##FORMU##5##6##), (##FORMU##6##7##), (##FORMU##7##8##), (##FORMU##8##9##), (##FORMU##9##10##), (##FORMU##10##11##), (##FORMU##11##12##) and (##FORMU##12##13##) is seen that the value of the impedance matching in relation to the optimal load (3) is specific for individual variants of secondary side rectifiers discussed in previous part of the paper. Figure ##FIG##5##6## shows comparison of the impedance matching values of discussed rectifier types and its relationship to the optimal value of the R_AC. From this figure is seen, what is the optimal value of the load resistance considering individual secondary side types of rectification.</p>", "<p id=\"Par30\">Table ##TAB##1##2## is listing these values for each type. At this point it must be noted that DC-DC connection on the secondary side can adapt the optimal value of R_AC due to the possibility of the regulation of the output voltage and/or current.</p>", "<title>Time-domain simulation</title>", "<p id=\"Par31\">In order to be able to realize the physical prototypes and to provide experimental measurements, first the simulation models in time domain have been realized. Figures ##FIG##6##7##, ##FIG##7##8##, ##FIG##8##9## and ##FIG##9##10## are showing circuit diagrams of considered secondary side rectifiers. The primary side of the WPT system is replaced by the voltage-sourced equivalent circuit, representing the functionality of the primary side inverter. All circuit parameters are defined in Table ##TAB##0##1##. Regarding U_type rectifier, the common mode inductors with very high magnetic coupling must be considered (k → 1).</p>", "<p id=\"Par32\">The simulation results shown on Figs. ##FIG##10##11## and ##FIG##11##12## are representing leg currents of the secondary side rectifier (I_a, I_b), load current (I_load), the current from rectifier to DCDC converter (I_dcdc) and the voltage on the secondary/receiving coil of the WPT system (U₂). Individual waveforms are represented for the nominal—steady state operation of the system.</p>", "<p id=\"Par33\">In the case of direct load connection (Fig. ##FIG##10##11##-left), the presented waveforms are referring to the common operation of diode-bridge rectifier. The currents I_a and I_b are forming the pulsation of the load current I_load. The voltage U₂ has naturally rectangular shape, what is caused by the operational principle of the diode rectifier and with capacitive filter on the DC side. At the same time, for the presented case R_load = R_{load opt}, U_1m = U_2m and I_1m = I_2m apply here.</p>", "<p id=\"Par34\">In the case of connecting a load via a combination of a diode rectifier and a DCDC converter (Fig. ##FIG##10##11##– right), which has the responsibility for resistance variation, the presented waveforms are similar to the situation when direct connection is considered (R_load = 6.37 Ω, duty-cycle = 0.75).</p>", "<p id=\"Par35\">For the situation, when I_type rectifier is considered, a phase shift of 90° is visible between the currents I_a and I_b. I_load is formed by these two leg currents, while the current ripple is less compared to direct connection. Due to the triangular character of the current, a very unfavorable waveform of the voltage is visible, if transmitting and receiving coil are under consideration. This time waveform of U₂ (Fig. ##FIG##11##12##—left) is typical for power supplies which behave as a very stiff current source. It is seen that at the moment of diode commutation, extreme rise of voltage exists, while during the gradual increase of the I_load the gradual decrease of U₂ applies. After this transient the U₂ voltage is practically zero. The amplitude of the U₂ pulse is given by Eq. (##FORMU##13##14##).</p>", "<p id=\"Par36\">In the case of the variant with the U_type rectifier, a phase-shift is 0° between the currents I_a and I_b. Similarly to previous situation, I_load is formed by the leg currents. Depending on the quality (coupling factor) of the common-mode inductor, the currents are half-wave in nature, which has a positive impact on the U₂ voltage waveform. After reaching right the I_load effective value, U₂ begins to fall (Fig. ##FIG##11##12##—right). The amplitude of the U₂ pulse is given by Eq. (##FORMU##14##15##).</p>", "<p id=\"Par37\">From the previous simulation analysis is seen, that the unfavorable effect for U_type and I_type rectifier is reflected within the time-waveform of the voltage on coupling coils of WPT system. Both types use inductors within the main circuit. It is therefore desirable to investigate the influence of the values of inductances on the operational behavior of I_type and U_type rectifiers. For the case of U_type rectifier, the variable parameter is coupling factor of the common mode choke (from 0.8 to 0.999). I_type rectifier has variation within the value of the inductance of both inductors within the range 1 µH–900 µH. Figure ##FIG##12##13## is showing time-waveforms for individual situations.</p>", "<p id=\"Par38\">As a result of this analysis, next assumption can be made:<list list-type=\"bullet\"><list-item><p id=\"Par39\">Reduction of the value of inductances of I_type rectifier inductors, below the value, whish is determined by Eq. (##FORMU##10##11##) leads to decrease of the average value of rectifier leg´s currents resulting in generation of circulation currents. This causes reduction of the commutation voltage, efficiency and the amount of the transferred power.</p></list-item><list-item><p id=\"Par40\">In the case of U_type rectifier, the reduction of the coupling factor below 0.97 leads to gradual transition from U_type rectifier to I_type rectifier. At first, the commutation voltage only increases, which later saturates and the average value of the currents begins to decrease rapidly.</p></list-item></list></p>", "<title>Experimental measurements</title>", "<p id=\"Par41\">The aim of the experimental measurements is to verify the properties of individual rectifier types, while efficiency performance of whole WPT system will be evaluated. The experimental set-up is shown in Fig. ##FIG##13##14##. Table ##TAB##2##3## shows the input–output parameter during measurements. Figure ##FIG##14##15## is representing the prototype of reconfigurable topology of secondary side rectifier, i.e. PCB enables to configure all of discussed types of rectifier.</p>", "<p id=\"Par42\">The measurements were processed automatically, i.e. with the help of the supervisor control system (PC), and after the setting of the measuring algorithm, individual devices were automatically controlled, e.g. electronic load, where the load of the WPT system changed in defined steps. Subsequently, the measured data were automatically uploaded to the computer, where graphical visualization have been performed.</p>", "<p id=\"Par43\">To confirm results from the simulation analyses, the measurement of time-waveforms was performed, while the influence of the type of rectifier was validated. Set <italic>R</italic>_{<italic>load</italic>} is the same for all the cases of Figs. ##FIG##15##16## and ##FIG##16##17## to imagine rectifier influence better, especially in connection with Figs. ##FIG##17##18## and ##FIG##18##19## and chapter 3.2. Recorded variables are:<list list-type=\"bullet\"><list-item><p id=\"Par44\">Voltage on the transmitting coil—light blue waveform;</p></list-item><list-item><p id=\"Par45\">Current of the transmitting coil—dark blue waveform;</p></list-item><list-item><p id=\"Par46\">Voltage on the receiving coil—green waveform;</p></list-item><list-item><p id=\"Par47\">Current on the receiving coil/leg of the rectifier—pink waveform.</p></list-item></list></p>", "<p id=\"Par48\">The goal of this investigation was to proof the time-waveforms of the simulation analysis, while focus is given on the voltage amplitudes on the secondary side receiving coil, as well as the current of the rectifier leg. Table ##TAB##3##4## is listing the values on the individual components. It is seen that the simulation expectations are confirmed, and the differences between the measurement and simulation are very low (considering value of the rectifier leg current the relative error is approximately 7.7% for I_type and 5% for U_type).</p>", "<p id=\"Par49\">Experimental verification is done for all four connections under these test conditions: DC load form 1 by 1 to 10/15 Ω and DC load current from 1 by 1 to 10/15 A (ideally). See Figs. ##FIG##17##18## and ##FIG##18##19##.</p>", "<p id=\"Par50\">The results from the experimental verification are presented in three ways. First, they are represented as efficiency map, next as the load current map and finally as the efficiency dependency on the load current in case of <italic>R</italic>_{<italic>DC</italic>} optimum for each WPT to battery connection case. The load current is representing eventual battery current, therefore electronic load was operated equally to the operation of battery charging.</p>", "<title>Discussion to experimental results</title>", "<p id=\"Par51\">From Fig. ##FIG##17##18## left is seen, that direct connection between coupling element and rectifier is advantageous only for the applications, where almost constant load is expected. For this specific value of load, the coupling elements are designed adequately. Alternative with DCDC converter between load and coupling element has the possibility to match the impedance for the whole range of the load values and power variations. The additional losses caused by high currents are compensated as well (Fig. ##FIG##17##18##—left and right bottom part). So, connection using DCDC converter is suitable for wide range of currents opposite to the others. The only limitation would be a small value of currents if low load resistance is considered camming from pulse converter operation background.</p>", "<p id=\"Par52\">The I_type connection of the rectifier is suitable for very small values of load resistances, i.e., for high values of secondary side currents (Fig. ##FIG##18##19## left). The area of the effective utilization of this configuration is slightly narrow compared to the other options, so the application with variable load is not preferable. The last configuration of the rectifier, U_type is applicable for the systems with higher resistive load. The effective area of its utilization is wider compared to the I_type rectifier; thus the use is preferable also for the applications with slightly variable load resistance. Bottom parts of Fig. ##FIG##18##19## shows efficiency dependence on load current at case of optimal <italic>R</italic>_{<italic>DC</italic>} too. Finally, I_type is more beneficial for the highest load currents and U_type for the medium load currents.</p>" ]

[ "<title>Discussion to experimental results</title>", "<p id=\"Par51\">From Fig. ##FIG##17##18## left is seen, that direct connection between coupling element and rectifier is advantageous only for the applications, where almost constant load is expected. For this specific value of load, the coupling elements are designed adequately. Alternative with DCDC converter between load and coupling element has the possibility to match the impedance for the whole range of the load values and power variations. The additional losses caused by high currents are compensated as well (Fig. ##FIG##17##18##—left and right bottom part). So, connection using DCDC converter is suitable for wide range of currents opposite to the others. The only limitation would be a small value of currents if low load resistance is considered camming from pulse converter operation background.</p>", "<p id=\"Par52\">The I_type connection of the rectifier is suitable for very small values of load resistances, i.e., for high values of secondary side currents (Fig. ##FIG##18##19## left). The area of the effective utilization of this configuration is slightly narrow compared to the other options, so the application with variable load is not preferable. The last configuration of the rectifier, U_type is applicable for the systems with higher resistive load. The effective area of its utilization is wider compared to the I_type rectifier; thus the use is preferable also for the applications with slightly variable load resistance. Bottom parts of Fig. ##FIG##18##19## shows efficiency dependence on load current at case of optimal <italic>R</italic>_{<italic>DC</italic>} too. Finally, I_type is more beneficial for the highest load currents and U_type for the medium load currents.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par53\">The main objective of this research was to investigate the possibilities of alternative solutions of the on-board electronics of the wireless power charging system. We are discussing here about the secondary side rectification of WPT system, whereby focus was given on four circuit topologies. The investigated variants were standard bridge diode rectifier, standard bridge diode rectifier supplemented by DC/DC converter at the output, modified diode bridge rectifier to current type (I_type) and modified diode bridge rectifier to voltage type (U_type). It was discovered that each of the rectifier has different properties related to the identification of optimal value of the load resistance of WPT. In other words, the possibilities for impedance matching adjustments have been identified. From the simulation and experimental results, the conclusion can be summarized that the derived variants of the bridge rectifiers, i.e. I_type and U_type are equivalent, but in detail the variant with a voltage output (with a common-mode inductor) is more suitable. It is simpler to design, takes up less space, does not exhibit large commutation overvoltage and has a voltage output. In the case of high-quality design and determination of load change limits, the variants are effectively comparable to the rectifier variant equipped by DC/DC converter. In general, I_type and U_type rectifier variants are more suitable for a fixed or slightly changing load than for a big battery charging, where CV/CC charging profile has significantly impact to the battery input equivalent load. Once the battery charging is considered, the most suitable option is the use of active impedance adaptation, i.e. the utilization of secondary side rectifier with DC/DC converter, when multiple times higher efficiency and its stability are achieved throughout the entire charging in the CC–CV cycle compared to other investigated topologies. The only disadvantage here can be operate within the region with small values of the charging currents, when DC/DC converter is forced to the discontinuous mode of operation resulting in the reduction of the system efficiency. However, this can be largely eliminated with appropriate design.</p>", "<p id=\"Par54\">Proposed I_type rectifier is suitable for low loads with high currents. For example, CC battery or supercapacitor charging in electronic and smaoll drives (e.g. micro drilling, actuators) applications. Proposed U_type rectifier is suitable for medium current application with slightly higher input impedance e.g., electronic application supplying, backup or small batteries charging small actuators supplying act. In contrary to the connection using DCDC converter—Big advantage of I_type and U_type rectifier is fully passive, cheap and small solution of impedance matching for a specifics applications with a small fluctuation of input equivalent impedance.</p>", "<p id=\"Par55\">Partial results of this research also show a certain feature of the derived topologies of the diode rectifier, for example enabling the transfer of Joule losses from the primary side of the WPT system to the secondary side. This ability was also proven by measurements, thus for special applications, the U_type rectifier may be a more suitable choice (airtight applications, etc).</p>" ]

[ "<p id=\"Par1\">This paper focuses on the operational analysis of wireless power transfer (WPT) system, while the topology of the secondary side rectifier represents the main element, for which the properties of WPT system are being investigated. Initially the system description and technical specifications are given. Because WPT systems are designed for a certain type and value of the load (impedance matching) in order to achieve the highest possible efficiency, the definitions for those values are identified for individual topologies of the secondary side rectifiers. Consequently, the results are compared and discussed and followed by the simulation analysis to prove the operational behavior in time-domain for each of investigated alternative of rectifier. Several relationships have been identified in relation to secondary side electrical variables, and discussion for stress-optimization are given as well. The simulation results are verified by the experimental measurements, while individual solutions for secondary side rectifiers are evaluated from efficiency point of view followed by the recommendations of the operational conditions.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-49305-9.</p>", "<title>Author contributions</title>", "<p>Conceptualization, M.F. and D.A.; methodology, M.Z.; validation, M.Z.; formal analysis, V.K.; investigation, V.K. and M.Z., data curation, M.Z.; writing—original draft preparation, M.F.; writing—review and editing, D.A. All authors have read and agreed to the published version of the manuscript.</p>", "<title>Funding</title>", "<p>This work was funded by funding program of the University of West Bohemia number SGS-2021-021, Agentúra na Podporu Výskumu a Vývoja, Slovakia, apvv-20-0500. This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic under the project OP VVV Electrical Engicxneering Technologies with High-Level of Embedded Intelligence CZ.02.1.01/0.0/0.0/18_069/0009855.</p>", "<title>Data availability</title>", "<p>All data generated or analysed during this study are included in this published article.</p>", "<title>Competing interests</title>", "<p id=\"Par56\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Block diagram and principal schematic of researched WPT system alternatives.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Equivalent circuit of the WPT system using series-series compensation.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Example of the graphical interpretation of the optimal value of load resistance (65 kW prototype of WPT system), left – dependency of output power, right – dependency of efficiency.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Equivalent schematics of WPT system with current type rectifier.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Equivalent schematics of WPT system with current type rectifier.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Impedance matching values of individual secondary side rectifiers.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Simulation model of direct connection type.</p></caption></fig>", "<fig id=\"Fig8\"><label>Figure 8</label><caption><p>Simulation model of direct connection type with DCDCregulation.</p></caption></fig>", "<fig id=\"Fig9\"><label>Figure 9</label><caption><p>Simulation model of I_type.</p></caption></fig>", "<fig id=\"Fig10\"><label>Figure 10</label><caption><p>Simulation model of U_type.</p></caption></fig>", "<fig id=\"Fig11\"><label>Figure 11</label><caption><p>Time-waveforms from simulation models for direct connection (left) and DCDC (right).</p></caption></fig>", "<fig id=\"Fig12\"><label>Figure 12</label><caption><p>Time-waveforms from simulation models for I_type rectifier (left) and U_type rectifier (right).</p></caption></fig>", "<fig id=\"Fig13\"><label>Figure 13</label><caption><p>Time-waveforms from simulation models for I_type rectifier (left) and U_type rectifier (right) during parametric change of the inductance values (I_type) and coupling factor (U_type).</p></caption></fig>", "<fig id=\"Fig14\"><label>Figure 14</label><caption><p>Experimental set-up for evaluation of the properties of secondary side rectifiers of the WPT system (coupling coils are in the middle of the experimental set-up).</p></caption></fig>", "<fig id=\"Fig15\"><label>Figure 15</label><caption><p>Reconfigurable prototype of secondary side rectifier (boar contains all discussed topologies).</p></caption></fig>", "<fig id=\"Fig16\"><label>Figure 16</label><caption><p>Time-waveforms from the experimental measurement during steady-state of operation at <italic>R</italic>_{<italic>load</italic>} = 5 Ω, left—direct connection, right—DCDC connection.</p></caption></fig>", "<fig id=\"Fig17\"><label>Figure 17</label><caption><p>Time-waveforms from the experimental measurement during steady-state of operation at <italic>R</italic>_{<italic>load</italic>} = 5 Ω, left—I_type connection, right—U_type connection.</p></caption></fig>", "<fig id=\"Fig18\"><label>Figure 18</label><caption><p>Character maps from experimental measurements of direct rectifier connection (left) and DCDC connection (right).</p></caption></fig>", "<fig id=\"Fig19\"><label>Figure 19</label><caption><p>Character maps from experimental measurements of I_type rectifier connection (left) and U_type rectifier connection.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Tested assembly and variants of experimental set-up.</p></caption><table frame=\"hsides\" rules=\"groups\"><tbody><tr><td align=\"left\" rowspan=\"2\">Compensation components</td><td align=\"left\">L</td><td align=\"left\">23 μH</td></tr><tr><td align=\"left\">C</td><td align=\"left\">3.3 nF</td></tr><tr><td align=\"left\">Variable load</td><td align=\"left\">R_trim</td><td align=\"left\">0–20 Ω</td></tr><tr><td align=\"left\" rowspan=\"4\">On-board electronics (Secondary side of WPT system)</td><td align=\"left\">Diode bridge</td><td align=\"left\">H-bridge SiC</td></tr><tr><td align=\"left\">Diode Bridge + DCDC</td><td align=\"left\">L_DCDC = 10 μH</td></tr><tr><td align=\"left\">I_type Bridge</td><td align=\"left\">2*L 10 μH, SiC</td></tr><tr><td align=\"left\">U_type Bridge</td><td align=\"left\">CMM = 900 μH, SiC</td></tr><tr><td align=\"left\" rowspan=\"2\">Off-board electronics (Primary side of WPT system)</td><td align=\"left\">Inverter</td><td align=\"left\">H-bridge SiC</td></tr><tr><td align=\"left\">Power supply</td><td align=\"left\">Universal</td></tr><tr><td align=\"left\" rowspan=\"4\">Electrical parameters</td><td align=\"left\">Voltage range</td><td align=\"left\">Up to 312 V</td></tr><tr><td align=\"left\">Current range</td><td align=\"left\">Up to 15 A</td></tr><tr><td align=\"left\">Power limit</td><td align=\"left\">500 W</td></tr><tr><td align=\"left\">Frequency</td><td align=\"left\">577 kHz</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Comparison of the values of optimal load resistance for individual secondary side rectifiers.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Variant</th><th align=\"left\">R_{load opt}</th></tr></thead><tbody><tr><td align=\"left\">Direct</td><td align=\"left\">11.5</td></tr><tr><td align=\"left\">DCDC</td><td align=\"left\">–</td></tr><tr><td align=\"left\">I_type</td><td align=\"left\">1.8</td></tr><tr><td align=\"left\">U_type</td><td align=\"left\">2.8</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Operational parameters, component values and instrumentation list of designed WPT system.</p></caption><table frame=\"hsides\" rules=\"groups\"><tbody><tr><td align=\"left\">Input voltage (V)</td><td align=\"left\" colspan=\"2\">Up to 312 V, based on battery voltage</td></tr><tr><td align=\"left\">Regulated current (A)</td><td align=\"left\" colspan=\"2\">Up to 15 A</td></tr><tr><td align=\"left\">Switching frequency (kHz)</td><td align=\"left\" colspan=\"2\">577 kHz</td></tr><tr><td align=\"left\">Output power (W)</td><td align=\"left\" colspan=\"2\">Up to 500 W</td></tr><tr><td align=\"left\" rowspan=\"2\">Coupling elements values</td><td align=\"left\">L₁ = L₂ = 23 μH</td><td align=\"left\">H-bridge SiC</td></tr><tr><td align=\"left\">C₁ = C₂ = 3,3 nF</td><td align=\"left\">Universal</td></tr><tr><td align=\"left\" rowspan=\"4\">Rectifiers components</td><td align=\"left\">Diode rectifier</td><td align=\"left\">H-bridge SiC</td></tr><tr><td align=\"left\">H-bridge SiC + DCDC</td><td align=\"left\">L_DCDC = 10 μH</td></tr><tr><td align=\"left\">I_type bridge</td><td align=\"left\">2*L of 10 μH, SiC</td></tr><tr><td align=\"left\">U_type bridge</td><td align=\"left\">CMM = 900 μH, SiC</td></tr><tr><td align=\"left\">Power source</td><td align=\"left\">California instruments</td><td align=\"left\">CSW 5550</td></tr><tr><td align=\"left\">Power analyzes</td><td align=\"left\">ZES zimmer</td><td align=\"left\">LMG 500</td></tr><tr><td align=\"left\">Electronic load</td><td align=\"left\">H&amp;H</td><td align=\"left\">ZS 7080</td></tr><tr><td align=\"left\">Oscilloscope</td><td align=\"left\">Tektronix</td><td align=\"left\">MSO 4104B</td></tr><tr><td align=\"left\">Control board</td><td align=\"left\">RICE</td><td align=\"left\">Include TMS320F28335</td></tr><tr><td align=\"left\">Laboratory source</td><td align=\"left\">TTI</td><td align=\"left\">EX354 RT</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Comparison of the values of the voltage and current on I_type and U_type rectifier.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Rectifier variant</th><th align=\"left\" colspan=\"2\">U₂ (Vp-p)</th><th align=\"left\" colspan=\"2\">I₂ (Ap-p)</th></tr><tr><th align=\"left\">Simulation</th><th align=\"left\">Measurement</th><th align=\"left\">Simulation</th><th align=\"left\">Measurement</th></tr></thead><tbody><tr><td align=\"left\">I_type</td><td align=\"left\">500</td><td align=\"left\">500</td><td align=\"left\">13</td><td align=\"left\">12</td></tr><tr><td align=\"left\">U_type</td><td align=\"left\">180</td><td align=\"left\">250 (180 without oscillations)</td><td align=\"left\">10.6</td><td align=\"left\">10.039</td></tr></tbody></table></table-wrap>" ]

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}_{0}$$\\end{document}</tex-math><mml:math id=\"M6\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi mathvariant=\"normal\">η</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:msub><mml:mi mathvariant=\"normal\">ω</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${f}_{0} = \\frac{1}{2\\uppi \\sqrt{LC}}$$\\end{document}</tex-math><mml:math id=\"M8\" 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display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>D</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">load</mml:mi><mml:mspace width=\"0.166667em\"/></mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>;</mml:mo><mml:mi>D</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo stretchy=\"false\">⟨</mml:mo><mml:mn>0</mml:mn><mml:mo>;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{L\\, AC}=\\frac{8}{{{\\uppi }^{2} {D}^{2}}^{2}} {R}_{\\mathrm{load\\, }eqv} ; D\\in \\langle 0 ;1\\rangle$$\\end{document}</tex-math><mml:math id=\"M14\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>A</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>8</mml:mn><mml:msup><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">π</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">load</mml:mi><mml:mspace width=\"0.166667em\"/></mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mo>;</mml:mo><mml:mi>D</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo stretchy=\"false\">⟨</mml:mo><mml:mn>0</mml:mn><mml:mo>;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{L \\,DC} \\ge {R}_{\\mathrm{load\\, }eqv}$$\\end{document}</tex-math><mml:math id=\"M16\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>D</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>≥</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">load</mml:mi><mml:mspace width=\"0.166667em\"/></mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${I}_{bat}\\epsilon (\\langle {I}_{bat\\mathrm{ \\,min}} ; {I}_{bat{\\text{max}}CC}\\rangle \\wedge \\langle {I}_{bat\\mathrm{ \\,min}} ; \\frac{{U}_{bat\\, max}}{{R}_{eqv}}\\rangle )$$\\end{document}</tex-math><mml:math id=\"M18\" display=\"block\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">bat</mml:mi></mml:mrow></mml:msub><mml:mi>ϵ</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mo stretchy=\"false\">⟨</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:mspace width=\"0.166667em\"/><mml:mi mathvariant=\"normal\">min</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>;</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mtext>max</mml:mtext><mml:mi>C</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">⟩</mml:mo></mml:mrow><mml:mo>∧</mml:mo><mml:mrow><mml:mo stretchy=\"false\">⟨</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:mspace width=\"0.166667em\"/><mml:mi mathvariant=\"normal\">min</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>;</mml:mo><mml:mfrac><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">eqv</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo stretchy=\"false\">⟩</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ10\"><label>10</label><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{U}_{DC}}{8 \\,n \\,{L}_{DC} {f}_{sw\\, DCDC}} \\ll {I}_{bat \\,min}$$\\end{document}</tex-math><mml:math id=\"M20\" display=\"block\"><mml:mrow><mml:mfrac><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">DC</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mn>8</mml:mn><mml:mspace width=\"0.166667em\"/><mml:mi>n</mml:mi><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">DC</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>w</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>D</mml:mi><mml:mi>C</mml:mi><mml:mi>D</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>≪</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ11\"><label>11</label><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${L}_{I\\_RECT}=\\frac{{R}_{load \\,eqv}}{{\\omega }_{0}} \\frac{\\left(\\pi -1\\right)}{\\pi }$$\\end{document}</tex-math><mml:math id=\"M22\" display=\"block\"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>I</mml:mi><mml:mi>_</mml:mi><mml:mi>R</mml:mi><mml:mi>E</mml:mi><mml:mi>C</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>a</mml:mi><mml:mi>d</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>e</mml:mi><mml:mi>q</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ω</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfrac><mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mi>π</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mfenced><mml:mi>π</mml:mi></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ12\"><label>12</label><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{zL \\,AC}=\\frac{{\\uppi }^{2}}{2} {R}_{\\mathrm{load\\, }eqv}$$\\end{document}</tex-math><mml:math id=\"M24\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mi>L</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>A</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">π</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mn>2</mml:mn></mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">load</mml:mi><mml:mspace width=\"0.166667em\"/></mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ13\"><label>13</label><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${R}_{L \\,AC}\\approx \\frac{32}{{\\uppi }^{2}} {R}_{\\mathrm{load\\, }eqv}$$\\end{document}</tex-math><mml:math id=\"M26\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>A</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>≈</mml:mo><mml:mfrac><mml:mn>32</mml:mn><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">π</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">load</mml:mi><mml:mspace width=\"0.166667em\"/></mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ14\"><label>14</label><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{\\text{U}}}_{2m}= L\\frac{{I}_{2rms}}{tc}=L\\frac{\\frac{{I}_{load}}{2\\sqrt{2}}\\frac{{\\pi }^{2}}{2}}{{L}_{itype}\\frac{{di}_{load}}{{R}_{load}{I}_{load}}}= L\\frac{\\frac{{I}_{load}}{2\\sqrt{2}}\\frac{{\\pi }^{2}}{2}}{{L}_{itype}\\frac{\\frac{1}{{2f}_{0}}\\frac{{I}_{load}{R}_{load}}{{L}_{itype}}}{{R}_{load}{I}_{load}}}= L\\frac{\\frac{{I}_{load}}{2\\sqrt{2}}\\frac{{\\pi }^{2}}{2}}{\\frac{1}{2{f}_{0}}}= L\\frac{{\\pi }^{2}{f}_{0}{I}_{load}}{2\\sqrt{2}}$$\\end{document}</tex-math><mml:math id=\"M28\" display=\"block\"><mml:mrow><mml:msub><mml:mtext>U</mml:mtext><mml:mrow><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mfrac><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">tc</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mfrac><mml:mrow><mml:mfrac><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mn>2</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mrow></mml:mfrac><mml:mfrac><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">itype</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">di</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mfrac><mml:mrow><mml:mfrac><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mn>2</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mrow></mml:mfrac><mml:mfrac><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">itype</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mrow><mml:mn>2</mml:mn><mml:mi>f</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub></mml:mfrac><mml:mfrac><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">itype</mml:mi></mml:mrow></mml:msub></mml:mfrac></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mfrac><mml:mrow><mml:mfrac><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mn>2</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mrow></mml:mfrac><mml:mfrac><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mfrac><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">load</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ15\"><label>15</label><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{\\text{U}}}_{2m}=L\\frac{{I}_{2rms}}{tc}= \\frac{\\frac{{I}_{load\\_m}}{\\sqrt{2}}}{\\frac{1}{2{f}_{0}}}=2L{f}_{0}{I}_{load}$$\\end{document}</tex-math><mml:math id=\"M30\" display=\"block\"><mml:mrow><mml:msub><mml:mtext>U</mml:mtext><mml:mrow><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mfrac><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mi 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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

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[ "<media xlink:href=\"41598_2023_49305_MOESM1_ESM.docx\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Ischemic heart disease is a leading cause of cardiovascular deaths globally, affecting over 126 million people and resulting in more than 9 million deaths annually^{##REF##31163980##1##}. Myocardial ischemia occurs when blood flow to the heart is obstructed due to either a partial or complete blockage of coronary arteries or reduced coronary blood flow^{##REF##31685419##2##,##REF##31002282##3##}. Although successful therapeutic interventions have been developed to minimize ischemic injuries and cell death (infarction) through timely restoration of blood flow (reperfusion)^{##REF##25857912##4##,##REF##6227225##5##}, reperfusion itself can also induce additional irreversible injury and death in heart tissue that survived the ischemic insult^{##REF##25857912##4##,##REF##4056048##6##}. Clinical studies have also demonstrated a high risk of heart failure development and mortality in ischemic survivors despite reperfusion therapies^{##REF##24004117##7##,##REF##23695652##8##}, suggesting limitations in the available treatments.</p>", "<p id=\"Par3\">One contributing factor to injury and contractile dysfunction during reperfusion of the ischemic heart is the high rates of fatty acid oxidation observed during reperfusion^{##REF##19303418##9##–##REF##3342476##12##}. This phenomenon can be attributed to at least two main factors. Firstly, circulating levels of fatty acids are elevated after cardiac bypass surgery or myocardial infarction^{##REF##688564##13##–##REF##8970405##17##} due to adrenergic stimulation of adipose tissue lipolysis^{##REF##4847245##18##,##REF##6979436##19##}. This elevated fatty acid supply increases cardiac fatty acid oxidation during reperfusion. Secondly, cardiac mitochondrial fatty acid uptake is increased during reperfusion after ischemia due to decreased malonyl-CoA levels^{##REF##24147975##20##,##REF##7615556##21##}. Malonyl CoA is an important inhibitor of carnitine palmitoyl transferase-1 (CPT-1), the key enzyme for mitochondrial fatty acid transport in the heart^{##REF##19242641##22##}. Cardiac malonyl CoA levels decrease during ischemia and reperfusion due to an ischemic-induced activation of AMP-activated protein kinase^{##REF##24147975##20##}, leading to uncontrolled mitochondrial fatty acid uptake and β-oxidation^{##REF##7615556##21##,##REF##17030679##23##}. Both circumstances lead to increased delivery and utilization of fatty acids in the myocardium during reperfusion after ischemia.</p>", "<p id=\"Par4\">High fatty acid oxidation rates during reperfusion of ischemic hearts contribute to contractile dysfunction^{##REF##1476176##10##,##REF##11849874##11##,##REF##6115579##24##,##REF##11849661##25##} and have also been shown to contribute to infarct size and mortality in patients^{##REF##16595593##26##,##UREF##1##27##}. The negative effects of excessive fatty acid usage as the sole fuel source are associated with an inefficient oxygen utilization and inhibition of myocardial glucose oxidation^{##REF##1476176##10##,##REF##11849874##11##,##REF##25008008##28##}. The suppression of glucose oxidation occurs in the presence of accelerated anaerobic glycolysis, leading to the uncoupling of glycolysis from glucose oxidation^{##REF##8380856##29##}. This uncoupling results in lactate accumulation and excess proton (H⁺) production, causing disturbances in intracellular Na⁺ and Ca²⁺ homeostasis, further worsening contractile dysfunction and post-ischemic injury^{##REF##8888686##30##,##REF##2193525##31##}.</p>", "<p id=\"Par5\">Despite being known for decades, effective therapeutic interventions to reverse the imbalanced fuel use in post-ischemic hearts are still limited in clinical practice. Changes in the lysine acetylation status of fatty acid metabolic enzymes is one of the regulatory mechanisms controlling flux through mitochondrial metabolic pathways^{##REF##20203611##32##–##REF##27261364##34##}. Studies by our group and others have shown that acetylation of fatty acid oxidation enzymes results in an increased myocardial fatty acid oxidation in animal models of chronic high-fat diet and diabetes^{##REF##24966184##33##,##REF##23030792##35##,##REF##26101264##36##}. In contrast, acetylation decreases glucose oxidation by inhibiting the pyruvate dehydrogenase enzyme^{##REF##23835326##37##,##REF##35924321##38##}. These data suggest that increased protein acetylation could contribute to the metabolic inflexibility seen in heart failure through the differential regulation of metabolic enzyme activities. In contrast, a recent study by Davidson et al. dismissed the role of mitochondrial protein hyperacetylation in transverse aortic constriction (TAC) induced heart failure^{##REF##32660330##39##}. Using a genetic model of markedly elevated cardiac mitochondrial protein hyperacetylation, the authors observed no significant impact of protein lysine acetylation changes on mitochondrial function and heart failure progression after TAC^{##REF##32660330##39##}. However, the acetylation status and activities of major mitochondrial metabolic enzymes were not specifically assessed in this study.</p>", "<p id=\"Par6\">It is largely unknown what impacts myocardial I/R could have on mitochondrial protein lysine acetylation, and whether acetylation changes contribute to the cardiac energy metabolic shifts observed during myocardial ischemia and reperfusion (I/R) is not known. Myocardial ischemia has the potential to induce metabolic changes that could also enhance protein hyperacetylation. Firstly, a decrease in NAD⁺ levels as well as the downregulation of its salvaging enzyme, nicotinamide phosphoribosyl transferase (NAMPT), have been reported in myocardial I/R^{##REF##26297248##40##,##REF##24905194##41##}. As NAD⁺ is a co-substrate for sirtuin deacetylase enzymes, including SIRT1 and SIRT3, decreased NAD⁺ levels during ischemia may reduce sirtuin activities, thereby causing hyperacetylation^{##REF##30653603##42##}. In addition, SIRT3 expression could also be downregulated following ischemia and reperfusion^{##REF##31858519##43##,##REF##25877446##44##}. Secondly, increased myocardial fatty acid oxidation during reperfusion could also lead to the accumulation of mitochondrial acetyl-CoA, a substrate for protein lysine acetylation. However, although some studies have indicated the general susceptibility of hearts from sirtuin (deacetylase) deficient mice to ischemic injuries^{##UREF##2##45##,##REF##28659809##46##}, the role of acetylation dysregulation of fatty acid oxidative enzymes in fatty acid oxidation in post-ischemic hearts has not been studied. We, therefore, determined whether cardiac lysine acetylation changes during ischemia and reperfusion, and whether this has a role in increasing fatty acid oxidation in the post-ischemic heart.</p>" ]

[ "<title>Methods</title>", "<title>Ethical approval and animal care</title>", "<p id=\"Par7\">Study protocols for using Sprague–Dawley rats were reviewed and approved by the Animal Care and Use Committee at the University of Alberta. All animal experiments were conducted in compliance with the guidelines set by the Canadian Council of Animal Care. The study methods and results are reported in accordance with the ARRIVE guidelines^{##REF##32663219##47##}. Rats were housed in a temperature-controlled animal facility with a 12-h light/dark cycle. Additionally, the rats were provided ad libitum access to water and a regular chow diet. To determine the appropriate sample size and statistical power, we used G*Power software (v3.1.9.4, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany)^{##REF##17695343##48##}. The following factors were taken into consideration for the calculation. Five percent significance level (alpha or type-I error) (two-tailed), 80% power, effect size, as well as statistical tests used in the study (paired <italic>t</italic>-test or one-way ANOVA). For effect size estimation, we used the mean and standard deviation differences obtained from past studies under comparable conditions^{##REF##8888686##49##,##REF##19303418##50##}. Computing this information into the G* power software yielded a total required sample size of 51 rats. These rats were allocated among three different groups: the aerobic control (n = 10), the end of ischemia groups (n = 7) and the ischemia and reperfusion group (n = 34).</p>", "<title>Isolated working rat heart perfusions</title>", "<p id=\"Par8\">Isolated working rat heart perfusions were performed as previously described^{##REF##1476176##10##,##REF##9339411##51##}. Briefly, after an intraperitoneal injection of sodium pentobarbital (60 mg/kg), hearts from male Sprague–Dawley rats (275 to 300 g) (Charles River, Kingston, Canada) were rapidly excised and immersed in ice-cold Krebs–Henseleit bicarbonate (KHB) solution. The aorta was isolated and cannulated, and the hearts were immediately perfused in the Langendorff mode (at 60 mmHg) with KHB solution containing (in mmol/l): NaCl 118, KCl 4.7, MgSO₄ 7H₂O 1.2, KH₂PO₄ 1.21, CaCl₂H₂O 2.4, glucose 5, and NaHCO₃ 25, (pH 7.4). The KHB solution was gassed with 95% O₂ and 5% CO₂, and the temperature was maintained at 37 °C. During this time, excess tissues covering the heart (e.g. pericardium, lung, trachea, etc.) were removed, and the left atrium opening was cannulated via the pulmonary vein. The heart was then switched to the working mode by clamping the aortic inflow line from the Langendorff reservoir and opening the preload and after-load lines. Subsequently, the heart was placed in a glass chamber with the lower part prefilled with a 100 ml recirculating modified KHB solution containing 1.2 mM palmitate bound to 3% bovine serum albumin (BSA) (Equitech-Bio Inc, Kerrville, TX), 5 mM glucose, and 100 μU/ml insulin (Eli Lilly Inc, ON, Canada). The KHB solution also included appropriately radio-labeled substrates, [U-¹⁴C]-glucose, [5-³H]-glucose or [9,10-³H]-palmitate (Perkin Elmer, Boston, MA) for the measurement of glucose oxidation, glycolysis or fatty acid oxidation, respectively. The aortic and coronary outflows were recirculated through a closed air-tight system to allow the collection of ¹⁴CO₂ from glucose (see below for details). Left atrial preload and aortic after-load were set at column heights equivalent to 11.5 mmHg and 80 mmHg, respectively.</p>", "<title>Assessment of ex vivo cardiac function</title>", "<p id=\"Par9\">Hearts were perfused in the working mode and unpaced^{##REF##9339411##51##}. Heart rate, peak systolic pressure, and left ventricular developed pressure were measured using a Gould P21 pressure transducer (Harvard Apparatus, Holliston, MA) connected to the aortic outflow line. Data were acquired using an MP100 system from AcqKnowledge (BIOPAC Systems Inc., California). Cardiac output and aortic flow rates (ml/min) were obtained by measuring the perfusate flow rate into the left atria and from the after-load lines using Transonic T206 ultrasonic flow probes (Transonic Systems Inc., New York), respectively. Coronary flow (ml/min) was calculated as the difference between cardiac output and aortic flow. All data were collected at 10 min intervals. Cardiac work was determined as a function of cardiac output and peak systolic pressure and was calculated as (joules^.min^–1.g dry wt^–1) = (peak systolic pressure (PSP)–11.5) × 133.322 x cardiac output (CO) × 0.000001 × 60/60. A conversion factor of 1.333 × 10^–4 was used to convert cardiac power values from mmHg per ml to joules.</p>", "<title>Ischemia–reperfusion protocol</title>", "<p id=\"Par10\">Hearts were initially perfused aerobically for 30 min, followed by 30 min of global no-flow ischemia and then 40 min of aerobic reperfusion as outlined previously^{##UREF##3##52##}. Global no-flow ischemia was induced by clamping off both the left atrial and aortic flow lines for 30 min. Following 30 min of no-flow ischemia, left atrial and aortic flows were restored, and the recovery of mechanical function was monitored for a further 40 min period. Functional data and metabolic samples were collected every 10 min before and after ischemia. At the end of each perfusion, hearts were snap-frozen with liquid nitrogen, weighed, and then stored at − 80 °C. After grinding the frozen heart tissue at freezing temperature, a portion of the tissue (up to 30 mg) was weighed and dried in the oven for 24 h to remove its water content. The ratio of dry to wet weight was also calculated.</p>", "<title>Measurement of energy metabolic rates</title>", "<p id=\"Par11\">For the determination of glycolysis, glucose oxidation and palmitate oxidation rates, the hearts were perfused with radioactive substrates: [ 5-³H]-glucose, [U-¹⁴C]-glucose or [9,10-³H]-palmitate, respectively. The flux rate for each substrate was determined by quantitatively collecting either myocardial ³H₂O or ¹⁴CO₂ produced during the perfusion period at 10 min intervals (see details below), as previously described^{##REF##8888686##30##}. The amount of radioactive ³H₂O and ¹⁴CO₂ was then quantified using a liquid scintillation counter (Beckman Coulter, LS6500). Buffer samples were collected through an injection port inserted between the buffer reservoir and the oxygenator. All samples were collected in duplicate at each time point. Metabolic rates were normalized to the dry mass of the heart to correct for variations in heart size. To minimize variation due to contractile performance, metabolic rates were also normalized to cardiac work. Glucose or fatty acid oxidation rates were expressed as nanomoles (nmol) of substrate oxidized per minute per gram dry heart weight. Glycolysis was expressed as nmol of glucose passing through glycolysis per minute per gram dry heart weight.</p>", "<p id=\"Par12\">For the determination of glucose oxidation rates, the amount of ¹⁴CO₂ released from U-¹⁴C glucose oxidation both into the perfusate and hyamine solution (in gaseous form) was quantified. The gaseous ¹⁴CO₂ released into the perfusate was directed to the air outlet through specialized tubing until trapped in 30 ml of 1 M hyamine hydroxide solution (PerkinElmer, Waltham, MA). Subsequently, 150 µl of the hyamine sample was taken and mixed with the vial containing 4 ml of scintillation fluid. In addition, the ¹⁴CO₂ dissolved in the form of H¹⁴CO^-₃ in the perfusate was extracted by injecting 1 ml of the perfusate sample into a 25-mL stoppered metabolic vial with a center hole on the top and containing 1 ml of 9 N H₂SO₄. The ¹⁴CO₂ released after the reaction was trapped on hyamine hydroxide-soaked filter paper (300 µl) in a scintillation vial, which was flipped upside down and fitted into the rubber stopper to seal the center hole. Following overnight incubation, the scintillation vial with the filter paper was then taken and filled with 4 ml of scintillation fluid for quantification of radioactivity in the liquid scintillation counter.</p>", "<p id=\"Par13\">Glycolysis and palmitate oxidation rates were measured by the rate of appearance of ³H₂O in the perfusate from either ⁵H-glucose or [9,10-³H] palmitate, respectively, using a vapor transfer method^{##REF##16741157##53##}. Briefly, 500 μl of water was added into a 7 ml scintillation vial, followed by the insertion of a capless 1.5 ml microcentrifuge tube. Then, a 200 μl perfusate sample was added to the microcentrifuge tube placed inside the scintillation vial and incubated at 50 °C for 24 h to allow vaporization. It was further cooled at 4 °C for another 24 h before wiping all the water droplets on the outer wall of each capless tube into scintillation vials and discarding the capless tube with its content. The ³H₂O transferred to the scintillation vial was quantified after the addition of 4 ml Ecolite scintillation fluid (MP Biomedicals, Solon, OH) in a liquid scintillation counter. The individual measurements were normalized for transfer efficiency, which was determined as the ratio between vaporized ³H₂O together with the samples and the specific activity of unmetabolized (unprocessed) ³H₂O.</p>", "<title>ATP production rates and tricarboxylic acid cycle (TCA) activity</title>", "<p id=\"Par14\">To determine the contribution of glucose and palmitate oxidation to the overall tricarboxylic acid (TCA) cycle activity, we calculated the amount of acetyl-CoA derived from glucose and palmitate oxidation rates. A value of 2 acetyl-CoAs per molecule of glucose oxidized and 8 acetyl-CoAs per molecule of palmitate oxidized was used. Total ATP production rates from glucose oxidation, palmitate oxidation and glycolysis were determined by assuming 29 mole ATP produced per mole of glucose oxidized, 105 mol ATP produced per mole of palmitate oxidized, and 2 mol of ATP produced per mole of glucose passing through glycolysis.</p>", "<title>Tissue extraction and western blotting</title>", "<p id=\"Par15\">Approximately 20–30 mg of frozen heart tissue was weighed and homogenized in ice-cold lysis buffer containing the following concentrations (mM): 50 Tris–HCl (pH 7.5), 5 ethylenediaminetetraacetic acid (EDTA), 0.5 ethylene glycol-bis(β-aminoethyl ether)-N,N,N′,N′-tetra acetic acid (EGTA), 150 NaCl, 5 nicotinamide, and 10 sodium butyrate. Additionally, the buffer contained 1% Triton X-100, 0.5% NP-40, 0.1% sodium dodecyl sulfate (SDS), 1% phosphatase inhibitor cocktail 1, 1% phosphatase inhibitor cocktail 2, 0.2% protease inhibitor and 0.02% trichostatin A (TSA). The samples were homogenized using a tissue homogenizer (OMNI International, Kennesaw GA) for 30–40 s in two rounds, followed by centrifugation at 10,000×<italic>g</italic> for 10 min. The resulting supernatant was collected, and the protein concentration was determined using Bio-Rad Protein Assay dye (Bradford reagent) (Bio-Rad #5000006) in the BioTek Synergy Mx Microplate Reader. Subsequently, protein aliquots were mixed with Laemmli buffer containing 50% glycerol, 2% SDS, 0.0025% bromophenol blue, 50 mM Tris–HCl (pH 6.8) with 16% (v/v) β-mercaptoethanol (BME) and heated at 80 °C for 7 min prior to separation by SDS–polyacrylamide gel electrophoresis (SDS-PAGE).</p>", "<p id=\"Par16\">Protein lysate samples (equivalent to 30 µg of protein) were loaded and separated by 10% SDS-PAGE. The separated proteins were then transferred onto nitrocellulose membranes overnight at a cold temperature. Subsequently, the membranes were blocked with 5% skim milk for 1 h at room temperature followed by two 10 min washes with 1 × Tris-buffered saline containing 0.1% Tween-20 detergent (TBST). The membranes were then probed with one of the following primary antibodies overnight: pan acetyl-lysine (9441 s, Cell Signaling Technology (CST)), pan lysine succinyl (PTM-401, PTM Biolabs), SIRT3 (5490 s, Cell Signaling Technology (CST)), PDH (3205 s, Cell Signaling Technology (CST)), LCAD (ab128566, Abcam), β-HAD (ab37673, Abcam), glycerol-3-phosphate dehydrogenase (ab80535, Abcam), PGAM2 (PA5-98051, ThermoFisher Scientific), and α-tubulin (T6074, Millipore Sigma). Afterwards, the membranes underwent two 10 min washes with 1 × TBST and were then incubated with the appropriate secondary antibodies (1:5000) for 1 h at room temperature. The protein bands were visualized using an Amersham enhanced chemiluminescence kit (Cell Signaling Technology (CST), Danvers, MA) and were imaged by autoradiography. Finally, the intensity of the protein bands were quantified through densitometry analysis using ImageJ software (NIH, US) and normalized to the appropriate loading control.</p>", "<title>Immunoprecipitation</title>", "<p id=\"Par17\">To investigate the changes in the acetylation status of key proteins involved in fatty acid and glucose metabolism, frozen heart tissue was homogenized as described above. Then, approximately 300 μg of protein lysate was pre-cleared using 50 μl of protein A/G-agarose beads (sc-2003, Santa Cruz Biotechnology, Inc.) for 1–2 h with gentle rotation. Next, the mixture was centrifuged at 3000×<italic>g</italic> for 10 min and the resulting supernatant was transferred into a new tube. To this, 2 μl of acetyl-lysine antibody (Cell Signaling Technology (CST), 9441) was added and incubated overnight at 4 °C with gentle agitation. The next day, 50 μl of A/G-agarose beads was added to each sample to pull down protein-antibody complexes. This mixture was then incubated for an additional 6–8 h under the same conditions. The samples were then centrifuged at 5000×<italic>g</italic> for 10 min to separate the bead-antibody-protein complex from the supernatant, which was discarded afterwards. The pellet was washed 3 times with the same lysis buffer used for homogenization with centrifugation at 5000×<italic>g</italic> for 10 min in between. Finally, the bead-antibody-protein complex was resuspended with 1 × Laemmli buffer and heated at 95 °C for 5 min to release the acetylated proteins from the antibody-bead complexes. Then, the samples were centrifuged at high speed (15,000×<italic>g</italic> for 12 min), and the supernatant containing acetylated protein was collected in new tubes. Western blot was then carried out to detect various acetylated protein targets. The proteins were separated by 10% SDS-PAGE, as described above. Both a negative control, A/G PLUS-Agarose beads bound to an anti-acetyl-lysine antibody without a protein sample, and a positive control, protein lysate sample without A/G PLUS-Agarose beads, were used. All the bands were normalized to the IgG heavy chain.</p>", "<title>NAD⁺ and NADH quantification</title>", "<p id=\"Par18\">The concentration of nicotinamide adenine dinucleotide (NAD⁺) and its reduced form NADH in left ventricle tissue lysate samples was determined using the Amplite™ Colorimetric NADH Assay Kit (AAT Bioquest, Sunnyvale, CA; cat #15273) following the guidelines provided by the manufacturer. Briefly, the Amplite™ NAD/NADH Ratio Assay Kit contains the NADH probe, a chromogenic sensor with maximum absorbance at 460 nm upon NADH reduction. The absorbance increases proportional to the concentration of NADH in the sample. The NADH probe detects NADH in an enzyme-free reaction, and the absorbance was read in a microplate reader at 460 nm. For NAD⁺ quantification, 25 µl of NAD Extraction Solution was added to the test samples, followed by Neutralization Solution. The mixture was then incubated for 15 min before the absorbance was read at 460 nm.</p>", "<title>Statistical analysis</title>", "<p id=\"Par19\">A paired, two-tailed Student’s <italic>t</italic> test, and one-way or two-way analysis of variance (ANOVA) were used to determine the statistical significance differences between pre-and post-ischemic values. An unpaired Student’s <italic>t</italic> test was used to assess significant differences between experimental groups. The data are presented as mean ± standard deviation (SD) unless otherwise specified. All statistical analyses were performed using GraphPad Prism V9 software (San Diego, CA). Differences were considered statistically significant when P &lt; 0.05.</p>" ]

[ "<title>Results</title>", "<title>Recovery of cardiac function is significantly impaired during aerobic reperfusion of ischemic hearts</title>", "<p id=\"Par20\">To analyze the relationship between the recovery of mechanical function and the metabolic phenotype in post-ischemic hearts, we first characterized the severity of mechanical dysfunction following 30 min of no-flow global ischemia. The recovery rate after 30 min of no-flow ischemia was approximately 53%. Hearts that did not recover (unable to overcome the after-load pressure), (47% or 16/34), after the initial 10 min of reperfusion were not included in the final analysis. The 30 min global no-flow ischemia resulted in incomplete recovery for most of the parameters assessed (Fig. ##FIG##0##1##). Following reperfusion, cardiac work and efficiency declined by 41% and 49%, respectively, compared to pre-ischemic values. Despite a gradual improvement observed over the 40 min reperfusion period, both parameters failed to achieve full recovery (Fig. ##FIG##0##1##b). After 30 min of ischemia, the hearts recovered only 59% of cardiac output and 43% of aortic outflow rates. Similarly, the recovery rates for most other parameters remained below 80% of their pre-ischemic values (Fig. ##FIG##0##1##c-k).</p>", "<title>Fatty acid oxidation dominates cardiac energy metabolism in post-ischemic heart</title>", "<p id=\"Par21\">Following 30 min of ischemia, reperfused hearts displayed a statistically significant rise in glycolysis rate compared to the pre-ischemic baseline values, showing a 1.5 fold higher increase (2772 vs 4336 nmol ^. g dry wt^-1\n^. min^–1, p &lt; 0.0001). This increase was further amplified to 295% when normalized to cardiac work (1295 ± 563 vs 5127 ± 4175 nmol ^. joules^–1) (Fig. ##FIG##1##2##a, Table ##TAB##0##1##). Conversely, the rates of glucose oxidation significantly decreased after reperfusion from 215.1 ± 75.16 to 107.1 ± 60.8 nmol ^. g dry wt^–1\n^. min^–1, p &lt; 0.05, dropping by 51% from baseline values (Fig. ##FIG##1##2##b). This trend persisted after normalization to cardiac work (− 28%, p &lt; 0.05) (Table ##TAB##0##1##). In contrast, there was a remarkable 71% surge in the rates of palmitate oxidation during the post-ischemic period compared to the baseline (970.4 ± 275.8 vs 1658.8 ± 773.2 nmol ^. g dry wt^-1\n^. min^–1, p &lt; 0.05) (Fig. ##FIG##1##2##c). This increase was further accentuated upon normalization to cardiac work, exhibiting a substantial rise of 175% after reperfusion (Table ##TAB##0##1##, Supplement Fig. ##SUPPL##0##S1##).</p>", "<p id=\"Par22\">ATP production rates and TCA cycle activity fully recovered in post-ischemic hearts (Fig. ##FIG##2##3##). However, the source of this ATP production changed during reperfusion. While fatty acid oxidation contributed to 90% of the total ATP production at baseline, this contribution was further elevated to 93% in reperfused ischemic hearts (Fig. ##FIG##2##3##a,b). Conversely, glycolysis and glucose oxidation initially accounted for only 4.9% and 6.1% of ATP production, respectively, before ischemia. However, following reperfusion, the contribution of glucose oxidation to ATP production was reduced to less than 2%, while the contribution from glycolysis slightly increased to 5.5% (Fig. ##FIG##2##3##a,b).</p>", "<p id=\"Par23\">During reperfusion, palmitate oxidation provided 98.3 ± 0.9% of the acetyl-CoA for the TCA cycle, in contrast to 94.9 ± 1.6% in pre-ischemia. In contrast, glucose oxidation contributed only a minor proportion of the acetyl-CoA for the TCA cycle during reperfusion (1.63%, down from 5.1% in the pre-ischemic period). In summary, both overall ATP production and acetyl-CoA for the TCA cycle were significantly increased in the post-ischemic hearts primarily attributable to heightened fatty acid oxidation rate and (glycolysis for ATP).</p>", "<title>Ischemia and reperfusion do not alter NAD⁺ and NADH levels in the heart</title>", "<p id=\"Par24\">There was no significant difference in the NAD⁺ content between control (non-ischemic) hearts and reperfused hearts. However, NAD⁺ values were slightly lower in the post-ischemic hearts compared to controls, although this difference did not reach statistical significance (3.103 ± 0.6 vs 2.7 ± 0.6 μmol ^. g dry wt^–1, p-value: 0.53). Similarly, the NADH levels also remained unaltered after ischemia (0.95 ± 0.3 vs 0.84 ± 0.50 μmol ^. g dry wt^–1; p-value: 0.84). Likewise, the NAD⁺/NADH ratio was not substantially influenced by ischemia, although a slight increase was observed in post-ischemic hearts (3.5 ± 1.4 vs 6.2 ± 6.4). Furthermore, there was a reduction in the overall NAD⁺ plus NADH content in post-ischemic hearts compared to control hearts (Fig. ##FIG##3##4##a–d).</p>", "<title>Acetylation and succinylation status are not altered in post-ischemic heart</title>", "<p id=\"Par25\">To determine whether the high fatty acid oxidation and decreased glucose oxidation in post-ischemic heart were associated with dysregulation of protein acetylation status, we analyzed the post-translational acetylation patterns of metabolic enzymes and proteins involved both in glucose and fatty acid metabolism. However, to our surprise, we found no significant differences in total acetylation (Fig. ##FIG##4##5##a,b) or succinylation status (Fig. ##FIG##4##5##c,d) between control, ischemic and post-ischemic hearts. We also assessed the expression of SIRT3 protein, the main mitochondrial deacetylase enzyme, in these groups. However, there was no alteration in SIRT3 levels among the groups (Fig. ##FIG##4##5##e,f). We further investigated whether the acetylation status is changed at the level of individual metabolic enzymes of fatty and glucose oxidation in response to ischemia and reperfusion. However, there were no significant differences in the acetylation status of two key enzymes of fatty acid oxidation, (long-chain acyl-CoA dehydrogenase (LCAD) and β-hydroxy acyl-CoA dehydrogenase (ꞵ-HAD), between the control and post-ischemic hearts. Similarly, we found no changes in pyruvate dehydrogenase (PDH) acetylation, the rate-limiting enzyme in glucose oxidation (Fig. ##FIG##5##6##a–h). We also examined the acetylation status of several glycolytic enzymes in non-ischemic and post-ischemic hearts. Only phosphoglycerate mutase 2 (PGAM2) and glyceraldehyde 3-phosphate dehydrogenase (GAPDH) were found to be acetylated, but again no significant changes in acetylation were observed in ischemic and post-ischemic hearts. We also evaluated the protein levels of each of these enzymes. However, no changes in protein levels were observed (Supplement Fig. ##SUPPL##0##S4##). These results suggest that acetylation may not have a regulatory role in the metabolic changes observed in post-ischemic hearts.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par26\">Mitochondrial protein acetylation can have a significant impact on cardiac energy metabolism (see review^{##REF##34409084##54##}). In this study, we assessed for the first time the post-translational acetylation dynamics of cardiac metabolic enzymes and their functional relevance in post-ischemic hearts. Contrary to our expectations, we found no changes in either the global or individual metabolic enzyme acetylation status after ischemia or reperfusion. Nevertheless, ischemia did result in a significant increase in fatty acid oxidation and glycolysis rates during reperfusion, along with the inhibition of glucose oxidation. We further demonstrated that the contribution of glucose oxidation to total ATP production and acetyl-CoA supply to the TCA cycle was significantly decreased in hearts reperfused after ischemia. These metabolic changes were accompanied by an incomplete recovery of cardiac work and cardiac efficiency during reperfusion. In line with the unaltered acetylation status, both NAD⁺ and NADH contents were also not significantly changed in reperfused ischemic hearts compared to non-ischemic hearts.</p>", "<p id=\"Par27\">Recently, the regulatory effects of lysine acetylation on the activities of cardiac metabolic enzymes have been elucidated in high-fat diet-fed and obese mice as well as in the hearts of diabetic animals^{##REF##24966184##33##,##REF##23030792##35##,##REF##28526709##55##}. In these studies, the hyperacetylation state is demonstrated to have dual effects: augmenting the activities of fatty acid oxidation enzymes including LCAD and ß-HAD, while concurrently repressing pyruvate dehydrogenase (PDH)^{##REF##35924321##38##}. Under these circumstances, it has also been speculated that acetyl-CoA generated from high rates of fatty acid oxidation drives the hyperacetylation of mitochondrial enzymes^{##UREF##4##56##}. Likewise, increased concentrations of fatty acids in the bloodstream and enhanced utilization in the heart have been observed following myocardial I/R, both in experimental and clinical studies^{##REF##8017285##14##,##UREF##0##16##,##REF##8970405##17##}. While the conventional explanation attributes the rise in catecholamine levels during ischemic stress to adipose tissue lipolysis and the mobilization of free fatty acids^{##REF##5212391##57##–##UREF##5##59##}, alternative findings suggest that the surge in plasma fatty acid levels may also be induced by heparin, particularly in the clinical setting^{##REF##15541248##60##,##REF##18305079##61##}. Heparin acts on lipoprotein lipase (LPL) in the endothelium, releasing it into the circulation and breaking down lipoproteins to release free fatty acids. Consequently, some researchers argue that earlier studies might have overestimated plasma fatty acid levels if conducted without LPL inhibition^{##REF##18305079##61##,##REF##10894838##62##}. Regardless, we used a high fatty acid concentration in the current study, similar to the levels seen in the hearts of HFD-fed and diabetic animals. However, despite the high rates of fatty acid oxidation in the post-ischemic heart in the current study, we did not observe any significant alteration in the acetylation status of LCAD, ꞵ-HAD and PDH enzymes.</p>", "<p id=\"Par28\">Several potential factors could theoretically contribute to an altered acetylation status in response to myocardial ischemia and reperfusion. Firstly, high fatty acid ß-oxidation rates during reperfusion, as demonstrated in the current study, may lead to the accumulation of acetyl-CoA, which promotes the nonenzymatic acetylation of mitochondrial proteins, as described above. This notion was corroborated through a well-designed isotope tracing experiment conducted by Pougovkina and colleagues^{##REF##24516071##63##}. Using radioactively labeled palmitate, the authors demonstrated that the excess acetyl-CoA generated from high rates of fatty acid oxidation was sufficient to drive global protein hyperacetylation^{##REF##24516071##63##}. More recently, these findings were further reinforced through a more intricate heart failure model in mice by Deng et al. where they showed an increased incorporation of fatty acid-derived acetyl-CoA into acetylated proteins following a high-fat diet^{##REF##33176578##64##}. Notably, it is also evident that this increased acetylation of fatty acid oxidation enzymes under such circumstances augments their enzymatic activity. However, the causes underlying inconsistencies in the changes or regulatory roles of acetylation within metabolic enzymes across diverse heart failure pathologies (such as ischemic versus diabetic or high fat-induced heart failure) remain less clear.</p>", "<p id=\"Par29\">Using cutting-edge high-resolution mass spectrometry techniques, acetyl-proteomics studies have unveiled a large number of hyperacetylated proteins enriched with myocardial metabolic enzymes and proteins in non-ischemic heart failure models^{##UREF##6##65##,##UREF##7##66##}. IP with specific lysine acetyl antibody followed by western blotting is also an effective method to analyze differences in acetylation dynamics in response to various interventions. In this study, we used this approach to assess the acetylation changes of major regulatory enzymes and proteins in glycolysis, glucose oxidation and fatty acid metabolism, along with the determination of flux analysis for each pathway and ex vivo cardiac function measurements in post-ischemic hearts. This enabled us to directly determine the functional consequences of acetylation modifications on metabolic rates and functional recovery. Surprisingly, we found that myocardial lysine acetylation remain unaltered by myocardial ischemia or reperfusion, indicating that changes in the acetylation status of fatty acid oxidative enzymes may not contribute to the high fatty acid oxidation rates seen in the post-ischemic heart.</p>", "<p id=\"Par30\">The high rates of cardiac fatty acid oxidation seen in obesity and diabetes are accompanied by an increase in the acetylation and activities of fatty acid oxidation enzymes^{##REF##24966184##33##,##REF##23030792##35##,##REF##26101264##36##}. Given this context, the lack of a concomitant increase in the acetylation of fatty acid oxidative enzymes amidst the high rates of fatty acid oxidation during reperfusion of ischemic hearts in the present study remains unclear. A plausible explanation for these disparities could be attributed to the presence of acidosis that occurs during ischemia. It is assumed that most mitochondrial protein acetylation occurs non-enzymatically in the presence of excessive acetyl-CoA and an alkaline pH^{##REF##23946487##67##}. However, a decline in intracellular pH during ischemia might impede the nonenzymatic acetylation process^{##REF##11849874##11##}.</p>", "<p id=\"Par31\">Reduced mitochondrial oxidative phosphorylation rates during myocardial ischemia compromises the conversion of NADH to NAD⁺, a critical co-factor for sirtuins^{##REF##22904042##68##}. Accordingly, increased NADH levels accompanied by a decline in NAD⁺ may occur following ischemia^{##REF##1614262##69##,##REF##10963731##70##}. This decrease in NAD⁺ levels, anticipated during both ischemia and reperfusion, could theoretically inhibit SIRT3 activity and thus could contribute to a hyperacetylation state. However, our observation contradicts this assumption as we observed no differences in either NAD⁺ or NADH levels during and after ischemia. Similar to our findings, other researchers have also reported unaltered NAD⁺ levels in hearts subjected to 20 min of ischemia ^{##REF##25008320##71##}. However, our results are in contrast to the previous studies, which reported a significant elevation in NADH level at the end of ischemia^{##UREF##8##72##,##REF##11123243##73##} and in reperfusion^{##REF##10963731##70##} and a decline in NAD⁺ values^{##REF##19240850##74##}. While further investigation is necessary to resolve these differences, various factors may contribute to these variable observations, including variation in the duration of ischemia, perfusion conditions, differences in timing and assay methods for NAD⁺/NADH measurements.</p>", "<p id=\"Par32\">Some studies have revealed a reduced expression of SIRT3 protein in post-ischemic myocardial tissue which could potentially contribute to a hyperacetylation state^{##REF##31858519##43##,##REF##25877446##44##,##REF##32722183##75##}. However, we did not observe any changes in the protein level of SIRT3 at the end of ischemia or at the end of reperfusion. Regardless of this lack of changes in SIRT3 expression, SIRT3 activity could theoretically be decreased due to changes in NAD⁺ levels during ischemia and reperfusion. Although we did not directly assess SIRT3 activity, the unaltered levels of both NAD⁺ and NADH along with unchanged acetylation patterns suggest that SIRT3 activity may not be affected by ischemia and reperfusion. Previous studies have evaluated myocardial ischemia–reperfusion injury in mice deficient of SIRT3^{##UREF##2##45##,##REF##28659809##46##,##UREF##9##76##}. However, these studies produced mixed results. While some reported an increased susceptibility of SIRT3 KO mice to I/R injury^{##UREF##2##45##,##REF##28659809##46##}, others found no significant differences in the severity of myocardial injury in SIRT3 KO vs WT control mice^{##REF##26524632##77##}. Nevertheless, in all of these studies, neither the metabolic alterations nor the acetylation status of metabolic enzymes were directly assessed.</p>", "<p id=\"Par33\">Similarly, previous studies have also shown that myocardial I/R may affect the activity and expression of SIRT1^{##REF##30381241##78##}. Several other studies also indicated that SIRT1 has a cardio-protective role during myocardial I/R by modulating oxidative stress, apoptosis and other pathways^{##REF##21060073##79##,##REF##26489513##80##}. In addition, it is suggested that SIRT1 may regulate PGC-1α and PPARα activities, which in turn influences the transcription of genes related to fatty acid metabolism^{##REF##17347648##81##,##REF##18036349##82##}. However, it is not clear whether SIRT1-mediated deacetylation affects acute energy metabolic changes during myocardial I/R. In our study, we didn’t analyze the SIRT1 levels and the acetylation status of SIRT1 targets in the nucleus, which may have an indirect effect on mitochondrial metabolic changes. However, considering the acute nature of our study, it is less likely that mechanisms mediated by SIRT1 may contribute the acute mitochondrial metabolic alterations seen in post-ischemic heart.</p>", "<p id=\"Par34\">For decades, the altered myocardial energy substrate utilization has been recognized as a significant contributor to the impaired recovery of cardiac function and subsequent heart failure development in post-ischemic hearts. In line with early studies^{##REF##11849874##11##,##REF##8380856##29##}, we observed an increase in fatty acid oxidation following ischemia accompanied by a decline in both cardiac work and cardiac efficiency. Significant efforts have been made to utilize cardiac energy substrate manipulation as an adjunct therapeutic avenue in post-ischemic heart failure. In agreement with this, several studies have demonstrated an improved cardiac efficiency and recovery in post-ischemic hearts through interventions such as inhibiting myocardial fatty acid oxidation using drugs such as etomoxir, perhexilne, trimetazidine, and malonyl CoA decarboxylase inhibitors, or by stimulating glucose oxidation with dichloroacetate (see Ref.^{##REF##28279520##83##} for review). However, while many promising outcomes emerged from preclinical studies, the translation of these findings into routine clinical practices has been less successful, leaving room for the development of effective interventions to optimize cardiac energy metabolism in post-ischemic hearts. In our study, we investigated the roles of emerging mechanisms of post-translational protein acetylation modifications of cardiac metabolic enzymes as a new strategy to modulate the heart’s metabolic substrate utilization in post-ischemic heart. Although recent studies described the critical roles of dysregulated cardiac protein acetylation in myocardial metabolic disturbances and non-ischemic heart failure development (see Ref.^{##REF##34409084##54##} for review), we found no changes in acetylation status despite perturbed cardiac energy metabolism in post-ischemic heart. The therapeutic potential of targeting protein acetylation in heart failure and other diseases is being researched. Several small molecule inhibitors and activators, acetyltransferases and deacetylases (sirtuins) have been developed and tested in preclinical studies to neutralize aberrant protein acetylation changes, thereby improving metabolic homeostasis and functional outcomes in heart failure and other diseases^{##UREF##10##84##}. Despite this, our data suggest that drugs that inhibit hyperacetylation, such as SIRT3 activators, may not be a therapeutic approach to decreasing fatty acid oxidation in post-ischemic hearts. However, since increased lysine acetylation levels have been linked with the worsening of metabolic diseases such as diabetes and obesity as well as several cancer types, targeting protein lysine acetylation modification may be a potential therapeutic strategy in these disease states^{##UREF##11##85##}.</p>", "<title>Limitations</title>", "<p id=\"Par35\">There are some limitations in the current study. Firstly, we used an immunoprecipitation method to assess acetylation changes in key regulatory enzymes of glycolysis, glucose oxidation and fatty acid metabolism. Unlike acetyl-proteomics approaches, this method lacks the ability to identify specific acetylation sites. Additionally, the immunoprecipitation method is suboptimal for detecting the full spectrum of protein acetylation changes that could potentially occur in response to I/R. However, since there were no significant changes in global or major regulatory enzymes' acetylation status across our study groups, the relevance of identifying acetylation sites or other protein acetylation events becomes less important. Secondly, our study focused exclusively on cardiac fatty acid and glucose metabolism. However, it is worth noting that other fuel substrates, including branched-chain amino acids and ketone bodies, might also contribute to cardiac dysfunction and injury after myocardial I/R. Future studies on the role of these substrates in the recovery of cardiac function after I/R, as well as on acetylation dynamics, will be important. Thirdly, although our acute ex vivo myocardial I/R model is sufficient to study the short-term effects of I/R on protein acetylation, this may not fully represent the chronic and in vivo responses to I/R. Further studies on the chronic impact of in vivo I/R on enzymes or proteins regulating acetylation balance are necessary to fully understand the regulatory role of post-translation protein acetylation in myocardial I/R. Moreover, the studies described here were performed only in male rats. However, ischemia/reperfusion injury is a very relevant clinical condition in female patients. Therefore, additional studies are needed to examine the regulatory roles of acetylation on cardiac energy metabolism in post-ischemic hearts from female rats. Lastly, we used global no-flow ischemia to induce severe ventricular dysfunction, as indicated by the incomplete recovery of the mechanical function upon reperfusion. However, we didn’t assess directly the irreversible injuries after 30 min of ischemia other than troponin I level estimation at the end of the reperfusion. Due to the short frame of time, our protocol may not have significant effect on cardiac troponin I release. Additionally, it is also important to recognize that regional and low-flow ischemia are also relevant in vivo and clinical settings. The extent to which the severity of ischemic injury affects the results observed in our study needs further investigation.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par36\">In our study, we revealed the following interesting observations. Firstly, we found increased fatty acid oxidation rates in post-ischemic hearts despite impaired recovery of contractile function and cardiac efficiency. Intriguingly, the acetylation status of enzymes involved in both fatty acid and glucose oxidation remain unchanged in post-ischemic hearts despite the high rates of fatty acid oxidation. This suggests that alterations in acetylation status might not exert a regulatory role in the altered rates of fatty acid oxidation in post-ischemic hearts. Furthermore, we observed that ischemia and reperfusion did not affect the NAD⁺ and NADH redox states. Overall, our study provides valuable insights into the role of lysine acetylation in regulating metabolic changes in post-ischemic heart.</p>" ]

[ "<p id=\"Par1\">High rates of cardiac fatty acid oxidation during reperfusion of ischemic hearts contribute to contractile dysfunction. This study aimed to investigate whether lysine acetylation affects fatty acid oxidation rates and recovery in post-ischemic hearts. Isolated working hearts from Sprague Dawley rats were perfused with 1.2 mM palmitate and 5 mM glucose and subjected to 30 min of ischemia and 40 min of reperfusion. Cardiac function, fatty acid oxidation, glucose oxidation, and glycolysis rates were compared between pre- and post-ischemic hearts. The acetylation status of enzymes involved in cardiac energy metabolism was assessed in both groups. Reperfusion after ischemia resulted in only a 41% recovery of cardiac work. Fatty acid oxidation and glycolysis rates increased while glucose oxidation rates decreased. The contribution of fatty acid oxidation to ATP production and TCA cycle activity increased from 90 to 93% and from 94.9 to 98.3%, respectively, in post-ischemic hearts. However, the overall acetylation status and acetylation levels of metabolic enzymes did not change in response to ischemia and reperfusion. These findings suggest that acetylation may not contribute to the high rates of fatty acid oxidation and reduced glucose oxidation observed in post-ischemic hearts perfused with high levels of palmitate substrate.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51571-0.</p>", "<title>Acknowledgements</title>", "<p>This work was supported by a Canadian Institutes for Health Research Foundation grant (CIHR, 154302) to GDL. EK was supported by a Maternal and Child Health (MatCH) scholarship program, an Alberta Diabetes Institutes studentship and a Faculty of Medicine and Dentistry Graduate Studentship at the University of Alberta. QGK was supported by an Alberta Innovates Postgraduate Fellowship in Health Innovation.</p>", "<title>Author contributions</title>", "<p>E.B.K. performed the animal experiments, biochemical assays and data analysis. M.A. contributed to the biochemical investigations. L.Z. performed NAD⁺ and NADH quantifications. Q.G.K. contributed to the immunoprecipitation analysis. G.D.L. developed the concepts and planned the experiments. E.B.K. wrote the original manuscript draft. G.D.L. reviewed and edited the original draft. All authors contributed to the final manuscript editing and revision. G.D.L. secured funds and supervised the project.</p>", "<title>Data availability</title>", "<p>The datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par37\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Incomplete recovery of mechanical function in isolated working rat heart after 30 min of global no-flow ischemia and 40 min of reperfusion. All hearts were stabilized and perfused aerobically for 30 min before ischemia. A total of 34 rat hearts were subjected to I/R protocol, from which 18 (~ 53%) of them recovered after ischemia. The hearts were perfused with 1.2 mM palmitate, 5 mM glucose, 100 μU/ml insulin, and radio-labeled substrates (<bold>a</bold>) Study protocol, (<bold>b</bold>) Recovery of cardiac work, (<bold>c</bold>) Cardiac troponin levels (cTn-I), (<bold>d</bold>) Heart rate, (<bold>e</bold>) Peak systolic pressure, (<bold>f</bold>) Developed pressure, (<bold>g</bold>) Cardiac output, (<bold>h</bold>) Aortic outflow, (<bold>i</bold>) Coronary flow, (<bold>j</bold>) Rate pressure product, (<bold>k</bold>) Cardiac work, and (<bold>l</bold>) Cardiac efficiency (n = 18: (<bold>b</bold>,<bold>d</bold>-<bold>i</bold>); n = 8: (<bold>b</bold>,<bold>l</bold>)). A Paired <italic>t</italic> test was used for pre-and post-ischemic comparisons (<bold>c</bold>–<bold>k</bold>), while a simple linear regression was used to demonstrate the changes in functional recovery over time (<bold>b</bold>). Data are expressed as mean ± SD. ****P &lt; 0.0001,***P &lt; 0.001, **P &lt; 0.01 compared to pre-ischemic values.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Impaired cardiac energy metabolism in post-ischemic rat hearts. The hearts were perfused with 1.2 mM palmitate pre-bound with % BSA, 5 mM glucose, and 100 μU/ml insulin (n = 12–13). ³H₂0 production from [5-³H]-glucose and [9,10-³H] palmitate were used to determine glycolysis and palmitate (fatty acid) oxidation rates, while ¹⁴CO₂ released from [U-¹⁴C]-glucose was used to determine glucose oxidation rates. Samples were collected at 10 min intervals before the ischemia and during the reperfusion. (<bold>a</bold>) Glycolysis (n = 9), (<bold>b</bold>) Glucose oxidation (n = 9), (<bold>c</bold>) Palmitate oxidation (n = 8). A Paired <italic>t</italic> test was used for pre and post-ischemic comparisons. Data are expressed as mean ± SD. ***P &lt; 0.001, *P &lt; 0.05 compared to pre-ischemic values.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Reduced contribution of glucose oxidation to the total ATP production and TCA activity in post-ischemic rat heart. Cardiac adenosine triphosphate (ATP) production rate and TCA cycle activity. (<bold>a</bold>) Rate of ATP production as calculated from glycolysis (n = 8), glucose oxidation (n = 8), and palmitate oxidation (n = 8) in the pre-and post-ischemic hearts perfused with 1.2 mM palmitate, 5 mM glucose, and 100 μU/ml insulin, (<bold>b</bold>) Percent contribution of each pathway to the total cardiac ATP production, (<bold>c</bold>) TCA cycle activity (acetyl-CoA produced for the TCA cycle) based on the calculation from glucose oxidation (n = 8), palmitate oxidation (n = 8), (<bold>d</bold>) Percent contribution of each pathway to TCA activity. A two-way ANOVA with Bonferroni correction for multiple comparisons was carried out for each panel in this figure. Data are expressed as mean ± SEM. ****P &lt; 0.0001,***P &lt; 0.001, **P &lt; 0.01, *P &lt; 0.05 compared to pre-ischemic baseline values.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Unchanged NAD⁺ and NADH levels during and after ischemia. The NAD⁺ and NADH levels were determined from heart tissue snap-frozen at the end of ischemia and reperfusion using an Amplite™ Colorimetric NADH Assay Kit (n = 7–9 for each). (<bold>a</bold>) Cardiac NAD⁺ content before and after ischemia, (<bold>b</bold>) Cardiac NADH content before and after ischemia, (<bold>c</bold>) Ratio of cardiac NAD⁺ to NADH, and (<bold>d</bold>) Overall nucleotide content. A paired t-test was used for pre-and post-ischemic comparisons. Data are expressed as mean ± SD. **P &lt; 0.01 *P &lt; 0.05 compared to pre-ischemic values.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Global lysine acetylation and succinylation status are not affected by ischemia and reperfusion. Samples were collected from aerobic hearts (controls) at the end of the ischemic period (end of ischemia), or at the end of reperfusion. (<bold>a</bold>–<bold>c</bold>) Representative blots for total protein lysine acetylation, total protein lysine succinylation, and SIRT3, (<bold>d</bold>–<bold>f</bold>) Densitometry analysis for each blot (n = 7–9). A one-way ANOVA with multiple comparisons was done for each panel in this figure.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>No change in the acetylation status of major glucose and fatty acid oxidation enzymes was observed in isolated working rat hearts after ischemia and reperfusion. The acetylation status of the individual cardiac metabolic enzymes was determined using the immunoprecipitation technique using an acetyl-lysine antibody. (<bold>a</bold>) Representative blots, and (<bold>b</bold>–<bold>d</bold>) Densitometry analysis of acetylated LCAD, ꞵ-HAD and PDH, (<bold>e</bold>) Representative blots, and (<bold>f</bold>–<bold>h</bold>) Densitometry analysis of acetylated PGAM2, PDK4 and GAPDH normalized to the IgG heavy chain as a loading control (n = 7–9). Data are presented as mean ± SD. Data were analyzed using one-way ANOVA with multiple comparisons. *p &lt; 0.05 was considered statistically significant.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Glycolysis, glucose oxidation, and palmitate oxidation rates normalized to cardiac work (nmol ^. joules^–1) before and after ischemia in isolated working rat hearts.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Conditions</th><th align=\"left\">Glycolysis (n = 9)</th><th align=\"left\">Glucose oxidation (n = 9)</th><th align=\"left\">Palmitate oxidation (n = 8)</th></tr></thead><tbody><tr><td align=\"left\">Baseline</td><td char=\".\" align=\"char\">1295.56 ± 563.41</td><td char=\".\" align=\"char\">83.47 ± 35.26</td><td char=\".\" align=\"char\">498.13 ± 173.37</td></tr><tr><td align=\"left\">Reperfusion</td><td char=\".\" align=\"char\">5127.78 ± 4175.42</td><td char=\".\" align=\"char\">62.43 ± 36.38</td><td char=\".\" align=\"char\">1608.88 ± 1243.93</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41598_2024_51571_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"41598_2024_51571_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"41598_2024_51571_Fig3_HTML\" id=\"MO3\"/>", "<graphic xlink:href=\"41598_2024_51571_Fig4_HTML\" id=\"MO4\"/>", "<graphic xlink:href=\"41598_2024_51571_Fig5_HTML\" id=\"MO5\"/>", "<graphic xlink:href=\"41598_2024_51571_Fig6_HTML\" id=\"MO6\"/>" ]

[ "<media xlink:href=\"41598_2024_51571_MOESM1_ESM.docx\"><caption><p>Supplementary Figures.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">COVID-19 is a respiratory infection caused by the SARS-CoV-2 virus, usually manifested by a dry cough, fever and dyspnoea. This virus can also cause acute respiratory distress syndrome (ARDS), which caused an alarming number of deaths which has been increasing with each wave of successive mutations (Delta, Omicron)^{##REF##32981448##1##–##REF##35132910##3##}. In addition to this, COVID-19 may also affect other systems in the human body, including the nervous system and the cardiovascular system, contributing to multiple organ failure and eventual death^{##REF##32109013##4##}.</p>", "<p id=\"Par3\">There are increasing reports in the literature of neurological changes caused by the SARS-CoV-2 virus, which can infect the central nervous system (CNS) via both transneuronal and haematopoietic routes^{##UREF##0##5##–##REF##32436101##8##}. The most commonly described neurological symptoms are headache, ataxia and seizures associated with the entry of the SARS-CoV-2 virus into the CNS and loss of sense of smell (anosmia) and taste (ageusia) associated with the peripheral nervous system (PNS) infection^{##REF##32474093##9##–##REF##32661794##12##}. The symptoms described above can occur before, during or even after the patient’s respiratory system is infected with SARS-CoV-2^{##REF##33212316##13##}. Furthermore, it has been found that patients with a severe COVID-19 infection have more neurological abnormalities than those with a mild infection^{##REF##33486564##7##}. Anosmia has a direct association with the PNS and, when present in patients with COVID-19, may explain and give a clue to the likely mechanism of the SARS-CoV-2 virus entry into the brain via the olfactory nerves. Initial neuroinvasive hypotheses included the ability of SARS-CoV-2 to directly access the CNS by invading the olfactory bulb^{##REF##32251791##11##}. The piriform cortex may be the virus' main route into the brain^{##REF##32563019##14##,##REF##18495771##15##}. Currently, it is thought that the spread of the virus from the environment to the CNS is possible via the sensory afferents which supply the trigeminal nerve, the lingual-pharyngeal nerve, the vagus nerve and the dorsal root ganglia (DRG)^{##REF##33257876##16##}. Another hypothesis for the penetration of the SARS-CoV-2 virus into the CNS is that it is possible through secondary systemic mechanisms such as inflammatory cytokines, hypoxemia and oxidative stress associated with acute respiratory distress syndrome^{##REF##33412255##17##}.</p>", "<p id=\"Par4\">Peripheral neuropathies appeared as a specific COVID-19 symptom in 59% patients^{##REF##37680484##18##,##REF##35232750##19##}. The SARS-CoV-2 virus enters cells via the angiotensin converting enzyme 2 (ACE2) receptor with which the virus spike protein binds^{##REF##32826754##20##}. Studies suggest that neurons are not highly infected with SARS-CoV-2 due to the lack of ACE2 expression, and that neuropathies may be caused by an inflammatory response affecting sensory neurons in a cell-autonomous manner^{##REF##35232750##19##,##REF##35180380##21##,##REF##34287509##22##}. Studies by Shiers et al.^{##REF##32826754##20##} have shown that about a quarter of human DRG neurons express ACE2 mRNA, and that ACE2 protein is also found in human DRG. Most of these neurons are nociceptors, which are thought to form free nerve endings in the skin or other organs, providing the entry point for the virus into the PNS.</p>", "<p id=\"Par5\">There are no studies in the literature that identify the sensory sensitivity of COVID-19 survivors, which is directly related to any changes in the PNS. The two main aims of the research, therefore, were to provide an objective assessment, using TENS, of the effect of COVID-19 on the sensory threshold, understood in this study as the minimum level of a consciously perceived electrical stimulus and to demonstrate the changes that may occur in the cutaneous sensory area and thus the effect of the SARS-CoV-2 virus on the PNS in COVID-19 patients. The subjective and hedonic interpretation of the sensations produced by the applied electrical stimulus in the subject was also assessed. An additional aim was to determine whether the time elapsed between the start of the disease, that is the time from the onset of the first acute symptoms of COVID-19, to the date of the objective measurement of the sensory threshold, affected the sensation of the applied electrical stimulus.</p>" ]

[ "<title>Methods</title>", "<title>Key elements of the study design</title>", "<p id=\"Par6\">The study included a medical history taken from the people who had been referred for TENS physiotherapy for pain.</p>", "<p id=\"Par7\">The exclusion criteria for the study were absolute contraindications to physiotherapy and electrotherapy procedures, i.e. sensory disturbances, discontinuity of the skin at the treatment site, heart disease, including the presence of metal implants (pacemakers), other included contraindications were tumours and conditions after their removal, and, in women, pregnancy. None of the exclusion criteria above applied to any of the patients referred for TENS treatment. Those who had had COVID-19 underwent an extended health interview with questions strictly related to the disease, including questions about the time elapsed since the first acute symptoms of the disease had appeared. On the day of patient qualification for the study, sensory threshold was measured according to the research procedure described in the next section, and information was collected on the hedonic and subjective sensation evoked by TENS.</p>", "<title>The sensitivity measuring procedure</title>", "<p id=\"Par8\">To assess the level of sensory threshold transcutaneous electrical nerve stimulation (TENS) was used. TENS is a non-invasive technique used for pain relief in clinical practice. Electrical current is delivered across the intact surface of the skin to active underlying nerves^{##REF##26526976##23##}. In this study, conventional TENS was used: low-intensity, high-frequency 100 Hz and 100 µs parameters and biphasic current waveform. The test was performed on the right upper limb, on the wrist flexor muscle group. The forearm was placed on the table in supination. The electrodes used for the test were 12 cm² in size and were placed in pads soaked in warm water. The intensity of the applied current, expressed in milliamperes (mA), was increased in increments of 0.1 mA until the subject reported a minimal, consciously felt electrical stimulus. When a signal indicated that the subject was feeling the applied electrical stimulus, the current intensity displayed on the apparatus was noted. The patient was then asked to indicate whether the stimulus was pleasant, neutral or unpleasant, and to describe the stimulus by choosing one of the following words: tingling, pricking, scratching, warmth/burning, pinching, numbness and tickling. The research was carried out in 2022.</p>", "<p id=\"Par9\">Use of TENS in the assessment of the sensory threshold is a subjective method, requiring an alert and co-operative patient. The method measures the level at which a subject reports sensing a physical stimulus (detection threshold) applied to the skin and is similar to Quantitative Sensory Testing (QST)^{##REF##26826097##24##} which is a subjective, psychophysical test developed to assess sensory nerve function and measure the level at which a subject reports sensing a physical stimulus (detection threshold) applied to the skin. TENS has been previously used in studies connected with the sensation of electrical stimulation. The studies were conducted on young and healthy subjects in order to assess gender differences in the sensation of external stimulation^{##UREF##1##25##–##UREF##3##27##}.</p>", "<p id=\"Par10\">Other methods of sensory testing can also be found in literature e.g. the “Gold Standard” for testing cutaneous sensation with calibrated von Frey filaments^{##REF##22661298##28##}, which is a tactile method used to perceive surface sensations (tactile sensation) and the Semmes–Weinstein monofilament test to assess the threshold of tactile sensitivity on the skin by using accurate handheld calibrated nylon thread that buckles once it has delivered a force of 10 g^{##REF##36618173##29##}. Tuning forks, which are the most commonly clinically used tool to test for vibratory sensation should also be mentioned^{##REF##24534830##30##}.</p>", "<p id=\"Par11\">Participants in the study.</p>", "<p id=\"Par12\">The method used for the inclusion of the study participants in the study groups is shown in Fig. ##FIG##0##1##.</p>", "<p id=\"Par13\">The final analysis included results from 211 people aged 22 to 79 years, mean ± standard deviation 56.9 ± 12.1 years. There were 110 women and 101 men and body mass index (BMI) was 25.5 ± 2.0 kg/m². They included patients presenting for outpatient physiotherapy for: 67 (31.8%) spinal degeneration, 27 (12.8%) back pain, 27 (12.8%) shoulder injury, 26 (12.3%) multi-joint degeneration, 18 (8.5%) gonarthrosis, 15 (7.1%) ankle sprain, 10 (4.7%) knee sprain, 10 (4.7%) other soft tissue disease, 7 (3.3%) coxarthrosis, 3 (1.4%) internal knee injury, 1 (0.5%) acquired musculoskeletal deformity.</p>", "<p id=\"Par14\">From this group of people, 131 declared that they had had COVID-19 and formed the COVID group, while the NON-COVID group of 80 people consisted of people who had not had COVID-19, thus forming the control group. Cutaneous sensation may deteriorate for many reasons including: age, contributing morphological changes, decreased numbers of both myelinated afferent fibres and cutaneous receptor end-organs, changes in the mechanics of the skin itself, including dehydration, altered skin elasticity, or poor peripheral blood flow^{##REF##22661298##28##}. Therefore the control group was selected to ensure that it had no statistically significant differences from the COVID group in terms of gender, age, height, BMI, presence of chronic diseases, regularly used medication and types of medication. The characteristics of the COVID and NON-COVID groups are shown in Tables ##TAB##0##1## and ##TAB##1##2##.</p>", "<title>Statistical analysis</title>", "<p id=\"Par15\">Statistica 13 software (Statsoft, Krakow, Poland) was used for statistical analysis. The Mann–Whitney U test and Spearman's rank correlation coefficient were used due to the lack of normality of the distribution assessed by the Shapiro–Wilk test and the different number of persons in the groups studied. The Chi² test was applied to categorised data. Results were considered statistically significant at <italic>p</italic> &lt; 0.05.</p>", "<p id=\"Par16\">Informed consent.</p>", "<p id=\"Par17\">Informed consent was obtained from all individual participants included in the study. This study was conducted in accordance with the Declaration of Helsinki, and approved by the Bioethical Committee of Andrzej Frycz Modrzewski Krakow University (permission number KBKA/4/O/2022).</p>" ]

[ "<title>Results</title>", "<p id=\"Par18\">A prior COVID-19 infection had a statistically significant impact on the changes in sensory sensitivity (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##1##2##). There was an increase in skin sensitivity, as assessed by electrical stimulation. The median sensory sensitivity in the COVID group was 11 mA and in the NON-COVID group was 14 mA. The time elapsed from the onset of the first acute symptoms of the disease to the date of measurement had a statistically significant effect on the skin sensitivity threshold value (R = 0.52, <italic>p</italic> &lt; 0.001) (Fig. ##FIG##2##3##). The lowest values of the sensory sensitivity threshold were observed in subjects whose first acute symptoms of COVID-19 disease occurred one month or less from the day the test was performed, the median sensitivity threshold for that time lapse being 7.9 mA (Table ##TAB##2##3##). As the time from onset to the present measurement increased, the sensitivity threshold value increased. For patients who declared that they had had their first acute COVID-19 symptoms more than 10 months before the measurement, the median sensitivity threshold took on a value of 12.0, but was still lower than the median current sensitivity threshold for NON-COVID subjects of 14.0.</p>", "<p id=\"Par19\">The hedonic evaluation of the stimulus in the group who had had COVID-19 was statistically significantly different from the hedonic evaluation in the NON-COVID group (Fig. ##FIG##3##4##). Of those who had had COVID-19, the stimulus was perceived as unpleasant by 23%, as neutral by 35%, and as pleasant by 42%, whereas in the group of people who said they had not had COVID-19, only 3% described the stimulus as unpleasant, 53% as neutral and 45% as pleasant. It was observed that the highest proportions of people with an unpleasant perception of the stimulus occurred in the group who had had COVID-19 either up to one month or between one and four months from the day of the measurements. For those with symptoms more than 4 months ago, the predominant response was that the sensation was pleasant (Table ##TAB##3##4##).</p>", "<p id=\"Par20\">The subjective description of the stimulus felt by COVID-19 survivors differed significantly from the subjective stimulus felt by NON-COVID subjects (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##4##5##). In the group who had had COVID-19, 73% described the stimulus as tingling, 20% as pinching, with the other terms being used sporadically. In the group of people who declared that they had not had COVID-19 almost all described the sensation as tingling 98%. Taking into account the time lapse between the onset of the first acute symptoms of COVID-19 and the day on which the sensory threshold was measured, those who had been ill either up to one month or between one and four months differed most from the NON-COVID subjects in their subjective perception of the stimulus (Table ##TAB##4##5##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par21\">This study showed that the longer the time lapse between the first acute symptoms of COVID-19 and the present study of sensitivity to an electrical stimulus, the higher the value of the current required to reach the sensory threshold, indicating a higher sensory threshold and reduced sensory sensitivity. It is not possible to compare the results of our own study with reports from the literature on sensory perception after COVID-19, as this type of study does not appear in the currently available databases of scientific publications. Due to the direct link of anosmia and ageusia with the PNS, it is worth paying special attention to these symptoms^{##REF##32564071##31##–##REF##32981023##34##} which tend to occur in the early stages of the disease, as they may, therefore, be useful diagnostic markers^{##REF##32640192##35##}. A comparison was made with data from other disorders of the PNS, i.e. anosmia and ageusia^{##REF##32563019##14##,##REF##32539586##36##,##REF##32369429##37##}. A similar time relationship was found regarding the return to normal for the sensory disorders, both taste and olfactory, accompanying COVID-19^{##REF##32563019##14##–##REF##35180380##21##}. For example, a study by Qiu et al.^{##REF##32539586##36##} observed that 10% of COVID-19 patients had olfactory or gustatory symptoms only, while 19% reported olfactory and/or gustatory disorders before any other COVID-19 symptom. The range of follow-up time was 3 weeks, during which time 43% of patients experienced improvement in olfactory or taste dysfunction^{##REF##35232750##19##}, a similar time to our study where the shorter the time lapse from the onset of the first acute symptoms of COVID-19 the more pronounced were the differences in the perception and evaluation of the stimulus administered with TENS stimulation.</p>", "<p id=\"Par22\">The electrical stimulus which accompanied the TENS stimulation and which was used in the research had a short impulse time expressed in microseconds and a high frequency. This was deliberately designed so that the sensation that accompanied its flow through the skin was a delicate, pleasant tingling sensation. Our own research showed that almost all people who had not had COVID-19 interpreted their sensations in exactly this way. For them, the stimulus was neutral or pleasant. However, it should be noted that in the group of people who had had COVID-19, there were people who also reported other sensations accompanying TENS stimulation, such as: pinching, scratching and stinging. There were also people who reported that they found that the applied stimulus was unpleasant. This hedonic evaluation of the TENS stimulus on the skin indicates that the skin sensitivity of COVID-19 survivors was higher than those who had not had COVID-19, which may support the hypothesis that COVID-19 and the SARS-CoV-2 virus have an effect on the increased sensitivity of survivors.</p>", "<p id=\"Par23\">There is also a lack of clear evidence in the literature on the impact of SARS-CoV-2 virus and, in turn, COVID-19 on the PNS. In a study by Flamier et al.^{##REF##37680484##18##} which aimed to investigate the effects of SARS-CoV-2 on the PNS and try to elucidate the neuropathies associated with COVID-19, human sensory neurons were generated from induced pluripotent stem cells and sequentially infected with SARS-CoV-2 strain WA1/2020 and the Delta and Omicron variants. It was shown that 20% of human sensory neurons were infected with SARS-CoV-2, with the Omicron variant having the lowest infection rate. The study also showed that although SARS-CoV-2 infects human sensory neurons, it does not actively replicate to shed progeny virions.</p>", "<p id=\"Par24\">The first researchers to describe cutaneous hypersensitivity as a clinical symptom of COVID-19 were Krajewski et al.^{##REF##33320278##38##,##REF##32464157##39##}, who, two months after the onset of the pandemic, collected data from nine patients, with an average age of 47.7 years who reported an increased sensitivity to stimulation<bold>.</bold> Most of the patients studied also showed the typical general symptoms of COVID-19, such as a dry cough and fever. Cutaneous hyperaesthesia most often appeared 2–3 days after the onset of general disease symptoms, but in one patient it was the first symptom of the disease. Another patient reported increased skin sensitivity 5 days after resolution of general COVID-19 symptoms. The duration of the skin hypersensitivity varied considerably between patients, ranging from one day to six months. However, Harsh et al.^{##UREF##4##40##} described the case of a 69-year-old female patient with a moderate COVID-19 infection in whom any form of touch exacerbated the phenomenon of significant cutaneous hypersensitivity, particularly in the abdomen and lower extremities. The hypersensitivity resolved spontaneously after eight days. Abrams et al.^{##REF##34766365##41##}, retrospectively. examined sensory symptoms in thirteen patients with painful paraesthesia and numbness that developed during, or after, a SARS-CoV-2 infection. Six of the thirteen patients had a definitive diagnosis of small fibre neuropathy, including two cases with dysautonomia on autonomic testing. Nerve conduction studies showed no evidence of large fibre polyneuropathy. Studart-Neto et al.^{##REF##32756734##42##} found that three (6.7%) of 45 COVID-19 patients with severe respiratory disease developed peripheral neuropathy. Mehan et al.^{##REF##32763902##43##} assessed patients with myositis after COVID-19, including lower extremity paraesthesia and back pain. After magnetic resonance imaging revealed oedema and enhancement of the paraspinal muscles, it was hypothesised, that myositis may be relatively common in COVID-19 patients and that paraesthesia in these patients may be due to this myositis. Andalib et al.^{##REF##33586020##44##} reviewed the literature on PNS symptoms associated with COVID-19. It was concluded that the reason for these PNS symptoms was because of dysregulation of the systemic immune response by the COVID-19 virus. It has also been proposed that, after the acute phase of the infection has passed, patients with COVID-19 often go on to develop systemic excessive inflammation with macrophage activation, also known as secondary hemophagocytic lymphohistiocytosis.</p>", "<title>Limitations</title>", "<p id=\"Par25\">The methodology used in this study makes it possible to conclude unequivocally that a history of COVID-19 influences the sensations associated with the application of an electrical stimulus using TENS. However, the main limitation of the present study was the fact that only a single measurement of current sensation was carried out on each patient, which makes it impossible to precisely determine changes in the perception of the stimulus over time, as the passage of time is influenced by various individual factors. Unfortunately, for practical reasons, it was not possible to perform multiple measurements on the same person, which would have increased the reliability of the conclusions. Furthermore, the time since COVID-19 was measured using intervals. An additional limitation of this study was that the SARS-CoV-2 virus subvariant could not be determined, and it is known^{##REF##36560633##45##} that disease symptoms are subject to modification in the case of different subvariants. Moreover, based only on an interview with the participant, the final classification into COVID and NON-COVID may have been subject to error, since the group of people who declared that they had not had COVID-19 may have included people who had had the disease asymptomatically without being aware that they had it. The conclusions presented below must be read in the light of these limitations. There are no studies in literature on sensory changes in post-COVID-19 patients, so there is a need for further research and comparison of results obtained by researchers and clinicians on the occurrence of these sensory changes (cutaneous hypersensitivity) in patients who have or have had COVID-19. Further evidence is needed to determine the prevalence of this phenomenon in COVID-19 patients, how long it takes to resolve and to clarify its pathogenesis.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par26\">Having COVID-19 causes a reduction in the threshold of sensory sensitivity, a more unpleasant perception of the electrical stimulus and a change in the subjective sensations induced by the current from tingling to pinching and/or other unpleasant sensations. The shorter the time lapse from the onset of the first acute symptoms of COVID-19 in the group of people who declared that they had suffered from the disease, the more pronounced were the differences in the perception and evaluation of the stimulus administered with TENS stimulation compared to the group of people who declared that they had not suffered from COVID-19. Thus, the study observed a hypersensitivity to sensory stimuli that diminished with time from the onset of the first acute symptoms of the disease.</p>" ]

[ "<p id=\"Par1\">COVID-19 affects not only the respiratory system but also other biological systems such as the nervous system. Usually, these changes are reported based on the patient's subjective description. The aim of our study, therefore, was to objectively determine the effect that the SARS-CoV-2 virus and COVID-19 disease has on sensory threshold and the hedonic and subjective perception of an electrical stimulus. The sensory threshold was tested on the inner forearm by applying non-invasive transcutaneous electrical nerve stimulation (TENS) with 100 Hz and 100 µs parameters and a biphasic current waveform. The study involved 211 participants, aged 22–79 years, with a mean age of 56.9 ± 12.1 years. There were 131 subjects in the COVID group, while the NON-COVID group, the control group, was matched to the COVID group in terms of gender, age, body mass index and presence of chronic diseases. The research was carried out in 2022. Sensory sensitivity was highest in the group that had suffered with COVID-19. The median sensory sensitivity was 11 mA in the COVID group and 14 mA (<italic>p</italic> &lt; 0.001) in the NON-COVID group, however, the current sensitivity threshold decreased over time (R = 0.52, <italic>p</italic> &lt; 0.001). Post COVID-19, the electrical stimulus was more often perceived as unpleasant: COVID versus NON-COVID (23% vs. 3%, <italic>p</italic> &lt; 0.001) and as a different sensation to tingling (27% vs. 2%, <italic>p</italic> &lt; 0.001). Post-COVID-19 patients have a lower sensory threshold, the electrical stimulus is more often described as unpleasant and in subjective feelings it is more often described as pinching. The differences between COVID and NON-COVID decrease with time since the onset of COVID symptoms.</p>", "<title>Subject terms</title>" ]

[]

[ "<title>Author contributions</title>", "<p>G.B. Conception design of the work, methodology, formal analysis, writing the manuscript.\nJ.W. Formal analysis, writing the manuscript, data curation, review and editing.\nM.H.-P. Formal analysis, writing the manuscript, review and editing, data interpretation.\nAll authors have read and agreed to the published version of the manuscript.</p>", "<title>Data availability</title>", "<p>The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par27\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Flowchart of the study patients’ recruitment.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>The sensory sensitivity threshold in the group of patients who declared that they had had COVID-19 (COVID), N = 131 and those who declared that they did not have COVID-19 (NON-COVID, N = 80). <italic>x</italic>—average, box—interquartile range, — median (Test: U Mann–Whitney).</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>The effect of the time lapse after the first acute symptoms of COVID-19 on the threshold of sensory sensitivity (R Spearman).</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Hedonic rating of the current-induced stimulus for the group of patients who declared that they had had COVID-19 (COVID, N = 131) and those who declared that they had not had COVID-19 (NON-COVID, N = 80) (Test: Chi²).</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Subjective description of the sensory sensitivity caused by the electrical current in the group of patients who declared that they had had COVID-19 (COVID, N = 131) and those who declared that they had not had COVID-19 (NON-COVID, N = 80) (Test: Chi²).</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Characteristics of age, height and BMI values in COVID and NON-COVID groups.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">Me</th><th align=\"left\">Q1</th><th align=\"left\">Q3</th><th align=\"left\">Min</th><th align=\"left\">Max</th><th align=\"left\">Average</th><th align=\"left\">SD</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\" colspan=\"9\">Age [years]</td></tr><tr><td align=\"left\"> COVID</td><td char=\".\" align=\"char\">61.0</td><td char=\".\" align=\"char\">49.0</td><td char=\".\" align=\"char\">65.0</td><td char=\".\" align=\"char\">22.0</td><td char=\".\" align=\"char\">75.0</td><td char=\".\" align=\"char\">57.0</td><td char=\".\" align=\"char\">11.8</td><td align=\"left\" rowspan=\"2\">0.993</td></tr><tr><td align=\"left\"> NON-COVID</td><td char=\".\" align=\"char\">60.5</td><td char=\".\" align=\"char\">49.0</td><td char=\".\" align=\"char\">65.5</td><td char=\".\" align=\"char\">25.0</td><td char=\".\" align=\"char\">79.0</td><td char=\".\" align=\"char\">56.9</td><td char=\".\" align=\"char\">12.8</td></tr><tr><td align=\"left\" colspan=\"9\">Height [cm]</td></tr><tr><td align=\"left\"> COVID</td><td char=\".\" align=\"char\">170.0</td><td char=\".\" align=\"char\">167.0</td><td char=\".\" align=\"char\">174.0</td><td char=\".\" align=\"char\">159.0</td><td char=\".\" align=\"char\">182.0</td><td char=\".\" align=\"char\">170.2</td><td char=\".\" align=\"char\">5.1</td><td align=\"left\" rowspan=\"2\">0.646</td></tr><tr><td align=\"left\"> NON-COVID</td><td char=\".\" align=\"char\">170.0</td><td char=\".\" align=\"char\">165.0</td><td char=\".\" align=\"char\">174.5</td><td char=\".\" align=\"char\">160.0</td><td char=\".\" align=\"char\">182.0</td><td char=\".\" align=\"char\">170.0</td><td char=\".\" align=\"char\">5.5</td></tr><tr><td align=\"left\" colspan=\"9\">BMI [kg/m²]</td></tr><tr><td align=\"left\"> COVID</td><td char=\".\" align=\"char\">26.4</td><td char=\".\" align=\"char\">25.4</td><td char=\".\" align=\"char\">27.6</td><td char=\".\" align=\"char\">23.0</td><td char=\".\" align=\"char\">32.0</td><td char=\".\" align=\"char\">26.6</td><td char=\".\" align=\"char\">2.0</td><td align=\"left\" rowspan=\"2\">0.969</td></tr><tr><td align=\"left\"> NON-COVID</td><td char=\".\" align=\"char\">26.5</td><td char=\".\" align=\"char\">24.9</td><td char=\".\" align=\"char\">28.0</td><td char=\".\" align=\"char\">22.7</td><td char=\".\" align=\"char\">32.8</td><td char=\".\" align=\"char\">26.5</td><td char=\".\" align=\"char\">2.1</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Number and percentage of subjects in COVID and NON-COVID groups by sex, BMI categories and chronic diseases, as well as time since COVID-19 onset; <italic>p </italic>level of statistical significance (Test: Chi²).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">COVID</th><th align=\"left\">NON-COVID</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\" colspan=\"4\">Sex</td></tr><tr><td align=\"left\"> Female</td><td align=\"left\">67 (51.1)</td><td align=\"left\">43 (53.8)</td><td align=\"left\" rowspan=\"2\">0.713</td></tr><tr><td align=\"left\"> Male</td><td align=\"left\">64 (48.9)</td><td align=\"left\">37 (46.3)</td></tr><tr><td align=\"left\" colspan=\"4\">BMI categories</td></tr><tr><td align=\"left\"> Healthy Weight (18.5–24.9)</td><td align=\"left\">29 (21.1)</td><td align=\"left\">21 (26.3)</td><td align=\"left\" rowspan=\"3\">0.456</td></tr><tr><td align=\"left\"> Overweight (25.0–29.9)</td><td align=\"left\">92 (70.2)</td><td align=\"left\">56 (70.0)</td></tr><tr><td align=\"left\"> Obesity (&gt; 30.0)</td><td align=\"left\">10 (7.6)</td><td align=\"left\">3 (3.8)</td></tr><tr><td align=\"left\" colspan=\"4\">Elapsed time from onset of first acute symptoms of COVID-19</td></tr><tr><td align=\"left\"> &lt; 1 month</td><td align=\"left\">23 (17.6)</td><td align=\"left\" rowspan=\"5\">–</td><td align=\"left\" rowspan=\"5\">–</td></tr><tr><td align=\"left\"> 1–4 months</td><td align=\"left\">29 (22.1)</td></tr><tr><td align=\"left\"> 4–7 months</td><td align=\"left\">3 (2.3)</td></tr><tr><td align=\"left\"> 7–10 months</td><td align=\"left\">28 (21.4)</td></tr><tr><td align=\"left\"> &gt; 10 months</td><td align=\"left\">48 (36.6)</td></tr><tr><td align=\"left\" colspan=\"4\">Chronic diseases</td></tr><tr><td align=\"left\"> Hypertension</td><td align=\"left\">33 (25.2)</td><td align=\"left\">18 (22.5)</td><td align=\"left\">0.658</td></tr><tr><td align=\"left\"> Diabetes</td><td align=\"left\">7 (5.3)</td><td align=\"left\">3 (3.8)</td><td align=\"left\">0.597</td></tr><tr><td align=\"left\"> Osteoporosis</td><td align=\"left\">1 (0.8)</td><td align=\"left\">0 (0.0)</td><td align=\"left\">0.433</td></tr><tr><td align=\"left\"> Gout</td><td align=\"left\">10 (7.6)</td><td align=\"left\">5 (6.3)</td><td align=\"left\">0.704</td></tr><tr><td align=\"left\" colspan=\"4\">Regularly used medication</td></tr><tr><td align=\"left\"> Yes</td><td align=\"left\">46 (35.1)</td><td align=\"left\">21 (26.3)</td><td align=\"left\">0.180</td></tr><tr><td align=\"left\" colspan=\"4\">Type of medication</td></tr><tr><td align=\"left\"> Polocard</td><td align=\"left\">8 (6.1)</td><td align=\"left\">6 (7.5)</td><td align=\"left\">0.693</td></tr><tr><td align=\"left\"> Lernidum</td><td align=\"left\">2 (1.5)</td><td align=\"left\">0 (0)</td><td align=\"left\">0.267</td></tr><tr><td align=\"left\"> Milurit</td><td align=\"left\">11 (8.4)</td><td align=\"left\">5 (6.3)</td><td align=\"left\">0.568</td></tr><tr><td align=\"left\"> Acard</td><td align=\"left\">4 (3.1)</td><td align=\"left\">2 (2.5)</td><td align=\"left\">0.814</td></tr><tr><td align=\"left\"> Siofor</td><td align=\"left\">1 (0.8)</td><td align=\"left\">1 (1.3)</td><td align=\"left\">0.723</td></tr><tr><td align=\"left\"> Nebilet</td><td align=\"left\">5 (3.8)</td><td align=\"left\">3 (3.8)</td><td align=\"left\">0.980</td></tr><tr><td align=\"left\"> Akineton</td><td align=\"left\">4 (3.1)</td><td align=\"left\">1 (1.3)</td><td align=\"left\">0.403</td></tr><tr><td align=\"left\"> Adeksa</td><td align=\"left\">3 (2.3)</td><td align=\"left\">0 (0)</td><td align=\"left\">0.173</td></tr><tr><td align=\"left\"> Metformax</td><td align=\"left\">2 (1.5)</td><td align=\"left\">0 (0)</td><td align=\"left\">0.267</td></tr><tr><td align=\"left\"> Prestarium</td><td align=\"left\">5 (4.6)</td><td align=\"left\">0 (0)</td><td align=\"left\">0.051</td></tr><tr><td align=\"left\"> Noriprel</td><td align=\"left\">6 (4.6)</td><td align=\"left\">6 (7.5)</td><td align=\"left\">0.374</td></tr><tr><td align=\"left\"> Ostenil</td><td align=\"left\">1 (0.8)</td><td align=\"left\">0 (0)</td><td align=\"left\">0.433</td></tr><tr><td align=\"left\"> Diaprel</td><td align=\"left\">2 (0.8)</td><td align=\"left\">2 (2.5)</td><td align=\"left\">0.301</td></tr><tr><td align=\"left\"> Telmizek</td><td align=\"left\">3 (0.8)</td><td align=\"left\">0 (0)</td><td align=\"left\">0.433</td></tr><tr><td align=\"left\"> Formetic</td><td align=\"left\">0 (0)</td><td align=\"left\">1 (1.3)</td><td align=\"left\">0.200</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table. 3.</label><caption><p>The threshold of sensory sensitivity in the group of people who had suffered with COVID-19 at various times before the measurement and in the group who declared that they had not had the illness (NON-COVID).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Time from onset of first acute symptoms of COVID-19</th><th align=\"left\">N</th><th align=\"left\">Me</th><th align=\"left\">Q1</th><th align=\"left\">Q3</th><th align=\"left\">Min</th><th align=\"left\">Max</th><th align=\"left\">Average</th><th align=\"left\">SD</th></tr></thead><tbody><tr><td align=\"left\"> &lt; 1 month</td><td align=\"left\">23</td><td char=\".\" align=\"char\">7.9</td><td char=\".\" align=\"char\">7.7</td><td char=\".\" align=\"char\">11.0</td><td char=\".\" align=\"char\">6.7</td><td char=\".\" align=\"char\">14.0</td><td char=\".\" align=\"char\">9.1</td><td char=\".\" align=\"char\">2.1</td></tr><tr><td align=\"left\">1–4 months</td><td align=\"left\">29</td><td char=\".\" align=\"char\">9.5</td><td char=\".\" align=\"char\">8.2</td><td char=\".\" align=\"char\">12.0</td><td char=\".\" align=\"char\">7.8</td><td char=\".\" align=\"char\">14.0</td><td char=\".\" align=\"char\">10.1</td><td char=\".\" align=\"char\">1.9</td></tr><tr><td align=\"left\">4–7 months</td><td align=\"left\">3</td><td char=\".\" align=\"char\">9.2</td><td char=\".\" align=\"char\">9.0</td><td char=\".\" align=\"char\">11.0</td><td char=\".\" align=\"char\">9.0</td><td char=\".\" align=\"char\">11.0</td><td char=\".\" align=\"char\">9.7</td><td char=\".\" align=\"char\">1.1</td></tr><tr><td align=\"left\">7–10 months</td><td align=\"left\">28</td><td char=\".\" align=\"char\">11.7</td><td char=\".\" align=\"char\">10.4</td><td char=\".\" align=\"char\">12.3</td><td char=\".\" align=\"char\">9.0</td><td char=\".\" align=\"char\">14.0</td><td char=\".\" align=\"char\">11.5</td><td char=\".\" align=\"char\">1.3</td></tr><tr><td align=\"left\"> &gt; 10 months</td><td align=\"left\">48</td><td char=\".\" align=\"char\">12.0</td><td char=\".\" align=\"char\">11.0</td><td char=\".\" align=\"char\">13.1</td><td char=\".\" align=\"char\">9.0</td><td char=\".\" align=\"char\">16.0</td><td char=\".\" align=\"char\">12.2</td><td char=\".\" align=\"char\">1.7</td></tr><tr><td align=\"left\">NON-COVID</td><td align=\"left\">80</td><td char=\".\" align=\"char\">14.0</td><td char=\".\" align=\"char\">12.1</td><td char=\".\" align=\"char\">14.3</td><td char=\".\" align=\"char\">8.1</td><td char=\".\" align=\"char\">18.0</td><td char=\".\" align=\"char\">13.1</td><td char=\".\" align=\"char\">2.0</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Hedonic rating of the current-induced stimulus in the group of patients who declared that they had had COVID-19 at various times before the measurement and those who declared that they had not had COVID-19 (NON-COVID).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"> &lt; 1 month</th><th align=\"left\">1–4 months</th><th align=\"left\">4–7 months</th><th align=\"left\">7–10 months</th><th align=\"left\"> &gt; 10 months</th><th align=\"left\">NON-COVID</th></tr></thead><tbody><tr><td align=\"left\">Unpleasant</td><td align=\"left\">11 (47.8)</td><td align=\"left\">17 (58.6)</td><td align=\"left\">0 (0.0)</td><td align=\"left\">1 (3.6)</td><td align=\"left\">1 (2.1)</td><td align=\"left\">2 (2.5)</td></tr><tr><td align=\"left\">Neutral</td><td align=\"left\">8 (34.8)</td><td align=\"left\">8 (27.6)</td><td align=\"left\">0 (0.0)</td><td align=\"left\">11 (39.3)</td><td align=\"left\">19 (39.6)</td><td align=\"left\">42 (52.5)</td></tr><tr><td align=\"left\">Pleasant</td><td align=\"left\">4 (17.4)</td><td align=\"left\">4 (13.8)</td><td align=\"left\">3 (100.0)</td><td align=\"left\">16 (57.1)</td><td align=\"left\">28 (58.3)</td><td align=\"left\">36 (45.0)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Subjective description of the sensory sensitivity caused by the electrical current in the group of patients who declared that they had had COVID-19 at various times before the measurements were taken and those who declared that they had not had COVID-19 (NON-COVID).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"> &lt; 1 month</th><th align=\"left\">1–4 months</th><th align=\"left\">4–7 months</th><th align=\"left\">7–10 months</th><th align=\"left\"> &gt; 10 months</th><th align=\"left\">NON-COVID</th></tr></thead><tbody><tr><td align=\"left\">Tingling</td><td align=\"left\">11 (47.8)</td><td align=\"left\">8 (27.6)</td><td align=\"left\">3 (100.0)</td><td align=\"left\">27 (96.4)</td><td align=\"left\">46 (95.8)</td><td align=\"left\">78 (97.5)</td></tr><tr><td align=\"left\">Pinching</td><td align=\"left\">10 (43.5)</td><td align=\"left\">15 (51.7)</td><td align=\"left\">0 (0.0)</td><td align=\"left\">0 (0.0)</td><td align=\"left\">1 (2.1)</td><td align=\"left\">1 (1.3)</td></tr><tr><td align=\"left\">Other</td><td align=\"left\">2 (8.7)</td><td align=\"left\">6 (20.7)</td><td align=\"left\">0 (0.0)</td><td align=\"left\">1 (3.6)</td><td align=\"left\">1 (2.1)</td><td align=\"left\">1 (1.3)</td></tr></tbody></table></table-wrap>" ]

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[ "<table-wrap-foot><p><italic>Me</italic> median, <italic>Q1</italic> first quartile, <italic>Q3</italic> third quartile, <italic>Min</italic> minimum, <italic>Max</italic> maximum, <italic>SD</italic> standard deviation, <italic>p </italic>level of statistical significance (Test: Mann–Whitney U).</p></table-wrap-foot>", "<table-wrap-foot><p><italic>N</italic> number of subjects, <italic>Me</italic> median, <italic>Q1</italic> first quartile, <italic>Q3</italic> third quartile, <italic>Min</italic> minimum, <italic>Max</italic> maximum, <italic>SD</italic> standard deviation.</p></table-wrap-foot>", "<table-wrap-foot><p>The percentage of individuals is in brackets next to the number of individuals.</p></table-wrap-foot>", "<table-wrap-foot><p>The percentage of people is given in brackets next to the number of people.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41598_2024_51596_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"41598_2024_51596_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"41598_2024_51596_Fig3_HTML\" id=\"MO3\"/>", "<graphic xlink:href=\"41598_2024_51596_Fig4_HTML\" id=\"MO4\"/>", "<graphic xlink:href=\"41598_2024_51596_Fig5_HTML\" id=\"MO5\"/>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par3\">Renal cell carcinoma (RCC) is one of the most malignant tumors worldwide, with ~400,000 new cases and almost 200,000 deaths annually^{##UREF##0##1##}. In the United States, 76,080 individuals were diagnosed as RCC in 2021, accounting for 4% of newly occurrent malignant tumors and 46.4% of urinary tumors^{##UREF##1##2##}. Eighty-five percent of the pathological diagnosis for RCC is clear cell renal cell carcinoma (ccRCC)^{##REF##15205579##3##}, consistent with the putative cell of origin for RCC using scRNA-seq analyses^{##REF##34099557##4##}. It is worth noting that the ccRCC showed a high risk of distant organ metastasis, and the five-year survival rate of RCC patients would significantly decrease from 93% to 12% when distant metastasis occurred^{##UREF##2##5##}. More than one-third of metastatic RCC patients were accompanied by bone metastases^{##REF##23962746##6##}.</p>", "<p id=\"Par4\">Bone metastatic renal cell carcinoma (BMRCC) patients are usually complicated by skeletal related events including pathological fractures, spinal cord compression, and hypercalcemia^{##REF##20854942##7##,##REF##17062708##8##}. Until now, the main treatment options for BMRCC in clinical application are extensive surgical resection and radiotherapy^{##REF##11445855##9##,##UREF##3##10##}. Approved bone-targeted systemic therapies like bisphosphonates and denosumab showed limited benefits to the improvement of overall survival^{##REF##24613250##11##}. Although certain target-based agents such as antiangiogenic therapy have shown promising effectiveness, the progression-free survival of BMRCC remains low of 4.7 months versus 11.2 months for those without bone metastases^{##UREF##4##12##}. Therefore, systematic molecular characterization of BMRCC by single-cell transcriptome data may help discover predictive biomarkers and identify therapeutic targets for improvement of BMRCC treatment.</p>", "<p id=\"Par5\">The intrinsic genetic heterogeneity and dynamic immunogenic features significantly affect the therapeutic outcomes. Previous studies have explored in-depth tumor microenvironment profiling of ccRCC at single-cell level^{##REF##28475899##13##}. Tumor epithelial cells of ccRCC have been reported to play an active role in promoting immune cell infiltration^{##REF##34099557##4##}, while high proportions of endothelial cells were associated with lack of response to immunotherapy in ccRCC^{##REF##34099557##4##}. The CD8⁺ T cells and macrophages were reported to be increased in the tumor micro-environment^{##REF##33504936##14##}. The cytotoxic T cell subsets expressed higher levels of co-inhibitory receptors and effector molecules in RCC patients with effective response to immune checkpoint blockade^{##REF##33711272##15##}, and the maintenance of expanded T cell clones were correlated with drug response to anti-PD-1 therapy^{##REF##34715028##16##}. In addition to the classical roles of phagocytosis and antigen presentation, myeloid cells could impact response to cancer therapy^{##REF##34635571##17##} and directly contribute to tumor progression and metastases^{##REF##33526920##18##}. Besides, macrophages in RCC with effective responses to immune checkpoint blockade exhibited pro-inflammatory characteristic^{##REF##33711272##15##}. Similarly, <italic>TREM2</italic>/<italic>APOE</italic>/<italic>C1Q</italic>-positive macrophage was identified as a potential prognostic biomarker for ccRCC recurrence by single-cell protein analysis^{##REF##34019793##19##}. In addition, exhausted CD8⁺ T cells and M2-like macrophages showed co-occurrence in advanced ccRCC and expressed ligands and receptors supporting T cell dysfunction and M2-like polarization^{##REF##33711273##20##}. As a primary hematopoietic organ, bone marrow represents a unique reservoir for several types of immune cells, which would dramatically influence the trajectory of malignant disease. However, our incomplete understanding of the tumor microenvironment and heterogeneity of BMRCC hinder the efficient translation of these findings iBMBnto therapeutic treatment.</p>", "<p id=\"Par6\">Although important insights have been drawn for bone metastases treatment in the past decades, there remain multiple longitudinal barriers to gain a better understanding of the cell compositions and interconnections in the bone metastatic microenvironment. Traditional bulk transcriptome investigation is limited by insufficient resolution to characterize specific cellular types and expression of ligands and receptors of diverse cell types due to the average measuring of cell populations. Here, we systematically collect both primary and bone metastatic tumor tissues from ccRCC and performed scRNA-seq to explore the ecosystem of tumor, immune and stromal cells. The current study will provide additional therapeutic targets given a deeper insight into the cellular and molecular characteristics of BMRCC.</p>" ]

[ "<title>Methods</title>", "<title>Patient information</title>", "<p id=\"Par30\">Fourteen patients who were pathologically diagnosed with clear cell renal cell carcinoma, were enrolled in this study. A total of fifteen samples were obtained with two bone metastatic samples (P11_M1, P11_M2) were collected from one single patient. Six out of fifteen samples were collected from primary tumor site and nine of fifteen samples were collected from bone metastatic tumor site. Their clinical characteristics are summarized in Supplementary Table ##SUPPL##0##1##. All samples were discarded tissue after surgery. Written informed consent was provided from each patient prior to sample collection. This study was reviewed and approved by the Institutional Review Board of Fudan University Shanghai Cancer Center.</p>", "<title>Sample collection</title>", "<p id=\"Par31\">The femur metastasis sample was resected from tumor mass around the bone after pathological fracture, and only metastasis tumor sample was obtained to avoid potential influence of bone healing process. Similarly, surgical resection of rib metastasis included resection of the affected rib, adjacent muscles, and any other tissues adherent to the tumor. The specimen was also obtained from tumor mass without involvement of the osseous tissue. For the sacral and spinal (vertebral) sample, en bloc resection was performed in those patients to minimize the tumor residue, following a posterior spinal fixation using spinal instruments. In most patients, the pedicle screw fixation was used for posterior stabilization, in order to achieve biomechanical stability after vertebral resection.</p>", "<title>Single-cell isolation, cDNA amplification and library construction</title>", "<p id=\"Par32\">Fresh samples isolated from patients in operation were preserved in MACS Tissue Storage Solution (Miltenyi Biotec) at 4 °C. Tumor tissues were cut into a range of 0.2–1.0 g small pieces and dissociated in 5 mL enzyme mix containing 4.7 ml RPMI 1640 (Gibco), 200 μL Enzyme H, 100 μL Enzyme R and 25 μL Enzyme A (Miltenyi Biotec, MACS Tumor Dissociation Kit, human). The samples were subsequently incubated in a 37 °C thermostatic shaker for 35 min. Then suspended samples were filtered through a 40-μm Cell-Strainer nylon mesh (BD) with 30 mL of RPMI 1640 and centrifuged at 300 × g for 7 min. After removing the supernatant, we used Red Blood Cell Lysis Solution (Miltenyi Biotec #130-094-183) and the Dead Cell Removal Kit (Miltenyi Biotec #130-090-101) to remove red blood cells and obtain live cells. Cell suspension was centrifugated at 300 × g for 7 min and the pellet was re-suspended in 1 mL PBS solution. Once the desired cell suspension was obtained, the sample was immediately placed on ice for subsequent GEMs preparation and reverse transcription. The single cell libraries were prepared according to the standard protocols and sequenced on Illumina NovaSeq 6000 Systems using paired-end sequencing (150 bp in length).</p>", "<title>Single-cell RNA-seq data processing</title>", "<p id=\"Par33\">The scRNA-seq data generated from the 10× Genomics platform were aligned and quantified using CellRanger (version 6.0.2) against the GRCh38 human reference genome. A raw gene expression matrix for each scRNA-seq sample was generated by CellRanger. Cell-free RNA was removed using SoupX (version 1.5.2), and doublets were predicted and filtered using DoubletFinder (version 2.0.3). Then these matrices were combined as an integral gene expression matrix for all samples using the Seurat package (version 4.0.5) implemented in R (version 4.1.0). Further quality control was applied to cells, cells with less than 500 detected genes, more than 8000 detected genes, 20000 UMI counts and 10% mitochondrial gene count were filtered (Supplementary Fig. ##SUPPL##0##2a##). RunHarmony function in R Seurat package was applied to remove batch effects between data from different sources. The integrated gene expression matrix was used for the downstream analyses. The differences in cell abundances among samples and groups was calculated using the Milo framework^{##REF##34594043##65##}.</p>", "<title>Identification of the major cell types and their subtypes</title>", "<p id=\"Par34\">The Seurat R package was applied to identify major cell types. First, scTransform function^{##REF##31870423##66##} was used to normalize the influence of sequencing depth, mitochondria and other factors. Then 3000 highly variable genes were generated, and used to perform principal component analysis (PCA). The top 30 principal components were calculated to reveal the main axes of variation and denoise the data. Cells were clustered by unsupervised graph-based clustering algorithm using their expression profiles. For visualization, UMAP and t-SNE dimensionality reduction were applied by using RunUMAP and RunTSNE functions. The cluster-specific marker genes were identified by running FindAllMakers function with default parameters. Ten major cell types were identified: T cells (<italic>CD3D</italic>, <italic>CD3E</italic>), nature killer T-like (NKT) cells (<italic>GNLY</italic>, <italic>FGFBP2</italic>), myeloid cells (<italic>CD14</italic>, <italic>FCGR3A</italic>, <italic>LYZ</italic>), nature killer (NK) cells (<italic>XCL2</italic>, <italic>KLRC1</italic>), endothelial cells (<italic>PLVAP</italic>, <italic>PECAM1</italic>), cancer cells (<italic>KRT18</italic>, <italic>VEGFA</italic>), cancer-associated fibroblasts (CAFs) (<italic>COL1A1</italic>, <italic>COL1A2</italic>), B cells (<italic>CD79A</italic>, <italic>MS4A1</italic>), mast cells (<italic>TPSB1</italic>, <italic>TPSAB1</italic>), and neutrophils (<italic>S100A8</italic>, <italic>S100A9</italic>). Second, to identify subclusters within major cell type, the cells belonging to each cell type were re-analyzed separately with scTransform, dimensionality reduction, and clustering by unsupervised graph-based clustering algorithm. Then the subclusters were annotated to cell subtypes by subcluster-specific marker genes shown in the corresponding figures and Supplementary Data ##SUPPL##2##1##.</p>", "<title>Tissue distribution of clusters</title>", "<p id=\"Par35\">The ratio of observed to expected cell numbers (Ro/e) was calculated for each cell type or subtype between primary ccRCC and BMRCC to quantify the tissue preference of each cell type or subtype^{##REF##30479382##67##,##REF##33545035##68##}. The expected cell numbers for each combination of cell type or subtype and tissues were obtained from the chi-square test. Ro/e &gt; 1 suggested that one cell type or subtype was identified as being enriched in a specific tissue.</p>", "<title>Copy number variations analysis for tumor cells</title>", "<p id=\"Par36\">To further investigate genetic heterogeneity between tumor cells in primary and bone metastatic tumors, inferCNV (<ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/broadinstitute/inferCNV\">https://github.com/broadinstitute/inferCNV</ext-link>) was used to infer copy-number alteration for all the tumor cells. The copy number variations scores of the fibroblasts and endothelial cells were also calculated as a copy number variations control. Then the whole copy number variations profiles were normalized by subtracting the average expression profiles of control. The scores were restricted to the range −1 to 1 by replacing all values &gt;1 with 1 and all values &lt;−1 with −1, and any score between −0.3 and 0.3 was set to 0.</p>", "<title>Transcription factor analysis</title>", "<p id=\"Par37\">Activated TFs regulons in each CD8⁺Tem subset were analyzed using SCENIC^{##REF##28991892##36##}. The pySCENIC package (version 0.11.2) was applied with raw count matrix as input. Briefly, the regulons were identified by RcisTarget and the co-expression network was calculated using GRNBoost2. Next, the regulon activity foreach cell was scored by AUCell.</p>", "<title>Trajectory analysis</title>", "<p id=\"Par38\">To characterize the developmental state of MDSC and macrophages, the Monocle (version 2.20.0) algorithm^{##REF##28114287##35##} was applied with significant genes (<italic>q</italic> &lt; 0.05, top 3000 genes) of the studied cells were identified by using the differentialGeneTest function. Cell differentiation trajectory was constructed on these signature genes with the default parameters of Monocle after dimension reduction and cell ordering.</p>", "<title>Polarization state and functional phenotypes analysis of macrophages subtypes</title>", "<p id=\"Par39\">To further define dichotomous M1/M2 dualistic polarization state and functional phenotypes of macrophages subtypes, gene sets associated with M1/M2 state and angiogenesis/Phagocytosis phenotypes (Supplementary Table ##SUPPL##0##3##) were analyzed by comparing the mean expression values of cells in each macrophages subtype.</p>", "<title>Cell–cell communication analysis</title>", "<p id=\"Par40\">To explore the potential interactome between different cell types in RCC tumor micro-environment, the CellPhoneDB algorithm^{##REF##30429548##41##} was used to infer cell-cell communication. Single-cell transcriptomic data of all macrophage subtype and immune inhibitory T cells (CD4-Treg, CD8-Tex, CD8-Tem1) was analyzed by using CellPhoneDB package (version 3.0.0). The mean value of interactions was assessed for BMRCC vs primary ccRCC.</p>", "<title>Function analysis</title>", "<p id=\"Par41\">Metascape^{##REF##30944313##69##} (<ext-link ext-link-type=\"uri\" xlink:href=\"https://metascape.org/gp/index.html\">https://metascape.org/gp/index.html</ext-link>) was used for functional enrichment of different gene sets. The GSVA R package (version 1.40.1)^{##UREF##20##70##} from Bioconductor was used to assign pathway activity (c2BroadSets), which were described in the molecular signature database^{##REF##16199517##71##}. Gene Set Enrichment Analysis (GSEA) in the clusterProfiler R package (version 4.0.5)^{##UREF##21##72##} to evaluate the activation of hallmark pathways from the molecular signature database.</p>", "<title>Bulk RNAseq datasts analysis</title>", "<p id=\"Par42\">RCC expression data, mutation information and clinal information were performed using TCGAbiolinks R packages^{##REF##26704973##73##}. For survival analysis, the top ten significant genes of each cell subtype were used as gene set to evaluate the correlation between each cell subtype and the survival state of RCC patients by Kaplan-Meier Plotter (<ext-link ext-link-type=\"uri\" xlink:href=\"https://kmplot.com/analysis/index.php?p=background\">https://kmplot.com/analysis/index.php?p=background</ext-link>). Mutation analysis was performed using maftools R package (version 2.8.5)^{##REF##30341162##74##}. The RCC FPKM data was analyzed to compare the expression levels of genes (<italic>CD47</italic>, <italic>SIRPA</italic>, and the mean of <italic>CD47</italic> and <italic>SIRPA</italic>) at different clinical stages for RCC patient.</p>", "<title>Immunofluorescence staining</title>", "<p id=\"Par43\">Formalin-fixed, paraffin-embedded (FFPE) tissues containing primary and bone metastatic tumors of RCC were sliced into 4 μm sections and stained with antibodies against FAP (abcam, ab218164, Rabbit pAb, 1:1000), Vimentin (CST, 5741, Rabbit mAb, 1:1000), CD8A (abclonal, A0663, Rabbit mAb, 1:1000), PD-1 (abclonal, A20217, Mouse mAb, 1:1000), GZMB (abclonal, A22993, Rabbit mAb, 1:1000), CD68 (abclonal, A23205, Rabbit mAb, 1:1000), NRP2 (proteintech, 11268-1-AP, Rabbit pAb, 1:1000), SPP1 (proteintech, 22952-1-AP, Rabbit pAb, 1:1000), CD47 (SCBT, sc-12730, Mouse mAb, 1:500), and SIRPA (abcam, ab260039, Rabbit mAb, 1:1000) according to the standard protocols.</p>", "<title>Statistics and Reproducibility</title>", "<p id=\"Par44\">Mann-Whitney U test and Student’s <italic>t</italic> test for non-parametric samples were used to calculate <italic>p</italic> values between the two groups. For TCGA datasets, <italic>P</italic> values between two conditions were adjusted for multiple test corrections using the Benjamini–Hochberg algorithm to control the false discovery rate using DESeq2.</p>", "<title>Reporting summary</title>", "<p id=\"Par45\">Further information on research design is available in the ##SUPPL##4##Nature Portfolio Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<title>Cell landscape of primary and bone metastatic renal cell carcinoma</title>", "<p id=\"Par7\">To explore the cellular and molecular basis of bone metastasis of renal cell carcinoma, we collected 6 primary and 9 bone metastatic tumors from 14 ccRCC patients for scRNA-seq analyses (Fig. ##FIG##0##1a##, Supplementary Fig. ##SUPPL##0##1a, b## and Supplementary Table ##SUPPL##0##1##). Among them, 3 BMRCC patients were treated with tyrosine kinase inhibitor (TKI) and PD-1 inhibitor (Supplementary Table ##SUPPL##0##1##). In addition, single-cell RNA-seq samples of 6 primary ccRCC in different stages, 6 healthy kidneys and 6 healthy bone marrows were enrolled in the study from public datasets^{##REF##31896769##21##–##REF##33711272##24##} for elucidating the unique characteristics of BMRCC. In total, we obtained single cell transcriptomes from a total of 258,084 cells. After stringent quality control, 33,119 cells from early primary tumors, 27,275 cells from advanced primary tumor, 64,582 cells from bone metastatic tumors (Supplementary Fig. ##SUPPL##0##2a## and Supplementary Table ##SUPPL##0##2##), 27,210 cells from healthy kidney, and 18,396 cells from healthy bone marrows were reserved. Integration of all the cells using unsupervised graph-based clustering revealed 11 major cell types (Fig. ##FIG##0##1b## and Supplementary Fig. ##SUPPL##0##2b, c##), which were further annotated based on canonical cell markers. Specifically, the immune cell types consisted of T cells (<italic>CD3D</italic> and <italic>CD3E</italic>), NKT cells (<italic>GNLY</italic> and <italic>FGFBP2</italic>), NK cells (<italic>XCL2</italic> and <italic>KLRC1</italic>), myeloid cells (<italic>CD14</italic>, <italic>FCGR3A</italic>, and <italic>LYZ</italic>), B cells (<italic>CD79A</italic> and <italic>MS4A1</italic>), mast cells (<italic>TPSB1</italic> and <italic>TPSAB1</italic>), and plasma cells (<italic>MZB1</italic> and <italic>JCHAIN</italic>). The non-immune cells included endothelial cells (<italic>PVALP</italic> and <italic>PECAM1</italic>), CAFs (<italic>COL1A1</italic> and <italic>COL1A2</italic>), and cancer cells (<italic>KRT18</italic> and <italic>VEGFA</italic>) (Fig. ##FIG##0##1c##).</p>", "<p id=\"Par8\">We next compared the relationship between the major cell types and BMRCC, with primary ccRCC and healthy bone marrows as references. We calculated an enrichment score using Ro/e analysis which compared the ratio of each cell type in BMRCC with that in primary ccRCC or healthy bone marrows (Fig. ##FIG##0##1d## and Supplementary Fig. ##SUPPL##0##2d–f##). The results showed that B cells, plasma cells and T cells were enriched in BMRCC tumors (Fig. ##FIG##0##1d, e## and Supplementary Fig. ##SUPPL##0##2d##), indicating the infiltration of lymphoid cells in the bone metastasis microenvironment. By contrast, NKT cells, mast cells and cancer cells were enriched in early- and late-stage primary ccRCC (Fig. ##FIG##0##1d, e##). Mast cells in tumors were thought to play a dual role in influencing the fate of tumor cells^{##REF##2591732##25##}, the enrichment of mast cells in primary ccRCC instead of BMRCC hinted that mast cells might exhibit diverse functions across different tumor environment. Interestingly, the treatment-naïve BMRCC patients showed increased infiltration of B cells and myeloid cells in comparison with the BMRCC patients with the immunotherapy treatment (Fig. ##FIG##0##1e, f##, and Supplementary Fig. ##SUPPL##0##2e##), suggesting that the immunotherapy treatment might help to reshape the immune microenvironment of BMRCC.</p>", "<title>Tumor cells in bone metastasis have stronger angiogenesis ability</title>", "<p id=\"Par9\">We next dissected the gene signatures of all tumor cells in the cohort and found that the primary and bone metastatic enriched cancer cells revealed distinct gene signatures (Fig. ##FIG##1##2a## and Supplementary Fig. ##SUPPL##0##3a–c##). Notably, genes with higher expression levels in the bone metastatic tumors demonstrated a pro-angiogenic signature, and were enriched in blood vessel development and <italic>VEGFA</italic>-<italic>VEGFR2</italic> signaling pathways (Fig. ##FIG##1##2##a, b and Supplementary Fig. ##SUPPL##0##3a, b##), suggesting the angiogenesis ability of cancer cells in the BMRCC. By contrast, subpopulations in the primary tumors exhibited higher expression of genes associated with response to oxygen levels, <italic>IL-18</italic> signaling pathway and <italic>TNF</italic> signaling pathway (Fig. ##FIG##1##2b##). In addition, higher MHC associated genes (e.g., <italic>HLA-B</italic> and <italic>HLA-C</italic>) were highly expressed in primary ccRCC (Supplementary Fig. ##SUPPL##0##3c##). major histocompatibility complex class II is critical for antigen presentation to T cells, and is important for the efficacy of immunotherapy^{##UREF##6##26##}. We also observed that the BMRCC patients treated with immunotherapy showed downregulation of <italic>TP53</italic>-regulated genes (e.g., <italic>TP53I3</italic>, <italic>COX6C</italic> and <italic>TPM2</italic>) (Supplementary Fig. ##SUPPL##0##3d##).</p>", "<p id=\"Par10\">To further investigate genetic heterogeneity between tumor cells in primary and bone metastatic tumors, we inferred copy-number alterations for all the tumor cells, with the fibroblasts and endothelial cells as normal ploidy controls (Supplementary Fig. ##SUPPL##0##3e##). We found aberrant copy-number alterations regions in the short arm of chromosome 3, long arm of chr13, and chr14. Specifically, extensive chromosomal gains were observed in the long arm of chr5 and chr16. Of note, deletions in chromosome 3p tended to be a universal truncal event in ccRCC, as this region contains the <italic>VHL</italic> tumor suppressor locus^{##REF##30372397##27##,##REF##24487277##28##}. TCGA-KIRC cohort confirmed that <italic>VHL</italic> gene was the most common mutation in ccRCC patients (Supplementary Fig. ##SUPPL##0##3f##). Interestingly, we also observed a copy number amplification on chromosome 8q in the bone metastatic samples (<italic>P</italic> &lt; 2.2e−16, Student’s <italic>t</italic> test) (Fig. ##FIG##1##2c## and Supplementary Fig. ##SUPPL##0##3e##). Functional analysis of genes located in the 8q amplification region showed a significant enrichment in <italic>WNT</italic> signaling pathway (Fig. ##FIG##1##2d##), an ancient and evolutionarily conserved pathway that regulates crucial aspects of cell fate determination and cell migration. Further examination showed that the activation of <italic>WNT</italic> signaling pathway in the BMRCC tumors was significantly higher than that of primary ccRCC tumors (Fig. ##FIG##1##2e##). These results suggested the important regulation roles of angiogenesis and <italic>WNT</italic> signaling pathway in the BMRCC cells and provided a potential therapeutic solution to targeting their activities in clinical treatment.</p>", "<title>Cancer-associated fibroblasts were associated with metastasis and poor prognosis of RCC</title>", "<p id=\"Par11\">As the most prevalent component in the tumor microenvironment, CAFs play diverse roles in driving tumorigenesis and affecting response to treatment^{##REF##30841909##29##}. Thus, we next compared the heterogeneity of CAFs between primary ccRCC and BMRCCs. Focused examination of the CAF compartment revealed 5 subclusters based on canonical cell markers (Fig. ##FIG##2##3a, b##). Common fibroblast marker genes such as <italic>S100A4</italic>, <italic>SPARCL1</italic> and non-specific mesenchymal markers <italic>VIM</italic> and <italic>SPARC</italic> were found to be expressed across all subgroups (Supplementary Fig. ##SUPPL##0##4a##). Gene ontology (GO) analysis using marker gene signatures in each subpopulation showed differential preferences for functional pathways (Fig. ##FIG##2##3c##). Specifically, developmental CAFs (dCAFs), with high expression of <italic>MYH11</italic> and <italic>MCAM</italic>, was functionally featured by muscle structure and tissue development (Fig. ##FIG##2##3b, c## and Supplementary Fig. ##SUPPL##0##4b##), and presented in both primary ccRCC and BMRCC (Fig. ##FIG##2##3d## and Supplementary Fig. ##SUPPL##0##4c##). While, inflammatory CAFs (iCAFs) was characterized by interferon alpha/beta signaling, regulation of myeloid cell differentiation, and major histocompatibility complex class I antigen presentation (Fig. ##FIG##2##3c## and Supplementary Fig. ##SUPPL##0##4d##), consistent with the characteristics of the recently described antigen-presenting CAF (apCAFs)^{##REF##31197017##30##}. Vascular CAFs (vCAFs) were featured by endothelium development and vasculogenesis (Fig. ##FIG##2##3c##).</p>", "<p id=\"Par12\">Both matrix CAF (mCAF_1 and mCAF_2) clusters were enriched in the BMRCC patients (Fig. ##FIG##2##3d, e##), with high expression levels of extracellular matrix proteins (<italic>COL5A2</italic>, <italic>AEBP1</italic>, <italic>COL1A1</italic>, <italic>COL1A2</italic> and <italic>COL3A1</italic>) (Fig. ##FIG##2##3c## and Supplementary Fig. ##SUPPL##0##4e##). In addition to extracellular matrix organization, mCAF_2 was also enriched in collagen fibril organization with expression of <italic>FAP</italic>, <italic>COMP</italic>, <italic>MMP13</italic>, and <italic>SFRP2</italic> (Fig. ##FIG##2##3c## and Supplementary Fig. ##SUPPL##0##4f##). Given the role of CAFs in the assembly of fibronectin that is highly abundant in extracellular matrix and strongly associated with metastasis^{##REF##28931556##31##}, mCAF_2 might be the CAF subtype affecting bone metastasis of renal cell cancer. Comparative analysis also revealed that the mCAF_2 subtype was more abundant in BMRCC (Fig. ##FIG##2##3d, e##). The higher abundance of mCAF_2 in BMRCC than in primary ccRCC was validated by immunostaining experiments (Fig. ##FIG##2##3f## ). Besides, mCAF_2 exhibited significantly higher enrichment score than mCAF_1 in the epithelial mesenchymal transition (Fig. ##FIG##2##3g##), which is closely related to cancer progression and metastasis^{##REF##27042694##32##}. The proportion of mCAF_2 was not decreased in BMRCC samples with treatment, suggesting the little influence of fibroblasts upon immunotherapy. The expression of mCAF_2 marker genes was higher in ccRCC patients with stage III/IV (Supplementary Fig. ##SUPPL##0##4g##). We next grouped the patients with ccRCC into two groups based on the expression level of marker genes of mCAF_2, and found that the group with high expression of mCAF_2 markers showed significantly worse prognosis (Supplementary Fig. ##SUPPL##0##4h##). These results suggested that the mCAF_2 cluster is strongly associated with BMRCC and could predict poor prognosis for RCC patients.</p>", "<title>Diversity of T cell subtypes in BMRCCs</title>", "<p id=\"Par13\">To reveal the intrinsic structure and potential functional subtypes of lymphoid cells, the T cell populations were further subdivided into 13 sub-clusters, including 5 clusters for CD4⁺ T cells, 8 clusters for CD8⁺ T cells and 1 mitotic T cell cluster (Fig. ##FIG##3##4a, b## and Supplementary Fig. ##SUPPL##0##5a##). Each of these clusters showed specific expression of unique signature genes (Fig. ##FIG##3##4c##). The proportions of CD8⁺ T cells were increased with tumor progression, and decreased in the BMRCC after treatment (Fig. ##FIG##3##4b##). Two clusters of inhibitor CD4⁺ T cells (CD4-Treg and CD4-Tex) were identified, CD4-Treg was characterized by specific expression of <italic>FOXP3</italic>, <italic>TNFRSF9</italic> and <italic>TIGIT</italic>, whereas CD4-Tex expressed high levels of <italic>CTLA4</italic>, <italic>PDCD1</italic> and <italic>CXCL13</italic> (Fig. ##FIG##3##4a## and Supplementary Fig. ##SUPPL##0##5b##). Both of them were dominant in bone metastatic tumors, and the proportion of CD4-Treg decreased in the BMRCC patients with treatment (Fig. ##FIG##3##4d##). We also found a large group of effect memory T cells (CD8-Tem) (Fig. ##FIG##3##4a, e##), which could be divided to two clusters (CD8-Tem1 and CD8-Tem2). CD8-Tem1 that had higher expression of <italic>GZMB</italic> and <italic>CTSW</italic> were enriched in bone metastatic tumors, whereas CD8-Tem2 cells were enriched in primary ccRCC with higher expression of <italic>KLRD1</italic>, <italic>KLRF1</italic>, and <italic>KLRG1</italic> (Fig. ##FIG##3##4d## and Supplementary Fig. ##SUPPL##0##5c##).</p>", "<p id=\"Par14\">The proportion of exhausted T cell cluster CD8-Tex, with high expression levels of <italic>PDCD1</italic> and <italic>HAVCR2</italic>, was increased in treatment-naive BMRCC samples (Fig. ##FIG##3##4d## and Supplementary Fig. ##SUPPL##0##5d##). Specifically, CD8-Tex of late-stage primary ccRCC exhibited higher expression of <italic>ENTPD1</italic>, which is related to terminal differentiation of T cells^{##REF##34914499##33##}. By contrast, <italic>PDCD1</italic>, <italic>CXCL13</italic>, and <italic>LGALS3</italic> were highly expressed in the CD8-Tex of BMRCC (Supplementary Fig. ##SUPPL##0##5d##), indicating the influence of metastatic niche in T cell subsets. In addition, CD8-Tex cells in the BMRCC samples highly expressed genes associated with interferon response, e.g., <italic>CCL5</italic>, <italic>CCL3</italic>, and <italic>ISG15</italic> (Fig. ##FIG##3##4f##). This observation was consistent with previous findings that intrinsic type I interferon signaling of CD8⁺ T cells skewed the differentiation to a terminal exhaustion state^{##UREF##7##34##}.</p>", "<p id=\"Par15\">Interestingly, we found that the proportions of CD8-Tex were decreased and CD8-Tem was increased, especially CD8-Tem1, in the BMRCC after treatment (Fig. ##FIG##3##4d##), which was verified by immunostaining assay (Supplementary Fig. ##SUPPL##0##5e##). Thus, we next explored the alteration of T cell profiles upon the treatment of PD-1 inhibitor in the BMRCC, and found that CD8-Tex cells in the treated samples showed much higher expression of T cell activation associated genes, including <italic>JUNB</italic>, <italic>CEBPB</italic>, and <italic>HLA-DQB1</italic> (Fig. ##FIG##3##4f##). Further cell trajectory analysis using Monocle2^{##REF##28114287##35##} revealed that CD8-Tem2 and CD8-Tem1 cells could differentiate into CD8-Tex cells in the treatment-naïve BMRCC (Fig. ##FIG##3##4g##). While, the CD8-Tex cells in the treated BMRCC patients demonstrated potential to differentiate back into CD8-Tem2 through CD8-Tem1 cluster (Fig. ##FIG##3##4h##). Moreover, the expression of CD8-Tem1 marker genes were higher in ccRCC patients of stage III/IV (Supplementary Fig. ##SUPPL##0##5f##). Survival analysis indicated that high expression level of CD8-Tem1 markers in primary ccRCC was significantly associated with poor prognosis (Supplementary Fig. ##SUPPL##0##5g##), whereas the high level of CD8-Tem2 indicated better prognosis (Supplementary Fig. ##SUPPL##0##5h##). These results suggested that immunotherapy might reshape the differentiation trajectory of CD8⁺ T cells into activated effector T cells in the bone metastases.</p>", "<p id=\"Par16\">To identify potential transcription factors (TFs) associated with the two different transition directions of CD8-Tem1 cells, we then performed gene regulatory network analysis using SCENIC^{##REF##28991892##36##} and uncovered a series of regulons differentially expressed in CD8-Tem1 cells between the treatment-naïve and treated BMRCC (Fig. ##FIG##3##4i##). Specifically, <italic>ZFP30</italic>, <italic>ZNF569</italic>, <italic>TCF7</italic>, <italic>MYBL1</italic>, and <italic>HOXB2</italic> were predominantly present in treatment-naïve BMRCC, while <italic>XBP1</italic>, <italic>BCL3</italic>, <italic>ARID5B</italic>, <italic>RELB</italic>, and <italic>NR2C1</italic> were featured by treated BMRCC (Fig. ##FIG##3##4i##). The targeted genes highly expressed in the CD8-Tem1 of treatment-naïve BMRCC were enriched in cellular metabolic processes and regulation of leukocyte differentiation, while those enriched in the treated group were associated with functions including cytosine signaling in immune system, T cell activation, immune effector process and type I interferon signaling pathway (Fig. ##FIG##3##4j##). Together, these results indicated that BMRCCs were enriched with infiltrated T cell subtypes with distinct status from the primary ccRCC, and treatment might affect the trajectory path of CD8-Tem cells by activating TFs for T cell activation in the BMRCC.</p>", "<title>Identification of myeloid cell subsets in primary and BMRCC</title>", "<p id=\"Par17\">To generate a deeper transcriptional landscape of tumor-infiltrating myeloid cells, which modulate key cancer-associated activities and comprise various subsets with divergent functions, including immune evasion and responses to different types of cancer therapy^{##REF##27339708##37##}. We further explored the subpopulations of myeloid cells and identified 4 major lineages (Fig. ##FIG##4##5a##). Myeloid-derived suppressor cells (MDSC), macrophages, dendritic cells (DC), and monocytes showed high expression of canonical cell markers, including <italic>S100A12</italic>, <italic>APOE</italic>, <italic>HLA-DQA2</italic>, and <italic>HES4</italic>, respectively (Fig. ##FIG##4##5b##). We next examined the composition of major lineages of tumor-infiltrating myeloid between the primary ccRCCs and BMRCCs (Fig. ##FIG##4##5c##). Monocytes and DCs were abundant in primary ccRCC, whereas MDSCs and macrophages were increased in BMRCC (Fig. ##FIG##4##5c##), supporting the notion that MDSCs are generated in the bone marrow from common myeloid progenitor cells^{##REF##26858199##38##}.</p>", "<p id=\"Par18\">Macrophages have been reported to differentiate from monocytes in primary tumors^{##REF##33711273##23##}, we next explored whether the differentiation trajectory of macrophages in the BMRCC remained the same as the primary ccRCC. Trajectory analysis using the identified MDSCs, monocytes and macrophages in primary ccRCC and BMRCCs as well as normal bone marrow tissues revealed a complete picture of the differentiation trajectories of myeloid cells in the ccRCC (Fig. ##FIG##4##5d##). The results showed that macrophages in healthy kidney, early- and late-stage primary ccRCC and healthy bone marrows are mostly differentiated from monocytes, while macrophages are mainly derived from MDSC in the BMRCC (Fig. ##FIG##4##5d##). These results revealed enrichment of different myeloid subtypes together with distinct differentiation trajectories in the BMRCC in comparison with the primary ccRCC.</p>", "<p id=\"Par19\">Further clustering of the bone metastasis-enriched tumor-infiltrating myeloid cells MDSCs and macrophages gave rise to 14 sub-populations with specific gene signatures, including 4 groups of MDSCs and 10 subtypes of macrophages (Fig. ##FIG##4##5e, f##, Supplementary Fig. ##SUPPL##0##6a–c##). We then compared infiltration of subgroups of myeloid cells between primary ccRCC with BMRCC (Supplementary Fig. ##SUPPL##0##6a, b##). We observed that MDSC-<italic>S100A12</italic> and Macro-<italic>NLRP3</italic>, Macro-<italic>MRC1</italic>, Macro-<italic>CX3CR1</italic>, Macro-<italic>BAG3</italic>, Macro-<italic>CCL18</italic>, and Macro-<italic>NRP2</italic> were enriched in the BMRCC, with primary ccRCC from early and late stages as comparison (Supplementary Fig. ##SUPPL##0##6a, b##). MDSCs were reported to have the ability to markedly influence the trajectory of malignant diseases^{##REF##26858199##38##,##REF##28052991##39##}. We then explored the cell transformation relationship between MDSC and macrophage subtypes in the BMRCC, and found that MDSC subgroups MDSC-<italic>S100A12</italic> and MDSC-<italic>VCAN</italic> were the potential origins of macrophages, which were further divided into two branches with different macrophage subgroups (Fig. ##FIG##5##6a## and Supplementary Fig. ##SUPPL##0##6d##). Notably, genes highly expressed at the start of the trajectory were enriched in GO terms including chemotaxis, regulation of growth and osteoblast differentiation (Fig. ##FIG##5##6b##), consistent with the upregulated expression of <italic>S100A9</italic>, <italic>S100A12</italic>, <italic>S100A4</italic> and <italic>S100A6</italic> in the MDSC-<italic>S100A12</italic> and MDSC-<italic>VCAN</italic> subtypes (Supplementary Fig. ##SUPPL##0##6e##). The expression of genes related to regulation of myeloid cell differentiation were increased at the transformation stage, accompanied by the transcriptional regulation by <italic>TP53</italic> (Fig. ##FIG##5##6b## and Supplementary Fig. ##SUPPL##0##6e##). Genes including <italic>APOE</italic>, <italic>CD81</italic>, <italic>CD9</italic> and <italic>GPNMB</italic> showing high expression levels at the end of differentiation process were significantly enriched in leukocyte migration and T cell activation pathways (Fig. ##FIG##5##6b## and Supplementary Fig. ##SUPPL##0##6e##), suggesting potential interaction between macrophages and T cells in the BMRCC.</p>", "<p id=\"Par20\">By defining the dichotomous M1/M2 dualistic polarization state and functional phenotypes of macrophages subtypes, we found that Macro-<italic>CCL18</italic> and Macro-<italic>MRC1</italic> subgroups, which differentiated in the same branch (Branch 1) at the developmental trajectory, exhibited higher M2 signature and preferential expression of genes involved in phagocytosis (Fig. ##FIG##5##6a, c##). For the subtypes of macrophages on Branch 2, Macro-<italic>NLRP3</italic> showed higher expression of phagocytosis signatures (Fig. ##FIG##5##6a, c##), whereas Macro-<italic>NRP2</italic> exhibited higher pro-angiogenic signatures and M2 signature (Fig. ##FIG##5##6a, d## and Supplementary Fig. ##SUPPL##0##6f##). Besides, the M2 signature expression levels of Macro-<italic>NRP2</italic> in the BMRCC were significantly higher than primary ccRCC of both early and late stages (Fig. ##FIG##5##6e##). In addition, high expression of Macro-<italic>NRP2</italic> was associated with poor prognosis of primary ccRCC patients (Supplementary Fig. ##SUPPL##0##6g##). The existence of Macro-<italic>NRP2</italic> in BMRCC was showed by mIHC (Fig. ##FIG##5##6f##). These results indicated that Macro-NRP2 had anti-inflammatory and M2 polarization characteristics in the BMRCC, and could also be used as a predictive marker for prognosis of ccRCC.</p>", "<title>Interaction between macrophages and T cells in the bone metastatic environment</title>", "<p id=\"Par21\">Given the dominance of macrophages in the BMRCC and their potential role for regulating T cell activities in the tumor microenvironment^{##REF##30718830##40##}, we next explored the cell-cell interactions between macrophage subtypes and immune-inhibitory T cells using CellPhoneDB^{##REF##30429548##41##}. Compared with primary ccRCC, we found specific receptor-ligand pairs between macrophages and immune-inhibitory T cells were enriched in BMRCC, including pro-migratory interaction (<italic>CCL4L2</italic>-<italic>VSIR</italic>), and immune-inhibitory interactions (<italic>SIRPA</italic>-<italic>CD47</italic>, <italic>LGALS9</italic>-<italic>HAVCR2</italic>, <italic>LGALS9</italic>-<italic>CD47</italic>, <italic>TNF</italic>-<italic>FAS</italic> and <italic>TNF</italic>-<italic>ICOS</italic>) (Fig. ##FIG##6##7a##). Among them, the interaction between <italic>SIRPA</italic>-<italic>CD47</italic> pairs was widespread across diverse types of macrophage and inhibitory T cells (Fig. ##FIG##6##7a##). In addition, the interaction between macrophages and inhibitory T cells though <italic>SIRPA</italic>-<italic>CD47</italic> increased with the malignant progression of ccRCC, with the lowest in the early stage of ccRCC and highest in the BMRCC (Fig. ##FIG##6##7b##). Further analysis showed that expression levels of <italic>CD47</italic> in immune inhibitory T cells were much higher in BMRCC than those of primary ccRCC, and PD-1 inhibitor treatment could not decrease the <italic>CD47</italic> expression (Fig. ##FIG##6##7c## and Supplementary Fig. ##SUPPL##0##7a##). <italic>SIRPA</italic> was found to be highly expressed in macrophages of BMRCC (Fig. ##FIG##6##7d## and Supplementary Fig. ##SUPPL##0##7b##), and expression level was further elevated in macrophages of treated BMRCC (Fig. ##FIG##6##7d## and Supplementary Fig. ##SUPPL##0##7b##). These results were confirmed by the higher expression of <italic>SIRPA</italic> and <italic>CD47</italic> in patients with late-stage ccRCC (Fig. ##FIG##6##7e##, Supplementary Fig. ##SUPPL##0##7c, d##). Consistently, compared with the primary ccRCC, we observed the simultaneous enrichment of <italic>SIRPA</italic> and <italic>CD47</italic> in the BMRCC by immunofluorescence staining (Fig. ##FIG##6##7f, g##). Interestingly, the co-expression of <italic>SIRPA</italic> and <italic>CD47</italic> was significantly associated with poor prognosis for ccRCC patients (HR = 1.39, <italic>P</italic> = 0.032) (Fig. ##FIG##6##7h##), while high expression of <italic>CD47</italic> or <italic>SIRPA</italic> only slightly contribute to poor prognosis of ccRCC patients (HR = 1.34, <italic>P</italic> = 0.054 for <italic>CD47</italic>; HR = 1.33, <italic>P</italic> = 0.078 for <italic>SIRPA</italic>) (Supplementary Fig. ##SUPPL##0##7e, f##). Taken together, the expression of <italic>SIRPA</italic>-<italic>CD47</italic> pair could serve as a potential bone metastasis signal with poor prognosis for RCC (Fig. ##FIG##6##7i##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par22\">Here, we provide a high-resolution landscape of human primary (early and advanced stages) and BMRCC, and the underlying molecular mechanisms for bone metastasis of RCC. Based on the scRNA-seq data, we compared the transcriptomic profiles of cancer cells from primary ccRCC with BMRCCs. We also observed major lineages of cell types together with subtypes of fibroblasts, myeloid cells and T cells that enriched in the BMRCC, which were supported by their association with poor prognosis. The <italic>SIRPA</italic>-<italic>CD47</italic> interaction between myeloid subgroups and specific T cell clusters pointed to molecular-targeted immunotherapy as potential therapeutic solutions to be further explored for the treatment of BMRCC.</p>", "<p id=\"Par23\">As the most common subtype of RCC, previous studies have applied scRNA-seq to identify cell of origin and transcriptomic differences among different cell types in ccRCC^{##REF##34099557##4##,##REF##28793269##42##}. Ke et al. reported that hypoxia response, lipid biosynthesis, and localization pathways were enriched in malignant renal cells compared with normal renal cells^{##REF##32396851##43##}. Here, we found cancer cells in BMRCC showed stronger migration ability and angiogenesis ability in comparison with primary tumor cells of RCC. Together, the alteration from metabolic capacity to migratory capacity might point to the malignant evolution of renal tumor cells to RCC metastasis.</p>", "<p id=\"Par24\">Our scRNA-seq analysis revealed that genes enriched in tumor cells with evident copy number amplifications were associated with the <italic>WNT</italic> signaling pathway in the bone metastatic environment. <italic>WNT</italic> signaling is critically involved in both the development and homeostasis of tissues via regulation of their endogenous stem cells^{##REF##21603945##44##}. In tumor microenvironment, aberrant <italic>WNT</italic> signaling was considered to play a key role in the initiation, maintenance and development of multiple cancers by regulating the behavior of cancer stem cells^{##REF##26775730##45##,##REF##27322325##46##}. Previous studies have demonstrated <italic>WNT</italic> signaling pathway as a good therapeutic target for primary renal cancer^{##UREF##8##47##,##REF##32104684##48##}. Potential therapeutic reagents targeting this pathway might work as efficient treatment solutions for BMRCC in clinic.</p>", "<p id=\"Par25\">CAFs are the most prominent stromal components in solid tumors and rarely studied in RCC. Four transcriptionally diverse subpopulations of CAFs were defined in breast cancer^{##REF##30514914##49##}, which three groups were also found in primary ccRCC and BMRCCs (Fig. ##FIG##2##3##). The iCAF cluster was a specific CAF subpopulation found in primary ccRCC and BMRCCs, and it was also described in pancreatic ductal adenocarcinoma^{##REF##31197017##30##}. Interestingly, we found a mCAF cluster (mCAF_2) with high expression of <italic>FAP</italic> and <italic>MMP13</italic> dominant in BMRCC (Supplementary Fig. ##SUPPL##0##4g##). <italic>FAP</italic> is a dimeric Type II transmembrane glycoprotein with proteolytic activity, and was reported to be highly expressed in tumor stroma^{##UREF##9##50##}. <italic>FAP</italic> was also considered as a promising target for radionuclide-based approaches for diagnosis and treatment of tumors^{##REF##33127618##51##}. Our results here showed that <italic>FAP</italic>⁺ CAFs might be associated with bone metastasis of RCC, and the underlying mechanism deserves further investigation.</p>", "<p id=\"Par26\">T cells are the most abundant and best-characterized population in the tumor microenvironment of solid tumors. Here we revealed the dominance of inhibitory T cells and higher expression of exhaustion-related genes in the BMRCC, consistent with previous findings that exhausted T cells are enriched in advanced tumors^{##UREF##10##52##,##REF##29634943##53##}. In addition to the <italic>PDCD1</italic>, the <italic>LAG3</italic> and <italic>CXCL13</italic> were also overexpressed in the bone metastatic samples. Previous studies have shown that <italic>CXCL13</italic> could reshape the lymphoid structures and promote response to immunotherapy in multiple advanced cancers^{##UREF##11##54##–##UREF##12##56##}. Thus, restoring the exhausted T cells provides a promising strategy for preventing tumor progression. Our results showed that the trajectory path of CD8-Tem1 reversed from CD8-Tex and differentiated into CD8-Tem2 cells after treatment, suggesting the effectiveness of PD-1 inhibitor to the BMRCC. The distinct differentiation directions of CD8-Tem1 in the BMRCC after treatment might be partially explained by the differential activation of TFs and their downstream gene expressions, which needs to be further explored for better understanding of potential regulatory mechanisms.</p>", "<p id=\"Par27\">In addition, we also found the enrichment of MDSCs and macrophages in the bone metastatic tumors of RCC. The MDSCs are a population of myeloid cells and immature myeloid cells could convert to immunosuppressive MDSCs under pathologic conditions^{##UREF##13##57##}. The abundance of MDSCs in the BMRCC might represent a pathogenic state of activation of monocytes in the bone metastasis environment. Our trajectory analysis revealed that both MDSCs and monocytes are both progenitors of macrophages, and macrophages differentiate from monocytes in the primary ccRCC, consistent with previous reports^{##REF##33711272##24##,58]}. The differentiation trajectory of macrophages from MDSCs in the BMRCC was also different from that of normal bone marrows, hinting that targeting MDSC may provide tangible clinical benefits in the BMRCC. We also identified a bone metastasis-enriched macrophage subtype with high expression of <italic>NRP2</italic> gene, which is a single transmembrane receptor and plays a key role in promoting tumor proliferation, invasion and metastasis by interacting with vascular endothelial growth factors^{##UREF##14##58##,##UREF##15##59##}. <italic>NRP2</italic> is not detectable in the bone marrow or monocytes of humans^{##UREF##16##60##,##UREF##17##61##}, and the expression of <italic>NRP2</italic> in myeloid cells is upregulated during the differentiation to macrophages^{##UREF##18##62##}. Consistent with our findings that Macro-<italic>NRP2</italic> was characterized by high expression of M2 macrophage features, a previous study reported that reduced expression of <italic>NRP2</italic> after LPS stimulation of macrophages triggers M1 polarization^{##UREF##19##63##}. Given the M2 polarization and pro-angiogenesis features of Macro-<italic>NRP2</italic> and its potential in regulating immune inhibitory T cells in the BMRCC, this macrophage subgroup emerged as a potential therapeutic target for further investigations in the BMRCCs. The <italic>CD47</italic> expression on inhibitory T cells might inhibit macrophage-mediated elimination in a manner that bears a superficial resemblance to the inhibition of macrophages by <italic>CD47</italic>⁺ cancer cells^{##REF##33711272##15##,##REF##32433947##64##}. The inhibition of macrophage function favors the survival of inhibitory T cells and cancer cells, which in turn contributes to the malignancy of tumors. Thus, the interaction between macrophages and inhibitory T cell clusters through <italic>SIRPA</italic> ligand and <italic>CD47</italic> receptor serves as an alternative way for understanding the bone metastasis of RCC.</p>", "<p id=\"Par28\">Limitations of this study include unpaired primary and bone metastatic biopsy tissues and the small sample size. The uncertainty in the development of bone metastatic tumors from the initial treatment of ccRCC limited the ability to collect paired primary and BMRCC samples from the same patient in clinical practice. The findings might thus be confounded by the variations of genetic background and somatic mutations. Although the inclusion of single-cell data from late-stage primary ccRCC, normal kidney and healthy bone marrow tissues could reduce some of the confounding factors, further studies are needed to investigate the gene signatures in patients after controlling such clinical variables. Besides, the small sample size of the cohort limited the power of statistical significance in the results. Biological variation between samples may be confusing some of the results and more study samples will be needed in the future to confirm these results. In addition, the BMRCC patients included in our cohort are treated with immunotherapy and TKIs, which hinders the possibility to explore the influence of single regimen. The treatment of collected samples are anti-vascular and anti-PD-1 therapy, so we mainly included the treatment for stratification in these cell cancer cells and T cells. The effect of these treatments on other cell types like CAF and macrophages might be indirect and complicated, further studies are needed for better understanding of different treatment options on the microenvironment of BMRCC. Furthermore, despite of the survival analysis using TCGA cohort suggested that the signatures enriched in BMRCC might be markers indicating malignant tumor progression, our results have shown BMRCC was different from late-stage primary ccRCC (Supplementary Fig. ##SUPPL##0##2d##, ##SUPPL##0##5d##, Fig. ##FIG##4##5c, f##, and Fig. ##FIG##5##6e##), raising the necessity of generating large cohorts of BMRCC samples for further exploration.</p>", "<p id=\"Par29\">In summary, our comprehensive characterization of cell landscape of BMRCC revealed that intra-tumoral heterogeneity of primary and bone metastatic ccRCC. Our study identified key cell subsets and molecular features enriched in the bone metastatic environment of ccRCC. The development trajectory and cell-cell interaction analyses also revealed immune cell subtypes served as targets for BMRCC. Although the descriptive nature of this study, our data offer a rich resource to better understand various cell types in BMRCCs and thus provide valuable insights for therapeutic solutions.</p>" ]

[]

[ "<p id=\"Par1\">Bone metastasis is of common occurrence in renal cell carcinoma with poor prognosis, but no optimal treatment approach has been established for bone metastatic renal cell carcinoma. To explore the potential therapeutic targets for bone metastatic renal cell carcinoma, we profile single cell transcriptomes of 6 primary renal cell carcinoma and 9 bone metastatic renal cell carcinoma. We also include scRNA-seq data of early-stage renal cell carcinoma, late-stage renal cell carcinoma, normal kidneys and healthy bone marrow samples in the study to better understand the bone metastasis niche. The molecular properties and dynamic changes of major cell lineages in bone metastatic environment of renal cell carcinoma are characterized. Bone metastatic renal cell carcinoma is associated with multifaceted immune deficiency together with cancer-associated fibroblasts, specifically appearance of macrophages exhibiting malignant and pro-angiogenic features. We also reveal the dominance of immune inhibitory T cells in the bone metastatic renal cell carcinoma which can be partially restored by the treatment. Trajectory analysis showes that myeloid-derived suppressor cells are progenitors of macrophages in the bone metastatic renal cell carcinoma while monocytes are their progenitors in primary tumors and healthy bone marrows. Additionally, the infiltration of immune inhibitory <italic>CD47</italic>⁺ T cells is observed in bone metastatic tumors, which may be a result of reduced phagocytosis by <italic>SIRPA</italic>-expressing macrophages in the bone microenvironment. Together, our results provide a systematic view of various cell types in bone metastatic renal cell carcinoma and suggest avenues for therapeutic solutions.</p>", "<p id=\"Par2\">Single-cell profiling of primary and bone metastatic renal cell carcinoma suggests variation in intratumoral heterogeneity between samples and the is a valuable resource for examining the underlying pathogenic mechanisms for these cancers.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s42003-024-05772-y.</p>", "<title>Acknowledgements</title>", "<p>This study was supported by the grants from National Natural Science Foundation of China (81872179, 82072972, 82173106, 82130115 and 82272035) and Shanghai Pujiang Program (20PJ1413000). We thank OE Biotech Co., Ltd (Shanghai, China) for the assistance in single-cell RNA sequencing.</p>", "<title>Author contributions</title>", "<p>Conceptualization, W.Y., Y.S. and S.S; Resources, W.Y., S.W., L.X., W.H., G.S., Z.S., W.C., Z.W., M.F., M.C., Y.J., T.H., Y.Z. and B.G.; Methodology, Y.S., S.W., F.M. and L.X.; Investigation, S.W., L.X. and F.M.; Formal Analysis, F.M., S.W., Y.H., J.M., YN.S. and L.X.; Validation, Y.S., F.M. and S.W.; Data Curation, Y.S., F.M., W.Y. and S.W.; Visualization, F.M., S.W. and L.X. Writing—Original Draft, F.M., S.W., L.X. and Y.S.; Writing—Review &amp; Editing, Y.S., F.M. and S.W.; Supervision, W.Y., Y.S., S.S. and J.Z.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par46\"><italic>Communications Biology</italic> thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editors: Eve Rogers and George Inglis.</p>", "<title>Data availability</title>", "<p>The scRNA-seq dataset of primary and bone metastasis RCCs developed by this study are available at the National Omics Data Encyclopedia (NODE) under accession number OEP004678^{##UREF##22##75##} (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.biosino.org/node/project/detail/OEP004678\">https://www.biosino.org/node/project/detail/OEP004678</ext-link>). Other sequencing data that support the findings of this study have been deposited in the National Center for Biotechnology Information Gene Expression Omnibus (GEO)^{##REF##11752295##76##} under the GEO Series accession number: GSE120221, GSE131685, the website under address: <ext-link ext-link-type=\"uri\" xlink:href=\"https://singlecell.broadinstitute.org/single_cell/study/SCP1288/tumor-and-immune-reprogramming-during-immunotherapy-in-advanced-renal-cell-carcinoma#study-summary\">https://singlecell.broadinstitute.org/single_cell/study/SCP1288/tumor-and-immune-reprogramming-during-immunotherapy-in-advanced-renal-cell-carcinoma#study-summary</ext-link>, and paper supplementary files under address: <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.sciencedirect.com/science/article/pii/S153561082100115X?via%3Dihub#sec5.2\">https://www.sciencedirect.com/science/article/pii/S153561082100115X?via%3Dihub#sec5.2</ext-link>. Source data are included in Supplementary Data ##SUPPL##3##2##.</p>", "<title>Code availability</title>", "<p>All computer code used in this study is publicly available. The code can be obtained by visiting 10.5281/zenodo.10321536^{##UREF##23##77##}.</p>", "<title>Competing interests</title>", "<p id=\"Par47\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>The major cell clusters revealed by the primary ccRCC and BMRCC.</title><p><bold>a</bold> Workflow showing the process of sample collection, single-cell dissociation, sorting, sequencing, and data analysis. <bold>b</bold> UMAP plot of all single cells from the primary ccRCC of early and advanced stages and BMRCC with or without treatment. Cell colors indicate unsupervised clustering subgroups. Shading ranges and colors indicate cell type. <bold>c</bold> Bubble heatmap displaying the expression levels of representative well-known markers across the cell types identified in the cohort. Dot size indicates fraction of cells with expression of the indicated gene, and colors represent the normalized expression levels. <bold>d</bold> Lollipop plot showing the tissue distribution of each major cell type by Ro/e analysis in the BMRCC compared with the primary ccRCC. Dot color indicate the cell type labeled. BMRCC-enriched types were characterized with Ro/e &gt; 1. Fisher’s exact test was used to compare significance. <bold>e</bold> The major cell type proportions among the primary ccRCC of early and advanced stages and BMRCC with or without treatment. Colors on the columns indicate cell type. <bold>f</bold> The major cell type proportions in the heathy bone marrows and BMRCC with or without treatment. Colors on the columns indicate cell type.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Cancer cell profiles in the primary ccRCC and BMRCC.</title><p><bold>a</bold> Heatmap showing the differentially expressed genes between primary ccRCC and BMRCCs. The single cells are ordered by their tissue origins marked by the legend column on the left. Color from red to blue indicates a high to low gene expression. <bold>b</bold> Bar plot showing functional enrichment of genes highly expressed in the primary ccRCC or BMRCC. The yellow columns indicate BMRCC group. The blue columns indicate primary ccRCC group. <bold>c</bold> Heatmap showing the copy number variations score of genes located in the chromosome 8. The cells are ordered by their tissue origins marked by the legend column on the left. Color from red to blue indicates a high to low gene expression. <bold>d</bold> Bar plot showing the enriched pathways of genes located on the chr8 amplified region by GSVA. The yellow columns indicate BMRCC group. The blue columns indicate primary ccRCC group. The <italic>x</italic>-axis showed t values calculated by limma regression. <bold>e</bold> Comparison of GSVA scores of the <italic>WNT</italic> signaling pathway between the primary ccRCC and BMRCC. Yellow columns indicate BMRCC group, blue columns indicate primary ccRCC group. Centre line indicates median, box represents first and third quantiles, and whiskers indicate maximum and minimum values. <italic>P</italic> value was calculated by Student’s <italic>t</italic> test, <italic>n</italic> = 11132 biologically independent cells. Effect size of Cohen’s d: 0.135.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>High proportion of mCAF cells in the BMRCC.</title><p><bold>a</bold> UMAP plot showing the subtyping of CAFs. Colors of the cell indicate the cell type marked by legend. <bold>b</bold> Heatmap showing the expression levels of top 10 marker genes for CAF subtypes. The single cells are ordered by cell types marked by the upper legend column. Color from yellow to purple indicates a high to low gene expression. <bold>c</bold> Dot plot showing the functionally enriched pathways of marker genes in each CAF subtype. Dot color and size indicate <italic>p</italic> value. <bold>d</bold> Bar plot showing the fraction of CAF subtypes in the primary ccRCC and BMRCC. Colors on the columns indicate cell type. <bold>e</bold> Comparison of the fraction of mCAF_1 and mCAF_2 cells among the primary ccRCC and BMRCC. Yellow columns indicate BMRCC group, blue columns indicate primary ccRCC group. Data presents the mean ± SEM. <italic>P</italic> values were calculated by wilcox rank sum test, <italic>n</italic> = 15 biologically independent samples. The effect size of Cohen’s d: mCAF_1: 0.118; mCAF_2: 0.822. <bold>f</bold> Immunostaining experiments showing the existence of mCAF_2 in BMRCC and primary ccRCC. The green color indicates the expression of VIMENTIN protein. The red color indicates the expression of FAP protein. <bold>g</bold> GSEA analysis showing the enrichment of top 5 ranked hallmark pathways between mCAF_1 and mCAF_2 subtypes. The colors of the line indicate the pathway of enrichment.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Inhibitory T cell subtypes were enriched in the microenvironment of BMRCC.</title><p><bold>a</bold> UMAP plot showing the 13 subtypes of T cells. The colors of the cell indicate the cell type marked by legend. <bold>b</bold> Bar plot showing the fractions of CD8⁺ T, CD4⁺ T and mitotic T cells in the primary ccRCC of early and advanced stages and BMRCC with or without treatment. Colors on the columns indicate cell type marked by legend. <bold>c</bold> Correlation heatmap showed the differences among T cell subtypes. Colors on heatmap indicate the correlation value. Color from pink to white indicates a high to low correlation. <bold>d</bold> The distribution of CD4⁺ T and CD8⁺ T subtypes among the primary ccRCC of early and advanced stages and BMRCC with or without treatment. Colors on the columns indicate cell type marked by legend. <bold>e</bold> Immunostaining experiments showing the existence of CD8-Tem in BMRCC. The green color indicates the expression of CD8 protein. The purple color indicates the expression of GZMB protein. <bold>f</bold> Violin plot showing the expression levels of indicated marker genes among the indicated groups. Colors on the columns indicate groups marked by <italic>x</italic>-axis. <bold>g</bold>, <bold>h</bold> Developmental trajectory of inhibitory T cell subtypes in the treatment-naïve (<bold>g</bold>) and treated (<bold>h</bold>) BMRCC. Colors of cell indicate the cell type markered by legend. <bold>i</bold> Differentially enriched TFs between the treatment-naïve and treated BMRCC. Colors on heatmap indicate TF AUC score of CD8-Tem1 in treatment-naïve and treated BMRCC group. Color from red to pink indicates a high to low AUC score. <bold>j</bold> Bar plot showing the enriched pathways of regulons of the TFs in CD8-Tem1 from the treatment-naïve and treated BMRCC. The red columns indicate BMRCC Untreat group. The green columns indicate BMRCC Treat group.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Different trajectory paths of macrophages between the primary ccRCC and BMRCC.</title><p><bold>a</bold> UMAP plot showing the four myeloid cell types in the cohort. The colors of the cell indicate the cell type marked by legend. <bold>b</bold> UMAP plot displaying the marker genes of macrophages (<italic>APOE</italic>), DC (<italic>HLA-DQA2</italic>), MDSC (<italic>S100A12</italic>), and monocytes (<italic>HES4</italic>). Orange color indicates higher expression of these genes, pale yellow indicates lower expression of these genes. <bold>c</bold> Bar plot showing the fractions of macrophages, DC, MDSC, and monocytes in the primary ccRCC of early and advanced stages and BMRCC. Colors on the columns indicate cell type marked by legend. <bold>d</bold> Developmental trajectory of macrophages, MDSC, and monocytes in the primary and bone metastatic ccRCC. Colors of cell indicate cell type marked by legend. <bold>e</bold> UMAP plot showing the MDSC and macrophage subtypes by re-clustering analysis. Colors of cell indicate cell type marked by legend. <bold>f</bold> Bar plot showing the fractions of MDSC and macrophage subtypes in the primary ccRCC of early and advanced stages and BMRCC. Colors on the columns indicate cell type marked by legend.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>The differential trajectory of myeloid cell subtypes in the BMRCC.</title><p><bold>a</bold> Developmental trajectory of MDSC and macrophage subtypes in the BMRCC. Colors of cell indicate cell type marked by legend. <bold>b</bold> The expression patterns of genes associated with the pseudotime and their functional enrichment. Colors on heatmap indicate the genes expression. Color from red to blue indicates a high to low expression. <bold>c.</bold> The expression levels of phagocytosis signatures among the macrophage subtypes in BMRCC. Colors on the columns indicate cell type marked by <italic>x</italic>-axis. <italic>P</italic> values were calculated by Kruskal−Wallis test, <italic>n</italic> = 5172 biologically independent cells. <bold>d</bold> Comparison of the M1- and M2-associated signature gene expression levels in the Macro-<italic>NRP2</italic> cells in BMRCC. Blue columns indicate M1 type, yellow columns indicate M2 type. <italic>P</italic> values were calculated by Student’s <italic>t</italic> test, <italic>n</italic> = 887 biologically independent cells. Effect size of Cohen’s d: 1.826. <bold>e</bold> The expression levels of M2-associated signature genes in Macro-<italic>NRP2</italic> among the primary ccRCC of early and advanced stages and BMRCC. Blue columns indicate primary ccRCC early group, yellow columns indicate primary ccRCC advanced group. The gray columns indicate BMRCC group. <italic>P</italic> values were calculated by Student’s <italic>t</italic> test, <italic>n</italic> = 1833 biologically independent cells. Effect size of Cohen’s d: primary ccRCC early group vs BMRCC: 1.059; primary ccRCC advanced group vs BMRCC: 0.811. <bold>f</bold> mIHC showing the existence of Macro-<italic>NRP2</italic> in BMRCC. The green color indicates the expression of SPP1 protein. The red color indicates the expression of NRP2 protein. The purple color indicates the expression of CD68 protein. Box-and-whisker plots (<bold>c</bold>–<bold>e</bold>): centre line indicates median, box represents first and third quantiles, and whiskers indicate maximum and minimum values.</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><title>Cell-cell communication between macrophages and immune inhibitory T cells.</title><p><bold>a</bold> Bubble plot showing the interaction activities of different ligand-receptor pairs across macrophage subtypes and immune inhibitory T cell subtypes. Dot size indicates –log 10 (<italic>P</italic> value). Dot color indicates mean of interaction activities. Dot color from red to yellow indicates a high to low interaction activity. <bold>b</bold> Heatmap displaying the interaction activities of <italic>SIRPA</italic>-<italic>CD47</italic> pair between macrophage and immune inhibitory T cell subtypes. Colors on heatmap indicate mean of <italic>SIRPA</italic>-<italic>CD47</italic> interaction activities. Color from red to blue indicates a high to low interaction activity. <bold>c</bold> Comparison of <italic>CD47</italic> expression levels in the inhibitory T cell subtypes among primary ccRCC of early and advanced stages and BMRCC with or without treatment. Blue columns indicate primary ccRCC_early group, yellow columns indicate primary ccRCC_advanced group, gray columns indicate BMRCC_Untreat group, red columns indicate BMRCC_Treat group. <italic>P</italic> values were calculated by wilcox rank sum test, <italic>n</italic> = 24157 biologically independent cells. Effect size of Cohen’s d: BMRCC_Treat vs BMRCC_Untreat: 0.027; primary ccRCC early vs BMRCC_Untreat: 0.516; primary ccRCC_advanced vs BMRCC_Untreat: 0.292; primary ccRCC_early vs primary ccRCC_advanced: 0.282. <bold>d</bold> Comparison of <italic>SIRPA</italic> expression levels in the Macro-<italic>NRP2</italic> subtype among primary ccRCC of early and advanced stages and BMRCC with or without treatment. Blue columns indicate primary ccRCC_early group, yellow columns indicate primary ccRCC_advanced group, gray columns indicate BMRCC_Untreat group, red columns indicate BMRCC_Treat group. <italic>P</italic> values were calculated by wilcox rank sum test, <italic>n</italic> = 1833 biologically independent cells. Effect size of Cohen’s d: BMRCC_Treat vs BMRCC_Untreat: 0.666; primary ccRCC early vs BMRCC_Untreat: 0.424; primary ccRCC_advanced vs BMRCC_Untreat: 0.187; primary ccRCC_early vs primary ccRCC_advanced: 0.262. <bold>e</bold> Comparison of <italic>CD47</italic> and <italic>SIRPA</italic> co-expression levels between the early (Stage I/II) and late (Stage III/IV) staged primary ccRCC in TCGA. Blue columns indicate stage I/II samples, yellow columns indicate stage III/IV samples. <italic>P</italic> values were calculated by wilcox rank sum test, <italic>n</italic> = 606 biologically independent samples. Effect size of Cohen’s d: 0.307. <bold>f</bold> Immunofluorescence staining showing the expression of <italic>CD47</italic> and <italic>SIRPA</italic> in the primary ccRCC and BMRCC. The green color indicates the expression of CD47 protein. The red color indicates the expression of SIRPA protein. The blue color indicates nucleus of cell. <bold>g</bold> Barplot showing the fluorescence intensity of CD47⁺ cells and SIRPA⁺ cells in primary ccRCC and BMRCC. Blue dots indicate primary ccRCC samples, red dots indicate BMRCC samples. <italic>P</italic> values were calculated by Student’s <italic>t</italic> test. <italic>n</italic> = 12 biologically independent samples. Effect size of Cohen’s d: CD47: 4.182; SIRPA: 2.912. <bold>h</bold> Kaplan–Meier plots showing the survival probability of primary ccRCC patients with high and low co-expression levels of <italic>CD47</italic> and <italic>SIRPA</italic>. Red line indicates patients expressed higher <italic>CD47</italic> and <italic>SIRPA</italic> co-expression. grey line indicates patients expressed lower <italic>CD47</italic> and <italic>SIRPA</italic> co-expression. <italic>P</italic> values were calculated by log-rank test. <bold>i</bold> The model of the action of macrophages and T cells through <italic>SIRPA</italic>-<italic>CD47</italic>. HR, hazard ratio. Box-and-whisker plots (<bold>c</bold>–<bold>e</bold>): Centre line indicates median, box represents first and third quantiles, and whiskers indicate maximum and minimum values.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM5\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Fen Ma, Shuoer Wang, Lun Xu.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"42003_2024_5772_MOESM1_ESM.pdf\"><caption><p>Supplementary Information</p></caption></media>", "<media xlink:href=\"42003_2024_5772_MOESM2_ESM.pdf\"><caption><p>Description of Additional Supplementary Files</p></caption></media>", "<media xlink:href=\"42003_2024_5772_MOESM3_ESM.xlsx\"><caption><p>Supplementary Data 1</p></caption></media>", "<media xlink:href=\"42003_2024_5772_MOESM4_ESM.xlsx\"><caption><p>Supplementary Data 2</p></caption></media>", "<media xlink:href=\"42003_2024_5772_MOESM5_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">The rapid development of technology, excessive consumption demand of people, irregular urbanization, uncontrolled population growth, developments in the industrial field, nuclear waste, and heavy metal accumulation cause pollution of natural resources and constitute the most important environmental problems of today. Dyestuffs, heavy metals, organic pollutants, radioactive pollutants, highly toxic substances, and pharmaceutical chemicals are the contents of industrial wastes that cause serious environmental problems^{##UREF##0##1##–##UREF##3##4##}.</p>", "<p id=\"Par3\">Dyes, heavy metals, and other waste materials used in many branches of industry, especially textiles, cosmetics, paper, pharmaceuticals, plastics, dye and leather threaten the environment by polluting water resources^{##REF##37041227##5##–##REF##35723574##8##}. The textile industry uses a variety of dyes, including basic, acid, reactive, direct, azo, mordant, vat, and dispersion dyes^{##UREF##5##9##}. Because they have the greatest color variation, the largest volumes, and the most adaptable properties of all the synthetic dyes, azo dyes take the top spot. Mordant Violet 40 dye is an example of a dye containing only one azo group, this dye can be found in the aquatic environment, is toxic and mutagenic to the ecosystem, may cause harmful effects on organisms, the effect relies upon the exposure time of the azo dye to the dye in water, as well as its concentration in water^{##UREF##5##9##,##REF##37880272##10##}.</p>", "<p id=\"Par4\">Treatment of wastewater containing heavy metals is still a difficult and serious environmental concern. One of the heavy metals whose compounds are extensively employed in the chemical industry is chromium^{##UREF##6##11##}. Some of the other application areas where chromium is used are the electroplating, textile, leather tanning, metal plating, production of organic chemicals, wood preservation, and chromate preparation industries^{##UREF##7##12##–##UREF##10##15##}. Hexavalent chromium and trivalent chromium are most common in the environment, also chromium possesses several oxidation states (from – 2 to + 6). Cr⁶⁺ is highly soluble in water and bioavailable, while Cr³⁺ is less soluble and stable^{##UREF##11##16##}. The Cr⁶⁺ ions, which is found to be toxic to stem cells and living organisms, harms human health because it is highly mutagenic and carcinogenic. Since chromium compounds are widely used and accumulated in natural environments, it is very important and necessary to remove them from the environment^{##UREF##12##17##}.</p>", "<p id=\"Par5\">Methods such as chemical precipitation, membrane filtration, electrochemical treatment, and adsorption are some of the traditional wastewater treatment technologies applied to remove heavy metals and dyestuffs from the water environment^{##UREF##13##18##–##UREF##16##22##}. Studies to discover new techniques in the field of environmental technology have been guided by the shortcomings, application challenges, or costs of current treatment approaches. Among the mentioned treatment technologies, adsorption is the most efficient in terms of development and applicability^{##UREF##17##23##,##UREF##18##24##}. The cost-effectiveness of the adsorption method, its ease of use, the easy separation of toxic organic–inorganic species from the aqueous environment, and the disposal of the separated toxic material without affecting the biological structures highlight the advantages of the method^{##UREF##19##25##,##UREF##20##26##}.</p>", "<p id=\"Par6\">Iron oxide (Fe₃O₄), titanium dioxide (TiO₂), aluminum oxide (Al₂O₃), copper oxide (CuO), zinc oxide (ZnO), and nickel oxide (NiO) nanomaterials are well-known metal-based nano adsorbents for heavy metal removal and dyestuff^{##UREF##21##27##–##UREF##23##30##}. By reducing the particle size, metal oxide nanoparticles were able to absorb more substances. To remove metal and organic pollutants simultaneously, metal oxide nanoparticles are injected into the skeleton of activated carbon or other porous materials^{##REF##36760304##31##}. By altering the pH of the fluid, it is also possible to recreate these metal-based nanoparticles, and after a few regenerations, they are sufficiently potent^{##UREF##24##32##}. Some of these metal oxides are iron oxide nanoparticles such as magnetite (Fe₃O₄), maghemite, hematite (<italic>α</italic>-Fe₂O₃), and akaganéite (<italic>β</italic>-FeOOH) were used as nano-sized adsorbents to remove some of heavy metals and dyes from water^{##UREF##25##33##–##UREF##27##35##}. Magnetic nanoparticles are becoming attractive for industrial and environmental applications due to their low cost, lossless recovery, and reusability^{##UREF##28##36##,##UREF##29##37##}. However, aggregation of magnetite nanoparticles in water is undesirable, which reduces their catalytic capabilities. Various methods have been developed to overcome the coagulation of nanoparticles. In order to overcome this limitation and increase the catalytic activity of magnetic nanoparticles, materials such as graphene, graphene oxide, activated carbon, silica, carbon nanotube, bentonite, kaolinite, montmorillonite, and zeolite, etc. with high adsorption ability and catalytic activity are used as solid supports^{##UREF##30##38##–##UREF##36##46##}. Thanks to the use of these materials as a support, the surface area of iron-based magnetic nanoparticles is increased and their distribution is facilitated. At the same time, nanomagnetic particles placed on these support materials have smaller particle sizes, less agglomeration, and higher thermal and chemical stability than those without support materials^{##UREF##37##47##,##UREF##38##48##}.</p>", "<p id=\"Par7\">Due to its high surface area and pores, activated carbon has a great potential to adsorb organic and inorganic compounds in the liquid and gas phases^{##UREF##39##49##}. Since activated carbon has a large surface area, it has a great affinity for absorbing many deformations. AC is one of the most effective, economical, and simplest adsorbents for pollutants in aqueous solutions^{##REF##32875202##50##,##UREF##40##51##}. Although it can be found in organic cells as an adsorbent, activated carbon is difficult to extract from its solution. Electric or magnetic fields cannot regulate activated carbon because it lacks polarity. It is aimed to overcome this problem by synthesizing many activated carbon composite adsorbents with magnetic properties^{##REF##33924445##52##–##UREF##41##54##}. Technology for treating water might potentially develop with the addition of magnetic characteristics to activated carbon. Adsorption and magnetic separation work in concert to offer a flexible and effective solution to problems with water quality, all the while enhancing the overall sustainability of water treatment procedures. The goal of this field's ongoing research and development is to improve and broaden the uses of magnetic activated carbon in the pursuit of more sustainable and clean water sources^{##REF##37880272##10##}. The magnetic property of activated carbon is introduced through the incorporation of magnetic nanoparticles, such as magnetite (Fe₃O₄). This property allows for easy separation of the adsorbent from the solution after adsorption. Magnetic activated carbon can be manipulated using an external magnetic field, making the process more efficient and environmentally friendly^{##UREF##5##9##,##REF##37880272##10##}.</p>", "<p id=\"Par8\">In this study, iron oxide nanomagnetic composite (CAC-IO) was prepared from fisher commercial activated carbon (CAC) by co-precipitation method. This work is the first to use this type of commercial activated carbon to produce magnetic activated carbon composite and use it in the adsorption of heavy metals and textile dyes. The CAC-IO was invesrigated as an adsorbent for toxic metal (Cr⁶⁺) and azo dye (Mordant Violet 40). However, to our knowledge, Mordant Violet 40 dye removal has only been published by us. The importance of CAC-IO is that it shows a high <italic>Q</italic>_m for the MV40 dye and Cr⁶⁺ ions compared to the published data. The nano-magnetic composite was synthesized by using different iron salts and different base solutions. The magnetic iron oxide nanocomposite was comparatively characterized by FTIR, BET, SEM, EDX TEM, VSM, and XRD techniques. Different adsorption and kinetic isotherm models were used to investigate the mechanism of adsorption of two pollutants Cr⁶⁺ions and Mordant Violet 40 (MV40) dye on the synthesized iron oxide nanocomposite (CAC-IO). The adsorption capacity of the CAC-IO nanocomposite was calculated using the Langmuir and Freundlich models. To ascertain the adsorption mechanism, pseudo-first-order (PFO), pseudo-second-order (PSO), and intraparticle diffusion (IPDM) models were applied.</p>" ]

[ "<title>Materials and methods</title>", "<title>Materials</title>", "<p id=\"Par9\">Activated charcoal powder was purchased from Fisher Scientific, UK. Iron (III) Nitrate Nona hydrate (98%), and Iron (II) chloride hydrate were obtained from LOBA Chemie Company, India. Ferrous Sulphate Heptahydrate (FeSO₄.7H₂O), Ferric chloride (FeCl₃), Ammonia solution (25%), Sodium hydroxide, Sodium carbonate and Ethanol were obtained from El Nasr Company, Egypt. Hydrogen peroxide (50%) was purchased from Gateway Company, Hydrochloric acid solution (37%) and Sulfuric acids (98%) were purchased from Merck Company; Potassium dichromate was purchased from Sigma Aldrich Company, USA. MV40 dye salt was purchased from ISMA dye Company, Kafer El Dwar, Egypt.</p>", "<title>Surface modification of commercial activated charcoal (CAC)</title>", "<p id=\"Par10\">CAC oxidation was performed to increase the active site and functional group on the surface of CAC to obtain better contact with iron oxide. Oxidation of commercial activated charcoal powder was achieved by placed of 100 g of CAC in 1800 mL of hydrogen peroxide solution (8%) in the presence of ozone flow for 2 h. The carbon suspension was then filtered with a vacuum. After sequential pumping, several times distilled water and ethanol were used, respectively, for washing until the pH stabilized (approximately neutral). The resulting wet powder was dried in an oven (105 °C) for 24 hto remove its moisture and then weighed to obtain 91 g of dried powder^{##UREF##42##55##,##UREF##43##56##}.</p>", "<title>Preparation of ıron oxide-commercial activated carbon nanocomposite (CAC-IO)</title>", "<p id=\"Par11\">Co-precipitation method was used to create an iron oxide nanocomposite from commercial activated carbon by dissolving 4.04 g of iron (III) nitrate nonahydrate (98%) and 1.2 g of iron (II) chloride hydrate in 500 mL of distilled water in 1000 mL added to 10 g of CAC powder in a round table flask (3.38:1:8.33 of Fe(NO₃)₃:FeCl₂:oxidized CAC, respectively)^{##REF##18838216##57##}. The obtained suspension was ultrasonically agitated in a sonicator at ambient temperature and normal atmospheric pressure for 30 min. The ultimate pH was 13.72 after adding 100 mL of sodium hydroxide solution (5 M) drop by drop over the course of 45 min. The flask containing the created composite was moved to be refluxed for 16 h at moderate temperatures after the base solution had been fully added. After cooling to ambient temperature, the iron oxide nanocomposite from commercial activated carbon was filtered and collected with a magnet. It was then repeatedly cleaned with distilled water before being exposed to 98% ethanol. The nanocomposite was dried in an electric oven, and the 11.63 g of CAC-IO powder were measured using a balance.</p>", "<title>Characterization</title>", "<p id=\"Par12\">The characterisation of CAC-IO nanocomposites has involved the application of a number of approaches. The surface functional group on the CAC-IO powder and CAC after treatment was identified using an FT-IR Spectrophotometer with an ATR unit. The samples' ATR-FTIR spectra were taken using a Bruker VERTEX 70 spectrophotometer in the range of 4000 to 400 cm^-1. The produced samples (CAC after treatment, CAC-IO) were measured using Nitrogen-adsorption isotherm to determine their surface area, pore volume, and pore size distribution. At 77 K, sample measurements were started after the pressure was brought to <italic>P</italic>/<italic>P</italic>_{<italic>o</italic>} = 0.99. Using the Belsorp Mini II, Version 1.2.5 surface area analyzer, the average pore diameters and total surface areas of the samples were calculated using the Brunauer, Emmett, and Teller (BET) equation. The surface morphology and porosity of CAC after treatment and CAC-IO samples were examined using an analytical Scanning Electron Microscope (JEOL JSM-6360LA). After the samples were powdered, they were coated with a gold layer to obtain clearer images and increase conductivity.</p>", "<p id=\"Par13\">The morphology and particle size of the CAC-IO sample were examined using ESL Transition Electron microscopy from Scientific Researches City. For this purpose, 2 mg of the powdered samples was taken and dissolved in 5 mL of ethanol and mixed in the centrifuge device. A drop of the resulting suspension was tested by dropping it onto a copper grid. The degree of crystallinity and phase compositions of prepared samples were determined by an X-ray diffraction device (model No, 202,964) from Beni Sweif University. The Cu-Kα radiation was used to generate the XRD pattern at 10 mA, 1.54Å wavelength, and 25 °C in the 2θ region of 10–80°.</p>", "<p id=\"Par14\">The magnetic property of the nanocomposite was realized with the VSM device at Beni Sweif University. It ranged from + 20 KOe to –20 KOe for the magnetic field of G. The amount of MV40 dye in aqueous solutions was measured using an Analyticjena Spekol 1300 UV–VIS Spectrophotometer (Model No. 4560002, Cole Parmer Instrument Co., USA).</p>", "<title>Adsorption experiments</title>", "<p id=\"Par15\">Separately, a volumetric flask was used to dissolve a specific quantity of K₂Cr₂O₇ and MV40 dye salts in 1000 mL of distilled water to create a stock solution of 1000 mg L^–1 of Cr⁶⁺ solution and MV40 dye. The stock solutions for the Cr⁶⁺ ions and MV40 dyes were produced separately from their diluted concentrations. The different Cr⁶⁺ ion concentrations and MV40 dye solution concentrations (100, 150, 200, 300, and 400 ppm) were added separately to the adsorption batches along with various concentrations of CAC-IO composite (1.0, 1.5, 2.0, and 2.5 g L^–1). Each concentration had a volume of 100 mL in a conical flask, and the adsorbent-adsorbate suspensions were agitated using a shaker at room temperature and 200 rpm for 180 min for each pollutant's specific equilibrium duration. To determine the amount of leftover Cr⁶⁺ ions and MV40 dye in each solution, a sample of each solution was obtained at regular intervals. In adsorption experiments, it took 3 h for the samples to reach equilibrium, and analyses were performed at the end of this period. Adsorption tests were carried out with 0.5 ml Cr⁶⁺ ions sample or 2 ml MV40 dye sample at intervals of 5, 10, 20, 30, 45, 60, 90, 120, 150, and 180 min. Then, the composites were separated from the solutions by centrifugation at 6000 <italic>rpm</italic> for 5 min, and a magnet was used to disperse the composites in the solution and prevent the samples from separating. Cr⁶⁺ ion and MV40 dye filtrates obtained after centrifugation were measured at absorbance wavelengths of 540 and 510 nm, respectively^{##UREF##1##2##,##REF##37880272##10##,##UREF##44##58##}, on a spectrophotometer device for concentration determination. The effects of parameters such as initial concentration of adsorbates, nanocomposite concentration , contact time, and pH, which affect the removal of Cr⁶⁺ ions and MV40 dye from aqueous solutions of the prepared iron oxide nanocomposite CAC-IO samples were examined.</p>", "<p id=\"Par16\">The experimental data from adsorption batches were tested by using different adsorption isotherm (Langmuir and Freundlich) and kinetic (PFO, PSO, IPDM) models. These models facilitated knowledge of the mechanism of adsorption in our study on nanocomposite adsorbent.</p>", "<p id=\"Par17\">The removal % (R%) can be calculated by Eq. (##FORMU##0##1##)^{##REF##37880272##10##}.where <italic>C</italic>_{<italic>o</italic>} and <italic>C</italic>_{<italic>t</italic>} are the initial and final concentrations of adsorbate in aqueous solution, respectively. Adsorption capacity <italic>q</italic> (mg g^-1) can be calculated from Eq. (##FORMU##1##2##).where <italic>m</italic> is the mass of the iron oxide nanocomposite in grams and <italic>V</italic> is the volume of the adsorbate solution in Liter (L).</p>", "<p id=\"Par18\">The pH of different solutions was measured at 1.0 g L^–1 of adsorbent concentration (CAC-IO), 100 mL solution of 100 mg L^–1 of Cr⁶⁺ ions, and MV40 dye concentrations individually for 3 h of contact time. The MV40 dye solutions and Cr⁶⁺ ion concentrations ranged in pH from very acidic to strongly basic solutions (pH = 1 to 11); the pH of the adsorbate solution under study was slightly different from this pH range.</p>" ]

[ "<title>Results and discussion</title>", "<title>Characterization of adsorbent</title>", "<title>FTIR analyses</title>", "<p id=\"Par19\">The produced materials (CAC, CAC after treatment, and CAC-IO) were characterized using the Fourier transform infrared technique, as shown in Fig. ##FIG##0##1##. The FTIR spectrum of CAC, CAC after oxidation, and CAC-IO nanocomposite showed a broad peak at 3049 and 3225 cm^–1 due to the OH bond, also a peak appeared at 1576, 1578, 1576 cm^–1 with small shifts due to the C=C stretching bond and the bands appeared at 1174, 1192 and 1221 cm^–1 assigned to C–O stretching from phenolic, alcoholic, etheric groups and to C–C bond, similar results was obtained by Bagheri et al. (2017)^{##REF##29137753##59##}. The fact that all spectra included peaks at 2354 cm^–1 caused by the C–C bond in the structure of activated carbon showed that the structure had not been damaged during the composite pyrolysis^{##REF##24727015##53##}. Due to the synthesis of nano-iron oxide, a new peak at 575 cm^–1 in the CAC-IO spectra had been developed. The appearance of the Fe–O stretching bond revealed that iron oxide nanoparticles had been deposited on the CAC-IO adsorbent surface. The peaks appeared at 886 and 793 cm^–1, which may be due to the δ(OH) and γ(OH) vibration in and out of the plane, respectively, indicated to geothite peaks^{##REF##18838216##57##,##UREF##45##60##–##UREF##47##62##}.</p>", "<title>BET analyses</title>", "<p id=\"Par20\">Using the BET equation, the surface area and pore information of the produced nanocomposite and its constituent material were calculated. The pore volume (<italic>V</italic>_{<italic>t</italic>}) for each adsorbent and its precursor materials was calculated using nitrogen adsorption at relative pressure <italic>P</italic>/<italic>P</italic>_{<italic>o</italic>} = 0.99. The pore diameters of commercial and synthesized activated carbon and nanocomposites were calculated.</p>", "<p id=\"Par21\">As seen in Table ##TAB##0##1## using BET analyses, the specific surface areas of CAC, CAC after oxidation, and CAC-IO were calculated as 1426.8, 985.58, and 1070 m² g^–1, respectively. The use of H₂O₂, a powerful oxidizing chemical, caused damage to the pores in CAC's structure, resulting in a reduction in surface area following oxidation^{##UREF##42##55##,##REF##17980401##63##,##UREF##48##64##}. As the surface area increases after adding Fe₃O₄, it expected that the Fe₃O₄ is attached to the functional group on the surface of CAC rather than inserted inside the pores.</p>", "<p id=\"Par22\">Figure ##FIG##1##2## showed the nitrogen adsorption–desorption isotherms of the precursor materials and showed that they were type (IV) isotherms^{##UREF##49##65##}. The structure of CAC and CAC after oxidation, as well as CAC-IO, were mesoporous^{##REF##21749733##66##}, according to the IUPAC classification, which is micropores (<italic>d</italic> &lt; 2 nm), mesopores (2 &lt; <italic>d</italic> &lt; 50 nm), and macropores (<italic>d</italic> &gt; 50 nm)^{##UREF##49##65##}.</p>", "<p id=\"Par23\">The CAC-IO nanomagnetic adsorbent's pore volume was 0.9155 cm³ g^–1. The findings demonstrated that the oxidation process and the resulting production of magnetic nanocomposites reduced the surface area of the commercial activated carbon (CAC), which was caused by the dispersion of iron oxide nanoparticles on the carbon surface, from 1426 m² g^–1 to 1070 m² g^–1.</p>", "<title>SEM-TEM analyses</title>", "<p id=\"Par24\">As shown in Figs. ##FIG##2##3##a,b, scanning electron microscopy was used to examine the surface morphology and shape of the adsorbent prepared after oxidation and its iron oxide nanocomposite (CAC-IO). The surface of CAC-IO showed roughness than that of CAC, which may explain the attachment of Fe₃O₄ to the surface functional group instead of being inserted into the surface pores. The TEM image of the CAC-IO nanocomposite obtained using the Transition Electron Microscopy (TEM-2100 Electron Microscope) to determine the nano-sized composite spacing and their shape at the nanoscale is shown in Fig. ##FIG##2##3##c. TEM image of CAC-IO nanocomposite showed the particle shape of nano iron oxide was spherical and agglomerated to each other. According to Fig. ##FIG##2##3##c, the particle size ranged from 4.12 to 19.5 nm, and smaller particles have a higher adsorption capacity.</p>", "<title>EDX analyses</title>", "<p id=\"Par25\">As shown in Table ##TAB##1##2##, the elements and iron oxide nanocomposites in the adsorbent produced during the treatment were identified and determined using the SEM–EDX equipment. The study of CAC after oxidation verified the existence of several components, including Carbon, Oxygen, Sodium, Silicon, and Chlorine with percentage ratios of 83.26, 15.38, 0.17, 1.05, and 0.14%, respectively, in the CAC structure. The iron element Fe has a weight ratio of 12.09% owing to the magnetic CAC-IO synthesis, and the examination of CAC-IO nanocomposites in Fig. ##FIG##3##4## confirms the presence of the same components in CAC after oxidation with a modified weight ratio. The production of iron oxide nanocomposites with iron components resulted in a reduction in the carbon content from 83.26 to 65.25%^{##REF##21749733##66##}.</p>", "<title>VSM analyses</title>", "<p id=\"Par26\">The magnetization curve of the synthesized magnetite iron oxide nanocomposite (CAC-IO) was measured to study the magnetic properties at room temperature in a magnetic field with a cycle of –20 to + 20 KOe. The highest saturation magnetization for CAC-IO was 7.4130 emu g⁻¹ as in Fig. ##FIG##4##5##, which is due to the high iron oxide content of the CAC-IO nanocomposite. The magnetic properties of CAC-IO (7.4130 emu/g) compared to the magnetic properties of pure Fe₃O₄ nanoparticles (~ 90 emu/g) may be expained by the formation of CAC composites with Fe₃O₄ nanoparticles, which has a substantial impact on the magnetic properties of Fe₃O₄. This phenomenon can be attributed to factors such as the surface area and elemental composition of Fe₃O₄ within the composite or to the percentage of Fe₃O₄ within the CAC-IO composite.</p>", "<title>XRD analyses</title>", "<p id=\"Par27\">XRD analyses of the prepared nanocomposites and their pure materials obtained under Cu-kα radiation at 25 °C are given in Figs. ##FIG##5##6##a,b. In Fig. ##FIG##5##6##a, the only peak that appeared at 26.14° is related to commercial activated carbon after oxidation, similar results were obtained according to Gholamvaisi et al<italic>.</italic> (2014)^{##UREF##50##67##}.</p>", "<p id=\"Par28\">Figure ##FIG##5##6##b indicates to CAC-IO nanocomposite that shows several peaks at different angles at 30.31, 35.66, 43.25, 57.42, and 63.04°, the maximum peak intensity was at 2θ = 35.66⁰ which indicates the presence of magnetite (Fe₃O₄) or maghemite nanoparticles in cubic crystal structure shapes according to reference card code 04-013-9811. After oxidation, no peak for CAC was seen in Fig. ##FIG##5##6##b; this could be because the surface of the carbon has agglomerated or been coated with magnetite or maghemite nanoparticles^{##UREF##51##68##}.</p>", "<p id=\"Par29\">The average crystalline size of the prepared CAC-IO was determined from the XRD results; it was calculated from Scherrer’s formula (Eq. (##FORMU##2##3##)),where <italic>L</italic> is the crystalline size, λ is the wavelength of the X-ray, <italic>B</italic> is the full width of half maximum of a diffraction peak, <italic>θ</italic> is the angle of diffraction and <italic>K</italic> is the Scherrer’s constant of the order of 0.89^{##REF##29137753##59##}.</p>", "<p id=\"Par30\">The XRD results show that the average crystal size of CAC-IO is 24.21 nm at 2θ = 35.66, which is in good agreement with the TEM results.</p>", "<title>Adsorption of Cr⁶⁺ ions and MV40 dye on CAC-IO nanocomposite</title>", "<title>Effect of pH</title>", "<p id=\"Par31\">In order to examine the effect of solution pH on adsorption, solutions were prepared at constant concentrations at various pHs, and the adsorption of a certain amount of adsorbent and a certain volume of pollutant solution at room temperature was studied. As a result of the studies, the effect of different pH solutions has revealed that the best removal percentage is on acidic pH. Figure ##FIG##6##7## shows that by increasing the pH of Cr⁶⁺ ions solutions from 1.6 to 11.24, the percentage of Cr⁶⁺ removal decreased from 99.58 to 45.45%, giving the maximum removal percentage at pH 1.6. The effect of pH value on the chromium species in the solution and its effect on the chromium removal % were previously studied^{##UREF##9##14##,##UREF##10##15##,##UREF##17##23##,##UREF##52##69##–##REF##20099060##72##}. pH Fig. ##FIG##6##7## also shows that the removal % decreased by increasing the pH of MV40 dye solutions from 1.3 to 10.97, giving a maximum removal percentage was 99.08% at pH 2.07,100 mg L^–1 of initial dye concentration with 1 g L^–1 of CAC-IO concentration and 3 h of contact time. This result is due to the electrostatic attraction between the positively charged CAC-IO surface and the negative charges on the dye molecules at acidic pH, but at higher pH, there was repulsion between the two opposite charges of the dye molecules and the adsorbent surface used. Similar results were obtained in Kalantry et al. (2015)^{##UREF##54##73##}.</p>", "<title>Effect of CAC-IO adsorbent concentration</title>", "<p id=\"Par32\">Different concentrations from CAC-IO nanocomposite (1, 1.5, 2, 2.5 g L^–1) were used to study the adsorbent concentration effect at 400 mg L^–1 of initial concentrations of Cr⁶⁺ ions and MV40 dye solutions, contact time is 3 h and fixed pH = 1.6 for Cr⁶⁺ ions solutions after adding the adsorbent while the dye solution pH was fixed at 2.07 for MV40 dye after adding the adsorbent separately. The resulting samples were drawn at intermittent times (10, 20, 30, 45, 60, 90, 120, 150, and 180 min) to separately analyze the final concentrations of Cr⁶⁺ ions and MV40 dye in solutions. Figure ##FIG##7##8## illustrates the chart used to examine the influence of nanocomposite concentration on the percentages of Cr⁶⁺ ions and MV40 dye removal from water, respectively. The result shown for Cr⁶⁺ adsorption revealed that by increasing the adsorbent concentration (CAC-IO) from 1 to 2.5 g L^–1, the removal percentage increased from 54.33 to 78.80%, so 2.5 g L^–1 of CAC-IO nanocomposite was considered to be the optimum concentration to remove 400 mg L^–1 of Cr⁶⁺ ions from aqueous media at optimum solution pH = 1.6, room temperature and equilibrium time = 3 h.</p>", "<p id=\"Par33\">This results from the presence of unsaturated adsorption sites on adsorbent (CAC-IO) during the adsorption process, also the decrease in adsorption capacity may be due to the aggregation of adsorbent particles due to the high concentration of it. This aggregation may result in a reduction in the adsorbent's overall surface area and an increase in the diffusional route length^{##REF##32326104##74##}. The chart for the adsorption of MV40 dye indicated that increasing the adsorbent concentration (CAC-IO) from 1.0 to 2.5 g L^–1 slightly enhanced the elimination percentage from 97.64 to 99.79%. At optimal solution pH = 2.07, room temperature, and equilibrium time is 3 h, 1.0 g L^–1 of CAC-IO nanocomposite was thought to be the best concentration to remove 400 mg L^–1 of MV40 dye from aqueous medium as shown in Fig. ##FIG##7##8##. However, there was no significant increase in the removal percentage of dye at concentrations larger than 1.0 g L^–1.</p>", "<title>Effect of initial adsorbate concentrations on CAC-IO nanocomposite</title>", "<p id=\"Par34\">Different five concentrations (100, 150, 200, 300, 400 mgL⁻¹) of Cr⁶⁺ ions and MV40 dye solutions were each examined during batch adsorption experiments at 1.0 g L^–1 CAC-IO concentration individually at fixed pH = 1.6 in case of Cr⁶⁺ ions adsorption and pH = 2.07 in case of MV40 dye adsorption at room temperature. Commercial activated carbon-iron oxide nanocomposite (CAC-IO) was used to study the impact of initial Cr⁶⁺ ions concentrations on the rate of adsorption in the range of 100 to 400 mg L^–1, as shown in Fig. ##FIG##8##9##a. It is obvious that the Cr⁶⁺ ions removal by different adsorbents doses (CAC-IO) was dependent on the initial Cr⁶⁺ ions concentrations, this is due to increasing the initial Cr⁶⁺ ions concentrations increased the amount of Cr⁶⁺ ions adsorbed on the adsorbent adsorption capacity (<italic>q</italic>_{<italic>e</italic>}).</p>", "<p id=\"Par35\">This increase is due to the resistance to the uptake of solute from Cr⁶⁺ ions solution decreased so the initial concentrations of Cr⁶⁺ solutions provide an important driving force to overcome the mass transfer resistance of Cr⁶⁺ ions between the aqueous and the solid phases^{##UREF##55##75##}. In the range of 100 to 400 mg L^–1, the impact of initial MV40 dye concentrations on the rate of adsorption by CAC-IO was examined, as shown in Fig. ##FIG##8##9##b. Additionally, the number of MV40 dye molecules adsorbed on the CAC-IO surface developed when initial dye concentrations were raised, which is why the MV40 dye removal by various adsorbent (CAC-IO) concentrations were reliant on those initial dye concentrations. As it was previously mentioned, this rise results from a reduction in the impedance to solute absorption from dye solution^{##UREF##55##75##}.</p>", "<title>Effect of contact time using CAC-IO</title>", "<p id=\"Par36\">An experiment was done to study the effect of contact time, 100 mg L^–1 of Cr⁶⁺ ions or MV40 dye initial concentrations were tested, and 2 g L^–1 CAC-IO adsorbent concentration (highest dose gave maximum removal %) in case of Cr⁶⁺ ions solutions and 1.0 g L^–1 CAC-IO adsorbent concentration in case of dye solutions at pH of Cr⁶⁺ ions and dye solutions, 1.6 and 2.07, respectively, and room temperature. The obtained samples were taken at interval times (10, 20, 30, 45, 60, 90, 120, 150, and 180 min) and analyzed by UV–visible spectrophotometer at 540 and 510 nm of maximum wavelengths of Cr⁶⁺ ions and MV40 dye, respectively.</p>", "<p id=\"Par37\">The rapid removal of Cr⁶⁺ ions after only 10 min (87.92%) in the initial phase of adsorption from 0 to 10 min and then the rate of removal gradually slowed down until the equilibrium state was reached after 180 min, as shown in Fig. ##FIG##9##10##a. The rate of removal of MV40 dye was very fast (98.49%) from 0 to 10 min, and then the rate of removal gradually slowed down until it reached a constant value at equilibrium, as shown in Fig. ##FIG##9##10##b.</p>", "<p id=\"Par38\">The results were interpreted that the higher availability of vacant sites on the adsorbent surface at the initial stage while by passing the time of experiments, these sites were occupied by the adsorbate molecules, and the number of vacant sites became few so the removal percent of Cr⁶⁺ ions and MV40 dye molecules become very slow, also it was shown that the variations of initial dye and Cr⁶⁺ ion concentrations did not significantly affect the removal rate to reach its equilibrium state.</p>", "<p id=\"Par39\">Finally, we concluded that the maximum removal % of Cr⁶⁺ solutions was 98.60% after 180 min and the initial Cr⁶⁺ concentration was 100 mg L^–1 using 2.0 g L^–1 of CAC-IO adsorbent concentration, while 99.92% was the highest dye removal percent after 180 min using only 1.0 g L^–1 of CAC-IO and 100 mg L^–1 of initial dye concentration.</p>", "<title>Adsorption isotherms</title>", "<p id=\"Par40\">As indicated in Fig. ##FIG##10##11##, Langmuir and Freundlich isotherms were examined for the distinct adsorption of Cr⁶⁺ ions and MV40 dye on CAC-IO nanocomposites. The adsorption isotherm data of Langmuir and Freundlich models obtained using Langmuir and Freundlich models are shown in Table ##TAB##2##3##. The interaction between adsorbates and adsorbents is represented by the properties of adsorption and the parameters of each isotherm model; this information reveals the nature of the interaction^{##UREF##56##76##}.</p>", "<p id=\"Par41\">The Langmuir model assumed that the adsorption was monolayer on a homogeneous adsorbent surface, that there was no interaction between the molecules that were adsorbed, and that the transmigration of the molecules that were adsorbed on the adsorbent surface was not permitted^{##UREF##57##77##}. The Langmuir linear Eq. (##FORMU##3##4##) can be expressed as follows (Eq. (##FORMU##3##4##)):where <italic>C</italic>_{<italic>e</italic>} is the concentration of adsorbate in solution (mg L^–1) at equilibrium, <italic>q</italic>_{<italic>e</italic>} is the adsorption capacity at equilibrium in mg g⁻¹, <italic>K</italic>_{<italic>a</italic>} is constant related to free energy of adsorption (L mg^–1), and <italic>Q</italic>_{<italic>m</italic>} is the maximum adsorption capacity at monolayer coverage in mg g^–1. An empirical linear equation of Freundlich Isotherm assumed that the adsorbent surface was heterogeneous; the equation was expressed as shown in Eq. (##FORMU##4##5##):where <italic>K</italic>_{<italic>f</italic>} (mg^1–1/n g^-1 L^1/n) and <italic>n</italic> are the Freundlich constants, they indicate the adsorption capacity and intensity of adsorption, respectively. The values of 1/<italic>n</italic> in Tables ##TAB##2##3##, ##TAB##3##4## are greater than zero and lower than 1, (0 &lt; 1/<italic>n</italic> &lt; 1) the adsorption is favorable^{##REF##22119217##78##}.</p>", "<p id=\"Par42\">The isotherm parameters obtained from both models due to Cr⁶⁺ ions adsorption on CAC-IO are listed in Table ##TAB##2##3##. It showed that the Cr⁶⁺ ions adsorption was best fitted by the Freundlich model as shown in Fig. ##FIG##10##11##a,b. The separation factor <italic>R</italic>_{<italic>L</italic>} was calculated by Eq. (##FORMU##5##6##).</p>", "<p id=\"Par43\">The separation factor value (<italic>R</italic>_{<italic>L</italic>}) determined the favorability of the adsorption process. It ranged from 0.02 to 0.48, so 0 &lt; <italic>R</italic>_{<italic>L</italic>} &lt; 1, this indicated that the adsorption of Cr⁶⁺ ions on the CAC-IO nanocomposite surface was favorable. The maximum adsorption capacity <italic>Q</italic>_{<italic>max</italic>} was 312.5 mg g^–1 at 1.0 g L^–1 of CAC-IO.</p>", "<p id=\"Par44\">The experimental results were fitted to both isotherm models (Langmuir and Freundlich) in the adsorption of MV40 dye on CAC-IO, as shown in Fig. ##FIG##10##11##c,d. The maximum adsorption capacity (<italic>Q</italic>_{<italic>m</italic>}) for the Langmuir model was 833.3 mg g^–1, as shown in Table ##TAB##3##4## and the correlation coefficients <italic>R</italic>² obtained from that model varied from 0.958 to 0.986, while those obtained from the Freundlich model ranged from 0.979 to 0.995. Due to the proximity of <italic>R</italic>² to 1, these results showed that the adsorption process was fit for both models, however, the Freundich model was better matched than the Langmuir model. Table ##TAB##3##4## also showed that the adsorption process of dye on CAC-IO adsorbent was favorable due to 1/<italic>n</italic> values being lower than 1 as discussed before. The separation factors <italic>R</italic>_{<italic>L</italic>} were ranged from 0.001 to 0.063. These results indicated that the MV40 dye adsorption on CAC-IO was multilayer.</p>", "<title>Adsortion kinetic studies</title>", "<p id=\"Par45\">Three kinetic models, such as the pseudo-first-order (PFO), pseudo-second-order (PSO), and Intraprticle Diffusion (IPDM) models, were used to study the adsorption kinetic data. The rate expression of Lagergren indicated PFOas shown in Eq. (##FORMU##6##7##)^{##UREF##58##79##,##UREF##59##80##}:</p>", "<p id=\"Par46\">where <italic>q</italic>_{<italic>t</italic>} (mg g⁻¹) is the amount of adsorbed Cr⁶⁺ ions on CAC-IO adsorbent in time <italic>t</italic> and <italic>k</italic>_{<italic>1</italic>}, (min⁻¹), is the first-order rate constant, <italic>q</italic>_{<italic>e</italic>} is the adsorption uptake at equilibrium. The straight line was obtained representing, log (<italic>q</italic>_{<italic>e</italic>} − <italic>q</italic>_{<italic>t</italic>}) as the y-axis and <italic>t</italic> as the x-axis (Fig. ##FIG##11##12##a–d). The <italic>q</italic>_{<italic>e</italic>} and <italic>k</italic>_{<italic>1</italic>} shown in Tables ##TAB##4##5## and ##TAB##5##6## were determined from the intercept and slope of the plot, respectively. The linear PSO was used^{##UREF##58##79##,##UREF##59##80##} as in Eq. (##FORMU##7##8##):where <italic>k</italic>_{<italic>2</italic>} (g mg^–1) (min^–1) is the pseudo-second-order rate constant. From the slope of the straight line <italic>t</italic>/<italic>q</italic>_{<italic>t</italic>} vs. <italic>t</italic> plot, as shown in Fig. ##FIG##11##12##b–e, we can obtain qe while <italic>K</italic>₂ obtained from its intercept.</p>", "<p id=\"Par47\">The kinetic parameter values of Cr⁶⁺ ions and MV40 dye adsorption on CAC-IO adsorbent were summarised in Tables ##TAB##4##5##, ##TAB##5##6## and ##TAB##6##7## separately. It showed that the adsorption process follows the PSO model according to correlation coefficient (<italic>R</italic>²) from 0.982 to 1.00 in the case of Cr⁶⁺ ions adsorption and <italic>R</italic>² = 1 for MV40 dye adsorption and closeness of the calculated equilibrium adsorption capacity (<italic>q</italic>_e)_calc to those obtained from the experimental value (<italic>q</italic>_e)_exp. However, <italic>R</italic>² values for the PFO model are not satisfactory. So, the PSO adsorption model is more confirmed for an explanation of the adsorption kinetics of Cr⁶⁺ ions and MV40 dye by CAC-IO nanomagnetic adsorbent separately. These results were interpreted that the adsorption process was chemisorption^{##REF##21163571##81##}. Chemisorption is the sharing or exchanging of electrons between the adsorbate and the active sites on the adsorbent^{##REF##21163571##81##}.</p>", "<p id=\"Par48\">To interpret the diffusion mechanism, the experimental results were analyzed and fitted to the intraparticle diffusion model (IPDM) which is expressed by the following Eq. (##FORMU##8##9##):where <italic>K</italic>_{<italic>diff</italic>} is the intraparticle rate constant (mg g⁻¹ min^0.5) and <italic>C</italic> is an intercept (mg g⁻¹) which indicates the boundary layer effect. Figure ##FIG##11##12##c–f shows a linear plot of <italic>q</italic>_{<italic>t</italic>} vs <italic>t</italic>^0.5, these figures showed that these parameters increased by increasing the initial concentration of Cr⁶⁺ ion solutions, and there was an increase of <italic>C</italic> due to the increase of the thickness of the boundary layer. It was seen that the linear plot didn’t pass through the origin, these indicate that intraparticle diffusion was not only the rate-determining step^{##REF##23597681##82##}.</p>", "<p id=\"Par49\">The IPDM was also tested on the adsorption of the MV40 dye on CAC-IO nanocomposite, the <italic>q</italic>_{<italic>t</italic>} vs <italic>t</italic>^0.5 plot was drawn as shown in Fig. ##FIG##11##12##f, and similar behavior was obtained as in the Cr⁶⁺ ions adsorption process in Fig. ##FIG##11##12##c, none of the lines didn’t pass through the origin and the intercepts <italic>C</italic> increased by increasing the initial concentrations of dye solutions from 100 to 400 mg L^–1 at each adsorbent dose as shown in Table ##TAB##6##7##. It was concluded that the IPDM was not the only rate-controlling step as discussed previously.</p>", "<title>Comparison of results with reported literature</title>", "<p id=\"Par50\">Table ##TAB##7##8## shows some of the previous literature done for removing Cr⁶⁺ ions from aquatic media and dyes. The maximum adsorption capacity was recorded in this Table at a certain temperature, it was found that CAC-IO nano adsorbent has the greatest <italic>Q</italic>_{<italic>max</italic>} recorded more than the mentioned literature at room temperature. These values were 312.5 and 833.3 mg g^–1 for Cr⁶⁺ ions and MV40 dye removal at fixed 1.0 g L^–1 of nano adsorbent concentration, respectively. From this comparison, it is obvious that the CAC-IO nanocomposite prepared from CAC was an excellent adsorbent for removing Cr⁶⁺ ions and MV40 dye from aqueous solutions.</p>", "<title>Regeneration of MG-OPAC</title>", "<p id=\"Par51\">To test the viability and reusability of CAC-IO as an adsorbent, desorption tests of the Cr6 + ions and MV40 dye from the CAC-IO adsorbent were carried out by 0.1 M NaOH and HCl as elution media. With increasing regeneration cycles in this situation, the desorption percentage dropped (Fig. ##FIG##12##13##a,b). The regenerated CAC-IO was used in six successive adsorption/desorption cycles for the two pollutants with Slightly better for Cr⁶⁺ ions. The amount of adsorption that was offered remained constant during the cycles; however, after six regenerations, the adsorption capacity of Cr⁶⁺ ions had decreased by 10.1%, while the desorption capacity decreased by 10.8% after six desorption cycles. On the other hand, After six regenerations, the adsorption capacity of MV40 dye had decreased by 14.1%, while the desorption capacity decreased by 13.9% after six desorption cycles. It implies that it might be employed as a long-lasting Cr⁶⁺ ions and MV40 dye adsorption process (Fig. ##FIG##12##13##a,b).</p>", "<title>Adsorption mechanism of Cr⁶⁺ ions and MV40 dye ions by CAC-IO</title>", "<p id=\"Par52\">In the case of Cr⁶⁺ ions and MV40 dye, the probable adsorption mechanism onto magnetic commercial activated carbon (CAC-IO) in acidic medium was explained in Fig. ##FIG##13##14##. The activated carbon possesses numerous surface functional groups such as hydroxyl (-OH), carboxyl (-COOH), and other polar moieties. These functional groups play a crucial role in attracting and holding the pollutant molecules. Cr⁶⁺ ions and MV40 dye are likely to have charged particles, as many pollutants are ionic or polar in nature. The activated carbon, being a porous material, has a large surface area with a distribution of positive and negative sites. After the oxidation of the CAC, many functional groups were formed on the adsorbent (CAC) surface like allene C=C=C, ketamine C=C=N, hydroxyl O–H, and C–N groups. CAC, with its graphitic structure, can form π-π interactions with these aromatic rings. This type of interaction enhances the adsorption capacity, especially when the activated carbon is magnetic. The mechanism of the removal of Cr⁶⁺ ions and MV40 dye in an acidic medium may be achieved via physical interaction due to electrostatic interaction between the positive hydrogen ions in the bulk solution and the nitrogen and oxygen functional groups on the CAC-IO surface, then surface charge became positive; subsequently electrostatic interaction was occurred between the positively charged surface and the predominant pollutant anionic species ([HCrO₄]^– and [MV40]^– dye).</p>" ]

[ "<title>Results and discussion</title>", "<title>Characterization of adsorbent</title>", "<title>FTIR analyses</title>", "<p id=\"Par19\">The produced materials (CAC, CAC after treatment, and CAC-IO) were characterized using the Fourier transform infrared technique, as shown in Fig. ##FIG##0##1##. The FTIR spectrum of CAC, CAC after oxidation, and CAC-IO nanocomposite showed a broad peak at 3049 and 3225 cm^–1 due to the OH bond, also a peak appeared at 1576, 1578, 1576 cm^–1 with small shifts due to the C=C stretching bond and the bands appeared at 1174, 1192 and 1221 cm^–1 assigned to C–O stretching from phenolic, alcoholic, etheric groups and to C–C bond, similar results was obtained by Bagheri et al. (2017)^{##REF##29137753##59##}. The fact that all spectra included peaks at 2354 cm^–1 caused by the C–C bond in the structure of activated carbon showed that the structure had not been damaged during the composite pyrolysis^{##REF##24727015##53##}. Due to the synthesis of nano-iron oxide, a new peak at 575 cm^–1 in the CAC-IO spectra had been developed. The appearance of the Fe–O stretching bond revealed that iron oxide nanoparticles had been deposited on the CAC-IO adsorbent surface. The peaks appeared at 886 and 793 cm^–1, which may be due to the δ(OH) and γ(OH) vibration in and out of the plane, respectively, indicated to geothite peaks^{##REF##18838216##57##,##UREF##45##60##–##UREF##47##62##}.</p>", "<title>BET analyses</title>", "<p id=\"Par20\">Using the BET equation, the surface area and pore information of the produced nanocomposite and its constituent material were calculated. The pore volume (<italic>V</italic>_{<italic>t</italic>}) for each adsorbent and its precursor materials was calculated using nitrogen adsorption at relative pressure <italic>P</italic>/<italic>P</italic>_{<italic>o</italic>} = 0.99. The pore diameters of commercial and synthesized activated carbon and nanocomposites were calculated.</p>", "<p id=\"Par21\">As seen in Table ##TAB##0##1## using BET analyses, the specific surface areas of CAC, CAC after oxidation, and CAC-IO were calculated as 1426.8, 985.58, and 1070 m² g^–1, respectively. The use of H₂O₂, a powerful oxidizing chemical, caused damage to the pores in CAC's structure, resulting in a reduction in surface area following oxidation^{##UREF##42##55##,##REF##17980401##63##,##UREF##48##64##}. As the surface area increases after adding Fe₃O₄, it expected that the Fe₃O₄ is attached to the functional group on the surface of CAC rather than inserted inside the pores.</p>", "<p id=\"Par22\">Figure ##FIG##1##2## showed the nitrogen adsorption–desorption isotherms of the precursor materials and showed that they were type (IV) isotherms^{##UREF##49##65##}. The structure of CAC and CAC after oxidation, as well as CAC-IO, were mesoporous^{##REF##21749733##66##}, according to the IUPAC classification, which is micropores (<italic>d</italic> &lt; 2 nm), mesopores (2 &lt; <italic>d</italic> &lt; 50 nm), and macropores (<italic>d</italic> &gt; 50 nm)^{##UREF##49##65##}.</p>", "<p id=\"Par23\">The CAC-IO nanomagnetic adsorbent's pore volume was 0.9155 cm³ g^–1. The findings demonstrated that the oxidation process and the resulting production of magnetic nanocomposites reduced the surface area of the commercial activated carbon (CAC), which was caused by the dispersion of iron oxide nanoparticles on the carbon surface, from 1426 m² g^–1 to 1070 m² g^–1.</p>", "<title>SEM-TEM analyses</title>", "<p id=\"Par24\">As shown in Figs. ##FIG##2##3##a,b, scanning electron microscopy was used to examine the surface morphology and shape of the adsorbent prepared after oxidation and its iron oxide nanocomposite (CAC-IO). The surface of CAC-IO showed roughness than that of CAC, which may explain the attachment of Fe₃O₄ to the surface functional group instead of being inserted into the surface pores. The TEM image of the CAC-IO nanocomposite obtained using the Transition Electron Microscopy (TEM-2100 Electron Microscope) to determine the nano-sized composite spacing and their shape at the nanoscale is shown in Fig. ##FIG##2##3##c. TEM image of CAC-IO nanocomposite showed the particle shape of nano iron oxide was spherical and agglomerated to each other. According to Fig. ##FIG##2##3##c, the particle size ranged from 4.12 to 19.5 nm, and smaller particles have a higher adsorption capacity.</p>", "<title>EDX analyses</title>", "<p id=\"Par25\">As shown in Table ##TAB##1##2##, the elements and iron oxide nanocomposites in the adsorbent produced during the treatment were identified and determined using the SEM–EDX equipment. The study of CAC after oxidation verified the existence of several components, including Carbon, Oxygen, Sodium, Silicon, and Chlorine with percentage ratios of 83.26, 15.38, 0.17, 1.05, and 0.14%, respectively, in the CAC structure. The iron element Fe has a weight ratio of 12.09% owing to the magnetic CAC-IO synthesis, and the examination of CAC-IO nanocomposites in Fig. ##FIG##3##4## confirms the presence of the same components in CAC after oxidation with a modified weight ratio. The production of iron oxide nanocomposites with iron components resulted in a reduction in the carbon content from 83.26 to 65.25%^{##REF##21749733##66##}.</p>", "<title>VSM analyses</title>", "<p id=\"Par26\">The magnetization curve of the synthesized magnetite iron oxide nanocomposite (CAC-IO) was measured to study the magnetic properties at room temperature in a magnetic field with a cycle of –20 to + 20 KOe. The highest saturation magnetization for CAC-IO was 7.4130 emu g⁻¹ as in Fig. ##FIG##4##5##, which is due to the high iron oxide content of the CAC-IO nanocomposite. The magnetic properties of CAC-IO (7.4130 emu/g) compared to the magnetic properties of pure Fe₃O₄ nanoparticles (~ 90 emu/g) may be expained by the formation of CAC composites with Fe₃O₄ nanoparticles, which has a substantial impact on the magnetic properties of Fe₃O₄. This phenomenon can be attributed to factors such as the surface area and elemental composition of Fe₃O₄ within the composite or to the percentage of Fe₃O₄ within the CAC-IO composite.</p>", "<title>XRD analyses</title>", "<p id=\"Par27\">XRD analyses of the prepared nanocomposites and their pure materials obtained under Cu-kα radiation at 25 °C are given in Figs. ##FIG##5##6##a,b. In Fig. ##FIG##5##6##a, the only peak that appeared at 26.14° is related to commercial activated carbon after oxidation, similar results were obtained according to Gholamvaisi et al<italic>.</italic> (2014)^{##UREF##50##67##}.</p>", "<p id=\"Par28\">Figure ##FIG##5##6##b indicates to CAC-IO nanocomposite that shows several peaks at different angles at 30.31, 35.66, 43.25, 57.42, and 63.04°, the maximum peak intensity was at 2θ = 35.66⁰ which indicates the presence of magnetite (Fe₃O₄) or maghemite nanoparticles in cubic crystal structure shapes according to reference card code 04-013-9811. After oxidation, no peak for CAC was seen in Fig. ##FIG##5##6##b; this could be because the surface of the carbon has agglomerated or been coated with magnetite or maghemite nanoparticles^{##UREF##51##68##}.</p>", "<p id=\"Par29\">The average crystalline size of the prepared CAC-IO was determined from the XRD results; it was calculated from Scherrer’s formula (Eq. (##FORMU##2##3##)),where <italic>L</italic> is the crystalline size, λ is the wavelength of the X-ray, <italic>B</italic> is the full width of half maximum of a diffraction peak, <italic>θ</italic> is the angle of diffraction and <italic>K</italic> is the Scherrer’s constant of the order of 0.89^{##REF##29137753##59##}.</p>", "<p id=\"Par30\">The XRD results show that the average crystal size of CAC-IO is 24.21 nm at 2θ = 35.66, which is in good agreement with the TEM results.</p>", "<title>Adsorption of Cr⁶⁺ ions and MV40 dye on CAC-IO nanocomposite</title>", "<title>Effect of pH</title>", "<p id=\"Par31\">In order to examine the effect of solution pH on adsorption, solutions were prepared at constant concentrations at various pHs, and the adsorption of a certain amount of adsorbent and a certain volume of pollutant solution at room temperature was studied. As a result of the studies, the effect of different pH solutions has revealed that the best removal percentage is on acidic pH. Figure ##FIG##6##7## shows that by increasing the pH of Cr⁶⁺ ions solutions from 1.6 to 11.24, the percentage of Cr⁶⁺ removal decreased from 99.58 to 45.45%, giving the maximum removal percentage at pH 1.6. The effect of pH value on the chromium species in the solution and its effect on the chromium removal % were previously studied^{##UREF##9##14##,##UREF##10##15##,##UREF##17##23##,##UREF##52##69##–##REF##20099060##72##}. pH Fig. ##FIG##6##7## also shows that the removal % decreased by increasing the pH of MV40 dye solutions from 1.3 to 10.97, giving a maximum removal percentage was 99.08% at pH 2.07,100 mg L^–1 of initial dye concentration with 1 g L^–1 of CAC-IO concentration and 3 h of contact time. This result is due to the electrostatic attraction between the positively charged CAC-IO surface and the negative charges on the dye molecules at acidic pH, but at higher pH, there was repulsion between the two opposite charges of the dye molecules and the adsorbent surface used. Similar results were obtained in Kalantry et al. (2015)^{##UREF##54##73##}.</p>", "<title>Effect of CAC-IO adsorbent concentration</title>", "<p id=\"Par32\">Different concentrations from CAC-IO nanocomposite (1, 1.5, 2, 2.5 g L^–1) were used to study the adsorbent concentration effect at 400 mg L^–1 of initial concentrations of Cr⁶⁺ ions and MV40 dye solutions, contact time is 3 h and fixed pH = 1.6 for Cr⁶⁺ ions solutions after adding the adsorbent while the dye solution pH was fixed at 2.07 for MV40 dye after adding the adsorbent separately. The resulting samples were drawn at intermittent times (10, 20, 30, 45, 60, 90, 120, 150, and 180 min) to separately analyze the final concentrations of Cr⁶⁺ ions and MV40 dye in solutions. Figure ##FIG##7##8## illustrates the chart used to examine the influence of nanocomposite concentration on the percentages of Cr⁶⁺ ions and MV40 dye removal from water, respectively. The result shown for Cr⁶⁺ adsorption revealed that by increasing the adsorbent concentration (CAC-IO) from 1 to 2.5 g L^–1, the removal percentage increased from 54.33 to 78.80%, so 2.5 g L^–1 of CAC-IO nanocomposite was considered to be the optimum concentration to remove 400 mg L^–1 of Cr⁶⁺ ions from aqueous media at optimum solution pH = 1.6, room temperature and equilibrium time = 3 h.</p>", "<p id=\"Par33\">This results from the presence of unsaturated adsorption sites on adsorbent (CAC-IO) during the adsorption process, also the decrease in adsorption capacity may be due to the aggregation of adsorbent particles due to the high concentration of it. This aggregation may result in a reduction in the adsorbent's overall surface area and an increase in the diffusional route length^{##REF##32326104##74##}. The chart for the adsorption of MV40 dye indicated that increasing the adsorbent concentration (CAC-IO) from 1.0 to 2.5 g L^–1 slightly enhanced the elimination percentage from 97.64 to 99.79%. At optimal solution pH = 2.07, room temperature, and equilibrium time is 3 h, 1.0 g L^–1 of CAC-IO nanocomposite was thought to be the best concentration to remove 400 mg L^–1 of MV40 dye from aqueous medium as shown in Fig. ##FIG##7##8##. However, there was no significant increase in the removal percentage of dye at concentrations larger than 1.0 g L^–1.</p>", "<title>Effect of initial adsorbate concentrations on CAC-IO nanocomposite</title>", "<p id=\"Par34\">Different five concentrations (100, 150, 200, 300, 400 mgL⁻¹) of Cr⁶⁺ ions and MV40 dye solutions were each examined during batch adsorption experiments at 1.0 g L^–1 CAC-IO concentration individually at fixed pH = 1.6 in case of Cr⁶⁺ ions adsorption and pH = 2.07 in case of MV40 dye adsorption at room temperature. Commercial activated carbon-iron oxide nanocomposite (CAC-IO) was used to study the impact of initial Cr⁶⁺ ions concentrations on the rate of adsorption in the range of 100 to 400 mg L^–1, as shown in Fig. ##FIG##8##9##a. It is obvious that the Cr⁶⁺ ions removal by different adsorbents doses (CAC-IO) was dependent on the initial Cr⁶⁺ ions concentrations, this is due to increasing the initial Cr⁶⁺ ions concentrations increased the amount of Cr⁶⁺ ions adsorbed on the adsorbent adsorption capacity (<italic>q</italic>_{<italic>e</italic>}).</p>", "<p id=\"Par35\">This increase is due to the resistance to the uptake of solute from Cr⁶⁺ ions solution decreased so the initial concentrations of Cr⁶⁺ solutions provide an important driving force to overcome the mass transfer resistance of Cr⁶⁺ ions between the aqueous and the solid phases^{##UREF##55##75##}. In the range of 100 to 400 mg L^–1, the impact of initial MV40 dye concentrations on the rate of adsorption by CAC-IO was examined, as shown in Fig. ##FIG##8##9##b. Additionally, the number of MV40 dye molecules adsorbed on the CAC-IO surface developed when initial dye concentrations were raised, which is why the MV40 dye removal by various adsorbent (CAC-IO) concentrations were reliant on those initial dye concentrations. As it was previously mentioned, this rise results from a reduction in the impedance to solute absorption from dye solution^{##UREF##55##75##}.</p>", "<title>Effect of contact time using CAC-IO</title>", "<p id=\"Par36\">An experiment was done to study the effect of contact time, 100 mg L^–1 of Cr⁶⁺ ions or MV40 dye initial concentrations were tested, and 2 g L^–1 CAC-IO adsorbent concentration (highest dose gave maximum removal %) in case of Cr⁶⁺ ions solutions and 1.0 g L^–1 CAC-IO adsorbent concentration in case of dye solutions at pH of Cr⁶⁺ ions and dye solutions, 1.6 and 2.07, respectively, and room temperature. The obtained samples were taken at interval times (10, 20, 30, 45, 60, 90, 120, 150, and 180 min) and analyzed by UV–visible spectrophotometer at 540 and 510 nm of maximum wavelengths of Cr⁶⁺ ions and MV40 dye, respectively.</p>", "<p id=\"Par37\">The rapid removal of Cr⁶⁺ ions after only 10 min (87.92%) in the initial phase of adsorption from 0 to 10 min and then the rate of removal gradually slowed down until the equilibrium state was reached after 180 min, as shown in Fig. ##FIG##9##10##a. The rate of removal of MV40 dye was very fast (98.49%) from 0 to 10 min, and then the rate of removal gradually slowed down until it reached a constant value at equilibrium, as shown in Fig. ##FIG##9##10##b.</p>", "<p id=\"Par38\">The results were interpreted that the higher availability of vacant sites on the adsorbent surface at the initial stage while by passing the time of experiments, these sites were occupied by the adsorbate molecules, and the number of vacant sites became few so the removal percent of Cr⁶⁺ ions and MV40 dye molecules become very slow, also it was shown that the variations of initial dye and Cr⁶⁺ ion concentrations did not significantly affect the removal rate to reach its equilibrium state.</p>", "<p id=\"Par39\">Finally, we concluded that the maximum removal % of Cr⁶⁺ solutions was 98.60% after 180 min and the initial Cr⁶⁺ concentration was 100 mg L^–1 using 2.0 g L^–1 of CAC-IO adsorbent concentration, while 99.92% was the highest dye removal percent after 180 min using only 1.0 g L^–1 of CAC-IO and 100 mg L^–1 of initial dye concentration.</p>", "<title>Adsorption isotherms</title>", "<p id=\"Par40\">As indicated in Fig. ##FIG##10##11##, Langmuir and Freundlich isotherms were examined for the distinct adsorption of Cr⁶⁺ ions and MV40 dye on CAC-IO nanocomposites. The adsorption isotherm data of Langmuir and Freundlich models obtained using Langmuir and Freundlich models are shown in Table ##TAB##2##3##. The interaction between adsorbates and adsorbents is represented by the properties of adsorption and the parameters of each isotherm model; this information reveals the nature of the interaction^{##UREF##56##76##}.</p>", "<p id=\"Par41\">The Langmuir model assumed that the adsorption was monolayer on a homogeneous adsorbent surface, that there was no interaction between the molecules that were adsorbed, and that the transmigration of the molecules that were adsorbed on the adsorbent surface was not permitted^{##UREF##57##77##}. The Langmuir linear Eq. (##FORMU##3##4##) can be expressed as follows (Eq. (##FORMU##3##4##)):where <italic>C</italic>_{<italic>e</italic>} is the concentration of adsorbate in solution (mg L^–1) at equilibrium, <italic>q</italic>_{<italic>e</italic>} is the adsorption capacity at equilibrium in mg g⁻¹, <italic>K</italic>_{<italic>a</italic>} is constant related to free energy of adsorption (L mg^–1), and <italic>Q</italic>_{<italic>m</italic>} is the maximum adsorption capacity at monolayer coverage in mg g^–1. An empirical linear equation of Freundlich Isotherm assumed that the adsorbent surface was heterogeneous; the equation was expressed as shown in Eq. (##FORMU##4##5##):where <italic>K</italic>_{<italic>f</italic>} (mg^1–1/n g^-1 L^1/n) and <italic>n</italic> are the Freundlich constants, they indicate the adsorption capacity and intensity of adsorption, respectively. The values of 1/<italic>n</italic> in Tables ##TAB##2##3##, ##TAB##3##4## are greater than zero and lower than 1, (0 &lt; 1/<italic>n</italic> &lt; 1) the adsorption is favorable^{##REF##22119217##78##}.</p>", "<p id=\"Par42\">The isotherm parameters obtained from both models due to Cr⁶⁺ ions adsorption on CAC-IO are listed in Table ##TAB##2##3##. It showed that the Cr⁶⁺ ions adsorption was best fitted by the Freundlich model as shown in Fig. ##FIG##10##11##a,b. The separation factor <italic>R</italic>_{<italic>L</italic>} was calculated by Eq. (##FORMU##5##6##).</p>", "<p id=\"Par43\">The separation factor value (<italic>R</italic>_{<italic>L</italic>}) determined the favorability of the adsorption process. It ranged from 0.02 to 0.48, so 0 &lt; <italic>R</italic>_{<italic>L</italic>} &lt; 1, this indicated that the adsorption of Cr⁶⁺ ions on the CAC-IO nanocomposite surface was favorable. The maximum adsorption capacity <italic>Q</italic>_{<italic>max</italic>} was 312.5 mg g^–1 at 1.0 g L^–1 of CAC-IO.</p>", "<p id=\"Par44\">The experimental results were fitted to both isotherm models (Langmuir and Freundlich) in the adsorption of MV40 dye on CAC-IO, as shown in Fig. ##FIG##10##11##c,d. The maximum adsorption capacity (<italic>Q</italic>_{<italic>m</italic>}) for the Langmuir model was 833.3 mg g^–1, as shown in Table ##TAB##3##4## and the correlation coefficients <italic>R</italic>² obtained from that model varied from 0.958 to 0.986, while those obtained from the Freundlich model ranged from 0.979 to 0.995. Due to the proximity of <italic>R</italic>² to 1, these results showed that the adsorption process was fit for both models, however, the Freundich model was better matched than the Langmuir model. Table ##TAB##3##4## also showed that the adsorption process of dye on CAC-IO adsorbent was favorable due to 1/<italic>n</italic> values being lower than 1 as discussed before. The separation factors <italic>R</italic>_{<italic>L</italic>} were ranged from 0.001 to 0.063. These results indicated that the MV40 dye adsorption on CAC-IO was multilayer.</p>", "<title>Adsortion kinetic studies</title>", "<p id=\"Par45\">Three kinetic models, such as the pseudo-first-order (PFO), pseudo-second-order (PSO), and Intraprticle Diffusion (IPDM) models, were used to study the adsorption kinetic data. The rate expression of Lagergren indicated PFOas shown in Eq. (##FORMU##6##7##)^{##UREF##58##79##,##UREF##59##80##}:</p>", "<p id=\"Par46\">where <italic>q</italic>_{<italic>t</italic>} (mg g⁻¹) is the amount of adsorbed Cr⁶⁺ ions on CAC-IO adsorbent in time <italic>t</italic> and <italic>k</italic>_{<italic>1</italic>}, (min⁻¹), is the first-order rate constant, <italic>q</italic>_{<italic>e</italic>} is the adsorption uptake at equilibrium. The straight line was obtained representing, log (<italic>q</italic>_{<italic>e</italic>} − <italic>q</italic>_{<italic>t</italic>}) as the y-axis and <italic>t</italic> as the x-axis (Fig. ##FIG##11##12##a–d). The <italic>q</italic>_{<italic>e</italic>} and <italic>k</italic>_{<italic>1</italic>} shown in Tables ##TAB##4##5## and ##TAB##5##6## were determined from the intercept and slope of the plot, respectively. The linear PSO was used^{##UREF##58##79##,##UREF##59##80##} as in Eq. (##FORMU##7##8##):where <italic>k</italic>_{<italic>2</italic>} (g mg^–1) (min^–1) is the pseudo-second-order rate constant. From the slope of the straight line <italic>t</italic>/<italic>q</italic>_{<italic>t</italic>} vs. <italic>t</italic> plot, as shown in Fig. ##FIG##11##12##b–e, we can obtain qe while <italic>K</italic>₂ obtained from its intercept.</p>", "<p id=\"Par47\">The kinetic parameter values of Cr⁶⁺ ions and MV40 dye adsorption on CAC-IO adsorbent were summarised in Tables ##TAB##4##5##, ##TAB##5##6## and ##TAB##6##7## separately. It showed that the adsorption process follows the PSO model according to correlation coefficient (<italic>R</italic>²) from 0.982 to 1.00 in the case of Cr⁶⁺ ions adsorption and <italic>R</italic>² = 1 for MV40 dye adsorption and closeness of the calculated equilibrium adsorption capacity (<italic>q</italic>_e)_calc to those obtained from the experimental value (<italic>q</italic>_e)_exp. However, <italic>R</italic>² values for the PFO model are not satisfactory. So, the PSO adsorption model is more confirmed for an explanation of the adsorption kinetics of Cr⁶⁺ ions and MV40 dye by CAC-IO nanomagnetic adsorbent separately. These results were interpreted that the adsorption process was chemisorption^{##REF##21163571##81##}. Chemisorption is the sharing or exchanging of electrons between the adsorbate and the active sites on the adsorbent^{##REF##21163571##81##}.</p>", "<p id=\"Par48\">To interpret the diffusion mechanism, the experimental results were analyzed and fitted to the intraparticle diffusion model (IPDM) which is expressed by the following Eq. (##FORMU##8##9##):where <italic>K</italic>_{<italic>diff</italic>} is the intraparticle rate constant (mg g⁻¹ min^0.5) and <italic>C</italic> is an intercept (mg g⁻¹) which indicates the boundary layer effect. Figure ##FIG##11##12##c–f shows a linear plot of <italic>q</italic>_{<italic>t</italic>} vs <italic>t</italic>^0.5, these figures showed that these parameters increased by increasing the initial concentration of Cr⁶⁺ ion solutions, and there was an increase of <italic>C</italic> due to the increase of the thickness of the boundary layer. It was seen that the linear plot didn’t pass through the origin, these indicate that intraparticle diffusion was not only the rate-determining step^{##REF##23597681##82##}.</p>", "<p id=\"Par49\">The IPDM was also tested on the adsorption of the MV40 dye on CAC-IO nanocomposite, the <italic>q</italic>_{<italic>t</italic>} vs <italic>t</italic>^0.5 plot was drawn as shown in Fig. ##FIG##11##12##f, and similar behavior was obtained as in the Cr⁶⁺ ions adsorption process in Fig. ##FIG##11##12##c, none of the lines didn’t pass through the origin and the intercepts <italic>C</italic> increased by increasing the initial concentrations of dye solutions from 100 to 400 mg L^–1 at each adsorbent dose as shown in Table ##TAB##6##7##. It was concluded that the IPDM was not the only rate-controlling step as discussed previously.</p>", "<title>Comparison of results with reported literature</title>", "<p id=\"Par50\">Table ##TAB##7##8## shows some of the previous literature done for removing Cr⁶⁺ ions from aquatic media and dyes. The maximum adsorption capacity was recorded in this Table at a certain temperature, it was found that CAC-IO nano adsorbent has the greatest <italic>Q</italic>_{<italic>max</italic>} recorded more than the mentioned literature at room temperature. These values were 312.5 and 833.3 mg g^–1 for Cr⁶⁺ ions and MV40 dye removal at fixed 1.0 g L^–1 of nano adsorbent concentration, respectively. From this comparison, it is obvious that the CAC-IO nanocomposite prepared from CAC was an excellent adsorbent for removing Cr⁶⁺ ions and MV40 dye from aqueous solutions.</p>", "<title>Regeneration of MG-OPAC</title>", "<p id=\"Par51\">To test the viability and reusability of CAC-IO as an adsorbent, desorption tests of the Cr6 + ions and MV40 dye from the CAC-IO adsorbent were carried out by 0.1 M NaOH and HCl as elution media. With increasing regeneration cycles in this situation, the desorption percentage dropped (Fig. ##FIG##12##13##a,b). The regenerated CAC-IO was used in six successive adsorption/desorption cycles for the two pollutants with Slightly better for Cr⁶⁺ ions. The amount of adsorption that was offered remained constant during the cycles; however, after six regenerations, the adsorption capacity of Cr⁶⁺ ions had decreased by 10.1%, while the desorption capacity decreased by 10.8% after six desorption cycles. On the other hand, After six regenerations, the adsorption capacity of MV40 dye had decreased by 14.1%, while the desorption capacity decreased by 13.9% after six desorption cycles. It implies that it might be employed as a long-lasting Cr⁶⁺ ions and MV40 dye adsorption process (Fig. ##FIG##12##13##a,b).</p>", "<title>Adsorption mechanism of Cr⁶⁺ ions and MV40 dye ions by CAC-IO</title>", "<p id=\"Par52\">In the case of Cr⁶⁺ ions and MV40 dye, the probable adsorption mechanism onto magnetic commercial activated carbon (CAC-IO) in acidic medium was explained in Fig. ##FIG##13##14##. The activated carbon possesses numerous surface functional groups such as hydroxyl (-OH), carboxyl (-COOH), and other polar moieties. These functional groups play a crucial role in attracting and holding the pollutant molecules. Cr⁶⁺ ions and MV40 dye are likely to have charged particles, as many pollutants are ionic or polar in nature. The activated carbon, being a porous material, has a large surface area with a distribution of positive and negative sites. After the oxidation of the CAC, many functional groups were formed on the adsorbent (CAC) surface like allene C=C=C, ketamine C=C=N, hydroxyl O–H, and C–N groups. CAC, with its graphitic structure, can form π-π interactions with these aromatic rings. This type of interaction enhances the adsorption capacity, especially when the activated carbon is magnetic. The mechanism of the removal of Cr⁶⁺ ions and MV40 dye in an acidic medium may be achieved via physical interaction due to electrostatic interaction between the positive hydrogen ions in the bulk solution and the nitrogen and oxygen functional groups on the CAC-IO surface, then surface charge became positive; subsequently electrostatic interaction was occurred between the positively charged surface and the predominant pollutant anionic species ([HCrO₄]^– and [MV40]^– dye).</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par53\">Iron oxide nanocomposite (CAC-IO) was prepared from commercial activated carbon (CAC) by co-precipitation method using different iron salts and different base solutions. The Cr⁶⁺ ions removal % from its solution by CAC-IO adsorbent was 98.60% at solution pH 1.6 and adsorbent concentrations 2.0 g L^–1. The removal % of MV40 dye was 99.92% by CAC-IO, at pH of dye solutions = 2.07, and adsorbent concentrations of 1.0 g L⁻¹ of CAC-IO at 100 mg L⁻¹ of initial dye concentration. The removal percentage of Cr⁶⁺ ions and MV40 dye was higher in acidic solutions than in basic solutions. CAC-IO nanocomposite has 7.4130 emu g^–1 magnetization saturation. <italic>Q</italic>_{<italic>max</italic>} of Cr⁶⁺ ions on CAC-IO was 312.50 mg g⁻¹ at 1.0 g L^–1, while in the case of MV40 dye, it was 833.3 mg g^–1 at 2.0 g L^–1 adsorbent concentration. Freundlich model was the most fitted on MV40 dye adsorption using CAC-IO; also it was the best fitted model in Cr⁶⁺ ions adsorption on CAC-IO. CAC-IO nanocomposite can be separated from aqueous media after treatment and adsorption process by a magnet. An encouraging development in water treatment technology is the incorporation of magnetic characteristics into activated carbon usch as preparation of CAC-IO. The combination of magnetic separation and adsorption offers a flexible and effective way to deal with problems related to water quality, all the while enhancing the overall sustainability of water treatment procedures. Pursuing cleaner and more sustainable water resources is the goal of ongoing research and development in this subject, which aims to broaden and improve the uses of CAC-IO. The prepared Iron oxide nanocomposite CAC-IO can be used for the adsorption of Cr⁶⁺ ions and MV40 dye from aqueous media. The regeneration of CAC-IO was effective up to six cycles, which explains the possibility of using the prepared CAC-IO in treating industrial wastewater with high effectiveness, which may lead to reducing the cost of treating industrial wastewater.</p>" ]

[ "<p id=\"Par1\">Iron Oxide-commercial activated carbon nanocomposite (CAC-IO) was prepared from commercial activated carbon (CAC) by the co-precipitation method, and the resulting nanocomposite was used as an adsorbent to remove hexavalent chromium (Cr⁶⁺) ions and Mordant Violet 40 (MV40) dye from wastewater. The produced materials (CAC, CAC after oxidation, and CAC-IO) were comparatively characterized using FTIR, BET, SEM, EDX TEM, VSM, and XRD techniques. The adsorption mechanism of Cr⁶⁺ ions and MV40 dye on CAC-IO was examined using Langmuir and Freundlich isotherm models.. Different models were applied to know the adsorption mechanism and it was obtained that Pseudo-second order fits the experimental data better. This means that the adsorption of the adsorbate on the nanocomposite was chemisorption. The maximum removal percent of Cr⁶⁺ ions by CAC-IO nanocomposite was 98.6% determined as 2 g L^–1 adsorbent concentration, 100 mg L^–1 initial pollutant concentration, solution pH = 1.6, the contact time was 3 h and the temperature was room temperature. The maximum removal percentage of Mordant Violet 40 dye (C.I. 14,745) from its solutions by CAC-IO nanocomposite was 99.92% in 100 mg L^–1 of initial dye concentrations, 1.0 g L^–1 of adsorbent concentration, solution pH = 2.07, the contact time was 3 h. The MV40 dye adsorption on CAC-IO was the most fitted to the Freundlich isotherm model. The maximum adsorption capacity was calculated according to the Langmuir model as 833.3 mg g^–1 at 2 g L^–1 of adsorbent concentration and 400 mg L^–1 of initial MV40 dye concentration. The Cr⁶⁺ ions adsorption on CAC-IO was more fitted to the Freundlich model with <italic>Q</italic>_{<italic>max</italic>}, equal to 312.50 mg g^–1 at 1 g L^–1 adsorbent concentration and 400 mg L^–1 of Cr⁶⁺ ions initial concentrations.</p>", "<title>Subject terms</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).</p>" ]

[]

[ "<title>Acknowledgements</title>", "<p>The authors acknowledge the lat Professor Dr. Hesham Zaki Ibrahim, Institute of Graduate Studies and Research, Alexandria University, who passed away prior to writing this manuscript for his supervision and valuable discussion with S.M.I.M. during the experimental work and writing of Ms. S.M.I.M.'s master's thesis.</p>", "<title>Author contributions</title>", "<p>S.M.I.M. conceived the experiments, conducted the experiments and wrote the main manuscript text; E.K.G. and M.Y. revised and edited the main manuscript; A.E.N. reviewed, revised and enhanced the discussion in the paper and submitted to the journal. All authors reviewed the manuscript.</p>", "<title>Funding</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB). This work was partially supported by The Science, Technology &amp; Innovation Funding Authority (STDF) of Egypt, project number SCSE-31235.</p>", "<title>Data availability</title>", "<p>The data presented in this study are available on the request from the corresponding author.</p>", "<title>Competing interests</title>", "<p id=\"Par54\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>FTIR spectrum for CAC, CAC after oxidation and CAC-IO nanocomposite.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>N₂ adsorption–desorption isotherm plot of CAC (<bold>a</bold>), CAC after oxidation (<bold>b</bold>) and CAC-IO nanocomposite (<bold>c</bold>).</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>SEM Images of CAC after oxidation (<bold>a</bold>) and CAC-IO nanocomposite (<bold>b</bold>) at 15 kV and 2000 × magnification and TEM image of CAC-IO nanocomposite (<bold>c</bold>) at 50 nm scale.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>EDX analyses chart of CAC after oxidation (<bold>a</bold>) CAC-IO nanocomposite (<bold>b</bold>).</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Magnetization curve for CAC-IO nanocomposite.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>XRD graph of CAC after oxidation (<bold>a</bold>) and CAC-IO (<bold>b</bold>).</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Effect of pH on the removal of Cr⁶⁺ ions and MV40 dye from aqueous media (Pollutant = 100 mg L⁻¹, adsorbent = 100 mg L^–1, Time = 3 h).</p></caption></fig>", "<fig id=\"Fig8\"><label>Figure 8</label><caption><p>Effect of different CAC-IO concentrations on the removal % of Cr⁶⁺ ions and MV40 dye using 400 mg L^–1 of pollutants' concentrations and 1.0 g L^–1 as CAC-IO concentrations.</p></caption></fig>", "<fig id=\"Fig9\"><label>Figure 9</label><caption><p>Effect of various concentrations of Cr⁶⁺ ions (<bold>a</bold>) and MV40 dye (<bold>b</bold>) on adsorption capacity <italic>qe</italic> (mg g^–1) for each CAC-IO concentration (pH of Cr⁶⁺ ions solutions = 1.6 and pH of MV40 dye solutions = 2.07).</p></caption></fig>", "<fig id=\"Fig10\"><label>Figure 10</label><caption><p>Effect of contact time on adsorption of Cr⁶⁺ ions (<bold>a</bold>) and MV40 dye (<bold>b</bold>) on CAC-IO nanocomposite at optimum dose = 2 g L^–1 (pH of Cr⁺⁶ ions solutions = 1.6 and pH of MV40 dye solutions = 2.07).</p></caption></fig>", "<fig id=\"Fig11\"><label>Figure 11</label><caption><p>Langmuir (<bold>a</bold>) Freundlich (<bold>b</bold>) isotherm profiles for Cr⁶⁺ ions and Langmuir (<bold>c</bold>) Freundlich (<bold>d</bold>) isotherm profiles MV40 dye of initial concentration (100–400 mg L^–1) on CAC-IO doses (1.00–2.50 g L⁻¹) at 25 ± 2 °C, contact time: 180 min).</p></caption></fig>", "<fig id=\"Fig12\"><label>Figure 12</label><caption><p>The plot of PFO (<bold>a</bold>) PSO (<bold>b</bold>) IPDM (<bold>c</bold>) of adsorption of Cr⁶⁺ ions and PFO (<bold>d</bold>) PSO (<bold>e</bold>) IPDM (<bold>f</bold>) of adsorption of MV40 dye by CAC-IO adsorbent (Initial concentration = (100–400 mg L^-1), Adsorbent dose = (2.0 g L⁻¹ for Cr⁶⁺ ions and 1.0 g L⁻¹ for MV40 dye), Temperature = 25 ± 2 °C).</p></caption></fig>", "<fig id=\"Fig13\"><label>Figure 13</label><caption><p>(<bold>a</bold>) Cr⁶⁺ ions desorption% from CAC-IO (2.0 g L^–1) and the regenerated CAC-IO was used to promote Cr⁶⁺ ions (100 mg L^–1) adsorption cycles using pH = 1.0, (<bold>b</bold>) MV40 dye was desorption% from CAC-IO (1.0 g L^–1) and the regenerated CAC-IO was used to promote MV40 dye (400 g L^–1) adsorption cycles using pH = 2.07.</p></caption></fig>", "<fig id=\"Fig14\"><label>Figure 14</label><caption><p>Probable mechanism for the Cr⁶⁺ and MV40 dye ions adsorption onto the CAC-IO in acidic medium.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Data of surface analyses of CAC, CAC after oxidation and CAC-IO.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Surface analyses</th><th align=\"left\">CAC</th><th align=\"left\">CAC after oxidation</th><th align=\"left\">CAC-IO</th></tr></thead><tbody><tr><td align=\"left\">Pore diameter (nm)</td><td align=\"left\">3.3411</td><td char=\".\" align=\"char\">3.4575</td><td align=\"left\">3.4226</td></tr><tr><td align=\"left\">Pore volume (cm³ g⁻¹)</td><td align=\"left\">1.1910</td><td char=\".\" align=\"char\">0.8519</td><td align=\"left\">0.9155</td></tr><tr><td align=\"left\">Surface area (m² g⁻¹)</td><td align=\"left\">1426</td><td char=\".\" align=\"char\">985.58</td><td align=\"left\">1070</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>The EDX of CAC after oxidation and CAC-IO nanocomposite.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Element</th><th align=\"left\">C</th><th align=\"left\">N</th><th align=\"left\">O</th><th align=\"left\">Na</th><th align=\"left\">Al</th><th align=\"left\">Si</th><th align=\"left\">Fe</th><th align=\"left\">Cl</th><th align=\"left\">Total</th></tr></thead><tbody><tr><td align=\"left\">wt% of CAC after oxidation</td><td char=\".\" align=\"char\">83.26</td><td align=\"left\">–</td><td char=\".\" align=\"char\">15.38</td><td char=\".\" align=\"char\">0.17</td><td align=\"left\">–</td><td char=\".\" align=\"char\">1.05</td><td align=\"left\">–</td><td char=\".\" align=\"char\">0.14</td><td align=\"left\">100</td></tr><tr><td align=\"left\">wt% of CAC-IO nanocomposite</td><td char=\".\" align=\"char\">65.25</td><td align=\"left\">2.53</td><td char=\".\" align=\"char\">15.71</td><td char=\".\" align=\"char\">3.29</td><td align=\"left\">0.33</td><td char=\".\" align=\"char\">0.55</td><td align=\"left\">12.09</td><td char=\".\" align=\"char\">0.27</td><td align=\"left\">100</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Adsorption isotherm data for Cr⁶⁺ ions adsorption on CAC-IO nanocomposite at room temperature.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Adsorption ısotherm model</th><th align=\"left\" rowspan=\"2\">Parameters</th><th align=\"left\" colspan=\"4\">Commercial activated carbon-iron oxide nanocomposites((CAC-IO) (g L^–1)</th></tr><tr><th align=\"left\">1.0</th><th align=\"left\">1.5</th><th align=\"left\">2.0</th><th align=\"left\">2.5</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"3\">Langmuir</td><td align=\"left\">R²</td><td align=\"left\">0.945</td><td align=\"left\">0.933</td><td align=\"left\">0.964</td><td align=\"left\">0.986</td></tr><tr><td align=\"left\"><italic>Q</italic>_{<italic>m</italic>} (mgg⁻¹)</td><td align=\"left\">312.50</td><td align=\"left\">196.08</td><td align=\"left\">151.52</td><td align=\"left\">133.33</td></tr><tr><td align=\"left\"><italic>K</italic>_{<italic>a</italic>}</td><td align=\"left\">0.01</td><td align=\"left\">0.03</td><td align=\"left\">0.10</td><td align=\"left\">0.14</td></tr><tr><td align=\"left\" rowspan=\"3\">Freundlich</td><td align=\"left\">R²</td><td align=\"left\">0.988</td><td align=\"left\">0.987</td><td align=\"left\">0.976</td><td align=\"left\">1.000</td></tr><tr><td align=\"left\"><italic>1/n</italic></td><td align=\"left\">0.51</td><td align=\"left\">0.44</td><td align=\"left\">0.24</td><td align=\"left\">0.31</td></tr><tr><td align=\"left\"><italic>K</italic>_{<italic>F</italic>} (mg^1−1/nL^1/ng⁻¹)</td><td align=\"left\">14.65</td><td align=\"left\">17.31</td><td align=\"left\">44.32</td><td align=\"left\">31.46</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Adsorption isotherm data for MV40 dye adsorption on CAC-IO nanocomposite at room temperature.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Adsorption ısotherm model</th><th align=\"left\" rowspan=\"2\">Parameters</th><th align=\"left\" colspan=\"4\">Commercial activated carbon-iron oxide nanocomposites((CAC-IO) (g L⁻¹)</th></tr><tr><th align=\"left\">1.0</th><th align=\"left\">1.5</th><th align=\"left\">2.0</th><th align=\"left\">2.5</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"3\">Langmuir</td><td align=\"left\">R²</td><td align=\"left\">0.984</td><td align=\"left\">0.986</td><td align=\"left\">0.958</td><td align=\"left\">0.960</td></tr><tr><td align=\"left\"><italic>Q</italic>_{<italic>m</italic>} (mg g⁻¹)</td><td align=\"left\">476.2</td><td align=\"left\">625.0</td><td align=\"left\">833.3</td><td align=\"left\">555.6</td></tr><tr><td align=\"left\"><italic>K</italic>_{<italic>a</italic>}</td><td align=\"left\">2.63</td><td align=\"left\">0.46</td><td align=\"left\">0.15</td><td align=\"left\">0.23</td></tr><tr><td align=\"left\" rowspan=\"3\">Freundlich</td><td align=\"left\">R²</td><td align=\"left\">0.983</td><td align=\"left\">0.979</td><td align=\"left\">0.995</td><td align=\"left\">0.983</td></tr><tr><td align=\"left\"><italic>1/n</italic></td><td align=\"left\">0.43</td><td align=\"left\">0.78</td><td align=\"left\">0.88</td><td align=\"left\">1.04</td></tr><tr><td align=\"left\"><italic>K</italic>_{<italic>F</italic>} (mg^1−1/nL^1/ng⁻¹)</td><td align=\"left\">285.10</td><td align=\"left\">200.26</td><td align=\"left\">107.57</td><td align=\"left\">100.02</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Comparison of the first- and second-order adsorption rate constants and calculated and experimental <italic>q</italic>_{<italic>e</italic>} values for various initial Cr⁶⁺ ions and CAC-IO concentrations.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"3\">Parameter</th><th align=\"left\" colspan=\"3\">Pseudo-first-order</th><th align=\"left\" colspan=\"4\">Pseudo-second-order</th></tr><tr><th align=\"left\">CAC-IO (g L⁻¹)</th><th align=\"left\">Cr⁶⁺ (mg L⁻¹)</th><th align=\"left\"><italic>q</italic>_{<italic>e</italic>} (exp.)</th><th align=\"left\"><italic>q</italic>_{<italic>e</italic>} (calc.)</th><th align=\"left\"><italic>k</italic>_{<italic>1</italic>} × 10³</th><th align=\"left\">R²</th><th align=\"left\"><italic>q</italic>_{<italic>e</italic>} (calc.)</th><th align=\"left\"><italic>k</italic>_{<italic>2</italic>} × 10³</th><th align=\"left\"><italic>h</italic></th><th align=\"left\">R²</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"5\">1.0</td><td align=\"left\">100</td><td char=\".\" align=\"char\">76.20</td><td char=\".\" align=\"char\">15.38</td><td char=\".\" align=\"char\">13.130</td><td char=\".\" align=\"char\">0.954</td><td char=\".\" align=\"char\">76.92</td><td char=\".\" align=\"char\">2.70</td><td char=\".\" align=\"char\">15.95</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">104.36</td><td char=\".\" align=\"char\">24.01</td><td char=\".\" align=\"char\">11.520</td><td char=\".\" align=\"char\">0.938</td><td char=\".\" align=\"char\">105.26</td><td char=\".\" align=\"char\">1.73</td><td char=\".\" align=\"char\">19.16</td><td char=\".\" align=\"char\">0.998</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">124.10</td><td char=\".\" align=\"char\">28.32</td><td char=\".\" align=\"char\">17.500</td><td char=\".\" align=\"char\">0.984</td><td char=\".\" align=\"char\">125.00</td><td char=\".\" align=\"char\">1.61</td><td char=\".\" align=\"char\">25.19</td><td char=\".\" align=\"char\">0.998</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">177.48</td><td char=\".\" align=\"char\">43.28</td><td char=\".\" align=\"char\">21.650</td><td char=\".\" align=\"char\">0.955</td><td char=\".\" align=\"char\">166.67</td><td char=\".\" align=\"char\">0.60</td><td char=\".\" align=\"char\">16.78</td><td char=\".\" align=\"char\">0.982</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">216.05</td><td char=\".\" align=\"char\">8.26</td><td char=\".\" align=\"char\">1.380</td><td char=\".\" align=\"char\">0.830</td><td char=\".\" align=\"char\">212.77</td><td char=\".\" align=\"char\">3.74</td><td char=\".\" align=\"char\">169.49</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\" rowspan=\"5\">1.5</td><td align=\"left\">100</td><td char=\".\" align=\"char\">60.77</td><td char=\".\" align=\"char\">15.88</td><td char=\".\" align=\"char\">12.900</td><td char=\".\" align=\"char\">0.870</td><td char=\".\" align=\"char\">61.35</td><td char=\".\" align=\"char\">2.43</td><td char=\".\" align=\"char\">9.16</td><td char=\".\" align=\"char\">0.998</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">79.45</td><td char=\".\" align=\"char\">15.81</td><td char=\".\" align=\"char\">16.350</td><td char=\".\" align=\"char\">0.927</td><td char=\".\" align=\"char\">80.00</td><td char=\".\" align=\"char\">3.09</td><td char=\".\" align=\"char\">19.76</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">95.84</td><td char=\".\" align=\"char\">28.33</td><td char=\".\" align=\"char\">17.040</td><td char=\".\" align=\"char\">0.910</td><td char=\".\" align=\"char\">98.04</td><td char=\".\" align=\"char\">1.46</td><td char=\".\" align=\"char\">14.03</td><td char=\".\" align=\"char\">0.998</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">135.55</td><td char=\".\" align=\"char\">19.18</td><td char=\".\" align=\"char\">11.980</td><td char=\".\" align=\"char\">0.986</td><td char=\".\" align=\"char\">135.14</td><td char=\".\" align=\"char\">2.20</td><td char=\".\" align=\"char\">40.16</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">165.00</td><td char=\".\" align=\"char\">18.08</td><td char=\".\" align=\"char\">10.360</td><td char=\".\" align=\"char\">0.815</td><td char=\".\" align=\"char\">166.67</td><td char=\".\" align=\"char\">1.93</td><td char=\".\" align=\"char\">53.48</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\" rowspan=\"5\">2.0</td><td align=\"left\">100</td><td char=\".\" align=\"char\">49.30</td><td char=\".\" align=\"char\">5.93</td><td char=\".\" align=\"char\">19.580</td><td char=\".\" align=\"char\">0.964</td><td char=\".\" align=\"char\">49.75</td><td char=\".\" align=\"char\">9.04</td><td char=\".\" align=\"char\">22.37</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">71.45</td><td char=\".\" align=\"char\">13.31</td><td char=\".\" align=\"char\">14.510</td><td char=\".\" align=\"char\">0.985</td><td char=\".\" align=\"char\">71.94</td><td char=\".\" align=\"char\">3.26</td><td char=\".\" align=\"char\">16.89</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">88.49</td><td char=\".\" align=\"char\">57.10</td><td char=\".\" align=\"char\">50.440</td><td char=\".\" align=\"char\">0.961</td><td char=\".\" align=\"char\">89.29</td><td char=\".\" align=\"char\">2.19</td><td char=\".\" align=\"char\">17.45</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">115.77</td><td char=\".\" align=\"char\">21.62</td><td char=\".\" align=\"char\">18.190</td><td char=\".\" align=\"char\">0.974</td><td char=\".\" align=\"char\">117.65</td><td char=\".\" align=\"char\">2.10</td><td char=\".\" align=\"char\">29.07</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">148.89</td><td char=\".\" align=\"char\">54.09</td><td char=\".\" align=\"char\">52.050</td><td char=\".\" align=\"char\">0.945</td><td char=\".\" align=\"char\">149.25</td><td char=\".\" align=\"char\">2.55</td><td char=\".\" align=\"char\">56.82</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\" rowspan=\"5\">2.5</td><td align=\"left\">100</td><td char=\".\" align=\"char\">39.21</td><td char=\".\" align=\"char\">2.57</td><td char=\".\" align=\"char\">20.270</td><td char=\".\" align=\"char\">0.948</td><td char=\".\" align=\"char\">39.37</td><td char=\".\" align=\"char\">21.43</td><td char=\".\" align=\"char\">33.22</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">58.79</td><td char=\".\" align=\"char\">10.10</td><td char=\".\" align=\"char\">22.110</td><td char=\".\" align=\"char\">0.972</td><td char=\".\" align=\"char\">59.52</td><td char=\".\" align=\"char\">5.68</td><td char=\".\" align=\"char\">20.12</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">70.79</td><td char=\".\" align=\"char\">14.98</td><td char=\".\" align=\"char\">13.820</td><td char=\".\" align=\"char\">0.980</td><td char=\".\" align=\"char\">71.43</td><td char=\".\" align=\"char\">2.73</td><td char=\".\" align=\"char\">13.95</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">103.04</td><td char=\".\" align=\"char\">18.16</td><td char=\".\" align=\"char\">12.670</td><td char=\".\" align=\"char\">0.923</td><td char=\".\" align=\"char\">104.17</td><td char=\".\" align=\"char\">2.06</td><td char=\".\" align=\"char\">22.37</td><td char=\".\" align=\"char\">0.999</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">126.07</td><td char=\".\" align=\"char\">18.87</td><td char=\".\" align=\"char\">14.510</td><td char=\".\" align=\"char\">0.953</td><td char=\".\" align=\"char\">126.58</td><td char=\".\" align=\"char\">2.35</td><td char=\".\" align=\"char\">37.59</td><td char=\".\" align=\"char\">0.999</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab6\"><label>Table 6</label><caption><p>Comparison of the first- and second-order adsorption rate constants and calculated and experimental qe values for various initial MV40 dye solutions and CAC-IO concentrations.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"3\">Parameter</th><th align=\"left\" colspan=\"3\">Pseudo-first-order</th><th align=\"left\" colspan=\"4\">Pseudo-second-order</th></tr><tr><th align=\"left\">CAC-IO (g L⁻¹)</th><th align=\"left\">MV40 (mg L⁻¹)</th><th align=\"left\"><italic>q</italic>_{<italic>e</italic>} (exp.)</th><th align=\"left\"><italic>q</italic>_{<italic>e</italic>} (calc.)</th><th align=\"left\"><italic>k</italic>_{<italic>1</italic>} × 10³</th><th align=\"left\">R²</th><th align=\"left\"><italic>q</italic>_{<italic>e</italic>} (calc.)</th><th align=\"left\"><italic>k</italic>_{<italic>2</italic>} × 10³</th><th align=\"left\"><italic>h</italic></th><th align=\"left\">R²</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"5\">1.0</td><td align=\"left\">100</td><td char=\".\" align=\"char\">99.92</td><td char=\".\" align=\"char\">1.05</td><td char=\".\" align=\"char\">24.410</td><td char=\".\" align=\"char\">0.792</td><td char=\".\" align=\"char\">100.00</td><td char=\".\" align=\"char\">71.43</td><td char=\".\" align=\"char\">714.29</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">149.66</td><td char=\".\" align=\"char\">1.83</td><td char=\".\" align=\"char\">18.190</td><td char=\".\" align=\"char\">0.978</td><td char=\".\" align=\"char\">149.25</td><td char=\".\" align=\"char\">29.93</td><td char=\".\" align=\"char\">666.67</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">199.58</td><td char=\".\" align=\"char\">8.64</td><td char=\".\" align=\"char\">87.510</td><td char=\".\" align=\"char\">0.846</td><td char=\".\" align=\"char\">200.00</td><td char=\".\" align=\"char\">41.67</td><td char=\".\" align=\"char\">1666.67</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">299.33</td><td char=\".\" align=\"char\">8.83</td><td char=\".\" align=\"char\">43.760</td><td char=\".\" align=\"char\">0.826</td><td char=\".\" align=\"char\">303.03</td><td char=\".\" align=\"char\">18.15</td><td char=\".\" align=\"char\">1666.70</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">397.90</td><td char=\".\" align=\"char\">20.39</td><td char=\".\" align=\"char\">50.210</td><td char=\".\" align=\"char\">0.651</td><td char=\".\" align=\"char\">400.00</td><td char=\".\" align=\"char\">12.50</td><td char=\".\" align=\"char\">2000.00</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\" rowspan=\"5\">1.5</td><td align=\"left\">100</td><td char=\".\" align=\"char\">66.50</td><td char=\".\" align=\"char\">1.55</td><td char=\".\" align=\"char\">60.570</td><td char=\".\" align=\"char\">0.903</td><td char=\".\" align=\"char\">66.67</td><td char=\".\" align=\"char\">48.91</td><td char=\".\" align=\"char\">217.39</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">99.72</td><td char=\".\" align=\"char\">121.41</td><td char=\".\" align=\"char\">275.440</td><td char=\".\" align=\"char\">0.931</td><td char=\".\" align=\"char\">100.00</td><td char=\".\" align=\"char\">83.33</td><td char=\".\" align=\"char\">833.33</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">132.94</td><td char=\".\" align=\"char\">4.32</td><td char=\".\" align=\"char\">27.640</td><td char=\".\" align=\"char\">0.837</td><td char=\".\" align=\"char\">133.33</td><td char=\".\" align=\"char\">46.88</td><td char=\".\" align=\"char\">833.33</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">199.44</td><td char=\".\" align=\"char\">1.76</td><td char=\".\" align=\"char\">81.760</td><td char=\".\" align=\"char\">0.691</td><td char=\".\" align=\"char\">200.00</td><td char=\".\" align=\"char\">62.50</td><td char=\".\" align=\"char\">2500.00</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">265.60</td><td char=\".\" align=\"char\">3.08</td><td char=\".\" align=\"char\">24.640</td><td char=\".\" align=\"char\">0.981</td><td char=\".\" align=\"char\">263.16</td><td char=\".\" align=\"char\">24.07</td><td char=\".\" align=\"char\">1666.67</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\" rowspan=\"5\">2.0</td><td align=\"left\">100</td><td char=\".\" align=\"char\">49.79</td><td char=\".\" align=\"char\">6.00</td><td char=\".\" align=\"char\">195.520</td><td char=\".\" align=\"char\">0.696</td><td char=\".\" align=\"char\">49.75</td><td char=\".\" align=\"char\">577.16</td><td char=\".\" align=\"char\">1428.60</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">74.66</td><td char=\".\" align=\"char\">1.50</td><td char=\".\" align=\"char\">95.570</td><td char=\".\" align=\"char\">0.989</td><td char=\".\" align=\"char\">74.63</td><td char=\".\" align=\"char\">299.27</td><td char=\".\" align=\"char\">1666.70</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">99.54</td><td char=\".\" align=\"char\">1.65</td><td char=\".\" align=\"char\">32.700</td><td char=\".\" align=\"char\">0.661</td><td char=\".\" align=\"char\">100.00</td><td char=\".\" align=\"char\">37.04</td><td char=\".\" align=\"char\">370.37</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">149.33</td><td char=\".\" align=\"char\">2.01</td><td char=\".\" align=\"char\">44.220</td><td char=\".\" align=\"char\">0.933</td><td char=\".\" align=\"char\">149.25</td><td char=\".\" align=\"char\">56.11</td><td char=\".\" align=\"char\">1250.00</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">198.95</td><td char=\".\" align=\"char\">67.44</td><td char=\".\" align=\"char\">276.820</td><td char=\".\" align=\"char\">0.874</td><td char=\".\" align=\"char\">200.00</td><td char=\".\" align=\"char\">125.00</td><td char=\".\" align=\"char\">5000.00</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\" rowspan=\"5\">2.5</td><td align=\"left\">100</td><td char=\".\" align=\"char\">39.76</td><td char=\".\" align=\"char\">0.27</td><td char=\".\" align=\"char\">73.010</td><td char=\".\" align=\"char\">1.000</td><td char=\".\" align=\"char\">39.84</td><td char=\".\" align=\"char\">1260.00</td><td char=\".\" align=\"char\">2000.00</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">59.76</td><td char=\".\" align=\"char\">0.30</td><td char=\".\" align=\"char\">26.250</td><td char=\".\" align=\"char\">0.997</td><td char=\".\" align=\"char\">59.88</td><td char=\".\" align=\"char\">253.54</td><td char=\".\" align=\"char\">909.09</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">79.70</td><td char=\".\" align=\"char\">2.22</td><td char=\".\" align=\"char\">110.770</td><td char=\".\" align=\"char\">0.978</td><td char=\".\" align=\"char\">80.00</td><td char=\".\" align=\"char\">142.05</td><td char=\".\" align=\"char\">909.09</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">119.53</td><td char=\".\" align=\"char\">0.66</td><td char=\".\" align=\"char\">82.910</td><td char=\".\" align=\"char\">0.989</td><td char=\".\" align=\"char\">119.05</td><td char=\".\" align=\"char\">352.80</td><td char=\".\" align=\"char\">5000.00</td><td char=\".\" align=\"char\">1.000</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">159.36</td><td char=\".\" align=\"char\">1.42</td><td char=\".\" align=\"char\">16.200</td><td char=\".\" align=\"char\">0.832</td><td char=\".\" align=\"char\">158.73</td><td char=\".\" align=\"char\">33.08</td><td char=\".\" align=\"char\">833.33</td><td char=\".\" align=\"char\">1.000</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab7\"><label>Table 7</label><caption><p>IPDM results of adsorption of Cr⁶⁺ ions and MV40 dye by CAC-IO adsorbent (Initial concentration = (100–400 mg L^–1), adsorbent doses = (1.0–2.5 g L⁻¹), Temp. = (25 °C)).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"2\">Parameter</th><th align=\"left\" colspan=\"3\">Cr⁶⁺ ions</th><th align=\"left\" colspan=\"3\">MV40 dye</th></tr><tr><th align=\"left\">CAC-IO (g·L⁻¹)</th><th align=\"left\">Pollutant (mg L⁻¹)</th><th align=\"left\"><italic>К</italic>_{<italic>dif</italic>}</th><th align=\"left\"><italic>C</italic></th><th align=\"left\">R²</th><th align=\"left\"><italic>К</italic>_{<italic>dif</italic>}</th><th align=\"left\"><italic>C</italic></th><th align=\"left\">R²</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"5\">1.00</td><td align=\"left\">100</td><td char=\".\" align=\"char\">1.440</td><td char=\".\" align=\"char\">57.51</td><td char=\".\" align=\"char\">0.923</td><td char=\".\" align=\"char\">0.111</td><td char=\".\" align=\"char\">98.57</td><td char=\".\" align=\"char\">0.720</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">2.170</td><td char=\".\" align=\"char\">75.57</td><td char=\".\" align=\"char\">0.895</td><td char=\".\" align=\"char\">0.163</td><td char=\".\" align=\"char\">147.74</td><td char=\".\" align=\"char\">0.910</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">2.070</td><td char=\".\" align=\"char\">96.45</td><td char=\".\" align=\"char\">0.951</td><td char=\".\" align=\"char\">0.208</td><td char=\".\" align=\"char\">197.10</td><td char=\".\" align=\"char\">0.647</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">4.440</td><td char=\".\" align=\"char\">119.48</td><td char=\".\" align=\"char\">0.995</td><td char=\".\" align=\"char\">0.416</td><td char=\".\" align=\"char\">294.36</td><td char=\".\" align=\"char\">0.808</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">3.460</td><td char=\".\" align=\"char\">197.11</td><td char=\".\" align=\"char\">1.000</td><td char=\".\" align=\"char\">0.391</td><td char=\".\" align=\"char\">393.11</td><td char=\".\" align=\"char\">0.816</td></tr><tr><td align=\"left\" rowspan=\"5\">1.50</td><td align=\"left\">100</td><td char=\".\" align=\"char\">1.050</td><td char=\".\" align=\"char\">45.94</td><td char=\".\" align=\"char\">0.967</td><td char=\".\" align=\"char\">0.147</td><td char=\".\" align=\"char\">64.91</td><td char=\".\" align=\"char\">0.555</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">1.320</td><td char=\".\" align=\"char\">62.59</td><td char=\".\" align=\"char\">0.917</td><td char=\".\" align=\"char\">0.035</td><td char=\".\" align=\"char\">99.35</td><td char=\".\" align=\"char\">0.719</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">2.010</td><td char=\".\" align=\"char\">68.91</td><td char=\".\" align=\"char\">0.993</td><td char=\".\" align=\"char\">0.481</td><td char=\".\" align=\"char\">129.10</td><td char=\".\" align=\"char\">0.672</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">1.550</td><td char=\".\" align=\"char\">113.84</td><td char=\".\" align=\"char\">0.978</td><td char=\".\" align=\"char\">0.319</td><td char=\".\" align=\"char\">196.86</td><td char=\".\" align=\"char\">0.758</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">1.880</td><td char=\".\" align=\"char\">140.25</td><td char=\".\" align=\"char\">0.984</td><td char=\".\" align=\"char\">0.273</td><td char=\".\" align=\"char\">262.42</td><td char=\".\" align=\"char\">0.765</td></tr><tr><td align=\"left\" rowspan=\"5\">2.00</td><td align=\"left\">100</td><td char=\".\" align=\"char\">0.500</td><td char=\".\" align=\"char\">43.09</td><td char=\".\" align=\"char\">0.884</td><td char=\".\" align=\"char\">0.015</td><td char=\".\" align=\"char\">49.62</td><td char=\".\" align=\"char\">0.602</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">1.210</td><td char=\".\" align=\"char\">55.89</td><td char=\".\" align=\"char\">0.937</td><td char=\".\" align=\"char\">0.038</td><td char=\".\" align=\"char\">74.25</td><td char=\".\" align=\"char\">0.530</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">1.590</td><td char=\".\" align=\"char\">67.39</td><td char=\".\" align=\"char\">0.975</td><td char=\".\" align=\"char\">0.046</td><td char=\".\" align=\"char\">98.87</td><td char=\".\" align=\"char\">0.625</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">1.820</td><td char=\".\" align=\"char\">93.08</td><td char=\".\" align=\"char\">0.951</td><td char=\".\" align=\"char\">0.115</td><td char=\".\" align=\"char\">148.02</td><td char=\".\" align=\"char\">0.782</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">1.120</td><td char=\".\" align=\"char\">131.73</td><td char=\".\" align=\"char\">0.912</td><td char=\".\" align=\"char\">0.097</td><td char=\".\" align=\"char\">197.87</td><td char=\".\" align=\"char\">0.572</td></tr><tr><td align=\"left\" rowspan=\"5\">2.50</td><td align=\"left\">100</td><td char=\".\" align=\"char\">0.270</td><td char=\".\" align=\"char\">36.06</td><td char=\".\" align=\"char\">0.804</td><td char=\".\" align=\"char\">0.011</td><td char=\".\" align=\"char\">39.65</td><td char=\".\" align=\"char\">0.601</td></tr><tr><td align=\"left\">150</td><td char=\".\" align=\"char\">0.800</td><td char=\".\" align=\"char\">49.09</td><td char=\".\" align=\"char\">0.903</td><td char=\".\" align=\"char\">0.023</td><td char=\".\" align=\"char\">59.50</td><td char=\".\" align=\"char\">0.856</td></tr><tr><td align=\"left\">200</td><td char=\".\" align=\"char\">1.270</td><td char=\".\" align=\"char\">53.91</td><td char=\".\" align=\"char\">0.975</td><td char=\".\" align=\"char\">0.046</td><td char=\".\" align=\"char\">79.18</td><td char=\".\" align=\"char\">0.584</td></tr><tr><td align=\"left\">300</td><td char=\".\" align=\"char\">1.640</td><td char=\".\" align=\"char\">81.18</td><td char=\".\" align=\"char\">0.923</td><td char=\".\" align=\"char\">0.024</td><td char=\".\" align=\"char\">119.27</td><td char=\".\" align=\"char\">0.502</td></tr><tr><td align=\"left\">400</td><td char=\".\" align=\"char\">1.360</td><td char=\".\" align=\"char\">107.08</td><td char=\".\" align=\"char\">0.984</td><td char=\".\" align=\"char\">0.173</td><td char=\".\" align=\"char\">157.30</td><td char=\".\" align=\"char\">0.845</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab8\"><label>Table 8</label><caption><p>A comparison of the highest pollutant removal capabilities of some adsorbents.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Name of adsorbent</th><th align=\"left\">Pollutant</th><th align=\"left\"><italic>Q</italic>_{<italic>m</italic>} (mg g⁻¹)</th><th align=\"left\">Ref</th></tr></thead><tbody><tr><td align=\"left\">Wheat straw and <italic>E. adenophorum</italic></td><td align=\"left\">Cr⁶⁺</td><td char=\".\" align=\"char\">88.57</td><td align=\"left\">^{##REF##27911906##83##}</td></tr><tr><td align=\"left\">Magnetite nanoparticles</td><td align=\"left\">Cr⁶⁺</td><td char=\".\" align=\"char\">34.9</td><td align=\"left\">^{##REF##26859095##84##}</td></tr><tr><td align=\"left\">Rice husk-derived magnetic sorbent (RHC-Mag-2)</td><td align=\"left\">Cr⁶⁺</td><td char=\".\" align=\"char\">157.7</td><td align=\"left\">^{##UREF##60##85##}</td></tr><tr><td align=\"left\">Active carbon derived from <italic>Lantana Camara</italic> Plant</td><td align=\"left\">Cr⁶⁺</td><td char=\".\" align=\"char\">26.25</td><td align=\"left\">^{##REF##30388094##86##}</td></tr><tr><td align=\"left\" rowspan=\"2\"><italic>Pterocladia capillacea</italic> red algae magnetic activated carbon</td><td align=\"left\">Cr⁶⁺</td><td char=\".\" align=\"char\">151.52</td><td align=\"left\" rowspan=\"2\">^{##REF##37880272##10##}</td></tr><tr><td align=\"left\">Mordant Violet 40</td><td char=\".\" align=\"char\">303.03</td></tr><tr><td align=\"left\">Activated carbon from mango kernel</td><td align=\"left\">Cr⁶⁺</td><td char=\".\" align=\"char\">7.80</td><td align=\"left\">^{##UREF##61##87##}</td></tr><tr><td align=\"left\">CAC-IO nanocomposite</td><td align=\"left\">Cr⁶⁺</td><td char=\".\" align=\"char\">312.50</td><td align=\"left\">This study</td></tr><tr><td align=\"left\">CAC-IO nanocomposite</td><td align=\"left\">Mordant Violet 40</td><td char=\".\" align=\"char\">833.30</td><td align=\"left\">This study</td></tr></tbody></table></table-wrap>" ]

[ "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R\\%=\\frac{({C}_{0}-{C}_{t})}{{C}_{0}}x100$$\\end{document}</tex-math><mml:math id=\"M2\" display=\"block\"><mml:mrow><mml:mi>R</mml:mi><mml:mo>%</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfrac><mml:mi>x</mml:mi><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$q=\\frac{\\left({C}_{0}-{C}_{t}\\right)*m}{V}*100$$\\end{document}</tex-math><mml:math id=\"M4\" display=\"block\"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>m</mml:mi></mml:mrow><mml:mi>V</mml:mi></mml:mfrac><mml:mrow/><mml:mo>∗</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ L = K\\lambda /B{\\text{Cos}}\\theta , $$\\end{document}</tex-math><mml:math id=\"M6\" display=\"block\"><mml:mrow><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>λ</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>B</mml:mi><mml:mtext>Cos</mml:mtext><mml:mi>θ</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ C_{e} /q_{e} = {1}/K_{a} Q_{m} + { 1}/Q_{m} \\times C_{e} , $$\\end{document}</tex-math><mml:math id=\"M8\" display=\"block\"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:msub><mml:mi>Q</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ {\\text{Ln}}q_{e} = {\\text{ln}}K_{f} + {1}/n{\\text{ln}}C_{e} , $$\\end{document}</tex-math><mml:math id=\"M10\" display=\"block\"><mml:mrow><mml:mtext>Ln</mml:mtext><mml:msub><mml:mi>q</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mtext>ln</mml:mtext><mml:msub><mml:mi>K</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi><mml:mtext>ln</mml:mtext><mml:msub><mml:mi>C</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ R_{L} = {1}/{1} + K_{a} C_{o} . $$\\end{document}</tex-math><mml:math id=\"M12\" display=\"block\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mi>o</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\text{log}}({q}_{e}-{q}_{t})=\\mathrm{log }({q}_{e})-\\frac{{k}_{1}}{2.303}t$$\\end{document}</tex-math><mml:math id=\"M14\" display=\"block\"><mml:mrow><mml:mtext>log</mml:mtext><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant=\"normal\">log</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>-</mml:mo><mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mn>2.303</mml:mn></mml:mrow></mml:mfrac><mml:mi>t</mml:mi></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\frac{t}{{q}_{t}})=\\frac{1}{{k}_{2}{q}_{e}^{2}}+\\frac{1}{{q}_{e}} \\left(t\\right),$$\\end{document}</tex-math><mml:math id=\"M16\" display=\"block\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mfrac><mml:mi>t</mml:mi><mml:msub><mml:mi>q</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfrac><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msubsup><mml:mi>q</mml:mi><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi>q</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ q_{t} = K_{diff} t^{{0.{5}}} + C, $$\\end{document}</tex-math><mml:math id=\"M18\" display=\"block\"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">diff</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>t</mml:mi><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Chickens have played a significant role in life science and medical research, serving not only as a nutritional resource but also subjects of study. They have made substantial contributions to drug discovery and fundamental medical research, including vaccine development and the discovery of oncogenes and proto-oncogenes, such as v-src and c-src^{##REF##17742872##1##–##REF##221907##3##}. Over the past 25 years, DT40 cells, derived from chicken B cells, have emerged as valuable models for functional gene studies, significantly advancing in life science research, including basic medical research concerning DNA repair, owing to their high homologous recombination (HR) activity and utility in establishing gene-targeted cell lines^{##REF##9108474##4##–##REF##35165266##14##}.</p>", "<p id=\"Par3\">DNA double-strand breaks (DSBs) induced by therapeutic ionizing radiation or heavy particle radiation pose severe threats to vertebrate cells, potentially leading to carcinogenesis, cell death, and cellular senescence^{##REF##10755664##15##–##REF##19133841##18##}. Two primary DNA repair pathways exist for DSB: Rad54-dependent HR and Ku (a heterodimer of Ku70 and Ku80)-dependent non-homologous end-joining (NHEJ)^{##REF##9108474##4##,##REF##9736627##5##}. In mammalian cells, including humans and mice, NHEJ is the predominant DSB repair mechanism^{##REF##10755664##15##–##REF##30574452##20##}. NHEJ initiates with Ku binding to DSB ends^{##REF##10755664##15##–##REF##19133841##18##}. Then, DNA-PKcs is recruited there, and XRCC4 and XRCC4-like factor (XLF, also known as NHEJ1 or Cernunnos) promote the ligase activity of DNA ligase IV to rejoin DSB ends^{##REF##10755664##15##–##REF##19133841##18##,##REF##16439205##21##,##REF##16439204##22##}. In birds, initial cloning and characterization of chicken <italic>Ku70</italic> (referred to as <italic>GdKu70</italic>) cDNA by Takata et al. revealed distinct features (DDBJ/EMBL/GenBank accession No. AB016529)^{##REF##9736627##5##}. By generating Rad54-knockout (KO), Ku70-KO, and Rad54/Ku70-double KO (DKO) DT40 cells, they demonstrated that <italic>GdKu70</italic> cDNA could partially compensate for radiosensitivity when introduced into Rad54/Ku70 DKO-DT40 cells. They also proposed that the predominant repair pathway depends on the cell cycle. Since then, <italic>GdKu70</italic> cDNA, its expressing cells, and derivatives have been instrumental in numerous studies across various life sciences, including radiation biology and DNA repair^{##REF##9108474##4##–##REF##35165266##14##}.</p>", "<p id=\"Par4\"><italic>Ku70</italic> cDNA has also been cloned in humans and other organisms, such as mice and dogs^{##REF##9736627##5##,##REF##2466842##23##–##REF##28163277##25##}. Chromosomal mapping has shown conserved linkage homology in species like chicken, human, mouse, rat, and hamster^{##REF##8258294##26##–##REF##11474179##29##}. GdKu70 contains an additional 18 amino acids at the N-terminal portion compared to human and mouse Ku70^{##REF##9736627##5##}. This extra segment is also absent in canine Ku70, suggesting its absence is common among mammalian species^{##REF##28163277##25##}. However, the biological significance of this avian-specific N-terminal portion remains uncertain. Understanding its role may shed light on why DT40 cells exhibit high HR activity and uncover avian-specific Ku functions.</p>", "<p id=\"Par5\">In the present study, we cloned chicken <italic>Ku70</italic> cDNA to explore the function and biological significance of the N-terminal-specific portion of chicken Ku70. Our data show that the chicken <italic>Ku70</italic> gene encodes 614 amino acids. Additionally, our findings indicated that Ku70 localizes in the nucleus as a heterodimer with Ku80 and accumulates at DNA damage sites immediately after injury in chicken cells. Notably, the chromosome 1 genome, housing the chicken <italic>Ku70</italic> gene, does not contain most of the 5′ flanking sequence for chicken <italic>Ku70,</italic> known as <italic>GdKu70</italic> and gained worldwide use. This study provides valuable information and experimental materials to unravel the diverse mechanisms by which Ku functions. Meanwhile, caution is advised when in interpreting the numerous important discoveries made using <italic>GdKu70</italic> cDNA and its expressed cells.</p>" ]

[ "<title>Methods</title>", "<title>Cell lines, cell culture, and transfections</title>", "<p id=\"Par17\">The adherent fibroblast-like cell line PGC29-fibro, derived from PGCs of the White Leghorn line (WL-M/O), was purchased from the NAGOYA UNIVERSITY through the National Bio-Resource Project of the MEXT, Japan. Two chicken cell lines, PGC29-fibro and the LMH cell line (Health Science Research Resources BANK, Osaka, Japan), were cultured in Dulbecco's modified Eagle's medium (Nacalai Tesque, Kyoto, Japan or NISSUI, Tokyo, Japan) supplemented with 60 μg/mL kanamycin and 10% fetal bovine serum. The cells were maintained in a humidified incubator at 37 °C under a 5% CO₂ atmosphere. Plasmids were transfected into the cells using Lipofectamine 3000 (Thermo Fisher Scientific, Waltham, MA, USA)^{##REF##31115163##55##,##REF##32214226##56##}. Following transfection, the cells were cultured for 2 d, and images of the cells were captured using an FV300 CLSM system (Olympus, Tokyo, Japan), as previously described^{##REF##31115163##55##,##REF##32214226##56##}.</p>", "<title>RNA preparation, cDNA synthesis, and RT-PCR analysis</title>", "<p id=\"Par18\">RNA was extracted from frozen chicken LMH cells using the RNeasy Mini Kit (QIAGEN Inc., Chatsworth, CA, USA). This RNA served as a template for cDNA synthesis, which was performed using the High-Capacity RNA-to-cDNA™ Kit (Thermo Fisher Scientific). PCR amplification with sense (Ku70-A-F: 5′-atggagatgtgggtgttgggg-3′ or Ku70-B-F: 5′-atggccgactgggtgtcctattatc-3′) and antisense (Ku70-R: 5′-tggcttagtctaactcggacatcgc-3′) primers was performed using the AmpliTaq Gold360 Master Mix (Applied Biosystems, Waltham, MA, USA) according to the manufacturer's instructions. The reaction conditions included initial denaturation at 95 °C for 5 min, followed by 35 cycles of denaturation at 95 °C for 30 s, annealing at 60 °C for 30 s, and extension at 72 °C for 30 s, with a final extension step at 72 °C for 7 min. The amplified DNA was analysed by 1% agarose gel electrophoresis.</p>", "<title>Chicken <italic>Ku70</italic> cloning and expression vector</title>", "<p id=\"Par19\">Oligonucleotide primers designed to amplify chicken <italic>Ku70</italic> cDNA were created to clone the coding sequence of Ku70 in-frame between XhoI and EcoRI sites of pEYFP-C1 (Takara Bio Inc., Shiga, Japan), based on the published <italic>Ku70</italic> cDNA sequence of <italic>G. gallus domesticus</italic> (chicken) (DDBJ/EMBL/GenBank accession No. AB016529.1)^{##REF##9736627##5##}. The sense primer (Ku70-Xho-F: 5′-CGCGGAACTCGAGCTatggccgactgggtgtcctattatc-3′) and antisense primer (Ku70-Eco-R: 5′-CCGTGAATTCttagcgcccactgaagtattcagtc-3′) incorporated XhoI and EcoR1 restriction enzyme sites, respectively. High-fidelity Platinum™ SuperFi™ DNA Polymerase (Thermo Fisher Scientific) was used for PCR amplification following the manufacturer's instructions. The PCR conditions included an initial denaturation step at 95 °C for 1 min, followed by 30 cycles of denaturation at 95 °C for 0.5 min, annealing at 60 °C for 0.5 min, and extension at 72 °C for 1 min. The PCR products were digested and ligated in-frame into the pEYFP-C1 vector using the DNA Ligation Kit, Mighty Mix (Takara Bio, Inc.), and the inserts were confirmed by sequencing.</p>", "<title>Western blot analysis</title>", "<p id=\"Par20\">The preparation of total protein extracts and western blot analysis was conducted as previously described^{##REF##31115163##55##–##REF##11152690##57##}, with some modifications. Specifically, the total proteins (50 μg per lane) were separated on an Extra PAGE One Precast Gel 5–20% (Nacalai Tesque). Subsequently, the membranes were blocked with Blocking One (Nacalai Tesque) for 30 min at room temperature. The following antibodies were employed: mouse anti-Ku70 monoclonal antibody (E-5, Santa Cruz Biotechnology, Santa Cruz, TX, USA), mouse anti-Ku80 monoclonal antibody (B-4, Santa Cruz Biotechnology), rabbit anti-GFP polyclonal antibody (FL, Santa Cruz Biotechnology), and mouse anti-β-actin monoclonal antibody (AC-15, Sigma-Aldrich, St. Louis, MO, USA). Secondary antibodies used included anti-mouse IgG, horseradish peroxidase (HRP)-linked whole antibody from sheep (GE Healthcare Bio-Sci. Corp., Piscataway, NJ, USA) or anti-rabbit IgG, HRP-linked whole antibody from donkey (GE Healthcare Bio-Sci. Corp.). Protein bands were detected following the manufacturer's instructions using Chemi-Lumi One Ultra (Nacalai Tesque) and visualized with the ChemiDoc XRS System (Bio-Rad, Hercules, CA, USA). The 3-Color prestained XL-ladder (APRO Science, Tokushima, Japan) served as the molecular weight marker.</p>", "<title>DNA damage induction using microlaser and immunofluorescence cell staining</title>", "<p id=\"Par21\">Local DNA damage was induced through a microlaser, and subsequent cell imaging was performed as previously outlined^{##UREF##1##51##,##REF##32214226##56##}. In brief, DSBs were generated locally using a 405 nm diode laser equipped with an FV300 CLSM system (Olympus). Live and fixed cells expressing EYFP-chicken Ku70, EYFP-chicken XLF, or EYFP alone were imaged using an FV300 CLSM system (Olympus). Immunocytochemistry was conducted as previously described^{##UREF##1##51##,##REF##31115163##55##,##REF##32214226##56##} with the use of the following antibodies: mouse anti-Ku70 monoclonal antibody (E-5, Santa Cruz Biotechnology), mouse anti-Ku80 monoclonal antibody (B-4, Santa Cruz Biotechnology), mouse anti-Ku70/Ku80 monoclonal antibody (162, NeoMarkers, Fremont, CA, USA), mouse anti-γH2AX monoclonal antibody (JBW301, Merck Millipore, Billerica, USA), and donkey anti-mouse IgG (H + L) Highly Cross-Adsorbed Secondary Antibody, Alexa Fluor™ Plus 555 (Thermo Fisher Scientific).</p>", "<title>Sequence analysis</title>", "<p id=\"Par22\">The <italic>GdKu70</italic> cDNA sequence (54 bp [bases 1–54; NM_204927.2] and 54 bp [bases 200–253; AB016529.1]) corresponding to the N-terminal sequence, which displayed an 18-amino acid protrusion unique to chickens compared to humans and mice, was subjected to a genomic search against the chicken public genome sequence GRCg6a/galGal6. This search was performed using the alignment tool BLAT provided by UCSC. Additionally, the homology search encompassing the <italic>GdKu70</italic> cDNA sequence (274 bp [bases 1–274; AB016529.1]), including the sequences encoding the 18 amino acids, was conducted using BLAT and BLAST (<ext-link ext-link-type=\"uri\" xlink:href=\"https://blast.ncbi.nlm.nih.gov/Blast.cgi\">https://blast.ncbi.nlm.nih.gov/Blast.cgi</ext-link>). The BLAST was employed to identify regions of local similarity between sequences. The Pairwise Sequence Alignment EMBOSS Needle was utilized to compare the amino acid sequence of chicken Ku70 with those of canine, human, and mouse Ku70 (The European Bioinformatics Institute [EMBL-EBI]; <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ebi.ac.uk/Tools/psa/)\">https://www.ebi.ac.uk/Tools/psa/)</ext-link>^{##REF##30976793##62##}.</p>" ]

[ "<title>Results</title>", "<title>The 5′ flanking nucleotide sequences corresponding to the first 18-amino acid coding portion of the reported chicken <italic>Ku70</italic> cDNA cannot be detected at RNA level</title>", "<p id=\"Par6\">Chicken Ku70 (<italic>GdKu70</italic>) cDNA has previously been cloned and extensively utilized for research^{##REF##11593023##6##,##REF##12087170##7##,##REF##16498404##9##–##REF##35017534##13##}. GdKu70 possesses an additional 18-amino acid extension at its N-terminus compared to human and mouse Ku70, although its biological significance remains uncertain^{##REF##9736627##5##}. To validate this, we compared the number of amino acids comprising Ku70 among chicken, human, mouse, and canine Ku70. Sequence alignment analyses using published data confirmed that GdKu70 harbors an additional 18 amino acids at its N-terminus compared to Ku70 in three mammalian species, including canine Ku70 (Fig. ##FIG##0##1##A). These results suggest the possibility that the 18-amino acid segment may have specific functions in chicken and bird cells, despite the absence of major specific functional domains within this region (Fig. ##FIG##0##1##B). To test this hypothesis, we initially analyzed the expression of chicken <italic>Ku70</italic> mRNA through RT-PCR. Specific primers designed for analyzing the chicken <italic>Ku70</italic> expression were based on a sequence previously identified as <italic>GdKu70</italic>^{##REF##9736627##5##} (Fig. ##FIG##0##1##C). Subsequently, RT-PCR analysis was conducted using RNA from chicken Leghorn male hepatoma (LMH) cells. This involved using 5′ end primers containing the <italic>GdKu70</italic> specific translation initiation codon (Ku70-A-F) or the predicted translation initiation codon in homologous positions with those of mammalian species (Ku70-B-F), along with a 3′ end primer (Ku70-R) (Fig. ##FIG##0##1##D). PCR products of the expected length were detected with the primer set Ku70-B-F/Ku70-R, but not with Ku70-A-F/Ku70-R. Additionally, we observed PCR products of the expected length using 5′ end primers (Ku70-Xho-F) and a 3′ end primer (Ku70-Eco-R) (Fig. ##FIG##0##1##E). These results imply that the 18-amino acid portion may not be expressed in the examined chicken cell line.</p>", "<p id=\"Par7\">To confirm the genome sequence, a cDNA sequence (54 bp; 200–253 [AB016529.1] and 1–54 [NM_204927.2]) corresponding to the N-terminal sequence, which displayed an 18-amino acid segment unique to chickens compared to humans, mice, and dogs, was subjected to a genomic search against the chicken public genome sequence GRCg6a/galGal6 using the Basic Local Alignment Search Tool (BLAST)-like Alignment Tool (BLAT; <ext-link ext-link-type=\"uri\" xlink:href=\"https://genome.ucsc.edu/cgi-bin/hgBlat\">https://genome.ucsc.edu/cgi-bin/hgBlat</ext-link>) (UCSC) (Fig. ##FIG##1##2##A). The results indicated that the QUERY sequence 200–233 matched perfectly with 6,479,579–6,479,612 on chromosomes 27, and 232–253 matched with 49,571,464–49,571,485 on chromosome 1, respectively. Note that residues 232 and 233 in the QUERY sequence overlap because they are both G sequences. As there is no ATG sequence in the QUERY sequence from 232 to 253, we propose that this sequence is situated in the 5′-untranslated region (UTR) of chicken <italic>Ku70</italic> with translation initiated from position 254 to 256 (atg), as deduced from the alignment analysis of human and mouse <italic>Ku70</italic> (Fig. ##FIG##0##1##A,B). Similar to the findings of Takata et al. (1998), our analysis confirmed that the sequence gccatgg, including this ATG sequence, corresponds to the optimal Kozac sequence, a consensus sequence located around the translation start site^{##REF##9736627##5##}. Furthermore, a homology search encompassing the sequence of <italic>GdKu70</italic> from 1 to 274, including the sequences encoding the 18 amino acids, was conducted using BLAT and BLAST. The results suggested the possibility that <italic>GdKu70</italic> results from the fusion of three genes originating from two chicken chromosomes and an unknown chromosome (Fig. ##FIG##1##2##B). Specifically, this fusion involves the sequence of unknown origin including EcoR1 recognition sequences, the sequence in the 3′-UTR of <italic>Gallus gallus</italic> nuclear factor, erythroid 2 like 1 (<italic>NFE2L1</italic>) [NM_001030756.1] on chromosome 27, and the sequence of chicken <italic>Ku70</italic> on chromosome 1. Of the 18 amino acids previously reported as specific to GdKu70, 11 amino acids are considered to be derived from the sequence of the 3′-UTR of <italic>NFE2L1</italic>. The remaining seven amino acids originate from the 5′-UTR of chicken <italic>Ku70</italic>.</p>", "<p id=\"Par8\">Next, we proceeded to clone and sequence chicken <italic>Ku70</italic> cDNA, encompassing an open reading frame, using 5′ end primers (Ku70-Xho-F) and a 3′ end primer (Ku70-Eco-R) (Fig. ##FIG##0##1##C,E). As illustrated in Fig. ##FIG##2##3##, we successfully isolated an 1,845-nucleotide open reading frame encoding the chicken Ku70 protein (614 amino acids). This valuable information has been deposited in the DDBJ/EMBL/NCBI database under the accession number LC750713.</p>", "<title>Comparative analysis of amino acid sequences between chicken Ku70 and mammalian Ku70</title>", "<p id=\"Par9\">To assess the amino acid sequence of chicken Ku70 in comparison to mammalian Ku70, a comparative analysis was conducted. Chicken Ku70 exhibits a shared amino acid identity (similarity) of 69.4% (84.4%), 69.5% (84.0%), and 66.9% (82.9%) with human, canine, and mouse Ku70, respectively (Supplementary Table ##SUPPL##0##S1##). In contrast, mouse Ku70 displays a higher amino acid identity (similarity) of 83.1% (90.7%) and 84.0% (90.8%) when compared to human and canine Ku70, respectively. Ku70 is a multifunctional protein, and its functions are potentially regulated, at least in part, by post-translational modifications (PTMs) in human cells, including acetylation, phosphorylation, SUMOylation, protein cleavage, and protein–protein interactions^{##REF##10755664##15##,##REF##12518983##16##,##REF##28163277##25##,##REF##33923616##30##–##REF##16440001##34##}. To investigate whether functional domains and modification sites are evolutionarily conserved in chicken Ku70, we compared the amino acid sequence of chicken Ku70 with that of other mammalian species (Fig. ##FIG##3##4##). Our analysis revealed that certain critical features, including a nuclear localization signal (NLS; 539–556), two SUMOylation consensus motifs (ψ-K-X-E: 509PKVE512 and 555PKVE558), and a protein cleavage motif (Granzyme A [GzmA] target motif [KTKTR301]), presented in human Ku70, are also conserved in chicken, canine, and mouse species. Additionally, another protein cleavage motif (Granzyme B [GzmB] target motif [ISSD79]), found in human Ku70, is conserved in chickens and mice but not in canines^{##REF##28163277##25##,##REF##10499920##33##–##REF##10413594##36##}. However, the Lys31 (K31), which is essential for 5′dRP/AP lyase activity in humans, is not conserved in chickens, suggesting that chicken Ku and canine Ku may lack this activity^{##REF##28163277##25##,##REF##20383123##37##}. Furthermore, experiments conducted in human and mouse cells have demonstrated that Ku70 function is partially regulated by phosphorylation by kinases activated in a cell cycle-dependent manner, as well as by kinases associated with DNA repair and apoptosis modulation^{##REF##28163277##25##,##REF##26337656##38##–##REF##22037767##42##}. Human Ku70, for instance, serves as a substrate for the tyrosine kinase Src, contributing to Ku70-dependent inhibition of apoptosis through phosphorylation of Ku70 at Tyr530 (Y530)^{##REF##27998981##43##}. Recent studies have indicated that human Ku70 is phosphorylated by PKC-α at Ser77/78 (S77/S78), which, in turn, suppresses Ku70 binding to DSBs^{##REF##34635772##44##}. Importantly, these phosphorylation sites are conserved across all the examined species. Fourthermore, we found that the CDK phosphorylation motif ([S/T]Px[K/R]: 401TPRR404), which is a target for cyclin B1/CDK1 and cyclin A2/CDK2, the putative cyclin E1/CDK2 phosphorylation site (T58), the DNA damage-induced phosphorylation sites (S33 and S155), and putative phosphorylation sites required for Ku70/Ku80 dissociation from DSBs (T307, S314 and T316) in human Ku70 are conserved in chicken, canine, and mouse species^{##REF##28163277##25##,##REF##26337656##38##–##REF##22037767##42##}. However, we observed that some phosphorylation sites in human Ku70, including the cyclin B1/CDK1 phosphorylation site (T428), DNA damage-induced phosphorylation site (S27), putative phosphorylation sites needed for Ku70/Ku80 dissociation from DSBs (T305 and S306), and cyclin A2/CDK2 phosphorylation sites (T428 and T455), are not conserved in chickens. Furthermore, among these phosphorylation sites, amino acid residues other than T428 are not conserved in chicken, canine, and mouse species. The two DNA-PK phosphorylation sites (S6 and S51) in human Ku70 are perfectly conserved in canine and mouse species, while S51 is not conserved in chicken^{##REF##28163277##25##,##REF##9362500##45##,##REF##10026262##46##}. Additionally, eight acetylation sites (K317, K331, K338, K539, K542, K544, K553, and K556) present in humans are also perfectly conserved in chickens and mice. However, the acetylation site K544 is not conserved in canine species^{##REF##28163277##25##,##REF##15023334##47##}. Furthermore, the ubiquitination site (K114) in humans is evolutionarily conserved in chicken, canine and mouse species^{##REF##28163277##25##,##REF##25921528##48##}. Finally, it is worth noting that human Ku70 was reported to be methylated at K570 by SET-domain-containing protein 4 (SETD4), with Ku70 methylation being crucial for Ku70 localization to the cytoplasm and subsequent inhibition of apoptosis^{##REF##35545041##49##}. However, this methylation event is conserved in all examined mammalian species but not in chickens.</p>", "<title>Subcellular localization of chicken Ku70</title>", "<p id=\"Par10\">To examine the subcellular localization of Ku70 in normal chicken cells, we conducted immunofluorescence analysis using confocal laser scanning microscopy (CLSM) in PGC29-fibro cells, a primordial germ cell (PGC) line derived from normal White Leghorn chickens. As shown in Fig. ##FIG##4##5##A, indirect immunofluorescence staining with the Ku70 antibody revealed fluorescence in the nucleoplasm while excluding the nucleolus in interphase cells. A similar nuclear staining pattern was observed when using the Ku80 antibody, indicating that Ku70 co-localizes with its heterodimeric partner Ku80 within the nuclei of chicken cells. To further corroborate this findings, we performed indirect immunofluorescence staining using an anti-Ku70/Ku80 antibody, which yielded consistent results with individual Ku70 and Ku80 antibodies. Notably, mitotic phase cells did not exhibit detectable fluorescence with any of the three antibodies (Fig. ##FIG##4##5##B), suggesting that the expression of chicken Ku70 and Ku80 may be lower in mitotic cells compared to interphase cells.</p>", "<p id=\"Par11\">To confirm the nuclear localization of chicken Ku70 expressed from the cloned <italic>Ku70</italic> cDNA in live chicken cells, we examined chicken LMH cells transiently expressing EYFP-chicken Ku70 or EYFP alone. Initially, the expression vectors pEYFP-<italic>chicken Ku70</italic> or pEYFP were transfected into the cells (Fig. ##FIG##5##6##A). Western blot analysis using anti-Ku70 and anti-GFP antibodies confirmed the expression of EYFP-chicken Ku70 in transfected cells (Fig. ##FIG##5##6##B). Additionally, we detected the expression of chicken Ku80 using an anti-Ku80 antibody. As shown in Fig. ##FIG##5##6##C, CLSM revealed that EYFP-chicken Ku70 is localized to the nucleoplasm in interphase cells, excluding the nucleolus. In contrast, in pEYFP-transfected cells, EYFP alone was distributed throughout the cell, except in the nucleolus. Collectively, our findings indicate that chicken Ku70 expressed from the cloned cDNA in this study localizes to the nucleus in interphase chicken cells.</p>", "<title>Recruitment of chicken Ku70 to DNA DSB sites</title>", "<p id=\"Par12\">The subcellular localization and accumulation of Ku70 and other NHEJ proteins at DNA DSBs have been well-studied in mammalian cells but not in chicken cells^{##REF##12518983##16##,##REF##19133841##18##,##REF##28163277##25##,##REF##10413594##36##,##REF##34635772##44##,##REF##35545041##49##–##REF##31115163##55##}. Additionally, the subcellular localization of DNA repair proteins involved in the NHEJ pathway and their changes after DNA damage have not been reported in avian cells. Recently, we demonstrated that chicken XLF localizes to the nucleus and accumulates at DSBs in chicken cells, while truncated XLF lacking the predicted Ku-binding motif dose not localize to DSBs^{##REF##25947322##53##,##REF##32214226##56##}. To ascertain whether chicken Ku70 accumulates at DSBs, we locally induced DSBs in PGC29-fibro cells expressing EYFP-chicken Ku70 or EYFP alone using a 405 nm laser (Fig. ##FIG##6##7##A). As illustrated in Fig. ##FIG##6##7##B, EYFP-chicken Ku70, but not EYFP alone, accumulated at the laser-microirradiated sites in live chicken cells during interphase. Microirradiation, coupled with immunostaining against γH2AX, a marker for DSB detection, revealed that EYFP-chicken Ku70 co-localized with γH2AX at microirradiated sites in chicken cells (Fig. ##FIG##6##7##C). Time-lapse imaging demonstrated that EYFP-chicken Ku70 began to accumulate at DSB sites within 5 s of irradiation (Fig. ##FIG##6##7##D). Furthermore, microirradiation combined with immunostaining for Ku80 showed that EYFP-chicken Ku70 accumulated and co-localized with Ku80 at DSBs in chicken cells (Fig. ##FIG##6##7##Ea). Additionally, we observed that the NHEJ repair protein XLF accumulated and co-localized with Ku, a heterodimer composed of Ku70/Ku80, at DSBs (Fig. ##FIG##6##7##Eb,c). These findings suggest that the NHEJ repair protein Ku70 forms a heterodimer with Ku80 in chicken cells, and Ku, along with other NHEJ repair proteins, such as XLF, may participate in DSB repair immediately after DNA damage. These results also highlight the utility of the chicken Ku70 cloned in this study for investigating the molecular mechanisms of DNA repair in chicken cells.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par13\">Chicken <italic>Ku70</italic> cDNA, known as <italic>GdKu70,</italic> and cell lines expressing it have been instrumental in various studies aiming to elucidate Ku70's function and its involvement in Ku70-dependent molecular mechanisms, including the NHEJ pathway and radiation/drug resistance^{##REF##9736627##5##–##REF##35017534##13##}. These investigations have led to significant discoveries, such as the selection mechanism of the DNA DSB repair pathway^{##REF##9736627##5##}. However, our findings in this study strongly suggest that <italic>GdKu70</italic> cDNA encodes an artificial Ku70 variant (GdKu70) and that GdKu70 is not expressed in chicken cells. Consequently, caution should be exercised when interpreting certain prior results obtained using <italic>GdKu70</italic> cDNA and its expressing cells.</p>", "<p id=\"Par14\">In this study, we conducted a new cDNA cloning of chicken <italic>Ku70</italic>, revealing that it consists of 614 amino acids. It is worth noting that Takata et al<italic>.</italic> previously reported that chicken <italic>Ku70</italic> encodes 632 amino acids, including an 18-amino acid portion specific to chicken Ku70^{##REF##9736627##5##}. However, our RT-PCR analysis suggests that <italic>GdKu70</italic> mRNA is not expressed in chicken cells. In a prior study, we demonstrated that chicken <italic>Ku70</italic> is localized on chromosome 1 using direct R-banding fluorescence in situ hybridization^{##REF##10640808##28##}. In our current study, genome information analysis utilizing the publicly available genome sequence, revealed that 233 bases, which nearly encompass the chicken-specific 18-amino acid portion in GdKu70, perfectly match a section of the 3′-UTR of <italic>NFE2L1</italic> on chromosome 27. Taken together, it appears that the <italic>GdKu70</italic> cDNA reported by Takata et al. is likely an artificial gene, in which 233 bases from the <italic>NFE2L1</italic> on chromosome 27 have fused to the 5′-UTR, corresponding to the region of chicken <italic>Ku70</italic> on chromosome 1. We also noted an unidentified region, including the EcoR1 recognition sequence, in the 5′-flanking of <italic>GdKu70</italic>^{##REF##9736627##5##}. In conclusion, the portion of chicken-specific 18 amino acids previously reported does not appear to be expressed in chicken cells. It is worth mentioning that Takata et al<italic>.</italic> (1998) reported isolating <italic>Ku70</italic> full-length cDNA and genomic DNA, which codes for GdKu70 from a chicken intestinal mucosa cDNA library (Clontech) and a liver genomic library (Stratagene), respectively^{##REF##9736627##5##}. Moreover, the identities of the clones were confirmed through sequencing. Nevertheless, it remains unclear why the same fusion occurred in the cDNA and genomic libraries derived from different organs and purchased from different companies.</p>", "<p id=\"Par15\">The multifunctional protein Ku70 plays critical roles not only in NHEJ but also in various mechanisms, including V(D)J recombination, telomere maintenance, and regulation of neuronal apoptosis^{##REF##10755664##15##,##REF##12518983##16##,##REF##33923616##30##–##REF##34746031##32##}. Understanding the regulation of Ku70's subcellular localization is crucial for comprehending its function, although this regulatory mechanism remains incompletely understood^{##REF##12518983##16##}. Our findings indicate that chicken Ku70 predominantly localizes in the cell nucleus during interphase. Furthermore, the heterodimer Ku, composed of Ku70 and Ku80, accumulates at DNA DSBs immediately after DNA damage in chicken cells. These observations strongly suggest that the subcellular localization and behavior of Ku following DSB damage are akin to those of human, mouse, and canine Ku^{##REF##19133841##18##,##REF##28163277##25##,##UREF##1##51##,##REF##25947323##52##}. The subcellular localization of Ku70 and the mechanisms controling it are important for the functional regulation of Ku70 and Ku in mammalian species, including humans^{##REF##12518983##16##,##REF##34746031##32##}. In human cells, the nuclear localization of Ku70 is mainly regulated by the importin complex binding to the Ku70 NLS and may, in part, depend on the Ku80 NLS through heterodimerization with Ku80^{##REF##10413594##36##,##REF##11152690##57##,##REF##11112693##58##}. Recent research has revealed that Ku70's cytoplasmic localization induced by methylation at K570 by SETD4 is essential for regulating Ku70's function in human cells^{##REF##35545041##49##}. Furthermore, we reported that acetylation of two lysine residues, K553 and K556, in the human Ku70 NLS can regulate its nuclear localization^{##REF##36620088##59##}. In this study, we confirmed that the structure of the human Ku70 NLS is conserved in chicken Ku70, as well as in canine and mouse Ku70. Among the PTM target amino acids involved in regulating the subcellular localization of human Ku70, the acetylation target lysins in the NLS were evolutionarily conserved in chicken Ku70, but the methylation target lysine regulated by SETD4 was not. Notably, our findings showed that both the acetylation target lysins and the methylation target lysine by SETD4 are conserved in the Ku70 of dogs and mice. Overall, our results suggest that while the NLS structure crucial for regulating the subcellular localization of human Ku70 is conserved in chicken Ku70, the regulatory mechanisms of PTMs that negatively modulate NLS-mediated nuclear localization may not be fully conserved in chicken cells. Further studies are needed to elucidate the differences between mammals and birds, including chickens.</p>", "<p id=\"Par16\">Studies involving chickens and chicken cells, such as DT40 cells, have made significant contributions to basic research in the life sciences and pre-clinical research^{##REF##17742872##1##–##REF##35165266##14##}. DT40 cells, in paticular, have served as valuable models for studying gene function and have significantly advanced research in life sciences, including DNA repair mechanisms and oncogenesis. Single KO and DKO DT40 cell lines targeting key NHEJ genes, such as <italic>Ku70, XRCC4, XLF, DNA-PKcs,</italic> and <italic>DNA-ligase IV</italic>, have already been generated and studied for their sensitivity to radiation and various drugs^{##REF##9736627##5##,##REF##11593023##6##,##REF##15279806##8##,##REF##18674614##60##}. Furthermore, it is now feasible to transplant genetically modified chicken PGCs into recipient embryos to generate genetically modified chick^{##REF##32776392##61##}. Detailed investigations using various NHEJ gene-KO DT40 cell lines and new genetically modified chicken models are expected to lead to the discovery of new pathological models resulting from mutations in chicken NHEJ genes and novel regulatory mechanisms related to Ku70 function. Recently, we demonstrated that one chicken breed, the Japanese Bantam (Chabo), has lost a portion of the NHEJ repair gene <italic>XLF</italic>, resulting in decreased DSB repair ability in its cell lines and brain tissue^{##REF##32214226##56##}. Furthermore, the pathogenesis in Chabo chickens resembles that of <italic>XLF</italic> deficiency syndrome in humans^{##REF##16439204##22##,##REF##32214226##56##}. These findings strongly indicate that chickens serve as valuable analytical models for studying human DNA repair pathways and gene-deficient diseases related to DNA repair. In conclusion, the information and materials obtained in this study are expected to significantly contribute not only to chicken research but also to preclinical and basic life science research in both human and veterinary fields.</p>" ]

[]

[ "<p id=\"Par1\">Ku70 is a multifunctional protein with pivotal roles in DNA repair via non-homologous end-joining, V(D)J recombination, telomere maintenance, and neuronal apoptosis control. Nonetheless, its regulatory mechanisms remain elusive. Chicken <italic>Ku70</italic> (<italic>GdKu70</italic>) cDNA has been previously cloned, and DT40 cells expressing it have significantly contributed to critical biological discoveries. GdKu70 features an additional 18 amino acids at its N-terminus compared to mammalian Ku70, the biological significance of which remains uncertain. Here, we show that the 5′ flanking sequence of <italic>GdKu70</italic> cDNA is not nearly encoded in the chicken genome. Notably, these 18 amino acids result from fusion events involving the <italic>NFE2L1</italic> gene on chromosome 27 and the <italic>Ku70</italic> gene on chromosome 1. Through experiments using newly cloned chicken <italic>Ku70</italic> cDNA and specific antibodies, we demonstrated that Ku70 localizes within the cell nucleus as a heterodimer with Ku80 and promptly accumulates at DNA damage sites following injury. This suggests that the functions and spatiotemporal regulatory mechanisms of Ku70 in chickens closely resemble those in mammals. The insights and resources acquired will contribute to elucidate the various mechanisms by which Ku functions. Meanwhile, caution is advised when interpreting the previous numerous key studies that relied on <italic>GdKu70</italic> cDNA and its expressing cells.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51501-0.</p>", "<title>Acknowledgements</title>", "<p>We would like to thank Editage (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.editage.jp\">www.editage.jp</ext-link>) for English language editing. This research was supported in part by JSPS KAKENHI grant Number JP22K06036. This work was also carried out with the support of National Institutes for Quantum Science and Technology and Saitama University.</p>", "<title>Author contributions</title>", "<p>M.K. and A.K. designed and managed the experiments. M.K., H.Y., Y.Y., and A.K. conducted experiments and evaluated the results. The computational analysis was done by M.K. and H.Y. M.K. wrote the manuscript, and H.Y., Y.Y. and A.K. read and agreed to the final document.</p>", "<title>Data availability</title>", "<p>The sequence of chicken <italic>Ku70</italic> cloned in this study has been deposited in the DDBJ/EMBL/NCBI database under accession number LC750713.</p>", "<title>Competing interests</title>", "<p id=\"Par23\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>(<bold>A</bold>) Chicken Ku70 (GdKu70) differs from mammalian Ku70 by having an additional 18 amino acids at the N-terminal end. A comparison of Ku70 sequences among chicken (<italic>Gallus gallus domesticus,</italic> GenBank accession No. [BAA32018.1])^{##REF##9736627##5##}, dogs (<italic>Canis lupus familiaris</italic>, GenBank accession No. [LC195221])^{##REF##28163277##25##}, humans (<italic>Homo sapiens,</italic> GenBank accession No. [NP_001460.1]), and mice (<italic>Mus musculus</italic>, GenBank accession No. [NP_034377.2]). (<bold>B</bold>) Sequences surrounding the chicken Ku70 (GdKu70) translation initiation codon as reported by Takata et al.^{##REF##9736627##5##}. An 18-amino acid stretch is appended to the N-terminus in the amino acid sequence of chicken Ku70 (GdKu70) compared to human and mouse Ku70 (highlighted in yellow in <bold>A</bold> and <bold>B</bold>). The reported translation initiation codon and the translation initiation codon predicted by comparison among mammals are shown in red and blue capital letters, respectively. Numbers indicate amino acids (top) and nucleotides (bottom). (<bold>C</bold>) Primers for the detection of chicken <italic>Ku70</italic> by RT-PCR analysis. Specific primer locations used for detecting chicken <italic>Ku70</italic> (<italic>GdKu70</italic>) are indicated. ATG (red capital) is the reported translation initiation codon, and ATG (blue capital) is the predicted translation initiation codon based on comparison with mammals. (<bold>D</bold>) RT-PCR analysis of chicken <italic>Ku70</italic> using two 5′ end primers containing the reported (Ku70-A-F) or predicted translation initiation codons (Ku70-B-F)^{##REF##9736627##5##}. The primer pairs (Ku70-A-F/Ku70-R and Ku70-B-F/Ku70-R) were used to amplify each DNA fragment. (<bold>E</bold>) RT-PCR analysis of the chicken <italic>Ku70</italic> coding sequence (CDS). The CDS of <italic>Ku70</italic> was amplified using high-fidelity Platinum™ SuperFi™ DNA Polymerase with the Ku70-Xho-F/Ku70-Eco-R primer set. The amplified DNA was analyzed by 1% agarose gel electrophoresis. M: Lambda phage DNA EcoRI/HindIII digestion marker.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Chicken <italic>Ku70</italic> (<italic>GdKu70</italic>) is a fusion product of three genes derived from chromosomes 1, 27, and an unknown chromosome. (<bold>A</bold>) A nucleotide sequence (54 [bases 200–253] bp in <italic>GdKu70</italic> [AB016529.1]) corresponding to the N-terminal sequence, which displays an 18-amino acid protrusion unique to chickens compared to humans, mice, and dogs, when aligned with the amino acid sequence of Ku70, was subjected to a genomic search against the chicken public genome sequence GRCg6a/galGal6 using the BLAT alignment tool. The results revealed that the QUERY sequence 200–233 perfectly matches with 6,479,579–6,479,612 of chromosome 27, and 232–253 perfectly matches with 49,571,464–49,571,485 of chromosome 1, respectively. (<bold>B</bold>) A homology search was conducted on a nucleotide sequence (274 [bases 1–274] bp in <italic>GdKu70</italic> [AB016529.1]) using BLAT and another alignment tool, BLAST. The sequences included the reported translation initiation codon (atg, 200–202) and the predicted translation initiation codon (atg, 254–256, bold red letters), based on a comparison among mammals. The results suggest that chicken <italic>Ku70</italic> (<italic>GdKu70</italic>) is a fusion product derived from three genes, i.e., an unknown gene including the EcoR1 recognition sequence (underlined) on the unknown chromosome (bases 1–7, green), the <italic>NFE2L1</italic> gene [NM_001030756.1] on chromosome 27 (bases 8–233, pink), and the <italic>GdKu70</italic> gene on chromosome 1 (bases 234–274, yellow). The 18 amino acids in GdKu70 are indicated by red capital letters [BAA32018.1]^{##REF##9736627##5##}.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Nucleotide and deduced amino acid sequences of chicken <italic>Ku70</italic> cDNA cloned in this study. The coding sequence of chicken <italic>Ku70</italic> consists of 1845 bp, encoding 614 amino acid residues. The data has been deposited in the DDBJ, EMBL, and GenBank with the accession number [LC750713]. The translation initiation codon (atg) is underlined, and the asterisk indicates the position of the termination codon (taa).</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Ku70 sequence alignment. The amino acid sequences of chicken Ku70 (<italic>Gallus gallus domesticus</italic>, [LC750713]) are aligned with those of dog (<italic>Canis lupus familiaris,</italic> [LC195221]), human (<italic>Homo sapiens</italic>, [NP_001460.1], and mouse (<italic>Mus musculus</italic>, [NP_034377.2]) Ku70. The location of the nuclear localization signal (NLS) sequence (NLS: 539–556), the Granzyme A (GzmA) target motif (KTKTR301), the Granzyme B (GzmB) target motif (ISSD79), the two canonical SUMOylation consensus motifs (ψ-K-X-E: 509PKVE512 and 555PKVE558), and the CDK phosphorylation motif ([S/T]Px[K/R]: 401TPRR404) in human Ku70 are shown^{##REF##28163277##25##,##REF##10499920##33##–##REF##10413594##36##,##REF##27402161##41##}. Additionally, the location of the candidate nucleophile needed for 5′dRP/AP lyase activity (K31), the DNA-PK phosphorylation sites (S6 and S51), the DNA damage inducible phosphorylation sites (S27, S33, and S155), the phosphorylation sites needed for Ku’s dissociation from DSB (T305, S306, T307, S314 and T316), the PKC α phosphorylation sites (S77 and S78), the Src phosphorylation site (Y530), the cyclin B1/CDK1 phosphorylation sites (T401 and T428), the cyclin A2/CDK2 phosphorylation sites (T401, T428, and T455), the cyclin E1/CDK2 phosphorylation site (T58), the ubiquitination site (K114), the acetylation sites (K317, K331, K338, K539, K542, K544, K553, and K556), the methylation site (K570), and the two SUMOylation sites (K510 and K556) in human Ku70 are marked with asterisks or underlined^{##REF##28163277##25##,##REF##25218447##35##,##REF##20383123##37##–##REF##35545041##49##}.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Expression and subcellular localization of Ku70 and its heterodimeric partner, Ku80, in chicken cells. (<bold>A</bold>,<bold>B</bold>) Subcellular localization of Ku70 and Ku80 in chicken PGC29-fibro cells. Cells were fixed and stained with anti-Ku70, anti-Ku80, or Ku70/Ku80 antibodies. Nuclear DNA was stained with DAPI. The stained cells were analyzed using confocal laser scanning microscopy. Cells in interphase and mitotic phase were discriminated using the morphology of cell nuclei visualized by DAPI staining as an indicator. (<bold>A</bold>) Nuclear localization of Ku70 and Ku80 in interphase cells. Left panel: Ku70 (upper), Ku80 (middle), and Ku70/Ku80 (lower) images; center panel: DAPI images; right panel: merged images. (<bold>B</bold>) Low Ku70 and Ku80 expression in mitotic cells. Left panel: Ku70 (upper), Ku80 (middle), and Ku70/Ku80 (lower) images; center panel: DAPI images; right panel: merged images. Arrowheads indicate cells in the mitotic phase.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Expression and subcellular localization of EYFP-chicken Ku70 in chicken living cells. (<bold>A</bold>) Scheme representing the EYFP-chicken Ku70 chimeric protein (EYFP-chKu70) and control protein (EYFP). (<bold>B</bold>) (<bold>a</bold>,<bold>b</bold>) EYFP-chKu70 expression in chicken LMH cells. Extracts from cells transiently expressing EYFP-chKu70 or EYFP were analyzed by western blotting using anti-GFP (<bold>a</bold>, top and second from bottom), anti-Ku70 (<bold>a</bold>, second from top), anti-Ku80 (<bold>b</bold>, top), and anti-β-actin (<bold>a</bold>,<bold>b</bold>, bottom) antibodies. NT, non-transfected cells. M, molecular weight marker (kDa). (<bold>C</bold>) Subcellular localization of EYFP-chKu70 in living chicken LMH cells. Cells transiently expressing EYFP-chKu70 or EYFP were examined using confocal laser microscopy. EYFP images of the same cells are shown alone (upper panel) or merged with corresponding differential interference contrast (DIC) (lower panel) images.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Accumulation of Ku70 to DSBs induced by laser microirradiation in chicken cells. (<bold>A</bold>) The localization and accumulation of EYFP-chicken Ku70 (EYFP-chKu70) at DSBs induced by 405-nm laser irradiation were examined in chicken cells. (<bold>B</bold>) Recruitment of EYFP-chKu70 to the microirradiated site induced by 405-nm laser irradiation in chicken cells. Imaging of live PGC29-fibro cells transfected with pEYFP-<italic>chKu70</italic> (upper panel) or pEYFP (lower panel) before (left panel) and after (right panel) microirradiation. Arrowheads indicate microirradiated sites. (<bold>C</bold>) Accumulation of EYFP-chKu70 at DSBs induced by laser microirradiation in PGC29-fibro cells. Immunostaining of microirradiated cells transfected with pEYFP-<italic>chKu70</italic> (upper panel) or pEYFP (lower panel) was performed using anti-γH2AX antibody 5 min post-irradiation. Left panel, EYFP-chKu70 (upper) or EYFP (lower); center panel, γH2AX; right panel, merged images. (<bold>D</bold>) Time-dependent EYFP-chKu70 accumulation in live PGC29-fibro cells, from 5 to 120 s after irradiation. (<bold>E</bold>) Immunostaining of microirradiated cells transfected with pEYFP-<italic>chKu70</italic> or pEYFP-<italic>chXLF</italic> using anti-Ku80, anti-Ku70, or anti-Ku70/Ku80 antibodies. The cells were fixed and stained with each antibody 5 min post-irradiation. Left panel, EYFP-chKu70 (<bold>a</bold>); EYFP-chXLF (<bold>b</bold> and <bold>c</bold>); center panel, Ku80 (<bold>a</bold>), Ku70 (<bold>b</bold>), and Ku70/Ku80 (<bold>c</bold>); right panel, merged images (<bold>a–c</bold>).</p></caption></fig>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">The period of adolescence can prove to be demanding for students, given that they encounter a range of transformations. These encompass biological and cognitive shifts arising from maturation, alterations in their social interactions with both peers and parents, and adjustments prompted by heightened academic demands and expectations from school^{##REF##10354802##1##–##UREF##0##4##}. Accordingly, secondary school students commonly experience increased levels of psychological stress and school burnout^{##UREF##1##5##–##UREF##3##7##}. However, there have been few studies investigating whether the self-perceived stress and overload symptoms are also related to biophysiological stress markers (e.g., cortisol, alpha-amylase, oxidative stress, telomere length). Even though students’ self-reported information is central to unlocking their feelings and thoughts, it is also susceptible to systematic error due to desired response behavior^{##UREF##4##8##}. By merging subjective and biophysiological stress metrics, it becomes possible to uncover intricate psychophysical mechanisms associated with stress. These insights could potentially form the foundation for interventions aimed at managing stress. While the exploration of biophysiological stress markers like cortisol and alpha-amylase has gained attention in the educational setting in recent times^{##REF##35583016##9##–##UREF##5##11##}, the examination of biophysiological indicators associated with stress and arousal, such as oxidative stress and telomere length, has predominantly been conducted in the realm of psychopathology and health studies. Nonetheless, delving into a wide range of biophysiological markers within the educational context alongside self-report data from school students offers encouraging avenues for valuable insights, supporting the healthy development of students by identifying factors that can have a minimizing effect on students’ stress and burnout.</p>", "<p id=\"Par3\">Both the buffering hypothesis^{##REF##3901065##12##} as well as the Conservation of Resources theory COR^{##REF##2648906##13##} posit that supportive social relationships have the potential to mitigate sensations of stress and overwhelm, serving as crucial assets for effectively managing challenging situations. Although there are numerous findings confirming the buffering hypothesis and COR with regard to the protective effects of social support e.g.,^{##UREF##6##14##–##REF##28853242##16##}, to the best of our knowledge, there has been no study to date that has also examined this approach in the interplay of self-perceived <italic>and</italic> biophysiological stress and arousal. The present study was designed to address this research desideratum by examining how social relationships with parents, teachers, and peers that are perceived as supportive moderate the relationship between subjective stress (e.g., school burnout, perceived stress) and biophysiological stress markers (e.g., cortisol, alpha-amylase, oxidative stress, telomere length).</p>", "<title>Subjective stress, cortisol, alpha-amylase, oxidative stress, and telomere length</title>", "<p id=\"Par4\">Psychological stress may arise if demands exceed an individual’s resources which is associated with increased threat appraisals and negative affect^{##REF##22155939##17##,##UREF##7##18##}. While psychological stress is not primarily related to a specific context, school burnout is experienced in relation to the academic context. Students often report school-related psychosomatic stress symptoms such as head-aches or dizziness if they feel pressured to receive high grades, worry about their academic performance, and feel overwhelmed by schoolwork^{##REF##22525486##19##,##UREF##8##20##}. Long-lasting and high levels of school-related psychosomatic stress symptoms make students more susceptible to school burnout, which includes exhaustion from schoolwork, feeling inadequate as a student, and adopting a cynical and detached attitude towards school^{##REF##18257974##21##,##UREF##9##22##}. Although psychological stress and school burnout are conceptualized and measured differently, the constructs are related^{##UREF##10##23##} and present a risk to students’ health and academic trajectories^{##UREF##11##24##–##REF##12778983##29##}.</p>", "<p id=\"Par5\">Several large-scale international surveys have demonstrated steadily increasing levels of self-reported psychological stress, school-related psychosomatic stress symptoms, and school burnout both in the cohort of secondary school students and over the last decade^{##REF##16750846##30##–##UREF##16##34##}. Because of this alarming increase, it is also central to combine research approaches and ask whether or to what extent self-perceived stress and burnout are related to a variety of biophysiological stress markers.</p>", "<title>Cortisol and alpha-amylase</title>", "<p id=\"Par6\">Cortisol belongs to the glucocorticoid class of hormones and is commonly referred to as the “stress hormone,” while amylase is an enzyme that has been investigated as a suitable candidate to measure stress-related arousal^{##REF##31900867##35##,##REF##17418498##36##}. While alpha-amylase has traditionally been studied in the context of stress, research outside the clinical context has revealed its involvement in both heightened arousal of positive emotions and negative emotions experienced by individuals^{##REF##21840370##37##}. Hence, while cortisol has been consistently linked to stress related arousal, alpha-amylase is not limited specifically to stress or negative emotional valence.</p>", "<p id=\"Par7\">While both biological indicators serve as valuable markers for detecting physiological changes in response to arousal, cortisol is reflective of the hypothalamic–pituitary–adrenal (HPA) axis and α-amylase is a reliable index of sympathetic-adrenal medullary (SAM) activity during arousal^{##REF##17418498##36##,##REF##24790712##38##}. As both reflect the reactivity of distinct bodily stress systems, some studies speak of an asymmetry between the HPA axis and SAM in a bodily response to arousal^{##REF##22859941##39##} that is related to an asymmetry between cortisol and α-amylase reactivity^{##REF##16879926##40##}. For this reason, both act differently with respect to timely release in response to a stress-induced task^{##REF##21470780##41##}, they relate differently to self-reported stress^{##REF##16301277##42##,##REF##15485637##43##}, and they may not be correlated according to the findings of some studies^{##REF##35774026##10##,##REF##17418498##36##,##REF##8842578##44##}.</p>", "<p id=\"Par8\">There is a general belief that long-term stress leads to an increase in cortisol levels^{##REF##9695136##45##}. In this case, the overactivation of the HPA axis for a prolonged period of time induces wear and tear on the stress systems, which relates to negative health outcomes^{##REF##17290796##46##,##REF##17201569##47##}. In this respect, Jamieson et al.^{##UREF##17##48##} demonstrated that both challenge and threat appraisals activate the HPA axis, while threat appraisals have a stronger activation potential than challenge. Lee and colleagues have described cortisol to be an end product of threat-type stress responses^{##REF##29992534##49##}. However, empirical studies on the relation between self-reported stress, cortisol and alpha-amylase levels among healthy individuals are rather complex.</p>", "<title>Oxidative stress</title>", "<p id=\"Par9\">Oxidative stress introduces an additional dimension to the detection of biophysiological stress responses. It reflects an asymmetry between the production of reactive oxygen species (commonly known as free radicals) and the protective actions of antioxidants^{##REF##10693912##50##}. Numerous human and animal studies point to a correlation between psychosocial stress and elevated oxidative stress levels, which consequently contribute to cellular and tissue damage within the body^{##REF##34489642##51##–##REF##8827060##54##}. Nonetheless, investigations into the connection among oxidative stress and subjective stress within the school context are so far uncommon.</p>", "<title>Telomere length</title>", "<p id=\"Par10\">Telomeres consist of repetitive DNA sequences that provide stability to the ends of chromosomes, gradually shortening as a result of cell division over time^{##REF##15680963##55##}. Moreover, a link has been established between psychosocial stressors and the hastening of biological aging. This linkage is attributed to chronic stress directly influencing cellular mechanisms associated with the emergence of different diseases and the reduction of telomere length^{##REF##30225068##56##,##UREF##18##57##}. While telomeres have primarily been the focus of clinical research, a recent study conducted in an educational context revealed that school students with longer telomeres were less likely to report experiencing burnout^{##REF##37489893##58##}.</p>", "<p id=\"Par11\">In sum, empirical findings—mainly in the field of psychopathology and health studies—have indicated that cortisol, α-amylase, oxidative stress, and the length of telomeres are reliable but distinct indicators of biological stress and arousal. However, research that links these biophysiological markers with school students’ reported stress and burnout remains underdeveloped. Establishing connections between subjective and biophysiological stress linked to social support variables offers a promising strategy for preventing students from encountering psychological stress and school-related burnout, thereby promoting healthy psychological and academic development. Therefore, it is essential to identify resources that are accessible within students’ immediate environment and protect them from experiencing strain, stress-related negative affect, and feelings of being overwhelmed by school. Research has demonstrated that nurturing relationships with parents, teachers, and peers constitute significant resources that can mitigate feelings of stress in school students.</p>", "<title>Social support and students’ stress</title>", "<p id=\"Par12\">Social support emerges as a potent and enduring coping strategy during challenging circumstances, recognized as a fundamental cornerstone of social, psychological, and biological well-being^{##UREF##19##59##}. Social buffering, which falls within the realm of social support, refers to the mechanism by which the presence of a similar species diminishes the activity of stress-related neurobiological systems^{##REF##26230646##60##}. In a human context, Cohen and Wills^{##REF##3901065##12##} introduced the buffering hypothesis, which proposes that relationships perceived as supportive serve to alleviate the impact of stress. Likewise, the Conservation of Resources Theory COR^{##REF##2648906##13##} posits that individuals endeavor to preserve their resources, including their capacity for well-being, which necessitates the utilization of resources such as supportive social relationships^{##UREF##19##59##}. Hence, feelings of psychological stress and school burnout draw on students’ resources and consequently prompt a need for more resources, such as supportive social relationships, to help regain and maintain well-being. Many empirical studies have investigated students’ stress levels and well-being—as a counterweight to stress—in relation to their supportive relationships with parents, teachers, and peers, but their results differ depending on the measures used to capture social support, the age group investigated, and the statistical models tested.</p>", "<p id=\"Par13\">For example, studies have found that parental support protects students from feeling overwhelmed by school and is related to low levels of student’s stress^{##UREF##6##14##,##REF##33453550##61##}. Parental support can buffer the impact of stress on adolescents and facilitate school enjoyment^{##REF##26257685##62##,##REF##30356633##63##}. Hostinar et al.^{##REF##24942038##64##} found that social support from parents was related to lower cortisol levels in elementary school students compared to support from a stranger after students participated in the Trier Social Stress Test (TSST) the same did not apply to secondary school students. Raphael and Paul^{##UREF##20##65##} demonstrated that parental support measured by parent–child discussions about the future, joint school activities and parental school involvement were related to low levels of stress among secondary school students, but only in the absence of parental psychological control. The time parents spend with their children has been linked positively to children’s well-being^{##REF##37077856##66##,##UREF##21##67##} and contributes to a lesser extend of problem behavior in adolescents^{##UREF##22##68##}.</p>", "<p id=\"Par14\">Besides support from parents, support from teachers has been shown to minimize the effect of stress on externalizing problems^{##UREF##23##69##} and contributes to students’ self-reported health related to stress^{##UREF##24##70##,##REF##32056920##71##}. A study with Chinese adolescents could show that teacher support improves students’ mental well-being and resilience^{##REF##32038425##72##}. Another study with German adolescents could show that perceived teacher support was positively related to students’ self-worth and physical well-being^{##REF##34925161##15##}. Empirical findings from the school context suggest that students’ stress levels are buffered by perceived support from teachers^{##REF##12778983##29##,##UREF##25##73##,##UREF##26##74##}.</p>", "<p id=\"Par15\">In addition, support from peers can minimize stress symptoms. Adams et al.^{##REF##21895364##75##} detected that the presence of a best friend was related to low levels of cortisol during the exposure to TSST in elementary students. Investigating sAA and the reported network size of students, Ponzi et al.^{##REF##25919481##76##} found that the ego reported network size was correlated with higher sAA levels, indicated higher physiological arousal of students with larger network sizes.</p>", "<p id=\"Par16\">In quantitative questionnaire studies, the link between social support by peers—also measured by classroom climate—and students’ stress has been demonstrated consistently. For instance, Torsheim and Wold^{##UREF##26##74##} revealed that support from peers was related to lower levels of school-related stress, a finding that was also confirmed by Hoferichter et al.^{##REF##36518954##77##}. Similarly, Hoferichter and colleagues^{##UREF##27##78##} demonstrated that from grades seven to nine, classmate support buffered the increase of anti-school attitudes, which was related to school-related stress. However, according to a health study conducted by the World Health Organization (WHO), between the ages of 11 and 15, perceived support from classmates declined in nearly all of the 43 countries and regions across Europe and North America that were included in the study. Consequently, alternative social support sources, e.g., parental and teacher support or friends outside school, may compensate for the decline of peer support within the classroom.</p>", "<p id=\"Par17\">In sum, secondary school students’ supportive relationships with parents, teachers, and peers represent valuable resources that help students overcome stressful situations and maintain their well-being. However, research on whether social support buffers the relationship between various measures of self-perceived stress and biophysiological markers linked to stress and arousal is still missing. In response to this need, the present study aligns with the recommendations of Hanssen et al.^{##REF##28603779##79##} who proposed that future research on psychosocial stressors among youth should explore various stressors and explore potential factors that may moderate them. Hence, the objective is to gain a deeper understanding of the attributes of stressors and associated symptoms and to identify factors that predict vulnerability and resilience among young individuals.</p>", "<title>Hypotheses</title>", "<p id=\"Par18\">Hypothesis 1: Following the COR theory and empirical evidence, it is expected that social support from parents, teachers and peers is associated with lower levels of students’ psychological stress and school burnout (i.e., (1) exhaustion and (2) cynicism &amp; inadequacy).</p>", "<p>Exploratory Research Question: Given the underdeveloped state of research regarding the connection between biophysiological stress and arousal markers (i.e., cortisol, alpha-amylase, oxidative stress, telomeres) and support from parents, teachers, and peers, we do not propose a hypothesis but instead adopt an exploratory approach. Thereby it is investigated if the social support variables moderate the relationships between student’s perceived stress and burnout with their levels of cortisol, alpha-amylase, oxidative stress, and telomere lengths.</p>" ]

[ "<title>Method</title>", "<title>Participants and procedure</title>", "<p id=\"Par20\">The current sample is part of a larger sample (<italic>N</italic> = 733) of students from schools in Northeastern Germany, who participated in a survey investigating many different aspects of school-related stress and support factors during regular class hours. Out of these students, 100 participants were randomly selected and invited for the collection of biomarkers. Written informed consent was given by the parents after full explanation of the study to them and their child, with 83% consenting for both the questionnaire study and biophysiological testing (<italic>N</italic> = 83, <italic>M</italic>_{<italic>age</italic>} = 13.72, SD = 0.67; 48% girls). The study was approved by the Ministry of Education and Child Day Care Mecklenburg-Pomerania, the data protection officer and the ethics committee of the university medical centre. All methods performed in accordance with relevant guidelines and regulations.</p>", "<p id=\"Par21\">To determine the participants’ salivary α-Amylase (sAA) and cortisol levels, they were instructed to collect a saliva sample independently after waking up using salivary cuvettes supplied by a team member of the study during the prior medical examination. Instructions were given on how to collect the sample correctly, i.e., to collect it immediately after waking up, before eating or drinking anything or brushing their teeth as well as how to recognize that they had collected an appropriate amount of saliva using indicators on the container.</p>", "<p id=\"Par22\">On the day of the measurements, the participants woke up on average at 8:00 AM (<italic>SD</italic> = 1.29 h) and visited the University of Greifswald to give a second set of saliva samples at 10:54 AM on average (<italic>SD</italic> = 1.06 h). Here the students also provided urine samples for oxidative stress analysis as well as saliva samples to analyse telomere length. The salivettes containing the sAA and cortisol samples were stored at − 20 °C, while the urine samples were stored on ice and frozen at − 80 °C before analysis. The telomere length saliva was kept at room temperature in Oragene·DNA (OG-500) collection kits. Sample collection at the university was conducted by trained staff.</p>" ]

[ "<title>Results</title>", "<p id=\"Par35\">Sample statistics are depicted in appendix Table 1.</p>", "<title>Correlation analyses</title>", "<p id=\"Par36\">The correlation analyses (see appendix Table 2) indicated a general pattern of negative correlations between the stress and support variables. Support and stress variables showed no consistent relationships between the biomarkers, with the exceptions of telomere length and stress variables, which exhibited an overall negative relationship.</p>", "<title>Moderation analyses</title>", "<p id=\"Par37\">In the following, we report moderation analyses with interactions significant at the p &lt; 0.05 level. Tables describing moderation analyses are included in appendix Tables 3 and 4.</p>", "<p id=\"Par38\"><italic>Perceived psychological stress and parental support</italic> Both perceived psychological stress (<italic>B</italic> = 1.33, <italic>crSE</italic> = 0.38, <italic>p</italic> = 0.001) and parental support (<italic>B</italic> = 1.58, <italic>crSE</italic> = 0.43, <italic>p</italic> &lt; 0.001) showed significant association with sAA, as well as a significant interaction related to sAA (<italic>B</italic> = -0.37, <italic>crSE</italic> = 0.12, <italic>p</italic> = 0.002) (appendix Table 3). The moderating effect is depicted in Fig. ##FIG##0##1## and indicates that with increasing levels of psychological stress, students’ sAA levels increase. In detail, parental support changes significantly the variation rate of sAA related to psychological stress. The link between psychological stress and sAA increases to a lesser extent among students with high support compared to students who perceive lower support from their parents. For students perceiving lower parental support, the increase of sAA related to an increase of psychological stress is much steeper. In case of high psychological stress, the relationship between parental support and sAA weakens.</p>", "<p id=\"Par39\"><italic>Inadequacy/cynicism scale and parental support</italic> The interaction of inadequacy/cynicism and parental support was significant (<italic>B</italic> = − 0.20, crSE = 0.10, <italic>p</italic> = 0.048), with both parental support (<italic>B</italic> = 1.06, crSE = 0.39, <italic>p</italic> = 0.007) and inadequacy/cynicism (<italic>B</italic> = 0.56, crSE = 0.32, <italic>p</italic> = 0.087) predicting larger sAA values (appendix Table 4). The moderating effect is shown in Fig. ##FIG##1##2## and indicates that higher levels of parental support predicted overall higher levels of sAA related to low or average levels of inadequacy/cynicism. The effect of parental support changes the nature of the interplay of psychological stress and sAA. Students who experienced high parental support exhibited a decline of sAA related to an increase in inadequacy/cynicism whereas for students who experienced lower parental support this relationship shows a positive slope. For students who exhibit very high levels of inadequacy/cynicism the relationship with parental support diminishes in general.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par40\">The present study was designed to investigate how a) parental, b) teacher and c) peer support moderate the relationships between I) self-reported psychological stress and school burnout, namely II) exhaustion, and III) inadequacy/cynicism with biophysiological markers of stress and arousal including A) cortisol, B) alpha-amylase, C) oxidative stress, and D) telomere length. The aim of the study was to investigate protective factors of student’s immediate social environment that could serve as resources to overcome stressors, as theoretical frameworks, including the buffering hypotheses^{##REF##3901065##12##} and the COR^{##REF##2648906##13##} suggest that perceived social support mitigates feelings of stress and that social buffering reduces the activity of neurobiological systems associated with stress^{##REF##26230646##60##}.</p>", "<p id=\"Par41\">According to hypothesis I, we expected a negative link between the social support variables and self-reported stress, exhaustion, and inadequacy/cynicism among students. This hypothesis was confirmed as students who perceived their parents, teachers, and peers as supportive reported lower levels of perceived psychological stress and inadequacy/cynicism. In addition, teacher support as well as peer support was linked to lower exhaustion among students. This finding is confirmed by various empirical studies that have investigated the protective role of parents^{##REF##26257685##62##,##REF##30356633##63##}, teachers^{##REF##12778983##29##,##UREF##25##73##,##UREF##26##74##}, and peers^{##UREF##26##74##,##REF##36518954##77##} when it comes to student’s perceived stress.</p>", "<p id=\"Par42\">Following an exploratory approach, this study found that parental support functioned as buffer within the relationship between perceived psychological stress and sAA. In detail, it was found that the more time students spent with their parents, e.g., playing board games, having dinner together and doing the household, the higher their sAA was when their psychological stress was low or at an average level. In this case, sAA may reflect positive emotional arousal as students actively engage in activities together with their parents on a regular basis. The intermediate model in appendix Table 3 also indicated that as psychological stress increases among students, sAA levels also increase, reflecting heightened negative emotional arousal linked to psychological stress. As Adam et al.^{##REF##21840370##37##} pointed out, sAA serves as a metric for assessing overall arousal levels, which can be triggered by either positive or negative emotions. Therefore, sAA is not exclusively associated with negative emotions or stress.</p>", "<p id=\"Par43\">Interestingly, as psychological stress escalates among students, those who regularly spend time with their parents demonstrate minimal fluctuations in their sAA levels, whereas students who have limited interaction with their parents experience a sharp increase in sAA levels. Hence, common activities within the child-parent relationship buffer against increased stress related to sAA.</p>", "<p id=\"Par44\">Parental support also acts as a protective buffer when the level of inadequacy and cynicism towards school rises in relation to sAA. Students who report an increasing sense of inadequacy at school and view school cynically tend to experience a decrease in sAA levels if they regularly spend time with their parents. Conversely, students who have limited interaction with their parents show a notable rise in sAA levels when cynicism and feelings of inadequacy at school increase. Again, parents function as buffer when it comes to students experiencing inadequacy and cynicism towards school as sAA levels are decreasing.</p>", "<p id=\"Par45\">This is the first study to investigate parental support, measured by the time students spend with their parents, as moderator in relation to sAA and increasing levels of stress as well as inadequacy and cynicism towards school. The findings indicate that the time spent together with their parents protects students from experiencing high physiological arousal related to increasing stress levels and feelings of inadequacy and cynicism towards school. Hence, to ensure a healthy development of students, it is recommended for parents to make time for their children. This study highlights that the time spent in child-parent relationships can be an integral part of their daily life and routine, often involving ordinary and non-entertaining activities. Until now, research relying on self-report data has primarily connected the amount of time parents spend with their children to children’s well-being and behavioral issues but has not yet tested the moderation of parental-child time linked to stress^{##REF##37077856##66##–##UREF##22##68##}. However, there are various studies indicating that parental support plays an essential role for students’ stress, test anxiety, and whether students enjoy schools^{##REF##26257685##62##,##REF##30356633##63##,##UREF##35##90##}.</p>", "<p id=\"Par46\">Interestingly, no significant interaction effects with teacher support, peer support, self-reported variables and biophysiological markers was detected, which may possibly be due to the instruments used here, which surveyed peer support in a very general way. It is possible that support by close friends or peer network constructs could rather show a significant effect, as it has already been found in other studies^{##REF##21895364##75##,##REF##25919481##76##}. Future studies should therefore test support by friends and social networks as a possible buffer. Another plausible interpretation for the lack of statistically significant interaction terms concerning peer support could also be attributed to the fact that stressed students may have a higher tendency to seek advice from adult professionals in comparison to their peers^{##REF##28814325##91##} and the fear of social stigmatization and embarrassment may hold them back to address their need for help towards their peers^{##REF##31965309##92##}.</p>", "<p id=\"Par47\">In sum, the results of the current study indicate that social support is related differently to students’ biophysiological markers, which are related to stress and arousal. Although theoretical models, such as the buffering hypothesis and COR propose that social support functions as resource in the face of stress, the current results suggest a more nuanced picture of social support perceived by students in relation to different stress contexts and biophysiological processes. Certainly, the connection between the variables of interest explored within intricate moderation models is complex. The variety of biophysiological stress and arousal markers as well as investigating different self-reported stress variables and sources of support allows us to draw a complex and complementary picture of how support relates to students’ self-reported stress and biophysiological markers.</p>", "<p id=\"Par48\">In the quest to derive potential implications for stress prevention and intervention, it becomes imperative to accurately pinpoint the specific form of perceived stress experienced by individual students. This precision is essential for tailoring targeted support from both teachers and parents effectively.</p>", "<title>Strength, limitations, future directions</title>", "<p id=\"Par49\">The current study is one of the few within the educational context that (a) combined several self-reported stress variables with a variety of biophysiological data, including hormones, enzymes, cell damage, and DNA of a healthy student cohort in Germany, (b) testing social support from parents, teachers and peers related to self-reported stress and biophysiological data.</p>", "<p id=\"Par50\">Like any research endeavor, it is important to take into account certain constraints when interpreting the findings. Due to the exploratory design and small sample size, which impose certain limitations on statistical power, the results must be interpreted with caution. Replication studies with a larger sample are necessary to verify or falsify these first steps of basic research. The usage of manifest variables, though facilitating analysis, reduces variability. The alternative, latent structuring equation modeling, was not feasible due to the relatively small sample size. Furthermore, the relatively low reliability of the teacher support scale needs to be considered. However, following Kopp and Lois^{##UREF##36##93##}, Cronbach’s alpha values above 0.50 are acceptable. Finally, the cross-sectional design of the study does not allow to detect any causal ordering of the variables. Accordingly, studies with a longitudinal design, which also measure biophysiological markers at several measurement points and follow students over a longer period to test potential changes in students’ subjective and biophysiological arousal, as well as changes in their perceived social support are necessary to detect potential causal relationships as well as developmental processes from childhood to adolescence. Overall, however, the present study lays an important foundation for understanding the role of social support in the interplay of different biophysiological markers and subjective stress variables in healthy secondary school students.</p>" ]

[]

[ "<p id=\"Par1\">During adolescence, students increasingly report suffering from stress and school burnout, which poses a risk to students’ healthy development. However, social support may counteract perceived stress according to the Buffering Hypothesis and the Conservation of Resources Theory. In search of factors that would support healthy student development, studies have primarily focused on self-report data and neglected biophysiological processes. Addressing this research desideratum, this study examined whether perceived social support buffers the interplay of self-reported stress considering biophysiological markers (i.e., cortisol, alpha-amylase, oxidative stress, and telomere length). 83 secondary school students (<italic>M</italic>_{<italic>age</italic>} = 13.72, <italic>SD</italic> = 0.67; 48% girls) from Germany participated in a questionnaire study and biophysiological testing. Moderation analyses in R revealed that support from parents moderated the relationships between psychological stress as well as cynicism and inadequacy at school linked to alpha-amylase.</p>", "<title>Subject terms</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>" ]

[ "<title>Measures</title>", "<title>Self-reported stress measures (predictors)</title>", "<p id=\"Par23\"><italic>Psychological Stress.</italic> This variable is a subscale of the Perceived Stress Scale PSS^{##REF##27216151##80##}, capturing the subjective stress level of the responder experienced during the last month. It consists of six items such as ‘How often did you feel nervous or “stressed” during the last month?’ on a five-point Likert scale ranging from 1 (‘never’) to 5 (‘very often’) with α = 0.87.</p>", "<p id=\"Par24\"><italic>School burnout inventory</italic> The School Burnout Inventory SBI^{##REF##18257974##21##} is a self-report questionnaire that inquires for symptoms of burnout in students, and as such for signs of adverse psychological consequences of long-term stress. The SBI measures burnout as a continuous variable and does not serve as diagnostic tool, e.g. by providing cut-offs for individuals at risk. The SBI consists of 9 items which are grouped into the three subscales ‘Cynicism’ (3 Items, e.g. ‘I constantly ask myself if my schoolwork is good for anything at all’), ‘Exhaustion’ (4 Items, e.g. ‘I feel overburdened by my schoolwork’) and ‘Inadequacy’ (2 Items, e.g. ‘I often feel like my schoolwork isn’t good enough’). Participants are asked to rate their agreement with these statements on a six-point Likert Scale ranging from 1 (‘Do not agree at all’) to 6 (‘Agree completely’). Following the literature^{##UREF##28##81##}, we used a two factor approach consisting of the factor 1. exhaustion α = 0.82 and 2., a combined factor of inadequacy and cynicism α = 0.73, called ‘inadequacy/cynicism’ this study.</p>", "<title>Biophysiological stress markers (outcomes)</title>", "<p id=\"Par25\">Salivary Alpha-Amylase and Salivary Cortisol were analyzed from morning and noon samples of participants. Oxidative stress was analyzed from urine provided at noon. Telomeres were analyzed from saliva provided at noon. For further description on the biophysiological measures and processing, see appendix on “Analyzes of biophysiological stress markers”.</p>", "<title>Self-reported social support variables (moderators)</title>", "<p id=\"Par26\"><italic>Parental Support.</italic> We used the Social Capital Instrument based on works of the Max Planck institute for Educational Research and the PISA survey instrument, described in Kunter et al.^{##UREF##29##82##}. This questionnaire consists of five activities parents engage in together with their children such as playing (i.e., board games), doing household chores, or having dinner together and asks the participant to rate how often these take place on a four-point Likert scale from 1 (‘never’) to 4 (‘very often’) with <italic>α</italic> = 0.80.</p>", "<p id=\"Par27\"><italic>Teacher and peer support</italic> The ‘Teacher Classmate Support Scale’ was used^{##REF##22207777##83##} and includes the Teacher Support subscale (four statements, incl. ‘Our teachers treat us fairly’) with <italic>α</italic> = 0.57. The Peer Support subscale (four statements, incl. ‘Most of my fellow students are friendly and ready to help’) with α = 0.78. Both subscales are arranged on a five-point Likert scale from 1 (‘don’t agree at all’) to 5 (‘agree completely’).</p>", "<title>Control variables</title>", "<p id=\"Par28\">\n<italic>Gender</italic> The biological sex was of interest in this study and was coded as 0 = female (<italic>n</italic> = 40) and 1 = male (<italic>n</italic> = 43).</p>", "<p id=\"Par29\"><italic>School type</italic> School type was divided into two possible answers: 0 = lower-track school (<italic>n</italic> = 41) and 1 = higher-track school (<italic>n</italic> = 42). While higher-track schools provide students with a school leaving exam after 12 years, enabling them to pursue university education, lower-track schools present different school leaving exams and typically equip students for vocational paths or applied studies.</p>", "<p id=\"Par30\"><italic>Time of awakening &amp; time since awakening.</italic> Time of awakening and time since awakening were included in the models for sAA and cortisol to account for their diurnal rhythm over the measurement day. The time variables were included as hours, with time since awakening equaling 0 for the morning measurement.</p>", "<title>Statistical analyses</title>", "<p id=\"Par31\">Statistical analyses were performed using R Statistical Software v4.2.3^{##UREF##30##84##}. All biomarkers were found to exhibit positive skewness and were transformed by natural logarithm to normalize their distributions. Descriptive statistics for the analyzed variables were calculated. To investigate the pairwise relationships of the variables of interest, bivariate Pearson correlations were calculated, along with significance tests for the obtained correlations.</p>", "<p id=\"Par32\">To investigate the moderating effects of the support variables on the relationships between the stress variables and the biomarker levels, moderation analyses were performed for all combinations of perceived stress and support variables for each biomarker type. Analyses were performed using linear models, with gender and study track included as covariates in all models. Models were built stepwise including: (a) covariates, (b) covariates and moderating variables and (c) covariates, moderating variables and their interaction. To investigate model fits, <italic>R</italic>², Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values were calculated.</p>", "<p id=\"Par33\">Since the students provided repeated measurements of cortisol and sAA during the measurement day, this necessitated accounting for within-subject effects for these analyses. First, due to both cortisol and sAA levels following known diurnal rhythms^{##REF##17418498##36##,##UREF##31##85##}, the time of awakening and time since awakening were included as covariates. Second, the inclusion of repeated observations from the subjects violates the assumption of independence of observations, leading to biased standard error estimates. To account for this, the standard errors of coefficient estimates were evaluated using cluster robust standard errors using the sandwich^{##UREF##32##86##,##UREF##33##87##} and lmtest^{##UREF##34##88##} packages. The cluster robust standard errors multiply residuals within each cluster, inflating the standard error estimates to the degree that the clustering is informative^{##REF##27149401##89##}.</p>", "<p id=\"Par34\">Variables included in the analysis were checked for missing and outlier values. The students age was missing in 21 out of 83 cases, which is why it was not included as a covariate. One observation was excluded from sAA analysis due to undetectable values (&lt; 1 μkatal/l) and two more due to improbably high values (&gt; 10,000 μkatal/l). Two missing values were found in cortisol measurements, three in telomere lengths and one each in the time of awakening and time since awakening covariates. Eight instances of incomplete data were found in questionnaire items. Missing values in the biomarkers and covariates were handled by listwise deletion, while questionnaire scales were calculated using available data, due to less than 2.5% of the data missing in each item. Separate data sets were formed for each biomarker type to retain maximum sample size for moderation analyses.</p>", "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51802-4.</p>", "<title>Acknowledgements</title>", "<p>We would like to thank the participating schools and students for supporting this study. We also would like to express our gratitude to Sirine Schreier and Lisa Yeung for helping with the data collection. We also thank Lou Maas and Anna-Lisa Jõgi for her professional advice.</p>", "<title>Author contributions</title>", "<p>F.H. acquired funding for the study, collected the data, came up with the research question and wrote the theoretical part of the ms and discussion. J.L. did the statistical data analyses and wrote the methods section. MH contributed to the statistical analyses. H.J.G. and D.R. contributed with their expertise and edited the manuscript. G.H. was in charge of the telomere analyses.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>", "<title>Data availability</title>", "<p>Data will be made available on serious request. Please contact the corresponding author of this study.</p>", "<title>Competing interests</title>", "<p id=\"Par51\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Interaction of Perceived Psychological Stress and Parental Support on sAA levels. Estimated simple slopes are plotted at mean and 1 SD above and below mean parental support levels. The level of sAA is expressed in logarithmized units.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Interaction of Cynicism and Inadequacy with Parental Support on sAA levels. Estimated simple slopes are plotted at mean and 1 SD above and below mean parental support levels. The level of sAA is expressed in logarithmized units.</p></caption></fig>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Chagas disease is caused by a flagellate parasite, <italic>Trypanosoma cruzi (T. cruzi)</italic>, first described in 1909 in a patient by Carlos Chagas. The World Health Organization estimates that approximately 7 million people are infected worldwide, a serious health problem in Latin America and nonendemic countries in North America (Mexico, Canada, and the United States), Europe (Spain), and the Western Pacific Region (Australia and Japan)^{##REF##28673423##1##}.</p>", "<p id=\"Par3\">The course of Chagas disease comprises two phases, the acute phase that lasts 2–4 months, followed by a chronic phase that can be categorized into indeterminate, cardiac, and/or digestive stages with different clinical manifestations^{##REF##11871482##2##}. Only 20–30% of patients develop symptoms after years to decades of clinical latency (indeterminate stage), showing no detectable parasitemia in microscopic evaluations at this stage. Myocardial damage in Chagas disease is a progressive process that can be classified according to the degree of myocardial involvement^{##REF##20399979##3##}.</p>", "<p id=\"Par4\">MicroRNAs (miRNAs) are a class of small noncoding RNAs (20–25 nucleotides) involved in gene regulation and expression at the posttranscriptional level produced by cells that can be found in extracellular vesicles and blood^{##REF##23036329##4##,##REF##33351798##5##}. miRNA transcription depends on RNA polimerase II, which generates a primary transcript (pri-miRNA) with hairpin structure. This pri-miRNA is processed by the Drosha complex to form the pre-miRNA that will be transported to the cytoplasm through the exportin-5. Then, it will be recognized and cut by Dicer and RNA-induced silencing complex (RISC) proteins to create the mature miRNA^{##REF##15145345##6##}. miRNAs are key for a set of molecular signaling pathways and cellular pathophysiological effects of different but interrelated disorders, such as cardiovascular diseases, cardiac hypertrophy, coronary heart disease, myocardial infarction^{##REF##25013816##7##–##REF##18723672##11##}, infections, type 1 diabetes, inflammatory, infectious and autoimmune processes, and cardiovascular risk factors^{##REF##28261201##12##–##REF##27693002##15##}. An advantage is that changes in miRNA levels in body fluids occur earlier than conventional biomarkers^{##REF##24533657##16##}. This makes them promising potential candidates as prognostic biomarkers of disease.</p>", "<p id=\"Par5\">miRNAs may play a major role in the control of gene expression in key pathological processes in chronic Chagas cardiomyopathy (CC)^{##REF##33351798##5##}. However, more studies are needed to understand the role of miRNAs in CC and there are only a few studies on miRNAs as biomarkers in this disease. These studies used quantitative reverse transcription PCR (RT‒qPCR) for specific miRNAs and suggested a role in the pathogenesis, diagnosis, and prognosis of Chagas disease^{##REF##29559958##17##,##UREF##1##18##}. Circulating miR-208a, a heart-specific miRNA playing a critical role in heart failure, was increased during the chronic indeterminate phase when compared to chronic cardiac clinical forms in Chagas disease individuals^{##REF##29559958##17##}. Additionally, circulating miR-19a-3p, miR-21-5p, and miR-29b-3p, previously associated with heart failure, cardiac fibrosis, and hypertrophy, were increased in chronic cardiac Chagas disease and correlated with cardiac injury^{##UREF##1##18##}. In addition, other authors described the dysregulation of different miRNAs in the cardiac tissue of patients with chronic Chagas cardiomyopathy^{##REF##24910366##19##}.</p>", "<p id=\"Par6\">Considering the urgent need of biomarkers in CC, and the absence of studies addressing the role of miRNAs in CC, in the present study, we aimed for the first time to identify new circulating miRNAs using an exploratory small RNA sequencing (Small RNA-Seq) approach and posterior RT-qPCRs in the plasma of chagasic patients at various stages of the disease. Therefore, these miRNAs could be used as biomarkers of chronic Chagas cardiomyopathy and likely involved in its development.</p>" ]

[ "<title>Methods</title>", "<title>Ethics statement</title>", "<p id=\"Par33\">This study was approved by the Bioethics Committee from the Faculty of Medical Sciences, National University of Rosario, Argentina (Resolution N° 5093/2018); the Ethical Committees of Ramón y Cajal University Hospital and <italic>Fundación Jimenez Diaz</italic> in Madrid (Spain, References FUN-BEN-2007-01 and 10/2016, respectively); and the Ethical Committee of Vall d’Hebrón University Hospital in Barcelona (Spain, Reference D-RTF080). All patients signed informed consent forms. Data on human subjects were analyzed anonymously, and clinical investigations were conducted according to the Declaration of Helsinki.</p>", "<title>Blood samples from patients</title>", "<p id=\"Par34\">This work corresponds to an observational, cross-sectional study, where the patients and healthy volunteers were recruited from 2011 to 2017 at the Chagas disease ambulatory section from the <italic>Hospital Provincial del Centenario</italic> (HPC, Rosario, Argentina), in 2018 at the <italic>Fundación Jiménez Díaz</italic> (FJD, Madrid, Spain), and in 2020 at the Vall d’Hebrón University Hospital (HVH, Barcelona, Spain). Twenty-eight chagasic patients from Spanish hospitals were from Bolivia, 1 from Brazil, and 1 from Paraguay. Exclusion criteria comprised patients with previous treatment with Benznidazole or Nifurtimox. Healthy control subjects were seronegative for the <italic>T. cruzi</italic>-specific test. The diagnosis was based on at least two positive serological tests (either by ELISA, hemagglutination, or immunofluorescence), together with clinical symptoms, chest X-ray, 12-lead resting electrocardiogram (ECG), and/or echocardiography. Routine laboratory studies were also included.</p>", "<p id=\"Par35\">A total of 66 subjects were included in the study: healthy controls (HC, n = 26) from endemic areas, indeterminate Chagas disease (ICD, n = 19), and mild and moderate Chagas cardiomyopathy (MCC, n = 21). Table ##SUPPL##4##S1## compiles all subjects included in the study classified by the hospital in which they were recruited. The criteria for the aggrupation of chagasic patients from HPC were as follows: ICD, symptomless, normal ECG and chest X-ray; MCC, presented no congestive heart failure with ECG showing incomplete or complete right bundle branch block, ventricular arrhythmia or normal heart size or only mild cardiomegaly (chest X-ray cardiothoracic ratio &lt; 0.55). For patients from FJD: ICD, without pathologic alterations; and MCC, with pathologic alterations in ECG and/or echocardiogram and/or complementary tests compatible with CC. For patients from HVH: ICD, Kuschnir classification 0 and MCC, Kuschnir classification I. Individual information of the patients is shown in Supporting Data ##SUPPL##0##S1##.</p>", "<title>Circulating miRNA extraction</title>", "<p id=\"Par36\">Blood samples from patients and healthy volunteers were collected. Plasma from blood samples of HPC and HVH was obtained from EDTA-treated blood. Serum was obtained from blood samples from FJD patients. All the samples were immediately stored at − 80 °C until miRNA extraction. To avoid impacts in the circulating miRNAs profile, as other studies have demonstrated^{##REF##28123561##54##,##REF##23745127##55##}, hemolysis processes were checked visually according to the hemolysis reference palette^{##UREF##4##56##}, and all the samples used in the study were free of hemolysis. In samples from HPC and FJD, miRNAs were extracted using a QIAamp miRNeasy Serum/plasma kit (Qiagen, Germantown, USA), and samples from HVH were extracted using a miRNeasy Serum/Plasma Advance Kit (Qiagen). A spike-in mix (Qiagen, RNA Spike-In Kit containing sp2, sp4, and sp5) was added as a control for sample quality and PCR efficiency. The procedures were carried out following the directions of the manufacturer. Small RNA-Seq was performed using samples from HPC, and two or three extractions of each sample were performed to obtain at least 25 ng per sample. Then, the different extractions of each sample were gathered together. The amount of RNA was quantified using RiboGreen. Pools were made for each group (HC, ICD, and MCC), and each group was composed of 5 samples. The pools were concentrated to obtain at least 25 ng in a final volume of 6 µl, which passed the quality assessment in the bioanalyzer and were sent for sequencing to the <italic>Parque Científico de Madrid</italic> (Madrid, Spain).</p>", "<title>Small RNA-Seq analysis</title>", "<p id=\"Par37\">The total RNA fraction corresponding to miRNAs (15-30 bases) was purified by size exclusion in polyacrylamide gels and the miRNeasy Micro Kit (Qiagen Cat. No. 217084). Subsequently, the sequencing libraries were prepared with the TruSeq kit (Illumina) for Small RNA-Seq analysis following the specific protocols of the Illumina technology (TruSeq) without modifications by the Genomics facility of the <italic>Parque Científico de Madrid</italic> (Madrid, Spain), and readings of 14-50 bases in length were generated in a single replicate using MiSeq technology (Illumina). Differential expression analysis and miRNA <italic>de novo</italic> finding were performed using the DEseq2^{##REF##25516281##57##} and miRDeep2^{##REF##21911355##58##} packages, respectively.</p>", "<title>miRNA analysis by RT‒qPCR</title>", "<p id=\"Par38\">RT‒qPCR analysis was performed at the <italic>Parque Científico de Madrid</italic> (Madrid, Spain). cDNA synthesis was performed with the miRCURY LNA RT Kit (Qiagen Cat. No. 339340) according to the manufacturer’s instructions. Then, 2 µl of purified total miRNAs (10 ng) from plasma or serum was used as input RNA and mixed with 0.5 µL synthetic RNA spike-in (sp6) before reverse transcription. The obtained cDNAs were diluted 1/40 in RNAse-free water before qPCR amplification. Real-time PCR amplification was performed using the miRCURY SYBR Green PCR Kit (Qiagen Cat. No. 339347) in the presence of PCR Locked Nucleic Acid (LNA) primers specific for spike-in sp2, sp4, sp5, and sp6, miR-103a-3p, miR-Contig-5468, miR-Contig-1519, miR-Contig-2269, miR-Contig-3244, miR-148a-3p, miR-224-5p and miR-181a-5p (Qiagen). Three replicates were run for each combination of genes and samples. To obtain Cp values, we used LightCycler® 480 Software following the 2nd derivative max method. The expression levels of target miRNAs were normalized to the expression of endogenous miR-103a-3p. The results refer to HC samples. Relative changes and statistical values of miRNA expression levels were calculated by the ΔΔC_t method using LightCycler® 480 Software without correction for assay efficiency. The results were expressed as log₁₀RQ (RQ = 2^–ΔΔCt).</p>", "<title>Statistical analysis of the small RNA-Seq and the RT‒qPCR</title>", "<p id=\"Par39\">The main limitation of the present study is the lack of technical replicates in small RNA-Seq; therefore, Basemean (normalized reads) was chosen as an additional filter to the adjusted p value as a measure of miRNA abundance. miRNAs with less than 100 normalized reads in the healthy controls and the patient samples were discarded for further analysis. All PCAs were performed using the R programming language (version 4.2.2). Bar plots and statistical significance were evaluated using GraphPad Prism (Version 8.0). After the Shapiro‒Wilk normality test, two-way ANOVA tests were applied as indicated in the figure legends (*p&lt;0.05, **p&lt;0.01, ***p&lt;0.001, ****p&lt;0.0001).</p>", "<title>Pathway analysis of the relevant miRNA targets</title>", "<p id=\"Par40\">Target prediction of the most significant miRNAs in our study (miR-148a-3p, miR-224-5p, and miR-Contig-1519) was performed with the miRDB web tool^{##REF##31504780##59##,##REF##30670076##60##}. Targets with a score equal to or higher than 90 were used for enrichment pathway analysis in the EnrichR web tool using the BioPlanet and Reactome databases^{##REF##27141961##22##,##REF##33780170##23##}.</p>" ]

[ "<title>Results</title>", "<title>Small RNA-Seq alignment and analysis</title>", "<p id=\"Par7\">To explore the circulating miRNA transcriptomic profile in chagasic patients, we performed exploratory small RNA-Seq of pools of miRNAs extracted from the plasma of healthy controls (HC), indeterminate Chagas disease (ICD), and mild and moderate Chagas cardiomyopathy (MCC) patients (n = 5 each) attending to the <italic>Hospital Provincial del Centernario</italic> (HPC, Rosario, Argentina). We aligned the reads to the human genome (<italic>H. sapiens</italic>, GRch38, version 25/03/2019) using Bowtie 2. The mean percent alignment of total reads aligned at least once to the human genome was 98.95% (Table ##SUPPL##4##S2##). Then, reads aligning to known miRNAs were determined using miRBase annotations (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.mirbase.org/ftp.shtml\">http://www.mirbase.org/ftp.shtml</ext-link>) and normalized (Supp. Data ##SUPPL##1##S2##).</p>", "<p id=\"Par8\">An initial analysis was performed to check whether we could find altered levels of miRNAs in the chagasic patients compared to the HCs. We performed a preliminary PCA study with normalized reads (Fig. ##SUPPL##4##S1##). PC components explained 100% of the variance of the data. As expected, ICD and MCC grouped separately from HC individuals, indicating that we would probably find candidate miRNAs for biomarkers.</p>", "<title>Identification of new miRNAs</title>", "<p id=\"Par9\">To identify new miRNAs in the small RNA-Seq, we used miRDeep2. We identified several potential new miRNAs (Table ##SUPPL##4##S3##, column 2). miRDeep2 considers the loop sequence and structure compatible with Dicer processing as well as the conservation of the seed sequence (among other stringent parameters) to predict sequences of potentially new miRNAs and structures.</p>", "<p id=\"Par10\">Potential new miRNAs identified in chagasic patients with at least 80% similarity were grouped into clusters, which are defined as potential precursors of miRNAs and/or mature miRNAs separated in the genome from other clusters by a minimum of 30 nucleotides^{##REF##18392026##20##} (Table ##SUPPL##4##S3##, column 3).</p>", "<p id=\"Par11\">Then, data were filtered according to star sequence, precursor, and loop structures, and only those with significant ranfold p-values were considered (Table ##SUPPL##4##S4##). These short sequences showed a total score and secondary structure consistent with valid mature miRNA sequences, suggesting that they could be considered potential new miRNAs. Moreover, using miRDeep2, we predicted the secondary structure of these 4 new miRNAs and validated them with the precursor structure (Fig. ##FIG##0##1##).</p>", "<p id=\"Par12\">Most canonical miRNAs are generated from long noncoding regions, and a miR gene can generate more than one mature miRNA able to target different genes (isomiRs). However, although less frequently, miRNAs can also be generated from coding regions^{##UREF##2##21##}. Three of the new miRNAs mapped to the following regions of the genome: miR-Contig-5468 to <italic>Homo sapiens</italic> CACTIN antisense RNA 1 (CACTIN-AS1), long noncoding RNA (from RefSeq NR_038865); miR-Contig-2269 to <italic>Homo sapiens</italic> SREK1 interacting protein 1 (SREK1IP1), mRNA (from RefSeq NM_173829); and miR-Contig-3244 to RNA, U2 small nuclear 29, pseudogene (from HGNC RNU2-29P), while miR-Contig-1519 mapped to a noncoding region.</p>", "<title>Validation by RT‒qPCR of the new circulating miRNAs</title>", "<p id=\"Par13\">To validate the presence of these newly predicted miRNAs in humans, we studied their expression in serum/plasma samples from patients from <italic>Fundación Jiménez Díaz</italic> (FJD, Madrid, Spain) and Vall d'Hebrón University Hospital (HVH, Barcelona, Spain). Only 2 out of 4 were confirmed: miR-Contig-1519 and miR-Contig-3244 were detected, while miR-Contig-2269 and miR-Contig-5468 were not detected by RT‒qPCR (Fig. ##FIG##1##2##A). Both miR-Contig-1519 and miR-Contig-3244 showed a marked decrease in chagasic asymptomatic and symptomatic patients of all the hospitals compared to healthy controls. Considering this result, we performed an analysis to study whether these new miRNAs could serve to discriminate patients with chronic Chagas disease from healthy individuals (Fig. ##FIG##1##2##B). The results showed that both ICD and MCC individuals grouped and separated from the HC subjects. Thus, all these results point to miR-Contig-1519 and miR-Contig-3244 as possible biomarkers of chronic Chagas disease, reducing their expression in patients.</p>", "<title>Levels of known circulating miRNAs of interest by RT‒qPCR</title>", "<p id=\"Par14\">After the analysis of new miRNAs, we also decided to perform a study of known miRNAs, with more than 100 normalized reads, searching for previous relationships with cardiovascular diseases in databases to complete our results. We decided to focus on some miRNAs that had been described as possible biomarkers of cardiomyopathy in other disease contexts but not in Chagas disease: miR-148a-3p, miR-181a-5p, and miR-224-5p.</p>", "<p id=\"Par15\">To investigate the potential of those circulating miRNAs as biomarkers of chronic Chagas disease, we performed RT‒qPCR in samples from patients of different Spanish hospitals (FJD and HVH), including HC, ICD, and MCC individuals (Fig. ##FIG##2##3##A). Interestingly, miR-148a-3p decreased significantly in both ICD and MCC subjects with respect to the HC. Otherwise, miR-244-5p showed a remarkable and significant increase in ICD and MCC. However, miR-181a-5p did not display any difference between the HC and ICD/MCC groups; hence, this miRNA has no potential as a biomarker. Furthermore, considering both the miR-148a-3p and miR-224-5p results, we performed an analysis to study whether these miRNAs could serve to discriminate patients with chronic Chagas disease from healthy individuals (Fig. ##FIG##2##3##B). The results displayed a clear difference between ICD and MCC patients grouped and separated from healthy individuals, indicating that these miRNAs could serve as discriminants for chronic Chagas disease patients.</p>", "<p id=\"Par16\">Considering these data and the previous resuts of the new circulating miRNAs (miR-Contig-1519 and miR-Contig-3244) that could also serve as biomarkers of Chagas disease we performed a principal component analysis (PCA) to study whether miR-148a-3p, miR-224-5p, miR-Contig-1519, and miR-Contig-3244 could be used together as a panel of biomarkers to discriminate chronic chagasic patients from healthy controls (Fig. ##FIG##3##4##). The results showed that both ICD and MCC individuals are different from HCs, although there were no differences between them, suggesting that these four miRNAs may serve to discriminate chronic Chagasic patients, independent of the presence or absence of symptoms.</p>", "<title>Target genes and pathways predicted for miR-Contig-1519, miR-Contig-3244, miR-148a-3p and miR-224-5p</title>", "<p id=\"Par17\">From the above results, we defined a potential signature defined by low miR-Contig-3244, miR-Contig-1519, and miR-148a-3p and high miR-224-5p levels in chronic Chagas disease and cardiomyopathy (ICD and MCC). However, to explore the possible value of these miRNAs in terms of their contribution to the pathology of chronic Chagas disease, we used bioinformatics tools to predict the possible target genes of these miRNAs and the corresponding pathways in which they could be involved. Using miRDB, we predicted the target genes for these miRNAs (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.mirdb.org\">http://www.mirdb.org</ext-link>) (Supporting Data ##SUPPL##2##S3##). We used the Target Search tool to determine the targets of the known miR-148a-3p and miR-224-5p that are present in the database of miRDB. For the new miRNAs, miR-Contig-1519 and miR-Contig-3244, we used the Custom Prediction tool that, according to the miRNA sequence, predicts the more likely targets. Then, we considered those targets with a score equal to or higher than 90 out of 100 and performed enrichment analysis using the EnrichR website (BioPlanet and Reactome databases).</p>", "<p id=\"Par18\">The EnrichR web tool allows enrichment analysis according to different databases to associate gene lists with specific diseases or pathways and returns an adjusted p value of the Fisher exact test after Benjamini‒Hochberg correction^{##REF##27141961##22##,##REF##33780170##23##}. We used the BioPlanet database since it integrates pathway annotations from available, manually curated sources with consistency and redundancy cross-evaluation^{##REF##31133849##24##} and the Reactome database, which provides a broad range of physiological and pathological biological processes in humans manually curated from the primary literature and peer-reviewed manuscripts^{##REF##33693880##25##}. The complete list of predicted significant pathways or biological processes likely dependent on these miRNAs of the signature is shown in Supporting Data ##SUPPL##3##S4##.</p>", "<p id=\"Par19\">The BioPlanet database results showed that the principal targets of these four miRNAs belong to different pathways, but most of them were related to transforming growth factor (TGF)-β signaling and the transcriptional activity of the downstream heterotrimer suppressor of mothers against decapentaplegic (SMAD)2/3-SMAD4 (Fig. ##FIG##4##5##A). Additionally, some of the targets were part of ERBB signaling and T-cell signal transduction. Considering the Reactome database results (Fig. ##FIG##4##5##B), signaling of TGF-β members and receptors were the most significant biological processes. The forkhead box O (FOXO)-mediated transcription was the third most significant, and we also detected a remarkable regulation of transcriptional pathways such as those related to RNA polymerase II. Finally, these four miRNAs also regulated clathrin-mediated endocytosis, one of the ways for the parasite to enter host cells, and signaling by the serine/threonine-protein kinase B-Raf (BRAF) and the rapidly accelerated fibrosarcoma (RAF)1.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par20\">Previous research about the role of specific miRNAs in <italic>T. cruzi</italic> infection have mainly used RT-qPCR analysis of blood or cardiac tissue. In our study we have performed for the first time an exploratory small RNA-Seq analysis in the plasma of chagasic patients with different degrees of cardiac pathology, and we identified and validated by RT‒qPCR new circulating miRNAs and a miRNA signature as a potential biomarker of chronic Chagas disease. This signature is characterized by low levels of miR-Contig-1519, miR-Contig-3244, and miR-148a-3p and high levels of miR-224-5p.</p>", "<p id=\"Par21\">Of the four novel circulating miRNAs identified, we were able to detect miR-Contig-1519 and miR-Contig-3244, and both levels significantly decreased in all the chagasic cohorts analyzed. In the case of miR-Contig-2269 and miR-Contig-5468, either technical problems involving primer design hampered their detection or because they may be short mRNAs lacking miRNA activity. Further studies are needed to probe if they are real miRNAs and/or see their effect during the <italic>T. cruzi</italic> infection. Considering miR-Contig-1519 and miR-Contig-3244, we confirmed their use to discriminate healthy individuals from chronic chagasic subjects, independently if they are indeterminate or patients with cardiomyopathy. Therefore, this result suggests a role of these two new miRNAs in humans that is not related to the progression of the disease but to the pathological response associated with <italic>T. cruzi</italic>, that should be further elucidated in posterior research considering their targets and the affected biological pathways to provide mechanistic insights into their functions.</p>", "<p id=\"Par22\">To complete our results and establish a more powerful signature of chronic chagasic patients, we also analyzed three known miRNAs that had been described for cardiomyopathies of other etiology but not for Chagas disease: miR-148a-3p, miR-181a-5p, and miR-224-5p.</p>", "<p id=\"Par23\">miR-148a-3p is implicated in immunopathologic conditions and could be a potential biomarker for different cardiac pathologies. According to some authors miR-148a-3p is a novel repressor of <italic>IKBKB</italic>, which encodes the inhibitor of nuclear factor kappa B (IκB) kinase β, that represses the nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) signalling pathway that plays a key role in the inflammatory cascade^{##REF##25630970##26##}. Also, overexpression of miR-148a-3p inhibited inflammatory factors and functional injury in vascular endothelial cells^{##UREF##3##27##}. Therefore, according to our data, a decrease in miR-148a-3p levels in chagasic patients could be related to an increase in endothelial and cardiac inflammation.</p>", "<p id=\"Par24\">Moreover, miR-148a-3p affects macrophage polarization and cytokine production: it regulates the activation and polarization of mouse macrophages targeting the phosphatase and tensin homolog (PTEN) through the phosphatidylinositol 3-kinase (PI3K) and protein kinase B (AKT) pathway in response to <italic>Schistosoma japonicum</italic> infection^{##REF##31726056##28##}. Indeed, macrophage polarization is a key in the immune response against of <italic>T. cruzi</italic> infection^{##REF##13679306##29##}. Also, this miRNA is a novel downstream molecule of Notch signalling, promoting the differentiation of monocytes into macrophages by the presence of granulocyte macrophage colony-stimulating factor (GM-CSF). Specifically, it enhances M1 macrophage (activated by the classic pathway) differentiation, inhibits M2 macrophage polarization (activated by the alternative pathway) and increases the ability to engulf and kill bacteria, mediated by excessive production of reactive oxygen species (ROS) through the PTEN/AKT pathway^{##REF##29085372##30##}. Therefore, the reduction in miR-148a-3p in some chronic chagasic patients could inhibit M1 macrophage polarization and ROS production, both related to the elimination of the parasite and its persistence in immune cells.</p>", "<p id=\"Par25\">We did not detect significant differences in the levels of miR-181a-5p between any of the groups, even though this miRNA is involved in cardiomyocyte apoptosis, a general problem of several cardiomyopathies^{##REF##31353329##31##}.</p>", "<p id=\"Par26\">We found increased levels of miR-224-5p in ICD and MCC patients compared to the HC group. According to previous studies, this miRNA is a potential target molecule for treating and diagnosing atherosclerosis^{##REF##33974917##32##}. Additionally, it is increased in heart failure^{##REF##33969020##33##}, coronary artery disease^{##REF##36980904##34##}, and circulating extracellular vesicles of patients with reduced coronary flow reserve, which is related to endothelial dysfunction^{##REF##35850658##35##}. The upregulation of this miRNA in chronic chagasic patients, even in the absence of cardiac symptoms, is a new revelation that should be studied in the future to understand its specific role in the progression of Chagas disease.</p>", "<p id=\"Par27\">Enrichment pathway analysis considering miR-Contig-3244, miR-Contig-1519, miR-148a-3p, and miR-224-5p targets was performed through the EnrichR webtool using the BioPlanet and Reactome databases. This analysis predicted that most of the targets are related to TGF-β signaling, including the transcriptional activity of the heterotrimer SMAD2/3-SMAD4. After their phosphorylation by TGF-β, these proteins form a heterotrimer that translocates to the nucleus to mediate intracellular TGF-β signal transduction^{##REF##9311995##36##}. In Chagas disease, TGF-β is involved the progression of the CC onset, promoting the heart cell invasion and intracellular replication by <italic>T. cruzi</italic>, host immune and the inflammation response, and posterior cardiac fibrosis. In fact, inhibitors of TGF-β signaling revert these effects and improve cardiac electric parameters in infected mice, although more studies in infected human cells or humanized animal models are needed to clarify its potential as therapeutic approach. Additionally, Chagas disease patients with higher TGF-β in serum display a worse clinical outcome suggesting a predictive value as a surrogate biomarker^{##REF##35186778##37##–##REF##36530434##39##}. Our results support these ideas, and further studies are necessary to understand the specific role and regulation that these four miRNAs may exert on TGF-β signaling and their implication as possible biomarkers and/or therapeutic approaches for Chagas disease.</p>", "<p id=\"Par28\">Another biological process regulated by these miRNAs was T-cell signal transduction. T cells are key for the immune response against the parasite. CD8+ T cells take part in the elimination of the parasite, although some evidence suggests that they are also involved in some of the clinical manifestations of Chagas disease, such as tissue damage and inflammatory processes. The balance between CD4+ Th1 and Th2 cells is also important during infection. Th1 cytokines contribute to the control and elimination of the parasite but produce an enhanced immune response, while Th2 cytokines are implicated in protective responses, although they allow host and parasite cell survival. However, some of the authors suggest that more research about the specific parasite targets of T cell memory response may contribute to the conceptualization and development of prophylactic or therapeutic vaccines^{##REF##34267750##40##–##REF##32925918##43##}. Therefore, studies focusing on these specific types of cells could help to discover the role of these four miRNAs in the dilemma of T-cell implication in Chagas disease.</p>", "<p id=\"Par29\">Additionally, our miRNAs regulate targets linked to clathrin-mediated endocytosis and RAF1/BRAF signaling. Clathrin-mediated endocytosis is one of the main ways of entry of <italic>T. cruzi</italic> into the host cell from the initial stages of infection until the formation of the parasitophorous vacuole, and its inhibition drastically reduces the internalization of trypomastigotes in phagocytic and epithelial cells^{##REF##31202818##44##}. Therefore, a critical change in this pathway may alter all the endocytic processes of the parasite and its posterior intracellular replication, although more studies with different <italic>T. cruzi</italic> strains and other cellular types that are infected by the parasite could help to confirm the relevance of the clathrin-mediated endocytosis in the infection process.</p>", "<p id=\"Par30\">Regarding RAF1/BRAF signaling, both proteins are upstream kinases and activators of the mitogen-activated protein kinase (MAPK) cascade, which contains the mitogen-activated protein kinase kinase (MEK) and their targets, the extracellular signal-regulated kinase (ERK) family. Although there are not specific studies focused on RAF1 or BRAF proteins in <italic>T. cruzi</italic> infections, some. Some researchers studied the MAPK cascade activation and role in Chagas disease MEK/ERK pathway increase in nervous system models by the interaction of the host cells with surface molecules of <italic>T. cruzi</italic> as members of the multigene family of trans-sialidases^{##REF##11726780##45##,##REF##32892338##46##}, while the inhibition of ERK1/2 phosphorylation produced a significant decrease in invasion and infection by this parasite in epithelial and cardiac muscle cells^{##REF##36897926##47##} and in cultured human umbilical vein endothelial and vascular smooth muscle cells^{##REF##15322023##48##}. Therefore, the regulation of targets of this pathway by these miRNAs may drastically alter the infection process of <italic>T. cruzi</italic> and should be studied in the future to discover its real potential as a treatment for Chagas disease.</p>", "<p id=\"Par31\">Interestingly, our results complement previous observations on miRNAs in different contexts of <italic>T. cruzi</italic> infection by other authors. For instance, studies in patients pointed to miR-146a as a biomarker of the indeterminate phase of Chagas disease^{##REF##34289913##49##}, and miRNA-155 deficiency exacerbated <italic>T. cruzi</italic> infection in mice, suggesting that miR-155 is an important immune regulatory molecule critical for the control of <italic>T. cruzi</italic> in the acute phase of the infection^{##REF##32312766##50##}. In addition, it has been reported that <italic>T. cruzi</italic> induces a differential miRNA profile in human placental explants that may be potential targets for the therapeutic control of congenital Chagas^{##REF##33240284##51##}. On the other hand, it has been reported that modulation of miR-145-5p and miR-146b-5p levels is linked to reduced parasite load in H9C2 <italic>T. cruzi</italic>-infected cardiomyoblasts, which points to a possible direct action of miRNAs in heart tissue^{##REF##35082354##52##}. Thus, all these reports highlight the importance of our results and previous findings by other groups about the role of miRNAs in Chagas disease.</p>", "<p id=\"Par32\">In summary, we have identified a signature of circulating known and new miRNAs as a potential biomarker and/or therapeutic target of the chronic phase of Chagas disease. Moreover, it is important to remember that miRNA expression could vary between individuals according to both transcriptional changes in gene expression and promoter hypermethylation, and post-transcriptional changes in miRNA processing mechanisms of regulation, as well as effects of exogenous (xenobiotics) or endogenous (hormones, cytokines) compounds^{##REF##27197967##53##}. We recognize the limitations of our study and results (sample size, mainly), which should be considered exploratory, and therefore, these miRNAs should be further explored in a larger cohort of individuals to validate their promising use as biomarkers, therapeutic targets, or clinical treatments. In addition, more studies including severe Chagas cardiomyopathy (SCC) patients could be useful to evaluate their prognostic value. We consider it necessary for Chagas disease since it is not possible to predict whether ICD and MCC patients will develop SCC.</p>" ]

[]

[ "<p id=\"Par1\">Chagas disease affects approximately 7 million people worldwide in Latin America and is a neglected tropical disease. Twenty to thirty percent of chronically infected patients develop chronic Chagas cardiomyopathy decades after acute infection. Identifying biomarkers of Chagas disease progression is necessary to develop better therapeutic and preventive strategies. Circulating microRNAs are increasingly reliable biomarkers of disease and therapeutic targets. To identify new circulating microRNAs for Chagas disease, we performed exploratory small RNA sequencing from the plasma of patients and performed de novo miRNA prediction, identifying potential new microRNAs. The levels of the new microRNAs temporarily named miR-Contig-1519 and miR-Contig-3244 and microRNAs that are biomarkers for nonchagasic cardiomyopathies, such as miR-148a-3p and miR-224-5p, were validated by quantitative reverse transcription. We found a specific circulating microRNA signature defined by low miR-Contig-3244, miR-Contig-1519, and miR-148a-3 levels but high miR-224-5p levels for patients with chronic Chagas disease. Finally, we predicted in silico that these altered circulating microRNAs could affect the expression of target genes involved in different cellular pathways and biological processes, which we will explore in the future.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51487-9.</p>", "<title>Acknowledgements</title>", "<p>We thank the personnel of the Genomics Service of <italic>Parque Científico de Madrid</italic> (Madrid, Spain) for their technical assistance.</p>", "<title>Author contributions</title>", "<p>M.F. and N.G. conceived the experiment(s), S.R.V., A.H-C., F.C-H., M.C.M. J.dM-S. and M.G-M. conducted the experiment(s), A.H-C. and F.C-H. analyzed the results. S.R.V, I.C., M.G, H.O.R-A., P.B-N., I.M., J.A.P-M., B. M-M., O.A.B. J.B, and A.R.P. recruited the samples. All authors reviewed the manuscript.</p>", "<title>Funding</title>", "<p>The funding was supported by Agencia Nacional e Promoción Científica y Tecnológica, PICT 2013-1892, Secretaría de Ciencia y Tecnología, Universidad Nacional de Rosario, 1MED410, Ministerio de Economía y competitividad and Fondo Europeo de Desarrollo Regional, SAF2016-75988-R (MINECO/FEDER), SAF2015-63868-R (MINECO/FEDER), Red de Investigación de Centros de Enfermedades Tropicales, RICET RD12/0018/0004, Consejería de Sanidad, Comunidad de Madrid, S-2010/BMD-2332, Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional, PGC2018-096132-B-I00.</p>", "<title>Data availability</title>", "<p>All raw sequencing data generated from human plasma in this study are accessible in the National Center for Biotechnology Information (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ncbi.nlm.nih.gov/\">https://www.ncbi.nlm.nih.gov/</ext-link>) under the BioProject PRJNA853048, with the following BioSample accessions: SAMN29358576, SAMN29358577, SAMN29358578, and SAMN29358579. Temporary submission ID: SUB11686132; release date: 2024-03-30, or after publication, whichever is first.</p>", "<title>Competing interests</title>", "<p id=\"Par41\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Predicted secondary structure of the hairpins corresponding to the new miRNAs using miRDeep2. Red: mature miRNA, blue: star sequence, orange: loop.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>RT-qPCR analysis of new circulating miRNAs. (<bold>A</bold>) Quantification of the levels of miRNA in serum/plasma samples from FJD and HVH patients. After the Shapiro‒Wilk normality test, two-way ANOVA tests were applied (*p&lt;0.05, **p&lt;0.01, ***p&lt;0.001, ****p&lt;0.0001). (<bold>B</bold>) Plot of HC, ICD, and MCC individuals considering miR-Contig-1519 and miR-Contig-3244 data.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>RT‒qPCR analysis of known circulating miRNAs. (<bold>A</bold>) Quantification of the levels of miRNAs in plasma/serum samples from FJD and HVH patients. After the Shapiro‒Wilk normality test, two-way ANOVA tests were applied (*p&lt;0.05, **p&lt;0.01, ***p&lt;0.001, ****p&lt;0.0001). (<bold>B</bold>) Plot of HC, ICD, and MCC individuals considering miR-148a-3p and miR-224-5p data.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>PCA of healthy controls and chronic Chagasic patients. PCA study of HC, ICD, and MCC individuals considering miR-148a-3p, miR-224-5p, miR-Contig-1519, and miR-Contig-3244 data. PC components explain 82.8% of the variance.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Pathways and biological processes predicted to be regulated by miR-148a-3p, miR-224-5p, miR-Contig-1519, and miR-Contig-3244. The results from the EnrichR-Bioplanet (<bold>A</bold>) and EnrichR-Reactome (<bold>B</bold>) databases are shown.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM5\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Silvina R. Villar, Alfonso Herreros-Cabello, Francisco Callejas-Hernández, Manuel Fresno and Núria Gironès.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41598_2024_51487_MOESM1_ESM.xlsx\"><caption><p>Supplementary Information 1.</p></caption></media>", "<media xlink:href=\"41598_2024_51487_MOESM2_ESM.xlsx\"><caption><p>Supplementary Information 2.</p></caption></media>", "<media xlink:href=\"41598_2024_51487_MOESM3_ESM.xlsx\"><caption><p>Supplementary Information 3.</p></caption></media>", "<media xlink:href=\"41598_2024_51487_MOESM4_ESM.xlsx\"><caption><p>Supplementary Information 4.</p></caption></media>", "<media xlink:href=\"41598_2024_51487_MOESM5_ESM.docx\"><caption><p>Supplementary Information 5.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">A shortage of intensive care capacities during the COVID-19 pandemic forced doctors to make disturbing decisions in which they had to prioritize which patient to save^{##REF##32202722##1##,##REF##32219367##2##}. Laypeople’s decisions in such triage scenarios^{##REF##17141139##3##} provide an opportunity for studying moral reasoning in less artificial contexts than traditional sacrificial dilemmas^{##UREF##0##4##–##REF##22405924##7##}, such as the trolley dilemma^{##UREF##1##8##,##UREF##2##9##}. Recent ethical guidelines for medical situations of extreme scarcity are mostly based on utilitarian considerations. To save the largest number of lives, they advocate saving those patients with the best prognosis^{##REF##32219367##2##}. In the absence of relevant distinctions, ethical guidelines recommend a random allocation of resources^{##REF##32202722##1##,##REF##19186274##10##} (but see^{##REF##33296502##11##}). Laypeople largely endorse such guidelines, but have been found to deviate from random allocations by incorporating and overtly discriminating based on a variety of patient features that should be ignored from a normative stance^{##UREF##3##12##–##REF##33372069##19##}. Although people disagree with discriminating policies^{##UREF##3##12##}, judgments of concrete cases and abstract principles may diverge (e.g.^{##REF##29265854##20##}), explaining widespread evidence for discrimination in other work^{##REF##34996450##13##,##REF##35849934##14##}. Beyond that, focusing on overt measures of discrimination may still underestimate the extent of biases and in-group favoritism due to implicit biases (i.e., biases that are not revealed when people are asked explicitly), social desirability, and under-reporting effects^{##REF##12172003##21##,##UREF##5##22##}. Thus, we move beyond assessing laypeople’s propensity for engaging in overt discrimination and study whether they reveal further biases by allowing them to use seemingly fair random allocations to discriminate covertly against less favored patients.</p>", "<p id=\"Par3\">It is well-established that people’s judgments and decisions rarely adhere strictly to norms of moral reasoning^{##REF##29265854##20##,##REF##17201791##23##–##UREF##6##25##}. People deviate from utilitarian norms of impartiality (e.g.,^{##REF##29265854##20##}) and egalitarian norms of equality^{##REF##23647311##24##}, and aim to avoid harming others, even if harming others would save a larger number of lives overall^{##REF##17201791##23##,##UREF##6##25##}. Laypeople also show a variety of pervasive biases, many of which align with their perceptions of how scarce medical resources should be allocated during crises (see^{##REF##35849934##14##}, for a review), and lead to systematic discrimination. Biases for health and longevity generally favor younger and healthier individuals, as shown in studies of QALY maximization (see^{##REF##15386656##26##}, for a review), survey experiments on the allocation of scarce medical resources^{##REF##23647311##24##,##REF##20424038##27##} and hypothetical triage scenarios during the COVID-19 pandemic^{##REF##34996450##13##–##UREF##4##16##,##REF##33388037##18##,##REF##33372069##19##,##REF##33380791##28##}. Individuals are especially disfavored if they are perceived to be responsible for their ill-health, as in the case of obese individuals^{##REF##31377501##29##} or with other medical conditions^{##REF##34996450##13##,##REF##33388037##18##} (but see^{##REF##36063591##30##}). People also tend to favor individuals who exhibit behaviors that are being perceived as ethical, are being described as cooperative and as contributing to society^{##UREF##7##31##}. Similarly, patients who refrain from delinquent behaviors^{##REF##34996450##13##,##UREF##4##16##}, got vaccinated^{##UREF##8##32##}, or abstained from risky (health) behavior^{##REF##33388037##18##} are more likely to be favored. Relatedly, decision makers in triage decisions are willing to consider family-ties and caretaking roles, favoring patients with dependents^{##REF##34996450##13##,##REF##33372069##19##}.</p>", "<p id=\"Par4\">Individuals generally tend to cooperate more willingly with related others^{##UREF##9##33##} and with others that are perceived to belong to one’s in-group in economic games, such as the Prisoner’s dilemma or Dictator games^{##REF##25762906##34##–##UREF##12##38##}. These biases and in-group favoritism permeate into moral judgments and decisions and affect who would be saved in sacrificial dilemmas^{##REF##23647311##24##,##UREF##13##39##–##UREF##15##44##}. Such dilemmas include trolley-type dilemmas with self-driving cars^{##REF##30356211##45##}, but also triage situations involving the allocation of scarce healthcare resources^{##UREF##16##46##}, where people also base their preferences on patients’ ethnic background^{##REF##33372069##19##}, citizenship^{##REF##34996450##13##,##UREF##17##47##}, whether patients recently migrated^{##UREF##18##48##}, political affiliations (but see^{##UREF##19##49##}), and shared nationality, especially when decision makers were more politically conservative^{##UREF##4##16##}.</p>", "<p id=\"Par5\">Manifestations of biases and favoritism need not be explicit and overt, but can remain implicit and operate in a covert fashion^{##REF##7878162##50##–##UREF##21##52##}, affecting both the offers in trust games^{##REF##21518877##53##} and sacrificial dilemma decisions^{##REF##21220339##54##}. Related to modern forms of racism (e.g.,^{##UREF##22##55##}), people supporting egalitarian norms more readily exhibit favoritism in situations that allow them to justify it, for instance, by punishing outgroup members more readily by rejecting unfair offers^{##UREF##23##56##–##UREF##24##58##}. Moreover, people strategically use seemingly fair equality norms—such as randomness—in self-serving ways. They use random allocations to avoid responsibility for their outcomes^{##UREF##25##59##}, and prefer the use of random devices to create plausible deniability^{##UREF##26##60##}. Similarly, people use the alleged outcome of a coin flip to justify unequal allocations^{##REF##10510506##61##} and judge equal allocations as less fair if an individual from their group was previously favored by an allocation decision^{##REF##9150585##62##}. Thus, people could use seemingly fair principles of random allocation to avoid responsibility, but also to justify biased decisions.</p>", "<p id=\"Par6\">As a facet of avoiding responsibility, a bias for inaction that favors omission over commission^{##UREF##27##63##,##UREF##28##64##} has been linked to the avoidance of harm in sacrificial dilemmas^{##UREF##1##8##,##UREF##2##9##,##REF##17201791##23##}. In triage decisions, people are generally reluctant to withdraw care from patients who already receive treatment^{##UREF##3##12##,##REF##33046588##15##,##REF##33372069##19##,##UREF##8##32##}. Effectively, this tendency manifests itself in a first-come, first-served principle, that is discouraged by ethical guidelines^{##REF##32202722##1##}. In contrast to this reluctance to withdraw, laypeople are more willing to harm a patient by withdrawing care from a patient with a worse medical prognosis^{##REF##33372069##19##}. Thus, deviations from norms of moral reasoning may be based on more general mechanisms of judgment and decision making, including in-group favoritism and omission bias, that may also affect the allocation of scarce medical resources.</p>", "<p id=\"Par7\">Prior research on triage decisions primarily focused on explicit biases and overt discrimination. This focus may be prone to underestimate the true extent of biases and in-group favoritism^{##REF##12172003##21##,##UREF##5##22##}. Beyond replicating and extending the evidence for overt discrimination, we also examine covert discrimination tendencies. A diagnostic case for comparing covert and overt discrimination decisions is provided by situations in which a pre-allocated medical resource can be re-allocated. When withdrawing care causes active harm, strategically advocating random re-allocation provides an opportunity for covert discrimination that may appear to adhere to ethical guidelines. Rather than explicitly showing a bias by overtly reallocating a ventilator to a favored patient, a higher willingness to opt for random allocation when a ventilator has been pre-allocated to a disfavored patient than when it has been pre-allocated to a favored patient may superficially satisfy equality norms or ethical guidelines^{##REF##32202722##1##,##REF##19186274##10##}. However, asymmetric use of random re-allocation would nonetheless violate impartiality by selectively increasing the survival chances of a favored patient, relative to keeping the ventilator pre-allocated to the unfavored patient. Thus, an asymmetric use of random re-allocation would provide an opportunity for covert discrimination, as it allows individuals to justify their choice and thus avoid blame by choosing a seemingly fair option^{##UREF##25##59##}. Previous studies relying on forced choice experiments, conjoint analysis (estimating the relevance of multiple features from the responses to forced binary choices^{##UREF##4##16##,##REF##33388037##18##}), and ratings of moral relevance^{##REF##34996450##13##,##UREF##18##48##}, either did not allow individuals to explicitly abstain from a decision, or did not provide them with an opportunity for covert discrimination by avoiding direct harm.</p>", "<p id=\"Par8\">The present study investigates whether laypersons advocate an overt allocation of scarce medical resources based on biases and in-group favoritism or covertly express their preferences through seemingly fair random re-allocation decisions. Participants decided for 19 patient pairs how a doctor should allocate the last remaining ventilator to one of two hypothetical patients during a viral pandemic. Since both patients were described to be in critical condition, saving one patient implied sacrificing the other patient. Each pair of patients differed only in one focal feature. As it was emphasized that patients did not differ in any other features (including medical prognosis), an impartial random ventilator allocation was the recommended normative response^{##REF##32202722##1##,##REF##19186274##10##}. In contrast to most prior work on triage decisions, participants could always opt for random ventilator allocation (see^{##REF##33372069##19##} for a similar approach). Using this setup enables us to disentangle two aspects of discrimination: first, comparing pairs of patients that differ in one distinctive feature allows for the assessment of interpersonal agreement on the bias towards favored vs. dis-favored patient characteristics. Second, stronger deviations from random allocations indicate more pervasive biases, whereas the extent of random allocations provides a measure of impartiality. To distinguish explicit biases in allocation decisions (by denying care to a disfavored patient) from implicit biases reflected in random re-allocation, we moved beyond the basic withholding condition (i.e., both patients arriving simultaneously), and included a withdrawal condition (i.e., one patient arriving before the other) at two time-points (3 and 4, out of a total of 6). In the withdrawal condition, the last ventilator had been pre-allocated to the patient who had arrived earlier, but this default could be revised by re-allocating it to the other patient or by opting for random re-allocation. This extends a similar study by Wilkinson et al.^{##REF##33372069##19##}, who also allowed for random allocation and used a withdrawal condition for patients with different survival probabilities. By varying the withdrawal condition for features that are orthogonal to patients’ survival probability, our study is the first to address covert discrimination in this setting. This novel approach to study covert discrimination reveals systematic and strong explicit biases towards the patients with features that were expected to be favored. This overt discrimination largely persists under withdrawal conditions, but we find no evidence for implicit biases revealed through the (mis-)use of randomness that could additionally harm disfavored individuals.</p>" ]

[ "<title>Materials and methods</title>", "<title>Participants</title>", "<p id=\"Par22\">In total, we recruited 2463 participants on Amazon Mechanical Turk (39.1% female, mean age of 37.2 years, ranging from 18 to 83 years; see Supplementary Table ##SUPPL##0##1## for a full sample description). We collected data on 6 time-points in 1-week intervals between March 2nd and May 23rd and on August 27th and September 3rd, 2020. Data were always collected during U.S. working hours (beginning from about 8 a.m. to about 2 p.m. and lasting no later than 5 p.m.) in order to control for possible effects of weekday and time of day on the participant pool^{##REF##29130029##71##}. Participants provided informed consent prior to participating in the study. Checks of plausibility and completion time, as well as self-reports of data quality were used to screen out participants who did not pay sufficient attention. We excluded the data from a total of 167 participants due to missing data, missed attention checks, or text-field entries suggesting automated responses. This resulted in a total sample of <italic>N</italic> = 2296 participants (or about 1362 participants in the withholding condition across timepoints, plus about 460 participants in each withdrawal condition at timepoints 3 and 4). The study adhered to the Declaration of Helsinki, relevant laws, and institutional guidelines, as certified by IRB of the University of Konstanz. The University of Konstanz’s IRB approved the study. All participants provided informed consent.</p>", "<title>Design</title>", "<p id=\"Par23\">Participants made a total of 19 hypothetical decisions to which of two patients a doctor should allocate the only available ventilator during a viral epidemic that had created a scarcity of medical resources. They could either decide to allocate the ventilator to one of the two patients or decide to use a randomization device (like a random lottery draw or fair coin flip). The two patients in each of the scenarios were described to differ in exactly one focal feature (implying no difference in survival probability). This allowed us to address the question how different patient features affect participants’ allocation decisions, without introducing noise through interaction effects or potential diversions of richer representations. Based on our expectations of who will be favored due to their feature (e.g., based on higher contributions to society) we distinguish between favored and disfavored patients in the following. For a list of patient pairs see Fig. ##FIG##0##1## (pairs are aligned so that the individual we expected to be saved with a higher probability is placed on the right). The instructions clearly stated that the patient who received the ventilator would be saved, whereas the other patient would die. In time-points 3 and 4 we additionally introduced a withdrawal condition and varied between-subjects whether the favored patient, the disfavored patient, or neither patient had been pre-allocated the last available ventilator. Thus, the decision became whether to retain the default allocation, withdraw and re-allocate the ventilator to the other patient, or opt for re-allocation by means of a randomization device. An example scenario can be found in the supplement (see Supplementary Fig. ##SUPPL##0##1##).</p>", "<title>Procedure</title>", "<p id=\"Par24\">Participants first provided informed consent, received instructions that they will be asked to make decisions about which one of two comparable patients differing in one key regard should receive life-saving treatment. Patient pairs were presented in a randomized order. Next, participants answered questions about their own risk and their severity perceptions of the current COVID-19 crisis, their own health, altruism, time and risk preferences, as well as demographic questions, including their state and county, their political views and religiosity. To allow for the detection of in-group effects, we asked participants to provide information on characteristics equal or related to the characteristics of our hypothetical patients (e.g., political orientation and religious beliefs). Moreover, they provided information on their county so that we were able to assess the objective severity of the COVID-19 crisis in their area of residence. Participants always had the option to leave questions blank.</p>", "<title>Data analyses</title>", "<p id=\"Par25\">Our two main outcomes were (a) the proportion of random allocations, with lower proportions indicating less impartiality patient feature, and (b) the proportion of allocations to the patient whom we expected to be favored among non-random allocations, with higher proportions indicating a bias towards the corresponding patient feature. Unless an analysis explicitly refers to a withdrawal condition, analyses are based on the withholding condition. None of the analyses were pre-registered. To compare allocation probabilities within patient features, we used binomial tests against 50% on either allocation alternative. In order to control for variation between participants and patient features, all other analyses used pairs of logistic mixed models (using lme4) for allocations to the patient who was expected to be favored (or keeping, see below) among non-random allocations (denoted by <italic>P(favored|non-random)</italic> in the formulas below) and random allocations. For allocations to favored patients, we included the proportion of non-random allocations as an additional predictor. Across these models, we report Wald-<italic>χ</italic>² tests (indicating the relevance of predictors) and calculated comparisons of interest from post hoc tests (using emmeans), correcting for multiple tests with a Sidak correction. All discrete variables were effect-coded and all continuous variables were <italic>z</italic>-standardized, with the exceptions of age, which was mean-centered. The first pair of models compared allocation patterns between patient features with fixed effects for patient features and time point of data collection, including a random effect for the participant, capturing unexplained variance between individuals (e.g., though differences in randomness aversion).</p>", "<p id=\"Par26\">Model of bias (including the probability of random responses for participants and features):</p>", "<p id=\"Par27\">Model of impartiality:</p>", "<p id=\"Par28\">Models describing our default conditions included random effects for both patient features and participants. The second pair of models compared the conditions of withholding and withdrawal for random allocations and the probability that the patient who already received care could keep the ventilator, including fixed effects for condition (withholding, withdrawing from favored, withdrawing from unfavored) and timepoint of data collection. Since situations of withholding lacked a patient receiving care, we used the probability that the expected to be favored patient received the ventilator as a comparison benchmark.</p>", "<p id=\"Par29\">Model of keeping the ventilator:</p>", "<p id=\"Par30\">Model of random allocations in situations of withdrawal:</p>" ]

[ "<title>Results and discussion</title>", "<title>Overt discrimination based on health and longevity, ethical behavior, family and caretaking, and demographics</title>", "<p id=\"Par9\">Across all features in the withholding condition (when both patients arrived simultaneously) we find evidence for feature-based discrimination on all 6 timepoints of data collection. Among the non-random allocations, we see strong agreement on a bias towards the patient with features that were expected to be favored [<italic>p</italic>(favored patient|random allocation) = 73<italic>.</italic>95%]. An average of 49<italic>.</italic>51% of nonrandom allocations across all features demonstrate a clear lack of an overall agreement on honoring impartiality. Thus, participants mostly agreed when expressing favoritism in the expected direction, but only a minority made consistently impartial allocation decisions (4.20% of participants always used random allocations, 7.20% of participants never did). At the same time, the extent of overt discrimination varied considerably between our 4 categories of patient features: health and longevity, ethical behavior, family and caretaking roles, and demographics. Figure ##FIG##0##1## illustrates both the lack of impartiality (by random allocations, shown as grey bars, being substantially below 100%) and the biases towards favored patients (by more overt choices of favored features, shown in yellow, than of disfavored features, shown in blue) (results are largely robust to differences between time-points, see “<xref rid=\"Sec6\" ref-type=\"sec\">Materials and methods</xref>” and Supplementary Sect. ##SUPPL##0##2.1.3##).</p>", "<p id=\"Par10\">Figure ##FIG##0##1## reveals interesting similarities and differences regarding the category and specific content of discriminating patient features (feature comparisons compare estimates of bias and impartiality from logistic mixed models and are controlled for all 6 timepoints of data collection, see Supplementary Table ##SUPPL##0##4## for the models and Supplementary Sect. ##SUPPL##0##2.1.3## for an exploration of an interaction with sets of time-points of data collection). Despite our emphasis that each pair of patients only differed in one central characteristic (i.e., not in their survival probability), participants showed particularly pervasive biases on most <italic>health and longevity</italic> features. Among features for which patient control is likely perceived to be low, there was a comparable amount of bias for a patient with hereditary diabetes and a patient in a wheelchair (<italic>OR</italic> = 0<italic>.</italic>96, <italic>p</italic> = 0<italic>.</italic>732), but impartiality towards the patient with diabetes was lower (<italic>OR</italic> = 0<italic>.</italic>45, <italic>p</italic> &lt; 0<italic>.</italic>001). Comparing age to hereditary diabetes, in turn, shows both an increased bias (<italic>OR</italic> = 1<italic>.</italic>94, <italic>p</italic> &lt; 0<italic>.</italic>001) and lower impartiality (<italic>OR</italic> = 0<italic>.</italic>55, <italic>p</italic> &lt; 0<italic>.</italic>001) for age. This replicates earlier findings that patient age is used to discriminate in favor of a younger person^{##REF##34996450##13##–##UREF##4##16##,##REF##33388037##18##,##REF##33372069##19##,##REF##33380791##28##} (but see^{##REF##36063591##30##}; supplementary analyses also show no systematic evidence for ageism among younger participants, see Supplementary Sect. ##SUPPL##0##2.3##). When considering presumably more controllable features, excess drinking and excess weight elicited stronger biases than hereditary diabetes (<italic>OR</italic> = 3<italic>.</italic>07, <italic>p</italic> &lt; 0<italic>.</italic>001 and <italic>OR</italic> = 1<italic>.</italic>46, <italic>p</italic> = 0<italic>.</italic>002 respectively), while bias against the excess-drinking patient was larger than against the excess-weight patient (<italic>OR</italic> = 2<italic>.</italic>11, <italic>p</italic> &lt; 0<italic>.</italic>001). When contrasting the feature age with less controllable alcohol consumption, relatively lower bias for age (<italic>OR</italic> = 0<italic>.</italic>63, <italic>p</italic> &lt; 0<italic>.</italic>001) could reflect the co-existence of general ageism with either prioritarian considerations for saving individuals in higher need^{##UREF##3##12##} or merit-based considerations in favor of the elderly^{##UREF##7##31##}, that are absent for alcohol consumption. Conversely, decreased impartiality for age (<italic>OR</italic> = 0<italic>.</italic>66, <italic>p</italic> &lt; 0<italic>.</italic>001) reflects the higher willingness to use age as a feature for these different reasons. Overall, these findings are in line with previous research findings that the elderly and individuals possibly responsible for their ill health (e.g., smokers, unvaccinated individuals, and those engaging in risky behaviors) were less likely to be saved^{##REF##34996450##13##–##UREF##4##16##,##REF##33388037##18##}. Thus, perceptions of life-quality and individual control jointly play a role in resource allocation decisions.</p>", "<p id=\"Par11\">With respect to <italic>ethical behaviors</italic>, we find consistent and clear biases towards patients that are being described as behaving more ethically (see Fig. ##FIG##0##1##). When patients differed in their charitable behavior and flu vaccination status, systematic choices of random allocations indicate that a majority of people honored impartiality in those cases (61.7% and 56.2%, respectively). However, this consensus on impartiality declined when one patient was described as an organ donor (50.4%) and further deteriorated when a patient was described to evade paying taxes (42.0%). Relative to the non-cooperative and delinquent case of tax evasion, the evidence for explicit biases based on other ethical features (e.g., vaccination and organ donation status) were weaker, presumably because they involve personal decisions without violating existing laws. Nevertheless, in-group effects (see Supplementary Sect. ##SUPPL##0##2.3##) suggest that those participants who reported the cooperative behavior themselves discriminated more in favor of the cooperative patient, possibly indicating instances of third-party punishment (e.g., like in the case of vaccination^{##UREF##8##32##}).</p>", "<p id=\"Par12\">Patient features implying <italic>family-ties and caretaking roles</italic> elicit substantive discrimination towards individuals who are embedded in family structures and occupy caretaking roles. The extent of biases increases and impartiality decreases from past caretaking to present caretaking. Regarding bias, we find no differences between married patients and those with adult children (<italic>OR</italic> = 1<italic>.</italic>03, <italic>p</italic> = 0<italic>.</italic>857), but increased biases towards patients with young children when compared to those with adult children (<italic>OR</italic> = 1<italic>.</italic>64, <italic>p</italic> = 0<italic>.</italic>001). However, participants became less impartial towards married patients than towards those with adult children (past caretaking, <italic>OR</italic> = 0<italic>.</italic>76, <italic>p</italic> = 0<italic>.</italic>003), and even less impartial towards patients with young rather than adult children (present caretaking, <italic>OR</italic> = 0<italic>.</italic>36<italic>, p</italic> &lt; 0<italic>.</italic>001). Strong favoritism for saving a mother with young children corroborates previous findings that patients with dependents are more likely to be saved^{##REF##34996450##13##,##UREF##29##65##,##UREF##30##66##}. The decrease in impartiality from being married over past caretaking may indicate that contributing potential children in the future raises a patient’s perceived deservingness (e.g.,^{##REF##34996450##13##}), but not to the extent of already having contributed children in the past.</p>", "<p id=\"Par13\">Finally, considering patients’ demographics and group membership, weak biases based on patients’ sex, ethnicity, and religiosity, and high impartiality on those features suggest that there were few signs of overt sexism or racism (but the observed biases can partly be related to in-group favoritism, see Supplementary Sect. ##SUPPL##0##2.3##). However, pronounced biases towards saving police officers and health professionals indicate favoritism for higher reputation jobs, thereby favoring health-professionals over police officers and business executives. Comparing health professionals to police officers shows a higher bias (<italic>OR</italic> = 1.86<italic>, p</italic> &lt; 0.001) and lower impartiality (<italic>OR</italic> = 0.69, <italic>p</italic> &lt; 0.001) for the former. This may reflect the instrumental value of healthcare workers during the pandemic, as reported in previous work^{##REF##35849934##14##,##REF##33372069##19##,##UREF##29##65##} and reflected in ethical guidelines^{##REF##32202722##1##,##REF##19186274##10##}. With respect to residency status, there was substantive bias for patients born and raised in the U.S. over patients described as refugees or work permit holders, although both features lacked consensus on impartiality. Similarly, previous work reported favoritism towards citizens^{##REF##34996450##13##}, non-immigrants^{##UREF##17##47##,##UREF##18##48##}, and patients of identical nationality^{##UREF##4##16##,##REF##33372069##19##}. If such expressions of favoritism were based on past rather than future contributions to society, we would expect work permit holders (who possibly could contribute soon) to be treated more favorably than refugees (who may not as easily contribute). However, neither was the bias for the individual born in the U.S. larger when compared to refugees rather than work permit holders (<italic>OR</italic> = 1.15, <italic>p</italic> = 0<italic>.</italic>348), nor was the corresponding impartiality decreased (<italic>OR</italic> = 0.93, <italic>p</italic> = 0<italic>.</italic>449). Participants’ reasoning could involve that those born and raised in the U.S. (or their parents) are already contributing to society (e.g., by paying taxes, see the role of tax evasion above). Alternatively, participants’ reasoning may reflect in-group favoritism or even racism that is openly shown, as it may appear to be justified based on perceived deservingness or past reciprocity^{##REF##33388037##18##,##UREF##7##31##}. In line with in-group favoritism, we find that impartiality was increased among more liberal participants, indicating that fewer of them discriminated (see Supplementary Sect. ##SUPPL##0##2.3##).</p>", "<p id=\"Par14\">Although our pattern of results is largely unchanged upon in- or exclusion of the latter timepoints, minor differences (see Supplementary Sect. ##SUPPL##0##2.3.1##) may hint at changes in the participant pool or attitudes towards triage decisions over the course of the pandemic. That a trend towards lower bias holds across patient features could imply that all participants became less willing to rely on random allocations, which was largely driven by increased allocations to the unfavored patient (thus reducing overall bias). Moreover, some of the reported effects seem to be partly driven by participants’ group membership and thus reflect in-group favoritism (see Supplementary Sect. ##SUPPL##0##2.3##). Such in-group effects affected only the magnitude of bias or impartiality measures, but never reversed the direction of the bias among participants sharing the features of the unfavored patient (with the exception of non-religious individuals, who exhibited a bias against religious patients). Thus, even when incorporating in-group favoritism, participants’ discrimination patterns are driven by overarching preferences for the favored patient.</p>", "<title>Overt but no covert discrimination: No sign of asymmetric re-allocation through randomness</title>", "<p id=\"Par15\">Given clear explicit biases on all of our patient features and a wide-spread willingness to deviate from impartial resource allocation, we now turn to potential implicit biases, as operationalized by the withdrawal conditions (in which the last ventilator had been pre-allocated by default to either a favored or unfavored patient who arrived earlier).</p>", "<p id=\"Par16\">Figure ##FIG##1##2## illustrates the willingness for allocating the ventilator in the withholding condition versus keeping it allocated or re-allocating it in the two possible withdrawal conditions. Overall, the allocation probability differed between conditions (according to a logistic mixed model with random effects for participants and patient features, <italic>χ</italic>²(2) = 167<italic>.</italic>858<italic>, p</italic> &lt; 0<italic>.</italic>001). The default patient was more likely to keep the ventilator than it was allocated to the favored patient in the withholding condition for both, favored or unfavored defaults (<italic>OR</italic> = 4<italic>.</italic>77<italic>, p</italic> &lt; 0<italic>.</italic>001 and <italic>OR</italic> = 1<italic>.</italic>63<italic>, p</italic> &lt; 0<italic>.</italic>001, respectively). This shows a strong default effect. A higher probability of keeping the ventilator for the favored default than for the unfavored default (<italic>OR</italic> = 2<italic>.</italic>93<italic>, p</italic> &lt; 0<italic>.</italic>001), indicates that the favoritism observed in situations of withholding generalized to situations of withdrawal. This extends the previously documented effects regarding resource withdrawal based on differential survival probability^{##REF##33372069##19##} and whether a patient was unvaccinated against COVID-19^{##UREF##8##32##}.</p>", "<p id=\"Par17\">Selectively opting for more random re-allocations for less favored patients provided participants with an opportunity for covert discrimination. Although we find an overall effect indicating a difference in random re-allocations between the withdrawal and withholding conditions [<italic>χ</italic>²(2) = 399<italic>.</italic>920<italic>, p</italic> &lt; 0<italic>.</italic>001], participants’ choices for seemingly impartial random re-allocations were not asymmetrically more likely for disfavored defaults (<italic>OR</italic> = 1<italic>.</italic>17, <italic>p</italic> = 0<italic>.</italic>562, with more random re-allocations towards the favored default). The overall effect merely reflects fewer random re-allocations relative to those in the withholding condition for both favored (<italic>OR</italic> = 0<italic>.</italic>15<italic>, p</italic> &lt; 0<italic>.</italic>001) and unfavored defaults (<italic>OR</italic> = 0<italic>.</italic>13<italic>, p</italic> &lt; 0<italic>.</italic>001). Consequently, we find no evidence that people systematically used egalitarian random allocations to rationalize their preference against an unfavored default by asymmetrically increasing seemingly fair random allocations, as reported for other settings^{##UREF##25##59##,##REF##10510506##61##}. Instead of engaging in covert discrimination, many participants appeared to use a first-come first-served rule, but still endorsed overt discrimination against the unfavored patient (with the collapsed pattern being robust for all patient features, and for different times of data collection, see Supplementary Sects. ##SUPPL##0##2.2.1## and ##SUPPL##0##2.2.3##).</p>" ]

[ "<title>Results and discussion</title>", "<title>Overt discrimination based on health and longevity, ethical behavior, family and caretaking, and demographics</title>", "<p id=\"Par9\">Across all features in the withholding condition (when both patients arrived simultaneously) we find evidence for feature-based discrimination on all 6 timepoints of data collection. Among the non-random allocations, we see strong agreement on a bias towards the patient with features that were expected to be favored [<italic>p</italic>(favored patient|random allocation) = 73<italic>.</italic>95%]. An average of 49<italic>.</italic>51% of nonrandom allocations across all features demonstrate a clear lack of an overall agreement on honoring impartiality. Thus, participants mostly agreed when expressing favoritism in the expected direction, but only a minority made consistently impartial allocation decisions (4.20% of participants always used random allocations, 7.20% of participants never did). At the same time, the extent of overt discrimination varied considerably between our 4 categories of patient features: health and longevity, ethical behavior, family and caretaking roles, and demographics. Figure ##FIG##0##1## illustrates both the lack of impartiality (by random allocations, shown as grey bars, being substantially below 100%) and the biases towards favored patients (by more overt choices of favored features, shown in yellow, than of disfavored features, shown in blue) (results are largely robust to differences between time-points, see “<xref rid=\"Sec6\" ref-type=\"sec\">Materials and methods</xref>” and Supplementary Sect. ##SUPPL##0##2.1.3##).</p>", "<p id=\"Par10\">Figure ##FIG##0##1## reveals interesting similarities and differences regarding the category and specific content of discriminating patient features (feature comparisons compare estimates of bias and impartiality from logistic mixed models and are controlled for all 6 timepoints of data collection, see Supplementary Table ##SUPPL##0##4## for the models and Supplementary Sect. ##SUPPL##0##2.1.3## for an exploration of an interaction with sets of time-points of data collection). Despite our emphasis that each pair of patients only differed in one central characteristic (i.e., not in their survival probability), participants showed particularly pervasive biases on most <italic>health and longevity</italic> features. Among features for which patient control is likely perceived to be low, there was a comparable amount of bias for a patient with hereditary diabetes and a patient in a wheelchair (<italic>OR</italic> = 0<italic>.</italic>96, <italic>p</italic> = 0<italic>.</italic>732), but impartiality towards the patient with diabetes was lower (<italic>OR</italic> = 0<italic>.</italic>45, <italic>p</italic> &lt; 0<italic>.</italic>001). Comparing age to hereditary diabetes, in turn, shows both an increased bias (<italic>OR</italic> = 1<italic>.</italic>94, <italic>p</italic> &lt; 0<italic>.</italic>001) and lower impartiality (<italic>OR</italic> = 0<italic>.</italic>55, <italic>p</italic> &lt; 0<italic>.</italic>001) for age. This replicates earlier findings that patient age is used to discriminate in favor of a younger person^{##REF##34996450##13##–##UREF##4##16##,##REF##33388037##18##,##REF##33372069##19##,##REF##33380791##28##} (but see^{##REF##36063591##30##}; supplementary analyses also show no systematic evidence for ageism among younger participants, see Supplementary Sect. ##SUPPL##0##2.3##). When considering presumably more controllable features, excess drinking and excess weight elicited stronger biases than hereditary diabetes (<italic>OR</italic> = 3<italic>.</italic>07, <italic>p</italic> &lt; 0<italic>.</italic>001 and <italic>OR</italic> = 1<italic>.</italic>46, <italic>p</italic> = 0<italic>.</italic>002 respectively), while bias against the excess-drinking patient was larger than against the excess-weight patient (<italic>OR</italic> = 2<italic>.</italic>11, <italic>p</italic> &lt; 0<italic>.</italic>001). When contrasting the feature age with less controllable alcohol consumption, relatively lower bias for age (<italic>OR</italic> = 0<italic>.</italic>63, <italic>p</italic> &lt; 0<italic>.</italic>001) could reflect the co-existence of general ageism with either prioritarian considerations for saving individuals in higher need^{##UREF##3##12##} or merit-based considerations in favor of the elderly^{##UREF##7##31##}, that are absent for alcohol consumption. Conversely, decreased impartiality for age (<italic>OR</italic> = 0<italic>.</italic>66, <italic>p</italic> &lt; 0<italic>.</italic>001) reflects the higher willingness to use age as a feature for these different reasons. Overall, these findings are in line with previous research findings that the elderly and individuals possibly responsible for their ill health (e.g., smokers, unvaccinated individuals, and those engaging in risky behaviors) were less likely to be saved^{##REF##34996450##13##–##UREF##4##16##,##REF##33388037##18##}. Thus, perceptions of life-quality and individual control jointly play a role in resource allocation decisions.</p>", "<p id=\"Par11\">With respect to <italic>ethical behaviors</italic>, we find consistent and clear biases towards patients that are being described as behaving more ethically (see Fig. ##FIG##0##1##). When patients differed in their charitable behavior and flu vaccination status, systematic choices of random allocations indicate that a majority of people honored impartiality in those cases (61.7% and 56.2%, respectively). However, this consensus on impartiality declined when one patient was described as an organ donor (50.4%) and further deteriorated when a patient was described to evade paying taxes (42.0%). Relative to the non-cooperative and delinquent case of tax evasion, the evidence for explicit biases based on other ethical features (e.g., vaccination and organ donation status) were weaker, presumably because they involve personal decisions without violating existing laws. Nevertheless, in-group effects (see Supplementary Sect. ##SUPPL##0##2.3##) suggest that those participants who reported the cooperative behavior themselves discriminated more in favor of the cooperative patient, possibly indicating instances of third-party punishment (e.g., like in the case of vaccination^{##UREF##8##32##}).</p>", "<p id=\"Par12\">Patient features implying <italic>family-ties and caretaking roles</italic> elicit substantive discrimination towards individuals who are embedded in family structures and occupy caretaking roles. The extent of biases increases and impartiality decreases from past caretaking to present caretaking. Regarding bias, we find no differences between married patients and those with adult children (<italic>OR</italic> = 1<italic>.</italic>03, <italic>p</italic> = 0<italic>.</italic>857), but increased biases towards patients with young children when compared to those with adult children (<italic>OR</italic> = 1<italic>.</italic>64, <italic>p</italic> = 0<italic>.</italic>001). However, participants became less impartial towards married patients than towards those with adult children (past caretaking, <italic>OR</italic> = 0<italic>.</italic>76, <italic>p</italic> = 0<italic>.</italic>003), and even less impartial towards patients with young rather than adult children (present caretaking, <italic>OR</italic> = 0<italic>.</italic>36<italic>, p</italic> &lt; 0<italic>.</italic>001). Strong favoritism for saving a mother with young children corroborates previous findings that patients with dependents are more likely to be saved^{##REF##34996450##13##,##UREF##29##65##,##UREF##30##66##}. The decrease in impartiality from being married over past caretaking may indicate that contributing potential children in the future raises a patient’s perceived deservingness (e.g.,^{##REF##34996450##13##}), but not to the extent of already having contributed children in the past.</p>", "<p id=\"Par13\">Finally, considering patients’ demographics and group membership, weak biases based on patients’ sex, ethnicity, and religiosity, and high impartiality on those features suggest that there were few signs of overt sexism or racism (but the observed biases can partly be related to in-group favoritism, see Supplementary Sect. ##SUPPL##0##2.3##). However, pronounced biases towards saving police officers and health professionals indicate favoritism for higher reputation jobs, thereby favoring health-professionals over police officers and business executives. Comparing health professionals to police officers shows a higher bias (<italic>OR</italic> = 1.86<italic>, p</italic> &lt; 0.001) and lower impartiality (<italic>OR</italic> = 0.69, <italic>p</italic> &lt; 0.001) for the former. This may reflect the instrumental value of healthcare workers during the pandemic, as reported in previous work^{##REF##35849934##14##,##REF##33372069##19##,##UREF##29##65##} and reflected in ethical guidelines^{##REF##32202722##1##,##REF##19186274##10##}. With respect to residency status, there was substantive bias for patients born and raised in the U.S. over patients described as refugees or work permit holders, although both features lacked consensus on impartiality. Similarly, previous work reported favoritism towards citizens^{##REF##34996450##13##}, non-immigrants^{##UREF##17##47##,##UREF##18##48##}, and patients of identical nationality^{##UREF##4##16##,##REF##33372069##19##}. If such expressions of favoritism were based on past rather than future contributions to society, we would expect work permit holders (who possibly could contribute soon) to be treated more favorably than refugees (who may not as easily contribute). However, neither was the bias for the individual born in the U.S. larger when compared to refugees rather than work permit holders (<italic>OR</italic> = 1.15, <italic>p</italic> = 0<italic>.</italic>348), nor was the corresponding impartiality decreased (<italic>OR</italic> = 0.93, <italic>p</italic> = 0<italic>.</italic>449). Participants’ reasoning could involve that those born and raised in the U.S. (or their parents) are already contributing to society (e.g., by paying taxes, see the role of tax evasion above). Alternatively, participants’ reasoning may reflect in-group favoritism or even racism that is openly shown, as it may appear to be justified based on perceived deservingness or past reciprocity^{##REF##33388037##18##,##UREF##7##31##}. In line with in-group favoritism, we find that impartiality was increased among more liberal participants, indicating that fewer of them discriminated (see Supplementary Sect. ##SUPPL##0##2.3##).</p>", "<p id=\"Par14\">Although our pattern of results is largely unchanged upon in- or exclusion of the latter timepoints, minor differences (see Supplementary Sect. ##SUPPL##0##2.3.1##) may hint at changes in the participant pool or attitudes towards triage decisions over the course of the pandemic. That a trend towards lower bias holds across patient features could imply that all participants became less willing to rely on random allocations, which was largely driven by increased allocations to the unfavored patient (thus reducing overall bias). Moreover, some of the reported effects seem to be partly driven by participants’ group membership and thus reflect in-group favoritism (see Supplementary Sect. ##SUPPL##0##2.3##). Such in-group effects affected only the magnitude of bias or impartiality measures, but never reversed the direction of the bias among participants sharing the features of the unfavored patient (with the exception of non-religious individuals, who exhibited a bias against religious patients). Thus, even when incorporating in-group favoritism, participants’ discrimination patterns are driven by overarching preferences for the favored patient.</p>", "<title>Overt but no covert discrimination: No sign of asymmetric re-allocation through randomness</title>", "<p id=\"Par15\">Given clear explicit biases on all of our patient features and a wide-spread willingness to deviate from impartial resource allocation, we now turn to potential implicit biases, as operationalized by the withdrawal conditions (in which the last ventilator had been pre-allocated by default to either a favored or unfavored patient who arrived earlier).</p>", "<p id=\"Par16\">Figure ##FIG##1##2## illustrates the willingness for allocating the ventilator in the withholding condition versus keeping it allocated or re-allocating it in the two possible withdrawal conditions. Overall, the allocation probability differed between conditions (according to a logistic mixed model with random effects for participants and patient features, <italic>χ</italic>²(2) = 167<italic>.</italic>858<italic>, p</italic> &lt; 0<italic>.</italic>001). The default patient was more likely to keep the ventilator than it was allocated to the favored patient in the withholding condition for both, favored or unfavored defaults (<italic>OR</italic> = 4<italic>.</italic>77<italic>, p</italic> &lt; 0<italic>.</italic>001 and <italic>OR</italic> = 1<italic>.</italic>63<italic>, p</italic> &lt; 0<italic>.</italic>001, respectively). This shows a strong default effect. A higher probability of keeping the ventilator for the favored default than for the unfavored default (<italic>OR</italic> = 2<italic>.</italic>93<italic>, p</italic> &lt; 0<italic>.</italic>001), indicates that the favoritism observed in situations of withholding generalized to situations of withdrawal. This extends the previously documented effects regarding resource withdrawal based on differential survival probability^{##REF##33372069##19##} and whether a patient was unvaccinated against COVID-19^{##UREF##8##32##}.</p>", "<p id=\"Par17\">Selectively opting for more random re-allocations for less favored patients provided participants with an opportunity for covert discrimination. Although we find an overall effect indicating a difference in random re-allocations between the withdrawal and withholding conditions [<italic>χ</italic>²(2) = 399<italic>.</italic>920<italic>, p</italic> &lt; 0<italic>.</italic>001], participants’ choices for seemingly impartial random re-allocations were not asymmetrically more likely for disfavored defaults (<italic>OR</italic> = 1<italic>.</italic>17, <italic>p</italic> = 0<italic>.</italic>562, with more random re-allocations towards the favored default). The overall effect merely reflects fewer random re-allocations relative to those in the withholding condition for both favored (<italic>OR</italic> = 0<italic>.</italic>15<italic>, p</italic> &lt; 0<italic>.</italic>001) and unfavored defaults (<italic>OR</italic> = 0<italic>.</italic>13<italic>, p</italic> &lt; 0<italic>.</italic>001). Consequently, we find no evidence that people systematically used egalitarian random allocations to rationalize their preference against an unfavored default by asymmetrically increasing seemingly fair random allocations, as reported for other settings^{##UREF##25##59##,##REF##10510506##61##}. Instead of engaging in covert discrimination, many participants appeared to use a first-come first-served rule, but still endorsed overt discrimination against the unfavored patient (with the collapsed pattern being robust for all patient features, and for different times of data collection, see Supplementary Sects. ##SUPPL##0##2.2.1## and ##SUPPL##0##2.2.3##).</p>" ]

[]

[ "<p id=\"Par1\">Disturbingly realistic triage scenarios during the COVID-19 pandemic provide an opportunity for studying discrimination in moral reasoning. Biases and favoritism do not need to be explicit and overt, but can remain implicit and covert. In addition to assessing laypeople’s propensity for engaging in overt discrimination, the present study examines whether they reveal implicit biases through seemingly fair random allocations. We present a cross-sectional online study comprising 6 timepoints and a total of 2296 participants. Each individual evaluated 19 hypothetical scenarios that provide an allocation dilemma between two patients who are in need of ventilation and differ only in one focal feature. Participants could either allocate the last ventilator to a patient, or opt for random allocation to express impartiality. Overall, participants exhibited clear biases for the patient who was expected to be favored based on health factors, previous ethical or caretaking behaviors, and in-group favoritism. If one patient had been pre-allocated care, a higher probability of keeping the ventilator for the favored patient indicates persistent favoritism. Surprisingly, the absence of an asymmetry in random allocations indicates the absence of covert discrimination. Our results demonstrate that laypeople’s hypothetical triage decisions discriminate overtly and show explicit biases.</p>", "<title>Subject terms</title>" ]

[ "<title>General discussion</title>", "<p id=\"Par18\">Across a variety of different patient features, we investigated how laypeople decided to withhold and withdraw care in the context of triage decisions. Replicating and extending previous work. participants’ withholding decisions showed overt discrimination. They predictably favored more healthy patients and patients with higher status jobs, like health professionals and police officers, but also prioritized patients who are socially embedded and in care-taking roles, as well as patients showing cooperative behaviors. Surprisingly, overt discrimination persisted in withdrawal situations in which a life-saving ventilator could be re-allocated. Rather than using random allocations to covertly express implicit biases, participants consistently made overt re-allocation decisions. Overall, pervasive explicit biases based on patient features profoundly shaped laypersons’ triage decisions, even in situations where the decision concerned the withdrawal of care.</p>", "<p id=\"Par19\">The pervasiveness of discrimination adds to a body of findings that laypersons do not strictly adhere to ethical guidelines^{##REF##34996450##13##–##UREF##4##16##,##REF##33372069##19##,##UREF##8##32##,##UREF##29##65##,##UREF##30##66##} that focus on patient prognosis^{##REF##32219367##2##,##REF##33296502##11##} and otherwise recommend random resource allocation^{##REF##32202722##1##,##REF##19186274##10##}. Analogous to judgments about whether social welfare is deserved^{##UREF##7##31##}, laypeople consider patients as deserving care to different degrees, based on their perceived level of control over the situation, but also based on societal contributions. Our results on excess weight and alcohol consumption add to mixed findings from conjoint experiments which either find^{##REF##33388037##18##} or do not find^{##REF##36063591##30##} evidence for these (seemingly) controllable features, but agree on the importance of different professions. Likewise, our findings on patients who recently migrated, but also on marriage, adult children, and young dependents could also reflect a judgment of deservingness due to past or future contributions to society. Interestingly, participants here incorporated features that they had indicated to be irrelevant when asked to judge their moral relevance^{##REF##34996450##13##}. They also discriminated based on patients’ social usefulness, although they largely rejected discriminating triage policies^{##UREF##3##12##}. This likely implies potential differences between judgements of abstract policies and concrete hypothetical decisions^{##REF##29265854##20##}, which could partially consist in opportunities to rationalize discrimination based on features of the specific situation. Additional analyses also show that allocation decisions also reflect the pervasive phenomenon of in-group favoritism^{##REF##25762906##34##–##UREF##12##38##}. The relevance of in-group favoritism for triage decisions has so far only been shown for nationality^{##UREF##4##16##} and cooperative behaviors, such as getting vaccinated^{##UREF##8##32##}. Strikingly, discrimination persisted in situations in which individuals had to decide about actively harming a patient by re-allocating a critical resource. However, people did not seize the opportunity to rationalize their favoritism through seemingly fair random allocations in withdrawal conditions. This is surprising for two reasons: first, people reliably seem reluctant to withdraw care in triage scenarios^{##UREF##3##12##,##REF##33046588##15##,##REF##33372069##19##,##UREF##8##32##}, avoid directly harming others in sacrificial dilemmas^{##UREF##1##8##,##UREF##2##9##,##REF##17201791##23##,##UREF##6##25##}, and exhibit a general preference for inaction over action^{##UREF##27##63##,##UREF##28##64##}. Second, the observed absence of covert discrimination is at odds with previous reports of the motivated use of randomness^{##UREF##25##59##–##REF##10510506##61##} and people’s use of different norms of fairness on outgroup individuals^{##UREF##23##56##,##REF##24121413##57##}.</p>", "<p id=\"Par20\">We cannot fully exclude that experimenter demand characteristics due to salient features or a general aversion against randomness^{##UREF##31##67##} may have led to an overestimation of the degree of discrimination, whereas for some features random allocations may have been more likely due to social desirability (e.g., ethnicity and sex). However, demand effects have been found to be lower in online experiments than in laboratory settings^{##UREF##32##68##}. A general avoidance of random allocations also conflicts with the fact that random allocations were typically the modal response in situations of withholding. Additionally, our discrimination patterns persisted in the withdrawal condition where there was no individual accountability for covert discrimination, which would reduce the potential impact of social desirability. Thus, even though the estimated probabilities of discrimination may be overestimated due to demand characteristics or randomness aversion, the rank order of features should be unaffected and reveal actual preferences. Participants’ proneness to openly show their favoritism, even in situations of withdrawal extends the mixed evidence that people are more willing to reallocate a resource from a patient unvaccinated against COVID-19^{##UREF##8##32##} or with a lower survival probability^{##REF##33046588##15##,##REF##33372069##19##}. In sum, discrimination appears to be pervasive and extends beyond features that can be aligned with ethical guidelines, like health-related outcomes and a person’s instrumental value in conditions of scarcity.</p>", "<p id=\"Par21\">Overall, investigations of hypothetical triage scenarios offer a valuable window into human moral reasoning, which may be subject to a variety of moral motives^{##REF##21244187##43##}. The willingness to engage in trade-offs between patient features and situational aspects is in line with broadly utilitarian cost–benefit calculations^{##REF##30064654##69##}, but violates norms of impartiality^{##REF##29265854##20##} and deontologic rules against harm^{##REF##29265854##20##,##UREF##6##25##,##REF##31911126##70##}. Future work should aim to improve our understanding of the conditions under which people rely on overt and covert forms of discrimination. Although here we were interested in comparing isolated features to get a clean estimate of which features are used, investigating patients described with feature combinations could reveal additional insights, such as trade-offs or interactions between features. This would also be beneficial for external validity, because typically patients will vary in several features. Our results on single features add valuable insights to laypeople’s perspectives on practical debates about triage scenarios^{##REF##35849934##14##}. Rather than directly translating into guidelines, participants’ willingness to overtly express biases and in-group favoritism provides a cautionary note: Results reveal that there are substantial discrepancies between ethical guidelines and people’s moral intuitions, resulting in challenging disagreements over particular decisions. At the same time, the fact that people’s biases are openly stated rather than covertly enacted enables policy makers to anticipate such discrepancies, allowing—but also requiring—them to better explain expert recommendations to the general public.</p>", "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-50385-w.</p>", "<title>Acknowledgements</title>", "<p>This research was funded by the University of Konstanz. N.G., W.G., H.N. and H.G. received additional funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy–EXC 2117–422037984. W.G., H.G., and N.G. received additional funding from DFG Grant Number 441541975.</p>", "<title>Author contributions</title>", "<p>N.G., H.N. and W.G. contributed to the conceptual development of the work and designed the experiments; N.G. programmed the experiments, collected the data, and analyzed the data with input from H.N., W.G., and H.G.; N.G. produced the first draft, all authors provided critical revisions, and approved of the final version.</p>", "<title>Data availability</title>", "<p>All data, code, and materials have been made publicly available at OSF and can be accessed at <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/pn239/\">https://osf.io/pn239/</ext-link>.</p>", "<title>Competing interests</title>", "<p id=\"Par31\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Discrimination reflected in proportions of random allocations vs. allocations to the favored and disfavored patient by patient feature. The right label corresponds to the patient who we predicted to be favored, and the left label to the patient who we predicted to be disfavored. All four feature clusters indicate that allocations varied between patient features. Asterisks on random allocations indicate that random allocations statistically deviated from 50%, reflecting a lack of impartiality, and asterisks on favored allocations indicate a higher likelihood for favored than for disfavored allocations among non-random allocations, reflecting systematic bias towards one patient (binomial tests against 50%, first asterisk uncorrected, second asterisk Bonferroni corrected for 19 tests). The offset of bars from the center indicate the degree of bias as the absolute difference between favored and disfavored allocations (in percent) and odds ratios (to the right of the bars) provide the effect size of each bias.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Probability of receiving the ventilator by condition across patient features. Probabilities to allocate the ventilator to either patients in withholding scenarios (top) vs. retaining or re-allocating it in a withdrawal scenario in which the ventilator has been pre-allocated to a favored default (middle) or to an unfavored default (bottom).</p></caption></fig>" ]

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open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">keep</mml:mi></mml:mrow></mml:mfenced><mml:mspace width=\"0.166667em\"/><mml:mo>∼</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>f</mml:mi><mml:mi>a</mml:mi><mml:mi>u</mml:mi><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">timepoints</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">participant</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">feature</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equd\"><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P\\left( {random} \\right) \\, \\sim b_{default \\, condition} + b_{timepoints} + \\sigma_{participant} + \\sigma_{feature} .$$\\end{document}</tex-math><mml:math id=\"M8\" display=\"block\"><mml:mrow><mml:mi>P</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">random</mml:mi></mml:mrow></mml:mfenced><mml:mspace width=\"0.166667em\"/><mml:mo>∼</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>f</mml:mi><mml:mi>a</mml:mi><mml:mi>u</mml:mi><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:mspace 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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41598_2023_50385_MOESM1_ESM.pdf\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">The use of medical literature to guide clinical practice as part of evidence-based medicine can reduce the number of medical error-related deaths in the US, which is over 98,000 annually, per IOM^{##REF##1404801##1##,##UREF##0##2##}. The assessment of the diagnostic accuracy of medical decision-making aids and tools is an important step towards this goal of improving patient safety and healthcare provision^{##UREF##1##3##,##UREF##2##4##}. Standard metrics, including sensitivity, specificity, negative predictive value (NPV), and positive predictive value (PPV), measure the predictive utility of medical decision-making tools^{##UREF##3##5##–##UREF##4##9##}. The sensitivity and specificity of diagnostic tests, such as the chest x-ray for pneumothorax, are well-established for common illnesses. However, with the myriad of conditions and diagnostic tools available, clinicians often face challenges in selecting the most appropriate order of tests for specific, time-sensitive clinical situations.</p>", "<p id=\"Par3\">Shannon entropy is a core concept in machine learning and information theory, particularly in decision tree modeling of data analytics and machine learning^{##REF##35195818##10##}. To date, numerous research-based biological and clinical solutions have been developed based on the principle of Shannon entropy, a measure of uncertainty^{##REF##36690689##11##–##UREF##8##17##}, including diagnostic accuracy evaluation. However, no diagnostic metrics that specifically measure the reduction of diagnostic uncertainty, which often leads to decision paralysis and the \"shotgun\" diagnostic approach^{##REF##36690689##11##}, over-testing, delayed diagnosis, and patient harm^{##REF##36690689##11##}, have been extensively applied and explored.</p>", "<p id=\"Par4\">Shannon entropy, defined by Eq. (##FORMU##0##1##), offers a solution:where ’s denote the probabilities of the possible outcomes of the event, and is taken to be zero when  = 0, justified by the fact that the limit of is zero as <bold> → </bold>0⁺. Shannon entropy is maximized for a uniform distribution. For <italic>binary</italic> events, in particular, as is the case in this study, the entropy <italic>H(x)</italic> is at its highest when the probabilities are exactly 0.5, that is, when there is the most uncertainty, and is at its lowest (zero) when the outcomes are certain, that is, when the outcome probabilities are one and zero, respectively. This corresponds to its application in a clinical setting, where the entropy, or uncertainty of a patient with respect to their diagnosis is maximal when they enter the hospital with no testing or diagnostic evaluation. Various diagnostic tools subsequently reduce this clinical uncertainty, ideally to a definitive diagnosis.</p>", "<p id=\"Par5\">In emergency medicine, removal of entropy using testing and imaging tools can clarify the patient's presentation and optimize medical decision-making in time-sensitive settings. Quantifying entropy removal can elucidate the utility and sequence of diagnostic tools in removing uncertainty in those clinical settings and first exclude urgent, lethal pathology. In this study, we aim to characterize the utility and validity of Shannon entropy removal to reanalyze the performance of 623 clinical decision support tools in a publicly available database^{##REF##27489373##18##} compared to traditional validity tools including sensitivity, specificity, PPV/NPV, Youden’s index, and diagnostic odds ratio.</p>" ]

[ "<title>Materials and methods</title>", "<title>IRB statement</title>", "<p id=\"Par6\">This study is exempt from IRB review of Massachusetts General Hospital and Harvard Medical School as research involves collecting and studying existing data of which sources are publicly available, and subjects cannot be identified directly or through identifiers linked to the subjects.</p>", "<title>Data compilation</title>", "<p id=\"Par7\">Diagnostic metrics (true and false positives and negatives, respectively) were compiled from an established online database of diagnostic accuracy, known as “Get the Diagnosis”, totaling 533 studies of 623 decision-making tools of 267 diagnoses^{##REF##27489373##18##}. Data collection was performed from November 17, 2022 through January 22, 2023. PubMed was utilized when studies cited from the online database were unable to be accessed directly; concomitant diagnostic tools were also separately explored for elements included in the database as applicable (for example, if studies that evaluated the diagnostic accuracy of mammography for breast cancer screening were included in the database, data was also compiled for low-dose computerized tomography (CT) scans for breast cancer screening; see Data availability statement for details). This data was used to calculate sensitivities, specificities, NPVs, and PPVs. In addition, the data was used to generate decision tree representations for each decision-making tool from which Shannon entropy and entropy removal were calculated (see “<xref rid=\"Sec5\" ref-type=\"sec\">Decision tree representation</xref>” and Fig. ##FIG##0##1## in addition to “<xref rid=\"Sec6\" ref-type=\"sec\">Entropy calculation</xref>”).</p>", "<p id=\"Par8\">In this study, patient-derived datasets were systematically bootstrapped using the decision tree data previously reported in the literature (see “<xref rid=\"Sec7\" ref-type=\"sec\">Machine learning modeling and analysis</xref>”). This data was specifically derived from the “Step-By-Step Approach to Febrile Infants” and the “Pediatric Emergency Care Applied Research Network (PECARN) Pediatric Head Injury/Trauma Algorithm”^{##UREF##9##19##–##UREF##10##21##}.</p>", "<p id=\"Par9\">Similar methods have been performed in other studies to generate health data for the evaluation of healthcare solutions from datasets, such as HES, A&amp;E, and MIMIC^{##UREF##11##22##,##UREF##12##23##}. In each case, synthetic datasets that preserved the statistical properties of the original real data were generated^{##UREF##13##24##}. This was accomplished by using the decision tree data provided in the original and validation papers of the respective studies and synthesizing a binary dataset of the relevant metrics of each respective algorithm (ex. leukocyturia, age less than 21 days, loss of consciousness, etc.) and their binary value (0 for absence, 1 for presence). Thus, the original data used in the study was recreated with each patient in the respective studies being simplified to only their characteristics relevant to the study in addition to being reduced to a set of binary values for machine learning modeling.</p>", "<title>Decision tree representation</title>", "<p id=\"Par10\">Decision trees are constituted of parent nodes that split to yield children nodes; these nodes and decision splits are able to be generated to produce decision tree representations for diagnostic tools by using the diagnostic metrics for medical decision-making tools from 2 × 2 diagnostic tables as in Fig. ##FIG##0##1##, where N is the sample size of the study, TP is the number of true positives, FP is the number of false positives, FN is the number of false negatives, and TN is the number of true negatives.</p>", "<title>Entropy calculation</title>", "<p id=\"Par11\">Using diagnostic metrics (N, TP, FP, etc.), Shannon entropy was calculated as below in Eqs. (##FORMU##8##2##) through (##FORMU##9##4##) for the parent node and children nodes, with n_positive and n_negative representing the number of positive and negative tests, respectively:</p>", "<p id=\"Par12\">Entropy removal was calculated by Eq. (##FORMU##11##5##), where entropy removal equals the difference between the entropy of the parent node (the total entropy of the system) and the weighted average entropy of the children nodes (proportional to n_positive and n_negative, respectively):</p>", "<p id=\"Par13\">Data provided in the validation study by Gomez et al. was utilized to generate a patient dataset for analysis of the Step-By-Step Approach to Febrile Infants^{##UREF##9##19##}. Data provided in the original study by Kupperman et al. was similarly utilized to generate two separate patient datasets for analysis of the PECARN Pediatric Head Injury/Trauma Algorithm: one for patients less than 2 years of age and another for patients greater than or equal to 2 years of age^{##REF##19758692##20##}.</p>", "<title>Machine learning modeling and analysis</title>", "<p id=\"Par14\">The Python MATLAB and scikit-learn packages were utilized in this study to generate, analyze the performance, and visualize machine learning models developed from the synthetic patient datasets (for more details regarding the machine learning models developed)^{##UREF##14##25##,##UREF##15##26##}. Decision tree-based diagnostic algorithms pose unique applications for Shannon entropy analysis of the decision-making tool in its entirety and its constituent steps/nodes, allowing for evaluation of each feature in the algorithm. A decision tree was produced for each patient dataset and these decision trees were subsequently analyzed for the entropy removal and feature importance of each step within the algorithm. In the context of machine learning, feature importance is defined as the relative importance of each feature when making a prediction and is calculated as the decrease in entropy weighted by the probability of reaching that node, as shown below in Eqs. (##FORMU##12##6##) and (##FORMU##13##7##):</p>", "<p id=\"Par15\">(ni_j = the importance of node j, w_j = weighted number of samples reaching node j, C_j = the impurity value of node j, left(j) = child node from left split on node j, right(j) = child node from right split on node j).</p>", "<p id=\"Par16\">(fi_i = the importance of feature I, ni_j = the importance of node j, ni_k = the importance of node k).</p>" ]

[ "<title>Results</title>", "<title>Entropy removals</title>", "<p id=\"Par17\">Entropy removal was calculated in addition to sensitivity, specificity, NPV, and PPV as well as diagnostic odds ratio and Youden’s index for 533 studies to evaluate the 623 medical decision-making tools.</p>", "<p id=\"Par18\">Entropy removal displayed significant but weak positive correlations with sensitivity and NPV and showed significant moderate positive correlations with specificity and PPV (<italic>p</italic> &lt; 0.001). Entropy removal exhibited significant strong positive correlations with comprehensive clinical diagnostic metrics, such as Youden’s index and logged diagnostic odds ratio (<italic>p</italic> &lt; 0.001). Z-score calculation for differences in correlations revealed significant differences between the respective correlations of Youden’s index and logged diagnostic odds ratio with entropy removal as compared to the correlations of the other explored diagnostic metrics with entropy removal (<italic>p</italic> &lt; 0.001). Figures ##FIG##1##2## and ##FIG##2##3## illustrate the correlation between different diagnostic metrics and entropy removal. Tables ##TAB##0##1## and ##TAB##1##2## provide the Pearson and Spearman correlation coefficients for entropy removal and the different diagnostic metrics, respectively. Tables ##TAB##2##3## and ##TAB##3##4## provide examples of comparisons of the different diagnostic accuracy metrics of tests evaluating for pneumothorax and thoracic aortic dissection, respectively. Table ##TAB##4##5## displays the results of entropy removal analysis of decision tree-based clinical algorithms and their constituent steps.</p>", "<p id=\"Par19\">The diagnostic metrics of different diagnostic tools that assess patients for the same pathology were able to be compared as in Tables ##TAB##2##3## and ##TAB##3##4##.</p>", "<title>Bootstrapping and stepwise entropy calculation</title>", "<p id=\"Par20\">Decision tree machine learning analysis of the generated patient datasets yielded the exact decision trees of the original algorithms, supporting the validity of the clinical algorithms. Table ##TAB##4##5## shows the results of machine learning analysis.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par21\">Our study demonstrates the potential utility of quantified entropy removal of medical diagnostic decision-making tools. Diagnostic tools that are 100% sensitive and 100% specific (or definitively diagnostic) also have an entropy removal of 100% as all entropy (uncertainty) is completely removed with regard to a particular pathology. In cases in which diagnostic tools are less than 100% sensitive and/or specific, our entropy removal calculations provide further insight into how much diagnostic value the tool provides. In other words, entropy removal may be used as a “meta-metric” to assess existing clinical diagnostic metrics. The strong positive correlations of entropy removal with established comprehensive measures of diagnostic accuracy (Youden’s index and logged diagnostic odds ratio) may support its validity while its distinctive advantages support its novelty. Entropy removal provided unique insight on the diagnostic value of medical decision-making tools beyond the limitations of Youden’s index and diagnostic odds ratio (which include the omission of disease prevalence in calculation as well as inherent limitations of calculation in the respective formulas), demonstrating its clinical utility with particular potential in the setting of Emergency Medicine where exclusion of critical diagnoses within time-limited emergencies is critical. This utility of entropy removal in assessment of the diagnostic value of medical decision-making tools can be also seen in comparing different tools that evaluate for the same pathology.</p>", "<p id=\"Par22\">Traditional measures of test quality, such as sensitivity and specificity, are not as easily used for comparing diagnostic strategies as entropy removal. For example, evaluation for thoracic aortic dissection via helical CT scan has a sensitivity of 97.64% and a specificity of 98.90%, whereas evaluation by way of MRI has a slightly lower sensitivity (93.33%) but a higher specificity (99.30%). Entropy removal calculation reveals that helical CT scan removes 87.23% of all entropy with respect to thoracic aortic dissection while MRI removes 81.36%, revealing the superior overall diagnostic value of a helical CT scan in assessment for thoracic aortic dissection. This demonstrates the ability of entropy removal to provide clarification and stratification that sensitivity and specificity do not offer. This advantage of entropy removal calculation can also be seen in the comparison between chest x-ray and low-dose CT scan for lung cancer screening, with CXR having a greater sensitivity (88.89% versus 73.38%) and low-dose CT having a greater specificity (92.60% versus 97.00%) but CXR having greater entropy removal (32.03% versus 28.20%).The superior imaging test for pneumothorax can also be identified by entropy removal calculations, as chest ultrasound yields a superior sensitivity (95.12% versus 55.83%) while supine AP chest x-ray provides a greater specificity (98.87% versus 100%), but chest ultrasound has greater entropy removal over supine AP chest x-ray (82.38% versus 40.94%). Entropy removal thus has the potential to provide an evidence-based foundation for the dynamic evaluation of patients, as it can potentially serve as the basis for guiding medical decision-making in the context of performing certain tests or utilizing particular tools in time restricted order to most effectively eliminate uncertainty regarding a patient’s acute care presentation.</p>", "<p id=\"Par23\">Quantifying the entropy removal capability of medical diagnostics also opens the door for further exploration in healthcare innovation, such as the quantification of the impact of clinical guidelines by analyzing and comparing the diagnostic value of decision-making tools and tests. Entropy removal calculation also has potential use in financial analysis of healthcare costs, as metrics such as entropy removal per cost could be calculated and used to evaluate healthcare cost efficiency. For example, metrics such as the percent entropy removed per US dollar (USD) by a diagnostic tool can be calculated. Using publicly available Medicare costs^{##UREF##16##27##}, a chest x-ray screening for lung cancer was found to remove 1.28% entropy per USD while a low-dose CT scan screening for lung cancer removed 0.27% entropy per USD. Similarly, a chest US evaluating for pneumothorax removes 3.30% entropy per USD while a CXR evaluating for pneumothorax removes 1.64% entropy per USD. As a final example, an US of the abdomen evaluating for nephrolithiasis removes 0.13% entropy per USD and a CT scan of the abdomen evaluating for nephrolithiasis removes 0.11% entropy per USD.</p>", "<p id=\"Par24\">With respect to entropy removal, in the examples above, it would be more cost-effective to pursue chest x-ray imaging to screen for lung cancer screening as well as to evaluate for pneumothorax as opposed to low-dose CT and ultrasound, respectively. With regard to nephrolithiasis assessment, a CT scan removes marginally more entropy than ultrasound, but has inferior cost-effectiveness (as measured by entropy removal per USD) compared to ultrasound. All these results have the potential to inform medical decision-making in various contexts, providing an alternative means of cost-effectiveness analysis in assessing the efficiency of healthcare systems.</p>", "<p id=\"Par25\">Furthermore, entropy removal can be used to evaluate the diagnostic quality of entire departments or systems. For example, the diagnostic performances of expert radiologists and residents regarding COVID-19 identification on chest x-rays was evaluated in a 2021 study, which found that attending radiologists diagnosed COVID-19 at a sensitivity of 78.98% and a specificity of 80.45% as opposed to resident radiologists (75.09% and 57.89%, respectively)^{##REF##34218365##28##}. Entropy removal calculations can be used to further evaluate the diagnostic quality of each respective subgroup, revealing that attending radiologists removed 24.55% of clinical uncertainty regarding COVID-19 via chest x-rays while residents only removed 7.55%.</p>", "<p id=\"Par26\">Shannon entropy, proposed as a big data metric^{##UREF##17##29##}, can evaluate diagnostic quality across entire hospitals or health networks, not just specific pathologies. The utility of Shannon entropy can be extended to other research applications where data points of true and false positives and negatives are reported. Beyond individual groups, entropy removal can gauge the performance of whole departments and networks, indicating healthcare innovation and quality. Additionally, it can highlight healthcare disparities by comparing diagnostic efficiency across various regions and patient groups.</p>", "<p id=\"Par27\">The generation of synthetic patient datasets from medical decision-making algorithms and subsequent analysis of these algorithms by decision tree machine learning analysis as performed in this study showed potential utility, as well, though with limitations (see limitations below). The resultant machine learning decision trees and calculated metrics from the algorithms evaluated in this study were in line with the medical decision-making algorithms used in practice and the results of this analysis can be understood to support and further validate these current clinical guidelines. The results also quantified the effectiveness of the individual constituent steps of the algorithms, providing measurable insight on the most clinically relevant information for patient assessment in the algorithms. If more data are provided in literature for the development and validation of medical decision-making algorithms, deeper analysis can be performed on these diagnostic tools in order to more thoroughly evaluate them.</p>", "<p id=\"Par28\">The limitations of this study include the fact that the findings outlined in this study are statistical and mathematical modeling that will require further application to clinical practice. While the application of Shannon entropy to medical diagnostics, as in this study, is a limited implementation of established information theory and machine learning concepts to publicly available data, the need for clinical validation still remains. For example, the presence of differences in entropy removal from established metrics does not necessarily establish that such differences are clinically meaningful or accurately reflect the performance of the decision support tools unless some prospective testing is done. While this was outside of the scope of this study, further investigation and validation exploring these phenomena is warranted. Furthermore, the stepwise evaluation of algorithms as described in the latter portions of this paper made use of bootstrapped (resampled) data, which is very internally consistent but also requires prospective and external validation. Larger data sets from healthcare electronic medical records could provide valuable insight using our entropic approach.</p>" ]

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[ "<p id=\"Par1\">Shannon entropy is a core concept in machine learning and information theory, particularly in decision tree modeling. To date, no studies have extensively and quantitatively applied Shannon entropy in a systematic way to quantify the entropy of clinical situations using diagnostic variables (true and false positives and negatives, respectively). Decision tree representations of medical decision-making tools can be generated using diagnostic variables found in literature and entropy removal can be calculated for these tools. This concept of clinical entropy removal has significant potential for further use to bring forth healthcare innovation, such as quantifying the impact of clinical guidelines and value of care and applications to Emergency Medicine scenarios where diagnostic accuracy in a limited time window is paramount. This analysis was done for 623 diagnostic tools and provided unique insights into their utility. For studies that provided detailed data on medical decision-making algorithms, bootstrapped datasets were generated from source data to perform comprehensive machine learning analysis on these algorithms and their constituent steps, which revealed a novel and thorough evaluation of medical diagnostic algorithms.</p>", "<title>Subject terms</title>" ]

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[ "<title>Author contributions</title>", "<p>S.H.: conceptualization, writing—review and editing, supervision. P.C.: methodology, formal analysis, investigation, data curation, writing—original draft. B.J.Y.: writing—review and editing. P.H.C.: writing—review and editing. D.C.: writing—review and editing, visualization. S.M.: writing—review and editing. K.C.B.: writing—review and editing. W.S.: formal analysis. P.S.: writing—review and editing, supervision. J.N.G.: writing—review and editing, supervision. A.R.: writing—review &amp; editing, supervision. J.L.: writing—review and editing, supervision.</p>", "<title>Data availability</title>", "<p>All data (including the specific studies and figures utilized in compiling diagnostic variables) have been uploaded into a public\nrepository which can be accessed at the following URL: <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.google.com/search?q=https%3A%2F%2Fdata.mendeley.com%2Fdatasets%2Fhgwdb4mtpw%2F2+3.0\">https://data.mendeley.com/datasets/hgwdb4mtpw/2 3.0</ext-link>^{##UREF##18##30##}.</p>", "<title>Competing interests</title>", "<p id=\"Par29\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Decision tree representation of 2 × 2 diagnostic table. Diagnostic variables (TP/FP/FN/TN) are utilized to represent a 2 × 2 table and its corresponding medical decision-making tool as a decision tree for entropy analysis.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Scatterplot of removed entropy and tool sensitivity and specificity. 623 medical decision-making tools were analyzed. (<bold>A</bold>) Sensitivity exhibits a 0.46 Pearson correlation and 0.55 Spearman correlation with entropy removal (<italic>p</italic> &lt; .001). (<bold>B</bold>) Specificity exhibits a 0.61 Pearson correlation and 0.74 Spearman correlation with entropy removal (<italic>p</italic> &lt; .001).</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Scatterplot of removed entropy and tool positive predictive value and negative predictive value. 623 medical decision-making tools were analyzed. (<bold>A</bold>) Positive predictive value exhibits a 0.60 Pearson correlation and 0.71 Spearman correlation with entropy removal (<italic>p</italic> &lt; .001). (<bold>B</bold>) Negative predictive value exhibits a 0.41 Pearson correlation and 0.46 Spearman correlation with entropy removal (<italic>p</italic> &lt; .001).</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Pearson correlation coefficients of diagnostic metrics and entropy removal.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Metric</th><th align=\"left\">Pearson coefficient</th></tr></thead><tbody><tr><td align=\"left\">Sensitivity</td><td char=\".\" align=\"char\">0.465</td></tr><tr><td align=\"left\">Specificity</td><td char=\".\" align=\"char\">0.607</td></tr><tr><td align=\"left\">PPV</td><td char=\".\" align=\"char\">0.600</td></tr><tr><td align=\"left\">NPV</td><td char=\".\" align=\"char\">0.407</td></tr><tr><td align=\"left\">Logged diagnostic odds ratio</td><td char=\".\" align=\"char\">0.909</td></tr><tr><td align=\"left\">Youden’s index</td><td char=\".\" align=\"char\">0.780</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Spearman correlation coefficients of diagnostic metrics and entropy removal.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Metric</th><th align=\"left\">Spearman coefficient</th></tr></thead><tbody><tr><td align=\"left\">Sensitivity</td><td char=\".\" align=\"char\">0.550</td></tr><tr><td align=\"left\">Specificity</td><td char=\".\" align=\"char\">0.741</td></tr><tr><td align=\"left\">PPV</td><td char=\".\" align=\"char\">0.712</td></tr><tr><td align=\"left\">NPV</td><td char=\".\" align=\"char\">0.456</td></tr><tr><td align=\"left\">Logged diagnostic odds ratio</td><td char=\".\" align=\"char\">0.945</td></tr><tr><td align=\"left\">Youden’s index</td><td char=\".\" align=\"char\">0.890</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Comparison of diagnostic metrics of tests for pneumothorax.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Pneumothorax evaluation</th><th align=\"left\">Entropy removal</th><th align=\"left\">Sensitivity (%)</th><th align=\"left\">Specificity (%)</th><th align=\"left\">NPV (%)</th><th align=\"left\">PPV (%)</th></tr></thead><tbody><tr><td align=\"left\">Chest US</td><td char=\".\" align=\"char\">82.38%</td><td char=\".\" align=\"char\">95.12</td><td align=\"left\">98.87</td><td align=\"left\">96.89</td><td char=\".\" align=\"char\">98.20</td></tr><tr><td align=\"left\">Supine AP CXR</td><td char=\".\" align=\"char\">40.94%</td><td char=\".\" align=\"char\">55.83</td><td align=\"left\">100</td><td align=\"left\">100</td><td char=\".\" align=\"char\">86.02</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Comparison of diagnostic metrics for thoracic aortic dissection evaluation.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Thoracic aortic dissection evaluation</th><th align=\"left\">Entropy removal (%)</th><th align=\"left\">Sensitivity (%)</th><th align=\"left\">Specificity (%)</th><th align=\"left\">NPV (%)</th><th align=\"left\">PPV (%)</th></tr></thead><tbody><tr><td align=\"left\">TEE</td><td char=\".\" align=\"char\">83.69</td><td char=\".\" align=\"char\">94.80</td><td char=\".\" align=\"char\">99.28</td><td char=\".\" align=\"char\">98.76</td><td char=\".\" align=\"char\">96.92</td></tr><tr><td align=\"left\">Helical CT</td><td char=\".\" align=\"char\">87.23</td><td char=\".\" align=\"char\">97.64</td><td char=\".\" align=\"char\">98.90</td><td char=\".\" align=\"char\">99.31</td><td char=\".\" align=\"char\">96.28</td></tr><tr><td align=\"left\">MRI</td><td char=\".\" align=\"char\">81.36</td><td char=\".\" align=\"char\">93.33</td><td char=\".\" align=\"char\">99.30</td><td char=\".\" align=\"char\">98.32</td><td char=\".\" align=\"char\">97.13</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Results of machine learning analysis for medical decision-making algorithms.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">MDM algorithm</th><th align=\"left\">ML model prediction accuracy</th><th align=\"left\">Entropy removal (percentage)</th><th align=\"left\">Most important metric (as defined by entropy removal)</th><th align=\"left\">Most important metric (as defined by feature importance)</th></tr></thead><tbody><tr><td align=\"left\">Step-by-step approach to febrile infants</td><td char=\".\" align=\"char\">0.963</td><td align=\"left\">0.0295 (11.9%)</td><td align=\"left\">Abnormal pediatric triangle assessment/ill-appearing (0.0117)</td><td align=\"left\">Abnormal pediatric triangle assessment/ill-appearing (0.395)</td></tr><tr><td align=\"left\">PECARN (age &lt; 2 years)</td><td char=\".\" align=\"char\">0.994</td><td align=\"left\">0.0130 (16.5%)</td><td align=\"left\">Altered mental status (0.00783)</td><td align=\"left\">Altered mental status (0.302)</td></tr><tr><td align=\"left\">PECARN (age ≥ 2 years)</td><td char=\".\" align=\"char\">0.990</td><td align=\"left\">0.0111 (16.8%)</td><td align=\"left\">Altered mental status (0.00729)</td><td align=\"left\">Altered mental status (0.655)</td></tr></tbody></table></table-wrap>" ]

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id=\"M4\"><mml:msub><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq2\"><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{i} \\times log_{2} \\left( {p_{i} } \\right)$$\\end{document}</tex-math><mml:math id=\"M6\"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq3\"><alternatives><tex-math 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id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{i}$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:msub><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq7\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{i}$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:msub><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$entropy_{parent \\,node} = \\left[ {\\frac{FP + TN}{N} \\times \\left( {log_{2} \\left( N \\right) - log_{2} \\left( {FP + TN} \\right)} \\right)} \\right] + \\left[ {\\frac{TP + FN}{N} \\times \\left( {log_{2} \\left( N \\right) - log_{2} \\left( {TP + FN} \\right)} \\right)} \\right]$$\\end{document}</tex-math><mml:math id=\"M18\" display=\"block\"><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:mfrac><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>N</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:mfrac><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>N</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$entropy_{child \\,node \\,1} = \\left[ {\\frac{TP}{{n_{positive} }} \\times \\left( {log_{2} \\left( {n_{positive} } \\right) - log_{2} \\left( {TP} \\right)} \\right)} \\right] + \\left[ {\\frac{FP}{{n_{positive} }} \\times \\left( {log_{2} \\left( {n_{positive} } \\right) - log_{2} \\left( {FP} \\right)} \\right)} \\right]$$\\end{document}</tex-math><mml:math id=\"M20\" display=\"block\"><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>h</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>d</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">TP</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">TP</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">FP</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">FP</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$entropy_{child \\,node \\,2} = \\left[ {\\frac{FN}{{n_{negative} }} \\times \\left( {log_{2} \\left( {n_{negative} } \\right) - log_{2} \\left( {FN} \\right)} \\right)} \\right] + \\left[ {\\frac{TN}{{n_{negative} }} \\times \\left( {log_{2} \\left( {n_{negative} } \\right) - log_{2} \\left( {TN} \\right)} \\right)} \\right]$$\\end{document}</tex-math><mml:math id=\"M22\" display=\"block\"><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>p</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>h</mml:mi><mml:mi>i</mml:mi><mml:mi>l</mml:mi><mml:mi>d</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">FN</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">FN</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">TN</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">TN</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} &amp; entropy \\,removal = \\left[ {\\left( {\\frac{FP + TN}{N} \\times (log_{2} \\left( N \\right) - log_{2} \\left( {FP + TN} \\right)} \\right) + \\left( {\\frac{TP + FN}{N} \\times (log_{2} \\left( N \\right) - log_{2} \\left( {TP + FN} \\right)} \\right)} \\right] \\\\ &amp; \\quad - \\left[ {\\left[ {\\left( {\\frac{{n_{positive} }}{N}} \\right)\\left( {\\frac{TP}{{n_{positive} }} \\times (log_{2} \\left( {n_{positive} } \\right) - log_{2} \\left( {TP} \\right))} \\right) + \\left( {\\frac{FP}{{n_{positive} }} \\times (log_{2} \\left( {n_{positive} } \\right) - log_{2} \\left( {FP} \\right))} \\right)} \\right]} \\right. \\\\ &amp; \\quad + \\left. {\\left[ {\\left( {\\frac{{n_{negative} }}{N}} \\right)\\left( {\\frac{FN}{{n_{negative} }} \\times (log_{2} \\left( {n_{negative} } \\right) - log_{2} \\left( {FN} \\right)} \\right) + \\left( {\\frac{TN}{{n_{negative} }} \\times (log_{2} \\left( {n_{negative} } \\right) - log_{2} \\left( {TN} \\right)} \\right)} \\right]} \\right] \\\\ \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M24\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd/><mml:mtd columnalign=\"left\"><mml:mrow><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>p</mml:mi><mml:mi>y</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:mfrac><mml:mrow><mml:mo>×</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi></mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>N</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>F</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:mfrac><mml:mrow><mml:mo>×</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi></mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>N</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>T</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>F</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>-</mml:mo><mml:mfenced open=\"[\"><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub><mml:mi>N</mml:mi></mml:mfrac></mml:mfenced><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">TP</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>×</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">TP</mml:mi></mml:mrow></mml:mfenced><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">FP</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>×</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">positive</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">FP</mml:mi></mml:mrow></mml:mfenced><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mfenced close=\"]\"><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub><mml:mi>N</mml:mi></mml:mfrac></mml:mfenced><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">FN</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mrow><mml:mo>×</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi></mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">FN</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"italic\">TN</mml:mi></mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mrow><mml:mo>×</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi></mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">negative</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mi>g</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"italic\">TN</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$ni_{j} = w_{j} C_{j} - w_{left\\left( j \\right)} C_{left\\left( j \\right)} - w_{right\\left( j \\right)} C_{right\\left( j \\right)}$$\\end{document}</tex-math><mml:math id=\"M26\" display=\"block\"><mml:mrow><mml:mi>n</mml:mi><mml:msub><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>f</mml:mi><mml:mi>t</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>j</mml:mi></mml:mfenced></mml:mrow></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>f</mml:mi><mml:mi>t</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>j</mml:mi></mml:mfenced></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>h</mml:mi><mml:mi>t</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>j</mml:mi></mml:mfenced></mml:mrow></mml:msub><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>h</mml:mi><mml:mi>t</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>j</mml:mi></mml:mfenced></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$fi_{i} = \\frac{{\\mathop \\sum \\nolimits_{j: \\,node \\,j \\,splits \\,on \\,feature i}^{{}} ni_{j} }}{{\\mathop \\sum \\nolimits_{k\\epsilon \\,all \\,nodes}^{{}} ni_{k} }}$$\\end{document}</tex-math><mml:math id=\"M28\" display=\"block\"><mml:mrow><mml:mi>f</mml:mi><mml:msub><mml:mi>i</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>:</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>j</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>s</mml:mi><mml:mspace 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[ "<table-wrap-foot><p>623 diagnostic tools were analyzed (<italic>p</italic> &lt; .001). <italic>Note</italic>: diagnostic odds ratio was logged for correlation analysis because it displayed an exponential relationship with entropy removal.</p></table-wrap-foot>", "<table-wrap-foot><p>623 diagnostic tools were analyzed (<italic>p</italic> &lt; .001). <italic>Note</italic>: diagnostic odds ratio was logged for correlation analysis because it displayed an exponential relationship with entropy removal.</p></table-wrap-foot>", "<table-wrap-foot><p>Chest ultrasound (US) for pneumothorax diagnosis showed greater entropy removal than supine anterior–posterior (AP) chest x-ray (CXR).</p></table-wrap-foot>", "<table-wrap-foot><p>Helical CT scan had the greatest entropy removal for thoracic aortic dissection when compared with transesophageal echocardiogram (TEE) and magnetic resonance imaging (MRI).</p></table-wrap-foot>", "<table-wrap-foot><p>Three medical decision-making algorithms were analyzed using bootstrapped data, revealing their robust diagnostic value and providing in-depth insight on each algorithm’s individual steps. PECARN: Pediatric Emergency Care Applied Research Network Pediatric Head Injury/Trauma Algorithm.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Shuhan He and Paul Chong.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">The unabated progress in science, technology, and innovation, combined with the exponential rate of change facilitated by the proliferation of computerized capabilities and artificial intelligence (AI), calls for reassessing the food science, technology, and engineering (FST&amp;E) education. The fourth industrial revolution (i.e., Industry 4.0) highlights significant progress in numerous fields, including robotics, smart sensors, AI, the Internet of Things (IoT), big data, cloud computing, safety, and production efficiency^{##UREF##0##1##}. Climate change, global population growth, high levels of food loss and food waste, and the risk of new disease or pandemic outbreaks are examples of numerous challenges that are potential threats to future food sustainability and the security of the planet that urgently need to be addressed^{##UREF##1##2##}.</p>", "<p id=\"Par3\">The projected global population growth reaching 10 billion people by 2050 highlights the acute need for new evaluations of FST&amp;E education system background to address mounting challenges and opportunities. The complexity and predicted immense size of future tasks call for new paradigms, an open innovation mentality, and a novel mindset promoting multidisciplinary collaborations and partnerships^{##UREF##2##3##}.</p>", "<p id=\"Par4\">Disruptions such as digital agriculture, the fourth industrial revolution (industry 4.0), food agility, big data, and AI have been utilized to characterize the changes in the way agro-food systems evolve and function, as well as in the approach they have been analyzed, measured, and monitored^{##REF##33401934##4##}. For instance, Wageningen University, one of the leading influential universities, has also taken an active strategy to align with the developments in IT and AI. Apart from the content-wise shift, skills such as critical thinking, creativity, and problem-solving are addressed by applying project-based evaluations^{##UREF##3##5##}. The industrial revolution (industry 4.0) and moving to industry 5.0 include new enabling technologies (e.g., big data, IoT, cloud computing) besides AI, digital twins, machine learning, virtualization, and others^{##UREF##4##6##}.</p>", "<p id=\"Par5\">Food science and technology (FST) and especially food engineering (FE) in academia face diminishing funding for research, dwindling critical masses in faculties (particularly at universities in the USA), decreasing student enrollment^{##UREF##5##7##} and impacting future cooperative extension education and research needs^{##UREF##6##8##}. This leads to the observation by some food-related education programs to be at a crossroads and the need to reassess their vision and expand the scope to grand societal drivers such as health and wellness (H&amp;W), the mutual host and the microbiome considerations, food security and safety, population growth, aging, water and land scarcity, and environmental concerns^{##REF##30805342##9##}. Other reasons for integrating stakeholders outside the food manufacturing industry have been proposed^{##UREF##7##10##,##UREF##8##11##}. Members of the FST&amp;E professions request a broader and more applied education that offers better opportunities for entrepreneurship^{##UREF##9##12##} .</p>", "<p id=\"Par6\">FST&amp;E professions are witnessing significant challenges as well as changes imposed by the accelerated rate of change and digital transformation. The expected changes will most probably affect FST&amp;E education as already projected previously^{##UREF##5##7##,##UREF##7##10##–##UREF##12##15##}. This forward-looking, combined with the radical changes witnessed during and post-COVID-19, calls for a change in traditional education and curricula paradigms. For instance, the new vision deploys concepts of FST&amp;E in the context of sustainable food processes, products for changing lifestyles and beliefs, innovation for H&amp;W, and novel methodologies that suit audiences of the digital age. Courses on entrepreneurship and innovation, novel education methods, and enforcing quality standards and certification have been also proposed for Europe^{##UREF##11##14##}.</p>", "<p id=\"Par7\">Engineering education is also experiencing dramatic changes. The traditional teaching model, where students are passive in the lecture room, gives way to more active, student-centered, and participatory approaches. Different modern education and learning techniques, such as blended and flip-classroom, active learning, use of technology in teaching, universal design, and student-centered education approach, among others, were previously reported^{##UREF##7##10##}. For instance, active learning utilizing a teaching app called TopHat (<ext-link ext-link-type=\"uri\" xlink:href=\"https://tophat.com/\">https://tophat.com/</ext-link>) to administer a daily quiz, encouraged group work and discussion, and peer evaluation was also reported^{##UREF##13##16##}.</p>", "<p id=\"Par8\">Active engineering learning promotes the acquisition of knowledge and essential soft skills such as teamwork, problem-solving abilities, and entrepreneurial mindsets^{##UREF##14##17##}. It also encourages the utilization of digital technologies such as simulation software and virtual laboratories^{##UREF##14##17##}. It is worth noting the pioneering virtual experiments and laboratories in food science, technology processing, and engineering area^{##UREF##15##18##}.</p>", "<p id=\"Par9\">Among novel methodologies suggested for engineering education are project-based learning, hybrid learning, the flipped classroom, and design thinking^{##UREF##7##10##,##UREF##16##19##–##UREF##18##21##} .</p>", "<p id=\"Par10\">The role of the food industry and other related sectors in contributing to and assisting educational institutions in designing curricula that provide the skills demanded by the job market was highlighted recently. It emphasized that current Bachelor´s and Master´s degrees follow programs that attempt to offer a practical perspective but still focus on the academic point of view. To bridge the gap between academia and industry, the University Extension Diploma in Food Technology (DEUTA) deepens into the food sector, seeking professional qualifications for participants. This is achieved by both first-hand know-how of food sector professionals and academics, along with an internship period in a food company. Collaborative courses strengthen academia-industry bonds, and employability is boosted thanks to internships and the network created^{##UREF##19##22##}.</p>", "<p id=\"Par11\">Innovation and entrepreneurship are key factors to provide added value for food systems. Based on the findings of the Erasmus+ Strategic Partnership BoostEdu (<ext-link ext-link-type=\"uri\" xlink:href=\"https://erasmus-plus.ec.europa.eu/\">https://erasmus-plus.ec.europa.eu/</ext-link> assessed May 16, 2023), three knowledge gaps were reported: (1) identify the needs for innovation and entrepreneurship (I&amp;E) in the food sector; (2) understanding the best way to organize learning; (3) providing flexibility in turbulent times. The results of the project, in particular during the COVID-19 pandemic, highlighted the need for flexible access to modules that are complementary to other sources and based on a mix of theoretical concepts and practical experiences. The main lessons learned concern the need for co-creation and co-learning processes to identify suitable practices for the use of innovative digital technologies^{##UREF##20##23##}. However, there are experts objecting to entrepreneurship courses being a subject of FST&amp;E curricula or that the curricula should be supported with outside presentations or invited talks on this topic. This contrary position could be probably explained by the contrast between academia and more applied and industrial occupations. As the vast majority of the FST&amp;E graduates are employed in various businesses where innovation and startup activities are becoming essential, entrepreneurship aspects should be considered in future education.</p>", "<p id=\"Par12\">New platforms, such as massive open online courses (MOOCs), webinars, blogs, Facebook, Instagram, and Twitter, have opened up new spaces for disseminating ideas, experiences, and training in food-related matters^{##UREF##21##24##}. Online and open learning permits access anytime and anywhere to formal classes, education modules on specific topics, and informal discussion sites^{##UREF##21##24##}. Thus effectively democratizing learning, disseminating knowledge to vast audiences, and coping with the educational demands during the COVID-19 pandemic^{##UREF##22##25##}.</p>", "<p id=\"Par13\">The overall objectives of this study were: 1. Assessing the current status of FST&amp;E education by using a computerized global survey; 2. Identifying current challenges and opportunities; and 3. Suggest recommendations (if needed) for additional directions and topics for future curricula.</p>" ]

[ "<title>Methods</title>", "<p id=\"Par58\">The approach employed encompassed a structured questionnaire, adopting a methodology akin to the one described earlier^{##UREF##9##12##,##UREF##12##15##}. The questionnaire is provided in the ##SUPPL##0##Supplementary information## data file. The online questionnaire survey utilized the Qualtrics© software (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.qualtrics.com/\">https://www.qualtrics.com/</ext-link>) and targeted global professionals (including students) across the food sector and nutrition. The key questions were formulated to capture the perspectives on professional values held by individuals in the studied fields. The initial questionnaire was pretested (these data were not utilized in the final analysis) using a pilot sample (<italic>n</italic> = 12) of selected food practitioners from academia and the food industry. This panel was selected based on previous personal and professional interactions. The pilot was employed to ensure the questionnaire’s consistency and to seek suggestions on additional topics that should be incorporated into the revised survey.</p>", "<p id=\"Par59\">The link of the webpage of the questionnaire was distributed by e-mails of numerous organizations (e.g., IUFoST, ISEKI-Food Association, SoFE, IFT) and food practitioners globally. The survey was conducted in English, avoiding any possible language ambiguities. It was completely anonymous and was open from the end of May until the end of July 2022. Both mobile and computerized feedback was offered.</p>", "<p id=\"Par60\">A 5-point Likert-type scale^{##UREF##23##26##} was applied and consisted of 1 (‘Very low’), 2 (‘Low’), 3 (‘Medium’), 4 (‘High’), and 5 (‘Very high’). For comparisons, the Likert-type scale assessments were transformed into a calculated average. The Likert-type scale is widely employed as a fundamental and commonly utilized psychometric instrument in educational and social sciences research, marketing research, customer satisfaction studies, opinion surveys, and numerous other fields. One topic included ranking (from 1 to 5; each rank could appear only once).</p>", "<p id=\"Par61\">Apart from the professional questions, the survey included demographic information such as gender, age group, location where the most advanced degree was obtained, or current place for study according to the following geographic categories: Western Europe, Eastern Europe, UK, North America including Canada, Mexico, South America, Asia/Middle East, China, Far East (excluding China), Oceania (Australia, New Zealand), and Africa. The questionnaire ended with an open-ended question asking for the interview’s possible suggestions for curriculum improvements. The data were analyzed using Microsoft Excel© spreadsheet (Redmont, Washington), JASP software (ver. 0.16.4, <ext-link ext-link-type=\"uri\" xlink:href=\"https://jasp-stats.org/\">https://jasp-stats.org/</ext-link>), and IBM SPSS Statistics for Windows (version 28; IBM Corp., Armonk, New York). For significant differences (<italic>p</italic> &lt; 0.05) among groups, one-way ANOVA with a post-hoc least significant difference (LSD) test was performed. A two-sided <italic>t</italic>-test was utilized to identify significant differences (<italic>p</italic> &lt; 0.05) between the averages of the two groups.</p>", "<p id=\"Par62\">The survey was written according to the authorization from the Committee for the Use of Human Subjects in Research through The Robert H. Smith Faculty of Agriculture, Food and Environment of The Hebrew University of Jerusalem (file: AGHS/01.15) as outlined previously^{##UREF##9##12##}. Before starting the study, the participants were informed that the responses were completely anonymous. Also, before starting the questionnaire, the consent of the participants was requested, and only those who agreed were able to start the study.</p>", "<title>Reporting summary</title>", "<p id=\"Par63\">Further information on research design is available in the ##SUPPL##1##Nature Research Reporting Summary## linked to this article.</p>" ]

[ "<title>Results and discussion</title>", "<title>Respondents</title>", "<p id=\"Par14\">The total number of respondents that started the questionnaire was 1022. Of these, 703 (68.8%) respondents (the panel) completed the survey. Data from respondents who failed to address all questions and had several missing values were omitted, as they ignored or preferred not to answer some of the questions. The relatively high number of excluded respondents was probably due to the language barrier. Although not explicitly asked, based on respondents’ IP addresses, 88 countries participated in the survey. The overall time for completing the survey was approximately 10–12 min.</p>", "<title>Demographics and geographic distribution</title>", "<p id=\"Par15\">Demographic data are presented in Table ##TAB##0##1##. The panel was evenly distributed: gender (female/male 1.15:1.00), age (excluding the 18–25 years group, 7.5%). Age distribution indicates good participation of the various groups and experiences.</p>", "<p id=\"Par16\">The geographical location of the respondents indicates a global representation, although some regions were more prevalent by the panel. Respondents from China, the Far East (excluding China), and Oceania also participated, but their overall percentage was relatively low (combined value of 4.4%). However, combining Asia and the Middle East respondents resulted in a significant representation (16.5%). The surprising outcome was the high number of African respondents (14.8), probably due to the good network of IUFoST contacts in Africa. Although participation was quite impressive in terms of global feedback (88 countries), the number of respondents in a specific region was quite low in some cases, and consolidation was necessary for further analysis. Nevertheless, the widespread number of respondents from a wide spectrum of countries demonstrated that the survey had a global distribution, offering a significant improvement compared with a previous study^{##UREF##12##15##}.</p>", "<title>Main professional activities and education</title>", "<p id=\"Par17\">The panel (703 respondents) professions consisted of food scientists and technologists (FSTs) 398 (56.6%), food engineers (FEs) 120 (17.1%), microbiologists (HMs) 25 (3.6%), nutritionists (HNs) 35 (5.0%), chemical engineers (CEs) 19 (2.7%), bioengineering/biotechnology (BBs) 7 (1.0%), business/marketing (BMs) 14 (2.0%), consultants (COs) 41 (5.8%), and others (food trade company, regulators, etc.) 41 (5.8%). As 73.7% of the respondents were FSTs and FEs, students, and graduates, the data reflect professional positions within FST&amp;E disciplines, as was also previously shown^{##UREF##12##15##}.</p>", "<p id=\"Par18\">The respondents were also asked to fill in all their degrees in the various education categories using up to 4 options (student, BSc/1st Degree, MSc/equivalent, and Ph.D./DSc). Fig. ##FIG##0##1## highlights the panel degrees distribution. The relatively high number of doctoral (Ph.D./DSc, 464, 29.9%) is not surprising considering the academic affiliation of most of the respondents (see Section “Affiliation”). It should be noted that many of the respondents hold more than one degree, explaining the high number of overall degrees of the panel (1550), as also depicted in Fig. ##FIG##0##1##.</p>", "<title>Affiliation</title>", "<p id=\"Par19\">The combined high majority of the respondents affiliated with educational and private research institutes (71.7%) provides a possible explanation for the extra number of doctoral degrees in the panel. Conversely, based on the respondents in the age group 41–55 and above 55 (37.8 and 28.7%, respectively) and the fact that a high percentage of the majority of the respondents hold a doctoral degree, the data are likely to reflect professional middle to high management levels and leadership positions within educational, institutions and possibly in the food industry. It should be noted that the number of respondents from industrial affiliation (food industry, food service, startups/FoodTech, and consultants, excluding government) was quite high (18.2%), probably projecting that although academia and industry are not equally represented, industrial affiliations are well represented (i.e., 128 responders).</p>", "<title>Topics affecting the future of the professional domain curricula</title>", "<p id=\"Par20\">The importance of 10 topics to be included in developing future curricula using the Likert-type scale^{##UREF##23##26##} was evaluated. The topics listed included post-COVID-2019 considerations and several other new concepts. Table ##TAB##1##2## shows that 7 topics were evaluated above 4.0 (‘High’) based on the calculated Likert-type scores average. The highest average scores were: ‘Critical thinking’ (4.50), followed by ‘Problem-solving projects’ (4.44), ‘Teamwork/collaboration’ (4.31), ´Innovation/Open innovation’ (4.29), and ‘Multidisciplinary’ (4.24). These data highlight possible changes that the FST&amp;E domains anticipate in the post-COVID-19 and remote or hybrid education/learning, as well as the further proliferation of innovation and OI.</p>", "<p id=\"Par21\">It is important to note that business-related topics were evaluated as less important, with Likert-type scores averaging below 4.0. These included: ‘Soft skills’ (3.90), followed by ‘Entrepreneurship’ (3.77), and ‘Business creation/networking’ (3.70). ‘Entrepreneurship’ and ‘Business creation/network’ could bring many benefits, such as fostering innovation, productivity, competitiveness, new business, OI, and socioeconomic development. Yet, these topics were considered among those of less importance, probably indicating that the panel was less oriented to business-related topics.</p>", "<p id=\"Par22\">The search for professionals with different skills to overcome the current and foreseen challenges relevant to the agri-food sector was previously studied^{##UREF##22##25##}. It was shown that problem-based learning (PBL), described as an instructional approach, promotes interdisciplinary and critical thinking with the potential to meet current challenges. PBL, aligned with an innovation program and contest, integrated into a master’s degree in FE to promote academic entrepreneurship, allowed the development of innovative products intending to solve problems faced by the agri-food sector^{##UREF##24##27##}. The latter information supports the current survey data that show that the highest perceived topics were ‘Critical thinking’ (4.50) and ‘Problem-solving projects’ (4.44). On the other hand, the relatively low perceived importance of entrepreneurship (3.77 ranked #9) could indicate that FSs, FTs, or FEs are currently considering business-related topics as a lower priority. Nevertheless, their Likert average scores were approaching ‘High’. It is important to note that promoting project-based learning by students on developing eco-designed business models and eco-innovated food products seems to be an essential lever for the sustainability transition^{##UREF##7##10##}. Although this is just one example, it highlights the importance of project-based learning^{##UREF##24##27##–##UREF##26##29##}.</p>", "<p id=\"Par23\">Project-based learning is an integrated part of the flipped classroom (FC) model, based on active learning, and consequently attracts much interest. The FC is a form of blended learning (BL) that reorganizes the workload in and outside the classroom and requires the active participation of students in learning activities before and during face-to-face lessons with teachers^{##UREF##7##10##,##UREF##27##30##}. The FC model has been applied since the 1990s to encourage student preparation before classes: team-based learning, peer or mentor instruction, and just-in-time education, where the teaching information is communicated via electronic means. This allows more class time to be devoted to active learning and formative assessment^{##UREF##28##31##}. A recent study highlighted a case study where an elective FC course on engineering, science, and gastronomy was implemented for undergraduate students that included in-class demonstrations by chefs. New education methodologies call for expanded computational abilities, ample access to online content, active learning, and student-centered approaches^{##UREF##7##10##}.</p>", "<p id=\"Par24\">A comparison between traditional project-based learning and hybrid project-based learning indicated a significant increase in fundamental formative knowledge, enhanced problem-solving abilities, and production of better-performing artifacts regarding the set of design skills for students undergoing hybrid project-based learning^{##UREF##25##28##}.</p>", "<p id=\"Par25\">In light of the feedback by the panel indicating that ‘Critical thinking development’ and ‘Problem-solving projects’ were the highest outcome (#1 and #2, respectively), combined with recent reports on the FC importance, it could be concluded that seeking new directions in learning/facilitating strategies that complement existing methods in order to enrich the learning experience of students is recommended.</p>", "<title>Academic partnership/collaboration</title>", "<p id=\"Par26\">The respondents were instructed to rank (from 1 to 5, corresponding to high to low; each rank could appear only once) the importance of partnership(s) and/or collaboration(s) with: ‘Food Industry´, ‘Nutrition sciences’, ‘Government, policymakers and/or local authorities’, ‘Private sector’, and ‘Other academic disciplines’. The ranking distribution is depicted in Fig. ##FIG##1##2##.</p>", "<p id=\"Par27\">Collaboration with the ‘Food industry’ was ranked the highest, while the collaboration with ‘Other academic programs’ was ranked lower. Furthermore, the top two rankings (‘Very high’ and ‘High’) were ‘Food industry’ (53%), ‘Nutrition’ (38%), ‘Government’ (36%), ‘Private institutes (35%) and ‘Other academic programs’ (33%).</p>", "<p id=\"Par28\">Collaboration with the nutrition sector was highly ranked. This demonstrates that the panel considered collaboration between FST&amp;E and nutrition highly important and is a direction that these domains should consider closely. The need to enhance and probably integrate or converge nutrition sciences and FST&amp;E is underscored due to the lack of present collaboration and the growing consumers’ awareness of H&amp;W and food processing.</p>", "<p id=\"Par29\">The role of the food industry as a key player in academic partnership and collaboration should be considered, particularly due to the negative aspects suggested by the NOVA ultra-food processes food classification. For instance, “<italic>By design, these products are highly palatable, cheap, ubiquitous, and contain preservatives that offer a long shelf life. These features, combined with aggressive industry marketing strategies, contribute to excessive consumption and make these products highly profitable for the food, beverage, and restaurant industry sectors that are dominant actors in the global food system</italic>”^{##UREF##29##32##}. This study demonstrates that the food industry plays significant positive roles in both collaboration and partnerships. It also plays a key part in internships described below (Section “Internships”).</p>", "<title>Topics importance to FST&amp;E</title>", "<p id=\"Par30\">The importance of 11 topics for FST&amp;E was assessed as listed in Table ##TAB##2##3##.</p>", "<p id=\"Par31\">The data exposed 5 top important topics to FST&amp;E. The topic of highest interest was ‘Sustainability, circular economy, and food waste management,’ followed by ‘Innovation/open innovation’ and ‘New product development’ (no statistically significant difference between these topics), ‘Consumer perception &amp; trust’ and ‘Nutrition sciences’ that were statistically different from the first two topics (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt;0.05), respectively. Worth noting the significant differences between FSTs and FEs in ‘Sustainability, circular economy, and food waste management’, ‘New product development’, ‘Consumer perception &amp; trust’, and ‘Nutrition Sciences’, where FSTs significantly assigned higher importance to these topics in comparison with FEs. However, no significant difference was found for ‘Innovation/open innovation’.</p>", "<p id=\"Par32\">‘Artificial Intelligence, machine learning’ was only ordered as #9 based on the Likert-type scores averages, and FEs considered it significantly higher than FSTs. It is safe to predict that the importance of AI will increase in the coming years once more and more applications and utilizations will emerge. Suffice to consider recent applications and the global AI market size growth from $65.48 billion in 2020, projected to reach $1581.70 billion by 2030, growing at a CAGR of 38.0% from 2021 to 2030 (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.alliedmarketresearch.com/artificial-intelligence-market\">https://www.alliedmarketresearch.com/artificial-intelligence-market</ext-link>).</p>", "<title>Importance to FST&amp;E curricula to meet future challenges and learning opportunities</title>", "<p id=\"Par33\">The importance of the curricula in meeting FST&amp;E future challenges and learning opportunities (in descending order) is highlighted in Table ##TAB##3##4##.</p>", "<p id=\"Par34\">Table ##TAB##3##4## shows five topics were considered to be of ‘Very high’ to ‘High’ importance: ‘Research project(s)’ (4.34), ‘Apprenticeships (e.g., industrial training)’ (4.28), ‘Adaptability (e.g., adjusting to change in real-time, managing biases, overcome challenges)’ (4.22), ‘Revision current programs’ (4.16), and ‘Employability’ (4.13). The other topics received lower scores.</p>", "<p id=\"Par35\">The significant difference between FSTs and FEs on ‘Research project(s)’, ‘Enhanced integration with nutrition’, and ‘Soft (life) skills’ is worth noting. On these topics, except for ‘Enhanced integration with nutrition’, FSTs scores were significantly higher when compared with FEs. The ´Enhanced integration with nutrition´ by both FSTs and FEs was ‘High’ (4.00) and above, projecting the absolute need for FST&amp;E to enhance its collaboration with nutrition, mainly due to the high importance of H&amp;W and its significant role.</p>", "<p id=\"Par36\">Adaptability is the potential to adjust and learn new skills in response to changing factors, conditions, cultures, and environments. It is a soft skill that both colleagues and superiors highly value. In the ever-changing needs and progress, businesses and employees must adapt quickly to unforeseen dynamic circumstances, innovation, and disruption. Adaptability means being flexible, innovative, open, and resilient, particularly under unforeseen conditions. Some key elements of being adaptable are confident but open to criticism, focusing on solutions rather than problems, collaborating with others, and learning from them (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.walkme.com/glossary/adaptability/\">https://www.walkme.com/glossary/adaptability/</ext-link>). For instance, the a<italic>daptability</italic> of FST developments implies a capacity to continuously change and improve its operations and food quality output in time and space^{##UREF##30##33##}. This explains the #3 place the panel considered adaptability.</p>", "<p id=\"Par37\">The panel perceived both ‘Revision of current programs’ and ‘Employability’ as high priority (#4 and #5, average of 4.16 and 4.13, respectively). These assessments should be considered carefully by academic programs in order to adapt to the fast changes driven by innovation, disruption, and digital progress.</p>", "<p id=\"Par38\">‘Enhanced integration with nutrition’ came in #6. However, FSTs and FEs indicated this topic is highly important (average of 4.00 and 4.21, respectively). Hence, FST&amp;E education programs should seek avenues to enhance integration with nutrition science. Possible collaborations should consider joint research programs and other partnerships and alliances.</p>", "<p id=\"Par39\">‘Business-related activities (e.g., creation, network, partnerships, collaboration)’ and ‘Soft (life) skills’ were #7–8. Nevertheless, their Likert-type average values were close to ‘High’. Hybrid teaching was perceived as the last (3.78). Apparently, this type of education is not very appealing. Yet, this should be reassessed after the Covid-19 pandemic has passed.</p>", "<p id=\"Par40\">Engineering education is also experiencing dramatic changes. The traditional teaching model, where students are passive in the lecture room, gives way to more active, student-centered, and participatory approaches. Different modern education and learning techniques, such as blended and flip-classroom, active learning, use of technology in teaching, universal design, and student-centered education approach, among others, were previously reported^{##REF##30805342##9##}. Hence, it is expected that Hybrid teaching and other advanced methods, including AI, will flourish soon and will become the norm.</p>", "<title>Internships</title>", "<p id=\"Par41\">The importance of internship to FST&amp;E students was evaluated considering 5 possibilities: ‘Academic internship,’ ‘Food industry internship,’ ‘Start-up/FoodTech company internship,’ ‘Other domains/industries,’ and ‘Internship in other countries.’ The data are depicted in Fig. ##FIG##2##3##.</p>", "<p id=\"Par42\">The internship was categorized into three statistically different groups (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05). The first group was internships in ‘Food Industry’ (4.60), followed by the second group: ‘Start-ups/Food Tech’ (4.04), ‘Other countries’ (3.98), and ‘Academia’ (3.96), and the third group ‘Others domains/industries’ (3.46). Comparing the difference between FSTs and FEs, respondents showed a significant difference (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05) for internships in ‘Food Industry’ (4.65 and 4.52), ‘Start-ups/Food Tech’ (4.11 and 3.89) and ‘Other domains/industries’ (3.46 and 3.26), respectively. It is not surprising that FSTs have consistently assigned higher values to internships, probably due to the possibility that they are more complimentary to hands-on experiences.</p>", "<p id=\"Par43\">Bridging the academia-industry gap in the food sector through collaborative courses and internships was recently studied. More than fifteen years of university extension diplomas in food technology Diplomas demonstrated how collaborative courses strengthen academia-industry bonds, and employability was boosted thanks to internships and the network created^{##UREF##31##34##}. Internships could support students in developing their identity, which is achieved by close contact with their future working tasks^{##UREF##32##35##}, enhancing familiarity with and nearness to their future profession^{##UREF##33##36##} and industry-based projects and governance^{##UREF##34##37##}. Also, student projects in collaboration with the industry make the students face a reality^{##UREF##19##22##}. In light of these benefits, it is clear why the internship in the food industry received such a high Likert-type average. This very high importance given by the panel to industry internships coincides with their ranking, as aforementioned in the previous section, highlighting the core role of the food industry in students’ education.</p>", "<title>Professional organization impact on FST&amp;E education</title>", "<p id=\"Par44\">The impact of professional organizations on food science/food technology/food engineering education, as well as strategy and vision data, are depicted in Fig. ##FIG##3##4##.</p>", "<p id=\"Par45\">Data analysis (<italic>t</italic>-test) of the impact of the various organizations or vision and strategy on education revealed that the statistically highest Likert-type average scores (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05) were given to the ‘Food industry’ (3.86). ‘IFT (Institute of Food Technologists)’ was in the 2nd statistical group (3.70), followed by the 3rd statistical group that included ‘IUFoST (International Union of Food Science &amp; Technology)’ (3.49), ‘Vision, strategy &amp; leadership of the university’ (3.49), ‘IFST (Institute of Food Science+Technology)’ (3.44), and ‘Government, public interest &amp; support’ (3.42). ‘EFFoST (The European Federation of Food Science and Technology)’ (3.40) was between the 3rd and the 4th group that included ‘ISEKI-Food (European Association for Integrating Food Science and Engineering Into the Food Chain),’(3.27). ‘SoFE (Society of Food Engineering)’ (2.96) was the next statistical group, and the last 6th group was ‘Others’ (2.65).</p>", "<p id=\"Par46\">It is quite surprising that the food industry obtained such a high perceived impact on education, especially because the number of respondents in the panel affiliated with academic and educational institutes was high (69.6%). This could be explained by the fact that most curricula are designed to align with the industrial requirement and/or the need to provide students with the essential tools for the food industry. As no in-depth interviews were conducted, these findings warrant additional consideration.</p>", "<p id=\"Par47\">IFT was in second place, significantly affecting FST&amp;E education. In light of the quite low number of respondents from North America and Canada (13.1%), this finding clearly projects the significant role IFT has in impacting global education and proliferation. The 3rd group included IUFoST, IFST (international and mainly UK organizations, respectively), ‘Vision, strategy &amp; leadership of the university’ and ‘Government, public interest &amp; support´. These different groups and elements were perceived as very important and apparently have a significant role in contributing to the education program. EFFoST was categorized between the 3rd and 4th groups, including ISEKI-Food (3.27). These organizations were perceived as lower compared with the previous organizations. SoFE was classified only in the 5th significantly different group. As SoFE appeals mainly to FEs, many panelists were probably unfamiliar with its activities.</p>", "<title>Education impact on professional expectations</title>", "<p id=\"Par48\">The impact of the respondents’ education curricula on their professional success, satisfaction, and meeting expectations data is depicted in Fig. ##FIG##4##5##.</p>", "<p id=\"Par49\">Education curricula showed two different statistical (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05) groups. The first group included ‘Success’ (4.03) and ‘Satisfaction’ (3.95). The second statistical group that was quite lower evaluated was ‘Meeting expectations’ (3.76). This finding could open new avenues for education institutes to conduct in-depth assessments of their alumni and graduates, focusing on improving their performances in order to better meet their graduates’ future expectations. This study also provides insights into new education and learning opportunities and new topics to be included in future curricula.</p>", "<p id=\"Par50\">When comparing FSTs with FEs, it was quite surprising that FSTs consistently rated all three attributes lower than FEs. In two cases, these differences were even significant: ‘Success’ (4.07 vs. 4.15, one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05), ‘Satisfaction’ (3.96 vs. 4.06), and ‘Meeting expectation’ (3.78 vs. 3.83, one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05). This lower assessment by FSTs highlights that the potential for curriculum improvements is high, and an in-depth evaluation should open new avenues for significant improvements.</p>", "<p id=\"Par51\">In conclusion, these main points are highlighted:<list list-type=\"bullet\"><list-item><p id=\"Par52\">Seven topics affecting the future of the profession domain curricula were evaluated between ‘High’ to ‘Very high’. The highest scores were found for: ‘Critical thinking’, followed by ‘Problem-solving projects,’ ‘Teamwork/collaboration’, ‘Innovation/Open innovation’, and ‘Multidisciplinary’.</p></list-item><list-item><p id=\"Par53\">The importance of Academic partnership/collaboration showed that ‘Food industry’, and ‘Nutrition’ were ranked the highest.</p></list-item><list-item><p id=\"Par54\">Significant positive roles of the food industry in collaboration and partnerships with the FST&amp;E domain were demonstrated. Significant findings were also related to internships, education, strategy, and vision effects of the food industry.</p></list-item><list-item><p id=\"Par55\">Collaboration between FST&amp;E and nutrition sciences indicated its high importance. Integrating or converging nutrition science and FST&amp;E is emphasized based on the lack of actual present collaborations.</p></list-item><list-item><p id=\"Par56\">Assessing the education curricula contribution showed two statistical groups. The first group included ‘Success’ and ‘Satisfaction’. ‘Meeting expectations’ was the second. New avenues to better meet future graduates’ and students’ expectations were identified.</p></list-item><list-item><p id=\"Par57\">Insights into novel education and learning opportunities and new topics to be included in future curricula have been identified.</p></list-item></list></p>" ]

[ "<title>Results and discussion</title>", "<title>Respondents</title>", "<p id=\"Par14\">The total number of respondents that started the questionnaire was 1022. Of these, 703 (68.8%) respondents (the panel) completed the survey. Data from respondents who failed to address all questions and had several missing values were omitted, as they ignored or preferred not to answer some of the questions. The relatively high number of excluded respondents was probably due to the language barrier. Although not explicitly asked, based on respondents’ IP addresses, 88 countries participated in the survey. The overall time for completing the survey was approximately 10–12 min.</p>", "<title>Demographics and geographic distribution</title>", "<p id=\"Par15\">Demographic data are presented in Table ##TAB##0##1##. The panel was evenly distributed: gender (female/male 1.15:1.00), age (excluding the 18–25 years group, 7.5%). Age distribution indicates good participation of the various groups and experiences.</p>", "<p id=\"Par16\">The geographical location of the respondents indicates a global representation, although some regions were more prevalent by the panel. Respondents from China, the Far East (excluding China), and Oceania also participated, but their overall percentage was relatively low (combined value of 4.4%). However, combining Asia and the Middle East respondents resulted in a significant representation (16.5%). The surprising outcome was the high number of African respondents (14.8), probably due to the good network of IUFoST contacts in Africa. Although participation was quite impressive in terms of global feedback (88 countries), the number of respondents in a specific region was quite low in some cases, and consolidation was necessary for further analysis. Nevertheless, the widespread number of respondents from a wide spectrum of countries demonstrated that the survey had a global distribution, offering a significant improvement compared with a previous study^{##UREF##12##15##}.</p>", "<title>Main professional activities and education</title>", "<p id=\"Par17\">The panel (703 respondents) professions consisted of food scientists and technologists (FSTs) 398 (56.6%), food engineers (FEs) 120 (17.1%), microbiologists (HMs) 25 (3.6%), nutritionists (HNs) 35 (5.0%), chemical engineers (CEs) 19 (2.7%), bioengineering/biotechnology (BBs) 7 (1.0%), business/marketing (BMs) 14 (2.0%), consultants (COs) 41 (5.8%), and others (food trade company, regulators, etc.) 41 (5.8%). As 73.7% of the respondents were FSTs and FEs, students, and graduates, the data reflect professional positions within FST&amp;E disciplines, as was also previously shown^{##UREF##12##15##}.</p>", "<p id=\"Par18\">The respondents were also asked to fill in all their degrees in the various education categories using up to 4 options (student, BSc/1st Degree, MSc/equivalent, and Ph.D./DSc). Fig. ##FIG##0##1## highlights the panel degrees distribution. The relatively high number of doctoral (Ph.D./DSc, 464, 29.9%) is not surprising considering the academic affiliation of most of the respondents (see Section “Affiliation”). It should be noted that many of the respondents hold more than one degree, explaining the high number of overall degrees of the panel (1550), as also depicted in Fig. ##FIG##0##1##.</p>", "<title>Affiliation</title>", "<p id=\"Par19\">The combined high majority of the respondents affiliated with educational and private research institutes (71.7%) provides a possible explanation for the extra number of doctoral degrees in the panel. Conversely, based on the respondents in the age group 41–55 and above 55 (37.8 and 28.7%, respectively) and the fact that a high percentage of the majority of the respondents hold a doctoral degree, the data are likely to reflect professional middle to high management levels and leadership positions within educational, institutions and possibly in the food industry. It should be noted that the number of respondents from industrial affiliation (food industry, food service, startups/FoodTech, and consultants, excluding government) was quite high (18.2%), probably projecting that although academia and industry are not equally represented, industrial affiliations are well represented (i.e., 128 responders).</p>", "<title>Topics affecting the future of the professional domain curricula</title>", "<p id=\"Par20\">The importance of 10 topics to be included in developing future curricula using the Likert-type scale^{##UREF##23##26##} was evaluated. The topics listed included post-COVID-2019 considerations and several other new concepts. Table ##TAB##1##2## shows that 7 topics were evaluated above 4.0 (‘High’) based on the calculated Likert-type scores average. The highest average scores were: ‘Critical thinking’ (4.50), followed by ‘Problem-solving projects’ (4.44), ‘Teamwork/collaboration’ (4.31), ´Innovation/Open innovation’ (4.29), and ‘Multidisciplinary’ (4.24). These data highlight possible changes that the FST&amp;E domains anticipate in the post-COVID-19 and remote or hybrid education/learning, as well as the further proliferation of innovation and OI.</p>", "<p id=\"Par21\">It is important to note that business-related topics were evaluated as less important, with Likert-type scores averaging below 4.0. These included: ‘Soft skills’ (3.90), followed by ‘Entrepreneurship’ (3.77), and ‘Business creation/networking’ (3.70). ‘Entrepreneurship’ and ‘Business creation/network’ could bring many benefits, such as fostering innovation, productivity, competitiveness, new business, OI, and socioeconomic development. Yet, these topics were considered among those of less importance, probably indicating that the panel was less oriented to business-related topics.</p>", "<p id=\"Par22\">The search for professionals with different skills to overcome the current and foreseen challenges relevant to the agri-food sector was previously studied^{##UREF##22##25##}. It was shown that problem-based learning (PBL), described as an instructional approach, promotes interdisciplinary and critical thinking with the potential to meet current challenges. PBL, aligned with an innovation program and contest, integrated into a master’s degree in FE to promote academic entrepreneurship, allowed the development of innovative products intending to solve problems faced by the agri-food sector^{##UREF##24##27##}. The latter information supports the current survey data that show that the highest perceived topics were ‘Critical thinking’ (4.50) and ‘Problem-solving projects’ (4.44). On the other hand, the relatively low perceived importance of entrepreneurship (3.77 ranked #9) could indicate that FSs, FTs, or FEs are currently considering business-related topics as a lower priority. Nevertheless, their Likert average scores were approaching ‘High’. It is important to note that promoting project-based learning by students on developing eco-designed business models and eco-innovated food products seems to be an essential lever for the sustainability transition^{##UREF##7##10##}. Although this is just one example, it highlights the importance of project-based learning^{##UREF##24##27##–##UREF##26##29##}.</p>", "<p id=\"Par23\">Project-based learning is an integrated part of the flipped classroom (FC) model, based on active learning, and consequently attracts much interest. The FC is a form of blended learning (BL) that reorganizes the workload in and outside the classroom and requires the active participation of students in learning activities before and during face-to-face lessons with teachers^{##UREF##7##10##,##UREF##27##30##}. The FC model has been applied since the 1990s to encourage student preparation before classes: team-based learning, peer or mentor instruction, and just-in-time education, where the teaching information is communicated via electronic means. This allows more class time to be devoted to active learning and formative assessment^{##UREF##28##31##}. A recent study highlighted a case study where an elective FC course on engineering, science, and gastronomy was implemented for undergraduate students that included in-class demonstrations by chefs. New education methodologies call for expanded computational abilities, ample access to online content, active learning, and student-centered approaches^{##UREF##7##10##}.</p>", "<p id=\"Par24\">A comparison between traditional project-based learning and hybrid project-based learning indicated a significant increase in fundamental formative knowledge, enhanced problem-solving abilities, and production of better-performing artifacts regarding the set of design skills for students undergoing hybrid project-based learning^{##UREF##25##28##}.</p>", "<p id=\"Par25\">In light of the feedback by the panel indicating that ‘Critical thinking development’ and ‘Problem-solving projects’ were the highest outcome (#1 and #2, respectively), combined with recent reports on the FC importance, it could be concluded that seeking new directions in learning/facilitating strategies that complement existing methods in order to enrich the learning experience of students is recommended.</p>", "<title>Academic partnership/collaboration</title>", "<p id=\"Par26\">The respondents were instructed to rank (from 1 to 5, corresponding to high to low; each rank could appear only once) the importance of partnership(s) and/or collaboration(s) with: ‘Food Industry´, ‘Nutrition sciences’, ‘Government, policymakers and/or local authorities’, ‘Private sector’, and ‘Other academic disciplines’. The ranking distribution is depicted in Fig. ##FIG##1##2##.</p>", "<p id=\"Par27\">Collaboration with the ‘Food industry’ was ranked the highest, while the collaboration with ‘Other academic programs’ was ranked lower. Furthermore, the top two rankings (‘Very high’ and ‘High’) were ‘Food industry’ (53%), ‘Nutrition’ (38%), ‘Government’ (36%), ‘Private institutes (35%) and ‘Other academic programs’ (33%).</p>", "<p id=\"Par28\">Collaboration with the nutrition sector was highly ranked. This demonstrates that the panel considered collaboration between FST&amp;E and nutrition highly important and is a direction that these domains should consider closely. The need to enhance and probably integrate or converge nutrition sciences and FST&amp;E is underscored due to the lack of present collaboration and the growing consumers’ awareness of H&amp;W and food processing.</p>", "<p id=\"Par29\">The role of the food industry as a key player in academic partnership and collaboration should be considered, particularly due to the negative aspects suggested by the NOVA ultra-food processes food classification. For instance, “<italic>By design, these products are highly palatable, cheap, ubiquitous, and contain preservatives that offer a long shelf life. These features, combined with aggressive industry marketing strategies, contribute to excessive consumption and make these products highly profitable for the food, beverage, and restaurant industry sectors that are dominant actors in the global food system</italic>”^{##UREF##29##32##}. This study demonstrates that the food industry plays significant positive roles in both collaboration and partnerships. It also plays a key part in internships described below (Section “Internships”).</p>", "<title>Topics importance to FST&amp;E</title>", "<p id=\"Par30\">The importance of 11 topics for FST&amp;E was assessed as listed in Table ##TAB##2##3##.</p>", "<p id=\"Par31\">The data exposed 5 top important topics to FST&amp;E. The topic of highest interest was ‘Sustainability, circular economy, and food waste management,’ followed by ‘Innovation/open innovation’ and ‘New product development’ (no statistically significant difference between these topics), ‘Consumer perception &amp; trust’ and ‘Nutrition sciences’ that were statistically different from the first two topics (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt;0.05), respectively. Worth noting the significant differences between FSTs and FEs in ‘Sustainability, circular economy, and food waste management’, ‘New product development’, ‘Consumer perception &amp; trust’, and ‘Nutrition Sciences’, where FSTs significantly assigned higher importance to these topics in comparison with FEs. However, no significant difference was found for ‘Innovation/open innovation’.</p>", "<p id=\"Par32\">‘Artificial Intelligence, machine learning’ was only ordered as #9 based on the Likert-type scores averages, and FEs considered it significantly higher than FSTs. It is safe to predict that the importance of AI will increase in the coming years once more and more applications and utilizations will emerge. Suffice to consider recent applications and the global AI market size growth from $65.48 billion in 2020, projected to reach $1581.70 billion by 2030, growing at a CAGR of 38.0% from 2021 to 2030 (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.alliedmarketresearch.com/artificial-intelligence-market\">https://www.alliedmarketresearch.com/artificial-intelligence-market</ext-link>).</p>", "<title>Importance to FST&amp;E curricula to meet future challenges and learning opportunities</title>", "<p id=\"Par33\">The importance of the curricula in meeting FST&amp;E future challenges and learning opportunities (in descending order) is highlighted in Table ##TAB##3##4##.</p>", "<p id=\"Par34\">Table ##TAB##3##4## shows five topics were considered to be of ‘Very high’ to ‘High’ importance: ‘Research project(s)’ (4.34), ‘Apprenticeships (e.g., industrial training)’ (4.28), ‘Adaptability (e.g., adjusting to change in real-time, managing biases, overcome challenges)’ (4.22), ‘Revision current programs’ (4.16), and ‘Employability’ (4.13). The other topics received lower scores.</p>", "<p id=\"Par35\">The significant difference between FSTs and FEs on ‘Research project(s)’, ‘Enhanced integration with nutrition’, and ‘Soft (life) skills’ is worth noting. On these topics, except for ‘Enhanced integration with nutrition’, FSTs scores were significantly higher when compared with FEs. The ´Enhanced integration with nutrition´ by both FSTs and FEs was ‘High’ (4.00) and above, projecting the absolute need for FST&amp;E to enhance its collaboration with nutrition, mainly due to the high importance of H&amp;W and its significant role.</p>", "<p id=\"Par36\">Adaptability is the potential to adjust and learn new skills in response to changing factors, conditions, cultures, and environments. It is a soft skill that both colleagues and superiors highly value. In the ever-changing needs and progress, businesses and employees must adapt quickly to unforeseen dynamic circumstances, innovation, and disruption. Adaptability means being flexible, innovative, open, and resilient, particularly under unforeseen conditions. Some key elements of being adaptable are confident but open to criticism, focusing on solutions rather than problems, collaborating with others, and learning from them (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.walkme.com/glossary/adaptability/\">https://www.walkme.com/glossary/adaptability/</ext-link>). For instance, the a<italic>daptability</italic> of FST developments implies a capacity to continuously change and improve its operations and food quality output in time and space^{##UREF##30##33##}. This explains the #3 place the panel considered adaptability.</p>", "<p id=\"Par37\">The panel perceived both ‘Revision of current programs’ and ‘Employability’ as high priority (#4 and #5, average of 4.16 and 4.13, respectively). These assessments should be considered carefully by academic programs in order to adapt to the fast changes driven by innovation, disruption, and digital progress.</p>", "<p id=\"Par38\">‘Enhanced integration with nutrition’ came in #6. However, FSTs and FEs indicated this topic is highly important (average of 4.00 and 4.21, respectively). Hence, FST&amp;E education programs should seek avenues to enhance integration with nutrition science. Possible collaborations should consider joint research programs and other partnerships and alliances.</p>", "<p id=\"Par39\">‘Business-related activities (e.g., creation, network, partnerships, collaboration)’ and ‘Soft (life) skills’ were #7–8. Nevertheless, their Likert-type average values were close to ‘High’. Hybrid teaching was perceived as the last (3.78). Apparently, this type of education is not very appealing. Yet, this should be reassessed after the Covid-19 pandemic has passed.</p>", "<p id=\"Par40\">Engineering education is also experiencing dramatic changes. The traditional teaching model, where students are passive in the lecture room, gives way to more active, student-centered, and participatory approaches. Different modern education and learning techniques, such as blended and flip-classroom, active learning, use of technology in teaching, universal design, and student-centered education approach, among others, were previously reported^{##REF##30805342##9##}. Hence, it is expected that Hybrid teaching and other advanced methods, including AI, will flourish soon and will become the norm.</p>", "<title>Internships</title>", "<p id=\"Par41\">The importance of internship to FST&amp;E students was evaluated considering 5 possibilities: ‘Academic internship,’ ‘Food industry internship,’ ‘Start-up/FoodTech company internship,’ ‘Other domains/industries,’ and ‘Internship in other countries.’ The data are depicted in Fig. ##FIG##2##3##.</p>", "<p id=\"Par42\">The internship was categorized into three statistically different groups (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05). The first group was internships in ‘Food Industry’ (4.60), followed by the second group: ‘Start-ups/Food Tech’ (4.04), ‘Other countries’ (3.98), and ‘Academia’ (3.96), and the third group ‘Others domains/industries’ (3.46). Comparing the difference between FSTs and FEs, respondents showed a significant difference (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05) for internships in ‘Food Industry’ (4.65 and 4.52), ‘Start-ups/Food Tech’ (4.11 and 3.89) and ‘Other domains/industries’ (3.46 and 3.26), respectively. It is not surprising that FSTs have consistently assigned higher values to internships, probably due to the possibility that they are more complimentary to hands-on experiences.</p>", "<p id=\"Par43\">Bridging the academia-industry gap in the food sector through collaborative courses and internships was recently studied. More than fifteen years of university extension diplomas in food technology Diplomas demonstrated how collaborative courses strengthen academia-industry bonds, and employability was boosted thanks to internships and the network created^{##UREF##31##34##}. Internships could support students in developing their identity, which is achieved by close contact with their future working tasks^{##UREF##32##35##}, enhancing familiarity with and nearness to their future profession^{##UREF##33##36##} and industry-based projects and governance^{##UREF##34##37##}. Also, student projects in collaboration with the industry make the students face a reality^{##UREF##19##22##}. In light of these benefits, it is clear why the internship in the food industry received such a high Likert-type average. This very high importance given by the panel to industry internships coincides with their ranking, as aforementioned in the previous section, highlighting the core role of the food industry in students’ education.</p>", "<title>Professional organization impact on FST&amp;E education</title>", "<p id=\"Par44\">The impact of professional organizations on food science/food technology/food engineering education, as well as strategy and vision data, are depicted in Fig. ##FIG##3##4##.</p>", "<p id=\"Par45\">Data analysis (<italic>t</italic>-test) of the impact of the various organizations or vision and strategy on education revealed that the statistically highest Likert-type average scores (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05) were given to the ‘Food industry’ (3.86). ‘IFT (Institute of Food Technologists)’ was in the 2nd statistical group (3.70), followed by the 3rd statistical group that included ‘IUFoST (International Union of Food Science &amp; Technology)’ (3.49), ‘Vision, strategy &amp; leadership of the university’ (3.49), ‘IFST (Institute of Food Science+Technology)’ (3.44), and ‘Government, public interest &amp; support’ (3.42). ‘EFFoST (The European Federation of Food Science and Technology)’ (3.40) was between the 3rd and the 4th group that included ‘ISEKI-Food (European Association for Integrating Food Science and Engineering Into the Food Chain),’(3.27). ‘SoFE (Society of Food Engineering)’ (2.96) was the next statistical group, and the last 6th group was ‘Others’ (2.65).</p>", "<p id=\"Par46\">It is quite surprising that the food industry obtained such a high perceived impact on education, especially because the number of respondents in the panel affiliated with academic and educational institutes was high (69.6%). This could be explained by the fact that most curricula are designed to align with the industrial requirement and/or the need to provide students with the essential tools for the food industry. As no in-depth interviews were conducted, these findings warrant additional consideration.</p>", "<p id=\"Par47\">IFT was in second place, significantly affecting FST&amp;E education. In light of the quite low number of respondents from North America and Canada (13.1%), this finding clearly projects the significant role IFT has in impacting global education and proliferation. The 3rd group included IUFoST, IFST (international and mainly UK organizations, respectively), ‘Vision, strategy &amp; leadership of the university’ and ‘Government, public interest &amp; support´. These different groups and elements were perceived as very important and apparently have a significant role in contributing to the education program. EFFoST was categorized between the 3rd and 4th groups, including ISEKI-Food (3.27). These organizations were perceived as lower compared with the previous organizations. SoFE was classified only in the 5th significantly different group. As SoFE appeals mainly to FEs, many panelists were probably unfamiliar with its activities.</p>", "<title>Education impact on professional expectations</title>", "<p id=\"Par48\">The impact of the respondents’ education curricula on their professional success, satisfaction, and meeting expectations data is depicted in Fig. ##FIG##4##5##.</p>", "<p id=\"Par49\">Education curricula showed two different statistical (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05) groups. The first group included ‘Success’ (4.03) and ‘Satisfaction’ (3.95). The second statistical group that was quite lower evaluated was ‘Meeting expectations’ (3.76). This finding could open new avenues for education institutes to conduct in-depth assessments of their alumni and graduates, focusing on improving their performances in order to better meet their graduates’ future expectations. This study also provides insights into new education and learning opportunities and new topics to be included in future curricula.</p>", "<p id=\"Par50\">When comparing FSTs with FEs, it was quite surprising that FSTs consistently rated all three attributes lower than FEs. In two cases, these differences were even significant: ‘Success’ (4.07 vs. 4.15, one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05), ‘Satisfaction’ (3.96 vs. 4.06), and ‘Meeting expectation’ (3.78 vs. 3.83, one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05). This lower assessment by FSTs highlights that the potential for curriculum improvements is high, and an in-depth evaluation should open new avenues for significant improvements.</p>", "<p id=\"Par51\">In conclusion, these main points are highlighted:<list list-type=\"bullet\"><list-item><p id=\"Par52\">Seven topics affecting the future of the profession domain curricula were evaluated between ‘High’ to ‘Very high’. The highest scores were found for: ‘Critical thinking’, followed by ‘Problem-solving projects,’ ‘Teamwork/collaboration’, ‘Innovation/Open innovation’, and ‘Multidisciplinary’.</p></list-item><list-item><p id=\"Par53\">The importance of Academic partnership/collaboration showed that ‘Food industry’, and ‘Nutrition’ were ranked the highest.</p></list-item><list-item><p id=\"Par54\">Significant positive roles of the food industry in collaboration and partnerships with the FST&amp;E domain were demonstrated. Significant findings were also related to internships, education, strategy, and vision effects of the food industry.</p></list-item><list-item><p id=\"Par55\">Collaboration between FST&amp;E and nutrition sciences indicated its high importance. Integrating or converging nutrition science and FST&amp;E is emphasized based on the lack of actual present collaborations.</p></list-item><list-item><p id=\"Par56\">Assessing the education curricula contribution showed two statistical groups. The first group included ‘Success’ and ‘Satisfaction’. ‘Meeting expectations’ was the second. New avenues to better meet future graduates’ and students’ expectations were identified.</p></list-item><list-item><p id=\"Par57\">Insights into novel education and learning opportunities and new topics to be included in future curricula have been identified.</p></list-item></list></p>" ]

[]

[ "<p id=\"Par1\">Progress in science, technology, innovation, and digital capabilities call for reassessing food science, technology, and engineering (FST&amp;E) education and research programs. This survey targeted global professionals and students across food disciplines and nutrition. Its main objectives included assessing the status of FST&amp;E higher education, identifying challenges and opportunities, and furnishing recommendations. Seven topics affecting the future of the FST&amp;E curricula were evaluated by the panel as ‘High’ to ‘Very high’, namely: ‘Critical thinking’, followed by ‘Problem-solving projects’, ‘Teamwork/collaboration’, ‘Innovation/Open innovation’ and ‘Multidisciplinary’. The importance of academic partnership/collaboration with the Food Industry and Nutrition Sciences was demonstrated. Significant positive roles of the food industry in collaboration and partnerships were found. Other essential food industry attributes were related to internships, education, strategy, and vision. Collaboration between FST&amp;E and nutrition sciences indicated the high standing of this direction. The need to integrate or converge nutrition sciences and FST&amp;E is emphasized, especially with the growing consumer awareness of health and wellness. The study provides insights into new education and learning opportunities and new topics for future curricula.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41538-023-00243-w.</p>", "<title>Acknowledgements</title>", "<p>The authors would like to thank the contribution of IUFoST (International Union of Food Science &amp; Technology), mainly to WG 1.2 ‘Emerging Issues, Key Focus Areas´ working group members, for pretesting, distributing, and spreading the survey. The author, C.L.M. Silva, would like to acknowledge the support by National Funds from FCT - Fundação para a Ciência e a Tecnologia through project UIDB/50016/2020.</p>", "<title>Author contributions</title>", "<p>I.S.S., C.L.M.S., and E.C. conceived and developed the questionnaire. E.C. data curation. E.C. and I.S.S. performed the validation and formal statistical analysis. I.S.S. and E.C. conducted the investigation and wrote the paper. C.L.M.S. provided expertize, feedback, and paper revision–supervision and project administration by I.S.S.</p>", "<title>Data availability</title>", "<p>The dataset obtained and analyzed during the current study is available from Prof. Eli Cohen upon request.</p>", "<title>Competing interests</title>", "<p id=\"Par64\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Respondents education fields: food scientists and technologists (FSTs), food engineers (FEs), microbiologists (HMs), nutritionists (HNs), chemical engineers (CEs), bioengineering/biotechnology (BBs), business/marketing (BMs), and others.</title><p>Overall degrees distribution (small insert).</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Ranking importance (‘Very high’, ‘High’, ‘Medium’, ‘Low’, ‘Very low’) distribution of ‘Academic partnerships/collaborations’.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Likert-type averages (1–5 scale) and one side (-) SD of internships importance for FST&amp;E (values with different small letters indicate significant differences between groups; one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05).</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Likert-type averages (1–5 scale) and one side (-) SD of organization/vision impact on FST&amp;E education (values with different letters indicated significant differences between groups; one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05).</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Likert-type averages (1–5 scale) and one side (-) SD of ‘Success’, ‘Satisfaction’, and ‘Meeting expectations’ (values with different letters indicated significant differences between groups; one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05).</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Respondents’ demographic.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th/><th>Frequency</th><th>%</th></tr></thead><tbody><tr><td>Respondents (panel)</td><td>703</td><td>100.0</td></tr><tr><td colspan=\"3\"><italic>Gender</italic></td></tr><tr><td> Male</td><td>322</td><td>45.8</td></tr><tr><td> Female</td><td>372</td><td>52.9</td></tr><tr><td> Others</td><td>9</td><td>1.3</td></tr><tr><td colspan=\"3\"><italic>Age groups (years)</italic></td></tr><tr><td> 18–25</td><td>53</td><td>7.5</td></tr><tr><td> 26–40</td><td>180</td><td>25.6</td></tr><tr><td> 41–55</td><td>266</td><td>37.8</td></tr><tr><td> Above 55</td><td>202</td><td>28.7</td></tr><tr><td colspan=\"3\"><italic>Geographic distribution where the most advanced degree was received or study</italic></td></tr><tr><td> Western Europe</td><td>195</td><td>27.7</td></tr><tr><td> Eastern Europe</td><td>97</td><td>13.8</td></tr><tr><td> UK</td><td>21</td><td>3.0</td></tr><tr><td> North America, including Canada</td><td>92</td><td>13.1</td></tr><tr><td> Mexico</td><td>11</td><td>1.6</td></tr><tr><td> South America</td><td>67</td><td>9.5</td></tr><tr><td> Asia/Middle East</td><td>85</td><td>12.1</td></tr><tr><td> China</td><td>12</td><td>1.7</td></tr><tr><td> Far East (excluding China)</td><td>7</td><td>1.0</td></tr><tr><td> Oceania (Australia, New Zealand)</td><td>12</td><td>1.7</td></tr><tr><td> Africa</td><td>104</td><td>14.8</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Topics affecting the future of the profession curricula in descending order based on Likert-type average (<italic>n</italic> = 703).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Order</th><th>Topic</th><th>Total panel</th><th>FSTs</th><th>FEs</th></tr></thead><tbody><tr><td>1</td><td>Critical thinking development</td><td>4.50^a</td><td>4.49</td><td>4.52</td></tr><tr><td>2</td><td>Problem-solving projects</td><td>4.44^a</td><td>4.45</td><td>4.45</td></tr><tr><td>3</td><td>Teamwork/collaboration</td><td>4.31^b</td><td>4.33</td><td>4.23</td></tr><tr><td>4</td><td>Innovation/open innovation</td><td>4.29^bc</td><td>4.33</td><td>4.20</td></tr><tr><td>5</td><td>Multidisciplinary</td><td>4.24^bc</td><td>4.18</td><td>4.18</td></tr><tr><td>6</td><td>Creativity</td><td>4.22^c</td><td>4.22</td><td>4.15</td></tr><tr><td>7</td><td>Project/time management</td><td>4.05^d</td><td>4.12^*</td><td>3.93^*</td></tr><tr><td>8</td><td>Soft (life) skills</td><td>3.90^e</td><td>3.94^*</td><td>3.70^*</td></tr><tr><td>9</td><td>Entrepreneurship</td><td>3.77^f</td><td>3.79</td><td>3.69</td></tr><tr><td>10</td><td>Business creation/network</td><td>3.70^f</td><td>3.72</td><td>3.56</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Topics importance to FST&amp;E curricula ordered based on the averages obtained by a Likert-type 1–5 scale.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Order</th><th>Topic</th><th>Total Panel</th><th>SD</th><th>FSTs</th><th>FEs</th></tr></thead><tbody><tr><td>1</td><td>Sustainability, circular economy food waste management</td><td>4.44^a</td><td>0.71</td><td>4.46*</td><td>4.24*</td></tr><tr><td>2</td><td>Innovation/open innovation</td><td>4.36^ab</td><td>0.71</td><td>4.39</td><td>4.34</td></tr><tr><td>3</td><td>New product development</td><td>4.32^b</td><td>0.78</td><td>4.41*</td><td>4.20*</td></tr><tr><td>4</td><td>Consumer perception &amp; trust</td><td>4.27^b</td><td>0.79</td><td>4.29*</td><td>4.08*</td></tr><tr><td>5</td><td>Nutrition Sciences</td><td>4.07^c</td><td>0.82</td><td>4.16*</td><td>3.82*</td></tr><tr><td>6</td><td>Startups/FoodTech</td><td>3.91^d</td><td>0.82</td><td>3.90</td><td>3.87</td></tr><tr><td>7</td><td>Entrepreneurship</td><td>3.82^d</td><td>0.90</td><td>3.84</td><td>3.68</td></tr><tr><td>8</td><td>Kaizen methodologies/continuous improvement</td><td>3.66^e</td><td>0.90</td><td>3.65</td><td>3.48</td></tr><tr><td>9</td><td>Artificial Intelligence, machine learning</td><td>3.65^e</td><td>0.89</td><td>3.60*</td><td>3.75*</td></tr><tr><td>10</td><td>Big Data, communication, robotics</td><td>3.58^e</td><td>0.90</td><td>3.50</td><td>3.57</td></tr><tr><td>11</td><td>Management/marketing</td><td>3.58^e</td><td>0.89</td><td>3.59</td><td>3.42</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Topics importance in meeting FST&amp;E future challenges and learning opportunities (in descending order based on Likert-type 1–5 scale average).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Order</th><th>Topic</th><th>Total panel</th><th>SD</th><th>FSTs</th><th>FEs</th></tr></thead><tbody><tr><td>1</td><td>Research project(s)</td><td>4.34^a</td><td>0.75</td><td>4.42*</td><td>4.21*</td></tr><tr><td>2</td><td>Apprenticeships (e.g., industrial training)</td><td>4.28^ab</td><td>0.77</td><td>4.29</td><td>4.21</td></tr><tr><td>3</td><td>Adaptability (e.g., adjusting to change in real-time, managing biases, overcoming challenges)</td><td>4.22^bc</td><td>0.79</td><td>4.21</td><td>4.18</td></tr><tr><td>4</td><td>Revision current programs</td><td>4.16^c</td><td>0.79</td><td>4.17</td><td>4.18</td></tr><tr><td>5</td><td>Employability</td><td>4.13^c</td><td>0.86</td><td>4.16</td><td>4.02</td></tr><tr><td>6</td><td>Enhanced integration with nutrition</td><td>3.92^d</td><td>0.84</td><td>4.00*</td><td>4.21*</td></tr><tr><td>7-8</td><td>Business-related activities (e.g., creation, network, partnerships, collaboration)</td><td>3.92^d</td><td>0.91</td><td>3.92</td><td>3.83</td></tr><tr><td>7-8</td><td>Soft (life) skills</td><td>3.89^d</td><td>0.87</td><td>3.95*</td><td>3.73*</td></tr><tr><td>9</td><td>Hybrid teaching</td><td>3.78^e</td><td>0.91</td><td>3.82</td><td>4.21</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>" ]

[ "<table-wrap-foot><p>Different small letters in the same column represent significant differences between groups (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05).</p><p>*Significant difference (two-side <italic>t</italic>-test between averages in the same row, <italic>p</italic> &lt; 0.05).</p></table-wrap-foot>", "<table-wrap-foot><p>Different small letters in the same column represent significant differences between groups (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05).</p><p>*Significant difference (two-side <italic>t</italic>-test between averages in the same row, <italic>p</italic> &lt; 0.05).</p></table-wrap-foot>", "<table-wrap-foot><p>Different small letters in the same column represent significant differences between groups (one-way ANOVA with post-hoc LSD test, <italic>p</italic> &lt; 0.05).</p><p>*Significant difference (two-side <italic>t</italic>-test between averages in the same row, <italic>p</italic> &lt; 0.05).</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41538_2023_243_Fig1_HTML\" id=\"d32e547\"/>", "<graphic xlink:href=\"41538_2023_243_Fig2_HTML\" id=\"d32e804\"/>", "<graphic xlink:href=\"41538_2023_243_Fig3_HTML\" id=\"d32e1274\"/>", "<graphic xlink:href=\"41538_2023_243_Fig4_HTML\" id=\"d32e1322\"/>", "<graphic xlink:href=\"41538_2023_243_Fig5_HTML\" id=\"d32e1353\"/>" ]

[ "<media xlink:href=\"41538_2023_243_MOESM1_ESM.pdf\"><caption><p>Supplementary information</p></caption></media>", "<media xlink:href=\"41538_2023_243_MOESM2_ESM.pdf\"><caption><p>Reporting summary</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">The germline is a unique lineage of cells that can be defined as all cells that have the possibility to propagate their genome to subsequent generations. This includes embryonic stem cells, primordial germ cells and germ stem cells, up to haploid mature gametes. Germline cells have properties that are often unique to their specific stage of germ cell development, such as stem cell proliferation and differentiation, meiosis, and gamete formation. Together these properties contribute to the capacity of the germline to pass a relatively intact genome to future generations. In contrast, somatic cells are restricted to only one generation and are not passed to future generations. Somatic cell death is ensured by senescence, which prevent uncontrollable cell growth [##REF##11413492##1##]. In cancer, this safeguard is circumvented and escaping senescence is an intrinsic hallmark of cancer [##REF##10647931##2##, ##REF##21376230##3##]. When it fails, a cell acquires a defining trait of the germline: the ability not to age. As the pathways that allow for escaping senescence are embedded in the genome for germline-specific use, it would be much easier for a developing cancer cell to aberrantly activate dormant processes, rather than evolve new pathways entirely [##REF##25043755##4##]. It is thus plausible that cancer cells utilize germline-specific processes to escape senescence. This is one of many examples of how a cancer cell may hijack germline specific processes to its benefit, more of which are discussed by [##REF##16034368##5##].</p>", "<p id=\"Par3\">We recently described a class of over one thousand germline-cancer genes (GC genes), which are defined as genes that are normally specific to the germline but are ectopically expressed in cancer [##REF##29907769##6##, ##REF##33348709##7##]. GC genes are involved in a wide variety of germline processes, including meiosis, gene regulation and DNA repair [##REF##29907769##6##, ##REF##33348709##7##]. In cancer, GC gene expression is observed in all of the 33 investigated tumor types of The Cancer Genome Atlas (TCGA) [##UREF##0##8##], but some cancers express more GC-genes than others. We previously found that the ectopic expression of GC genes in cancer is associated with a poor clinical prognosis in lung adenocarcinoma [##REF##33348709##7##]. Similar associations have been found by others in non-small cell lung cancer, prostate cancer and renal clear cell carcinoma [##REF##29190970##9##–##REF##25733303##14##]. Despite these clinical observations, little is known about how germline specific processes may contribute to the malignant properties of cancer.</p>", "<p id=\"Par4\">We here aim to investigate the relationship between GC gene expression and malignancy, as defined by therapy resistance, proficient DNA repair and proliferation rate. To this end, we used our list of GC-genes to create a model that allowed us to compare the phenotype of cancer cells that express many GC genes to cancer cells that express few GC genes. We tested the hypothesis that the observed clinical outcomes associated with more aggressiveness and resistance to therapy [##REF##29190970##9##–##REF##25733303##14##] can be observed in our model as well. In addition, we propose that one gene, TRIP13, is predominantly responsible for the malignant phenotype observed in some cell lines.</p>" ]

[ "<title>Materials and methods</title>", "<title>Selection of cell lines as a model for comparing the effect of GC genes</title>", "<p id=\"Par5\">To investigate the effect of GC gene expression in cancer on response to chemotherapy and irradiation, induced double-stranded break repair and proliferation, we selected 4 lung adenocarcinoma (LUAD) cell lines with high GC gene expression (GC_high) and 4 LUAD cell lines with low GC gene expression (GC_low). The selection of groups was made by using R2 [##UREF##2##15##] to obtain LUAD-specific signature scores for each LUAD cell line in the Cancer Cell Line Encyclopaedia (CCLE) [##REF##22460905##16##]. This score represents the average percentile of GC gene expression ranks for each cell line, and thus takes into account the high expression levels of GC genes and the low expression of non-GC genes. Using this approach, we previously reported that LUAD contains the largest variation of GC gene expression of all cancer cell lines in the CCLE, allowing for comparison of phenotypical traits within one type of cancer [##REF##33348709##7##]. To specifically rank LUAD cell lines based on GC gene expression levels, we derived a new signature score based on 422 GC genes that are expressed in LUAD (Fig. ##FIG##0##1##) [##REF##29907769##6##, ##REF##33348709##7##]. In order to minimize baseline differences between cell lines, we applied several additional criteria. First, the cell lines must be epithelial and adherent. Second, they must be from the same source United States’ National Cancer Institute (NCI). Third, the cells must be cultured in identical growth medium (RPMI-1640). In order to adequately compare phenotypes, the top 4 and bottom 4 cell lines that fulfill these criteria were selected (Fig. ##FIG##0##1## &amp; Supplementary Data ##SUPPL##0##1##). These 8 LUAD cell lines were commercially obtained from the American Type Tissue Collection (ATCC), of which H2085 and H1573 did not survive standardized culture conditions, and were excluded from further analysis (Table ##TAB##0##1##).</p>", "<title>Cell culture</title>", "<p id=\"Par6\">Cells were maintained in 5% CO₂ at 37°C in RPMI-1640 medium (Thermo Fisher Scientific), supplemented with 5% foetal bovine serum (Thermo Fisher Scientific) for H1693 and H1573 or 10% for the other 6 cell lines. Other supplements were 1% HEPES (Gibco), 1% Pen-Strep (Gibco), and 2.2% glucose (Gibco). Cells were refreshed every 3 days and passaged routinely for use until passage 20. Cells in culture tested negative for mycoplasma contamination during the entire study.</p>", "<title>Clonogenic assay</title>", "<p id=\"Par7\">Clonogenic assays were performed as described previously [##REF##17406473##17##]. For each cell line, an appropriate number of cells was plated in triplicates in 6-well plates (3000 cells for H1563, H1703 &amp; H1437, 6000 cells for H2347 &amp; H2122, and 14.000 cells for H1693). 4 h after plating, cells were exposed to 0 to 8 Gy of ionizing radiation (IR) in a CellRad system (Precision X-Ray) or 0 to 8 μM cisplatin. Cells were cultured in 3 ml medium, 2 ml of which was gently replaced after 7 days. Once the negative control condition (i.e. 0 Gy or 0 μM cisplatin respectively) showed formation of colonies of 50 cells, which was after approximately 14 days for all cell lines, medium was removed and cells were gently washed with phosphate-buffered saline (PBS), and fixed and stained with 6% glutaraldehyde +0.5% crystal violet in PBS. The numbers of colonies with &gt;50 cells were electronically counted with ImageJ and manually confirmed.</p>", "<p id=\"Par8\">Instead of using increasing dosages of treatment, we used 4 conditions to assess cells’ ability to form new colonies: no treatment, 1 Gy of IR, 10 μmol of the TRIP13 inhibitor DCZ0415 (HY-130603, Bio-Connect) [##REF##31732653##18##] and 1 Gy + 10 μM DCZ0415.</p>", "<title>Immunofluorescent staining of γ-H2AX and RAD51</title>", "<p id=\"Par9\">Cells were cultured on multi Nunc Lab-Tek II chambered slides (Thermo Fisher Scientific) for 24 h, after which they were exposed to 1 Gy of irradiation in a CellRad system (Precision X-Ray). Cells were fixated at various time points after irradiation (30 min–24 h) in 4% paraformaldehyde for 10 min and subsequently permeabilized in PBS with 0.1% triton-X for 15 min. Non-specific adhesion sites were blocked for 45 min in 0.25% Tween-20/PBS with 1% bovine serum albumin, followed by the addition of primary antibodies against γ-H2AX (1:10.000, 05-636, Millipore) or RAD51 (1:50, PA5-27195, Thermo Fisher Scientific), or isotype immunoglobulin G in the case of negative controls. After overnight incubation at 4 °C, the cells were washed and incubated with the corresponding host-specific secondary antibodies goat anti mouse Alexa Fluor 488 (1:1.000, A11029, Thermo Fisher Scientific) or goat anti Rabbit Alexa Fluor 532 (1:1000, A11009, Life Technologies), and counterstained with DAPI. The slides were mounted with Prolong Gold anti-fade (Thermo Fisher Scientific) and visualized using a Leica DM5000B microscope. γ-H2AX and RAD51 foci within the cell nucleus were counted manually in at least 100 cells per condition. This was repeated 3 times for statistical analysis.</p>", "<title>Western blotting</title>", "<p id=\"Par10\">Cells were seeded in 6-well plates. Once 80% confluency was reached, media was discarded and cells were washed twice with phosphate-buffered saline. Cells were treated with 1 mL 0.25% trypsin and incubated for 5 min, after which the corresponding media was added to dilute the trypsin. The mixture was pipetted from the plates to tubes. Proteins were extracted from the cells using a RIPA buffer and the addition of protease- and phosphatase-inhibitors. Protein expression was quantified with the Qubit Protein Assay Kit (Thermo Fisher Scientific). Western blot analysis was performed using the LI-COR Odyssey imaging system (LI-COR Biosciences) as previously reported [##UREF##3##19##]. The primary antibodies were mouse anti-TRIP13 (1:1000, ab128171, Abcam), rabbit anti-GAPDH (1:400; FL-335, Santa Cruz Biotechnology), mouse anti-TUBULIN (1:1000; T9026, Sigma), rabbit anti-RAD51 (1:1000; PA5-27195, Thermo Fisher Scientific) mouse anti-KU70 (1:1000; ab2172-500, Abcam), rabbit anti-Ligase IV (1:1000； ab193353, Abcam). Band intensities were assessed using Image Studio Lite (Version 5.2).</p>", "<title>Proliferation assay</title>", "<p id=\"Par11\">Cells were cultured in 96 well-plates. After 4 h, cells were exposed to IR in a CellRad system and/or 10 μmol TRIP13 inhibitor DCZ0415. When cells reached 50–60% confluency, the 5-ethynyl-2’-deoxyuridine (EdU) was added to the culture for 2 h. Quantification of EdU-positive cells was performed using the Cell Proliferation Kit (C10337, Thermo Fisher Scientific) as previously described [##REF##28576919##20##] and represented by the mean ± SEM of 3 independent experiments. Images were analyzed using Leica Application Suite X and counting of nuclei and EdU stains was performed electronically in ImageJ.</p>", "<title>Quantitative-real time PCR (Q-PCR)</title>", "<p id=\"Par12\">Total RNA was extracted from control and treated cells using the RNeasy Mini Kit (Qiagen) according to the manufacturer’s protocol. The RNA samples (<italic>n</italic> = 3 for all cell lines) were reversely transcribed using the SensiFAST cDNA Synthesis Kit (Bioline). The synthesized cDNA was then used for Q-PCR reactions, using the Roche LightCycler 480 platform in a 384-well plate format. The Q-PCR reaction was performed in a 10ul volume system including 2X LightCycler 480 SYBR Green I Master (Roche). <italic>GAPDH</italic>, <italic>ACTB</italic> and <italic>TUBA1C</italic> were used as reference genes. The data were analyzed using the delta Ct method. The primers for Q-PCR analysis are listed in Supplementary Table ##SUPPL##1##1##.</p>", "<title>Cell scratch (wound healing) assay</title>", "<p id=\"Par13\">Cells were cultured in Incucyte® image lock 96 well-plates (Satorius BA-04855). When the cells reached around 90% confluency, the Incucyte 96-well wound marker tool (Sartorius 4563) was used following the protocol provided by the manufacturer. After a scratch was automatically set, the cells were gently washed to remove detached cells and medium was refreshed. Wound healing was assessed using the Incucyte Live Cell Analysis System and quantified using ImageJ (version 2.0).</p>", "<title>Generation of knockout cell line with CRISPR-Cas9</title>", "<p id=\"Par14\">The plasmids containing CRISPR targeting <italic>TRIP13</italic> (sc-404006-NIC; Santa Cruz Biotechnology) or Control CRISPR/cas9 (sc-418922; Santa Cruz Biotechnology) was delivered to the cells using a Neon electroporator (Thermo Fisher Scientific), following the manufacturer’s guidance.), The program used for electroporation was voltage 1100, width 20 ms and pulse 2. Two days after electroporation, GFP+ cells were sorted by fluorescence-activated cell sorter (FACS, BD Biosciences). Single GFP positive cells were cultured for seven to eight weeks, and colonies were screened by Sanger sequencing and Western blotting using the anti-TRIP13 antibody (1:1000; ab128171, Abcam).</p>", "<title>Generation of TRIP13 overexpression cell line</title>", "<p id=\"Par15\">H1563 cells were transfected (Neon electroporator (Thermo Fisher Scientific) with <italic>TRIP13</italic> CRISPR Activation Plasmid (sc-404006-ACT; Santa Cruz Biotechnology) or Control CRISPR plasmid (sc-437275; Santa Cruz Biotechnology). After 48 h, transfected cells were selected using 1ug/mL puromycin (Enzo Life Sciences, ALX-380-028). <italic>TRIP13</italic> overexpression was screened by Q-PCR and Western blot analysis.</p>", "<title>Cell viability assay</title>", "<p id=\"Par16\">Cells were seeded in triplicate in 96-well plates. At around 70–80% confluency the cells were treated with 10 uM DCZ0415. Cell viability was measured using the Alamar Blue assay (BUF012B, BIO-RAD) according to the manufacturer’s protocol.</p>", "<title>Statistical analysis</title>", "<p id=\"Par17\">The data obtained were analyzed in Prism Graph Pad and Microsoft Excel. Two-sided T-tests were performed with α = 0.05, unless stated otherwise. Variance was tested for using the F-test of equality of variances, and the T-test without assuming equal variance was used in case of F &gt; 0.05. Results were corrected for multiple testing using the Bonferroni correction where appropriate.</p>" ]

[ "<title>Results</title>", "<title>GC_high cell lines are more resistant to IR</title>", "<p id=\"Par18\">To investigate the association between GC gene expression and therapy resistance, six lung adenocarcinoma (LUAD) cell lines were grown in standardized culture conditions to be used as a model to test the effect of GC gene expression: three with high GC gene expression (GC_high) and three with low GC gene expression (GC_low) (Materials &amp; methods). To investigate the association between GC gene expression and therapy resistance, we subjected all six cell lines to a clonogenic assay. This experiment results in surviving fraction of cells that is able to form new colonies after exposure to ionizing radiation (IR) or cisplatin, resulting in a survival curve of each cell line (Fig. ##FIG##1##2##). We observed that GC_high cell lines were more capable of colony formation following IR, compared to GC_low cell lines, especially at 0.5 Gy (<italic>p</italic> = 0.006) and 1 Gy (<italic>p</italic> = 0.02). While on average the GC_low cell lines are more sensitive to low dose irradiation than the GC_high cell lines, one GC_low cell line (H1437) appeared particularly resistant to IR above 1 Gy (Fig. ##FIG##1##2a##). For cisplatin, we did not observe a correlation between the cell lines’ ability to form new colonies and GC gene score (Fig. ##FIG##1##2c/d##).</p>", "<title>GC_high cell lines efficiently repair IR-induced DSBs</title>", "<p id=\"Par19\">To investigate whether the increased resistance to IR observed in the GC_high cell lines is due to more efficient repair of DNA double-strand breaks (DSBs), we quantified the number of double-stranded breaks (DSBs) in all cell lines through γ-H2AX staining at 0.5, 1.5, 3, 6 and 24 h after exposure to 1 Gy of IR (Fig. ##FIG##2##3a##). We observed that the foci were resolved more slowly in two GC_low cell lines (H1563 and H2122), compared to the GC_high cell lines (Fig. ##FIG##2##3b##). The GC_low cell line H1437 clearly followed the DSB repair rate of the GC_high cell lines (Fig. ##FIG##2##3b##). Nevertheless, taken together, GC_high cell lines repair DNA significantly faster than GC_low cell lines (Fig. ##FIG##2##3c##).</p>", "<title>GC_high cell lines display more IR-induced RAD51 foci</title>", "<p id=\"Par20\">In addition to γH2AX, to investigate differences in DSB repair via homologous recombination (HR), we quantified RAD51 foci formation and resolution at 0.5, 1.5, 3, 6 and 24 h after exposure to 1 Gy of IR. The number of RAD51 foci was lower in the three GC_low cell lines compared to the GC_high cell lines (Fig. ##FIG##2##3d, e##, Supplementary Fig. S##SUPPL##1##1##). Interestingly, in contrast to γH2AX, the GC_low but TRIP13 high cell line (H1437) did not follow RAD51 foci resolution of the GC_high cell lines. Taken together, GC_high cell lines repair DNA significantly faster than GC_low cell lines (Fig. ##FIG##2##3c##) and display more RAD51 foci (Fig. ##FIG##2##3f##).</p>", "<p id=\"Par21\">To investigate whether the GC_high or GC_low cells may differentially repair DSBs via non-homologous end-joining (NHEJ), we treated the six cell lines with the previously characterized DNA-PKcs inhibitor NU7026 [##UREF##4##21##]. We measured its effect on cell survival after 1 Gy of irradiation and found that NU7026 reduced the cancer cell surviving fraction in all cell lines. Importantly, survival of the cell lines with a high GC gene score was not affected significantly different than survival of the cell lines with a low GC gene score (Supplementary Fig. S##SUPPL##1##2A##).</p>", "<title>GC_high cell lines maintain a higher rate of proliferation following IR</title>", "<p id=\"Par22\">To test for a difference in cell proliferation between GC_high and GC_low cell lines, we stained cells with DNA synthesis marker 5-ethynyl-2’-deoxyuridine (EdU). This assay showed that GC_high and GC_low cell lines did not differ in EdU incorporation (<italic>p</italic> = 0.43) (Fig. ##FIG##3##4a##). However, after exposure to 1 Gy of IR, GC_low cell lines absorbed 32% less EdU than their non-irradiated counterpart cells, while GC_high cell lines absorb only 19% less (<italic>p</italic> = 0.033, Fig. ##FIG##3##4a/b##). These results indicate that GC_high cell lines maintain a higher rate of proliferation following IR.</p>", "<title>GC_high cell lines show higher expression of pluripotency markers and higher invasion potential</title>", "<p id=\"Par23\">To investigate the effect of GC genes on pluripotency we analyzed expression of <italic>OCT4</italic>, <italic>Nanog</italic> and <italic>SOX2</italic> using Q-PCR analysis of all our 6 LUAD cell lines (<italic>n</italic> = 3 for all cell lines). The GC_high cell lines showed a clear and significant increase in expression of these genes (Supplementary Fig. S##SUPPL##1##3A–C##). To quantify cell invasion potential, we performed a scratch assay using the Incucyte® imagelock 96-well plates and live cell imaging system (<italic>n</italic> = 3 for all cell lines). The GC_high cells appeared to display a higher invasion potential (Supplementary Fig. S##SUPPL##1##3D, E##).</p>", "<title>TRIP13 expression may be responsible for radioresistance</title>", "<p id=\"Par24\">Because GC_high cell lines appear to be more radioresistant than GC_low cell lines, and more efficiently repair IR-induced DSBs, we hypothesized that this effect is induced by genes that are normally functional in meiotic recombination. Nine meiotic genes are associated with both gene ontology terms ‘meiosis’ (GO:0051321) and ‘double-strand break repair’ (GO:0006302), and their expression differs between the 6 LUAD cell lines (Fig. ##FIG##4##5a##). Of these, the gene TRIP13 was of particular interest because it (i) showed the highest expression in all cell lines, (ii) it showed the largest difference in expression between GC_low and GC_high cell lines, (iii) it could be confirmed as GC gene on the protein level using the Human Protein Atlas (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.proteinatlas.org\">http://www.proteinatlas.org</ext-link>), and (iv) is highly expressed in the GC_low cell line that behaves as GC_high (H1437) with regard to its relatively high resistance to irradiation and rapid DSB repair. Moreover, a retrospective survival analysis of 515 LUAD patients included in the Cancer Genome Atlas [##UREF##0##8##] shows that the RNA expression level of TRIP13 is associated with a poor prognosis (<italic>p</italic> = 0.001, Fig. ##FIG##4##5b##). We confirmed the differential expression of TRIP13 between GC_high and GC_low cell lines at the protein level using Western Blot analysis, quantified by relative expression compared to GAPDH (Fig. ##FIG##4##5c/d##). Among the GC_low cell lines, H1437 stood out again, as also observed in prior experiments.</p>", "<title>TRIP13 inhibition strongly impairs cell survival and proliferation</title>", "<p id=\"Par25\">To test whether the differences in proliferation and response to irradiation are affected by the expression of TRIP13, we repeated the aforementioned experiments with addition of DCZ0415, a newly discovered compound that has been shown to inhibit TRIP13 [##REF##31732653##18##]. We measured the effect of inhibiting TRIP13 on cell survival and found that the addition of 10 µM DCZ0415 to the growth media reduced the cancer cell surviving fraction in all cell lines by an average of 64% (CI_95% 55–73%, Fig. ##FIG##5##6a##). Of all cell lines, the surviving fraction after TRIP13 inhibition was most decreased in H1703 and H1437, both of which show the highest TRIP13 expression of all 6 cell lines. To see whether the effect of DCZ0415 correlates with TRIP13 expression, we compared the reduction of the surviving fraction after treatment with DCZ0415 to the initial level of TRIP13 RNA expression. The reduction of the surviving fraction after treatment with 10 µM DCZ0415 indeed strongly correlates with the initial level of <italic>TRIP13</italic> RNA expression (Fig. ##FIG##5##6b##, R² = 0.94).</p>", "<p id=\"Par26\">As TRIP13 is involved in meiotic DSB repair [##REF##17696610##22##], we proceeded to test the influence of DCZ0415 on the radioresistance of the six LUAD cell lines. TRIP13 expression is strongly correlated with the surviving fraction following 1 Gy of IR (Fig. ##FIG##5##6c##). Combining 1 Gy of IR treatment with 10 µM DCZ0415 was able to impair the surviving fraction by an average of 81% across all cell lines (CI_95% 77–84%), compared to 1 Gy of IR alone (Fig. ##FIG##5##6d##). This increase in impaired colony formation did not correlate with the initial <italic>TRIP13</italic> RNA expression (R² = 0.003, Fig. ##FIG##5##6e##). In summary, TRIP13 inhibition by DCZ0415 correlates with a reduction of the surviving fraction, both with and without IR. In summary, TRIP13 inhibition by DCZ0415 correlates with a reduction of the surviving fraction, both with and without IR. TRIP13 expression appeared associated with increased radioresistance, and its inhibition by DCZ0415 led to a relatively stronger reduction of the surviving fraction of cells that express higher levels TRIP13.</p>", "<p id=\"Par27\">Because it has been demonstrated that phosphorylation of TRIP13 at Y56 sensitizes head and neck cancer to the EGF receptor inhibitor cetuximab [##REF##34111559##23##], we performed the clonogenic assay in all six cell lines, treated with or without cetuximab. We found that cetuximab indeed clearly affected survival of the high TRIP13 expressing cell lines (Supplementary Fig. S##SUPPL##1##2B##). However, although H2122 seemed unaffected by cetuximab, also the cell line H1563 (GC_low, low TRIP13) was strongly affected by cetuximab. Hence, although cetuximab affects LUAD cells, the relation between this effect and GC gene or TRIP13 expression remains inconclusive.</p>", "<p id=\"Par28\">To control that DCZ0415 specifically inhibits TRIP13, we used CRIPSR-CAS9 to remove <italic>TRIP13</italic> from one cell line. For this we chose the cell line H1703 (GC_high, high TRIP13). Using single cell cloning and Sanger sequencing, we were able to pick up one clone that displayed two disrupted <italic>TRIP13</italic> alleles (Supplementary Fig. S##SUPPL##1##4A–C##). Using Western blot analysis, we found that the TRIP13 protein was removed in these cells (Supplementary Fig. S##SUPPL##1##4D, E##).</p>", "<p id=\"Par29\">Using this cell line (TRIP13^KO), we performed the cell viability assay to detect whether <italic>TRIP13</italic> removal would decrease sensitivity to DCZ0415. As control we used cells treated with scrambled guide RNAs during the CRISPR-CAS9 procedure. Removal of TRIP13 clearly decreased the response to DCZ0415, suggesting that DCZ0415 indeed specifically inhibits TRIP13 (Supplementary Fig. S##SUPPL##1##5A##).</p>", "<p id=\"Par30\">In addition, we used the GC_low /low TRIP13 cell line H1563, to overexpress <italic>TRIP13</italic>. For this we used the TRIP13 CRISPR activation plasmid, including the synergistic activation mediator (SAM) transcription activation system, to overexpress TRIP13 or the CRISPR Activation plasmid encoding the deactivated Cas9 (dCas9) nuclease as control (Supplementary Fig. S##SUPPL##1##4F–H##). Using these cell lines, we performed the clonogenic assay to quantify the cells’ survival 14 days after irradiation with 2 Gy or without irradiation. (Supplementary Fig. S##SUPPL##1##5B, C##). Overexpression of TRIP13 indeed led to increased survival in response to IR.</p>", "<title>TRIP13 inhibition decreases RAD51 induction after irradiation</title>", "<p id=\"Par31\">To investigate the mechanism by which TRIP13 is making the GC_high cell lines more resistant to IR, we performed Western blot analyses on all six cell lines after irradiation, with and without DCZ0415 treatment. First, we analyzed expression of HR marker RAD51. Except for H1563, irradiation induced RAD51 in all cells, irrespective of GC gene score. TRIP13 inhibition by DCZ0415 decreased the levels of RAD51 in all cells, quantified by relative expression compared to TUBULIN (Supplementary Fig. S##SUPPL##1##6A, B##). We performed the same experiment to investigate the presence of non-homologous end-joining (NHEJ) proteins KU70 and Ligase IV. In contrast to RAD51, DCZ0415 treatment did not affect expression of KU70 or Ligase IV, quantified by relative expression compared to GAPDH (Fig. S##SUPPL##1##6C–E##).</p>", "<title>TRIP13 correlates with cell proliferation before and after irradiation</title>", "<p id=\"Par32\">Finally, in addition to measuring the colony formation ability of cancer cells, we also repeated the EdU proliferation assay after addition of DCZ0415 (Fig. ##FIG##5##6f##). This assay showed that addition of DCZ0415 led to a 15% reduction of EdU positive cells in GC_low cell lines, compared to 46% in GC_high cell lines (<italic>p</italic> &lt; 0.001). H1437, which is a GC_low cell line with a high TRIP13 expression level, showed a 35% reduction in EdU absorption following the DCZ0415 treatment. Similarly, GC_high cell line H1703 shows a 49% reduction in EdU absorption following DCZ0415 treatment. We then repeated the EdU assay to observe the added effect of TRIP13 inhibition to irradiation. Compared to 1 Gy of IR alone, the addition of 10 µM DCZ0415 shows a significant decrease in EdU absorption in all GC_high cell lines, but not in GC_low cell lines (Fig. ##FIG##5##6g##). In conclusion, TRIP13 expression is associated with cell proliferation, and its inhibition by DCZ0415 led to a reduction in cell proliferation of cells that express higher levels TRIP13.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par33\">We here find that LUAD cells that express a relatively high number of GC genes (GC_high) can rapidly repair DSBs, show higher rates of proliferation and are more resistant to IR, compared to LUAD cells that express a relatively low number of GC genes (GC_low). Due to increased radioresistance of GC_high cell lines in response to irradiation, but not cisplatin, we speculate that this increased malignancy may be attributed to (pseudo-)meiotic activity that is encoded by GC genes. The DNA damage response in meiosis involves GC genes that, when upregulated by cancer cells, enhance their ability to withstand DSBs that are induced by IR. One gene strongly associated with increased IR resistance in our cells appeared to be TRIP13, and we here show that the putative TRIP13 inhibitor DCZ0415 leads to a decreased DNA damage response, which may allow for improved cancer treatment options.</p>", "<p id=\"Par34\">In addition, we find that GC_high cells have higher expression of the pluripotency markers <italic>OCT4</italic>, <italic>Nanog</italic> and <italic>SOX2</italic>. Moreover, they show a higher invasion potential measured using the wound healing assay. However, since two cell lines, representing both the GC_high and GC_low groups, display a very high invasion potential, future research on both stemness and invasion potential is warranted.</p>", "<p id=\"Par35\">Maybe the most well-known germline-specific feature is meiosis, the highly specialized cell division that ultimately results in the formation of haploid gametes [##REF##29385397##24##]. Meiosis includes the induction of hundreds of DSBs that are required for crossover formation [##REF##9039264##25##]. These DSBs are effectively dealt with by meiotic recombination, which not only requires genes involved in somatic homologous recombination, but also involves many meiosis specific genes. Among these meiosis specific genes are GC genes we previously identified, such as RAD51AP1, HORMAD1, DMC1 and SMC1β [##REF##29907769##6##, ##REF##33348709##7##]. While meiosis is tightly controlled in germ cells, the ectopic expression of such GC genes in cancer may result in the aberrant activation of pseudomeiotic processes, such as partial meiotic recombination or maybe even faulty assembly of the synaptonemal complex [##REF##36300921##26##, ##REF##36681477##27##]. For example, TEX12 is a gene that normally mediates synaptonemal complex assembly, but ectopic expression in somatic cells contributes to oncogenic centrosome amplifications [##REF##34880391##28##]. Another example is Aurora kinase C (AURKC), which is required for the spindle assembly checkpoint during meiosis, but leads to increased migration and oncogenic transformation when ectopically expressed in somatic cells [##REF##34461108##29##]. Ectopic expression of meiotic genes that are normally involved in cell cycle checkpoints or DNA damage repair could thus have a major influence on how cancer cells respond to DNA damaging agents, such as irradiation.</p>", "<p id=\"Par36\">We observed that GC_high cell lines are more susceptible to DNA damage caused by IR, which predominately induces DSBs. Using immunofluorescence with γ-H2AX following irradiation, we found that DSB repair is indeed more efficient in GC_high cell lines. It could thus be hypothesized that GC genes induce partial meiotic recombinational repair of DSBs. From a bioinformatic analysis it indeed appeared that partial activation of meiotic recombinational processes can lead to increased repair of DSBs in cancer cells, which would ultimately lead to more genomic instability and further oncogenesis [##REF##36300921##26##]. One gene involved in the DNA damage response that shows high differential expression between GC_high and GC_low cell lines is RAD51-associated protein 1 (RAD51AP1), which directs RAD51 towards DNA damage to initiate meiotic recombination [##UREF##5##30##]. Loss of RAD51AP1 leads to defective homologous recombination and genome instability [##REF##35652094##31##], while upregulation of RAD51AP1 has been associated with a poor prognosis in several kinds of adenocarcinoma [##REF##33403046##32##]. Indeed, we find that GC_high cell lines display higher amounts of RAD51 foci in response to irradiation induced DSBs. Because inhibition of non-homologous end-joining (NHEJ) does not significantly affect the GC_high cells more than the GC_low cells, it seems that expression of GC genes predominately has an effect on homologous recombination (HR).</p>", "<p id=\"Par37\">Another meiotic and DNA repair response associated gene that shows a high differential expression between GC_high and GC_low cell lines is TRIP13 (Thyroid Hormone Receptor Interacting Protein 13), which is an AAA-ATPase that acts as a chaperone in a variety of cellular processes [##REF##9927482##33##]. It is highly expressed during embryogenesis, in testicular tissue and a variety of cancers [##REF##17696610##22##, ##REF##25613900##34##]. While TRIP13 gene expression was not detectible in the GTEx data that was used to identify GC genes [##REF##29907769##6##, ##REF##33348709##7##], TRIP13 is expressed at a low yet functional level in mitosis, where its role is likely to disassemble the mitotic spindle checkpoint complex [##REF##22712476##35##, ##REF##25895724##36##]. The effects of TRIP13 inhibition are widespread because TRIP13 is a key orchestrator of the HORMA domain protein family, which includes the genes MAD2L2, MAD2L1, HORMAD1, HORMAD2, ATG13, ATG101, CMT2. These proteins regulate a variety of signaling processes, including mitosis, meiotic recombination, DNA damage repair, and autophagy [##REF##35041460##37##]. HORMA domain proteins can be active or inactive, depending on the availability of their C-terminal binding site. When bound to a closure motif, the HORMA domain protein becomes active and able to bind a substrate. Reversion from the active to the inactive state occurs through TRIP13, together with MAD2 (or p31 ^comet) [##REF##33122436##38##]. One HORMA domain protein is MAD2L2 (or Rev7), a crucial component of the Shieldin complex that binds at DSBs sites to suppress recombination and allows for NHEJ to take place. The presence of TRIP13 during DSB repair leads to the inactivation of Rev7 and the disassembly of Shieldin complexes [##REF##32420796##39##]. As a result, NHEJ is inhibited and recombination becomes the preferred DNA repair pathway [##REF##33122436##38##–##REF##31915374##40##]. Sustained expression of TRIP13, as is frequently observed in cancer, thus provides cancer cells with an alternative DNA repair mechanism through recombination [##REF##33122436##38##]. During meiosis, recombination is promoted by TRIP13, as it facilitates depletion of the meiosis-specific HORMA domain proteins HORMAD1 and HORMAD2 from the chromosome axes as synapsis occurs, leading to further progression of meiotic recombination and cross-over formation [##UREF##6##41##, ##REF##22549958##42##].</p>", "<p id=\"Par38\">To understand the role of TRIP13 in meiosis, Li &amp; Schimenti reduced TRIP13 expression in mice, leading to meiotic arrest due to accumulation of DNA damage in spermatocytes caused by dysfunctional recombination at the pachytene stage [##REF##17696610##22##]. Later, Roig et al. were able to induce a more severe TRIP13 mutation that, in addition to impaired recombination, also leads to impaired synapsis of the homologous chromosomes and the lack of XY-body formation [##REF##20711356##43##]. Despite the role of TRIP13 in mitosis, TRIP13-mutant mice were viable and looked no different from TRIP13-wildtype mice, except for reduced testis size. Humans with biallelic mutations in TRIP13 are highly susceptible to Wilms tumor and chromosome missegregation due to impairment of the spindle assembly checkpoint [##REF##28553959##44##]. In addition, human TRIP13-mutant oocytes cannot complete meiosis [##REF##32473092##45##]. On the other hand, upregulating TRIP13 in non-malignant cells leads to an oncogenic phenotype [##UREF##4##21##], which may be accounted for by two distinct mechanisms. First, sustained TRIP13 expression may lead to the inappropriate silencing of mitotic checkpoints, thereby allowing for rapid proliferation. Second, overexpression of TRIP13 may induce the function it has in meiotic prophase, inhibiting NHEJ and promoting of homologous recombination. As such, TRIP13 overexpression leads to the activation of HORMA domain proteins to induce chromosomal instability and is associated with a poor prognosis in several types of cancer [##UREF##4##21##, ##REF##16921376##46##–##REF##31396344##48##]. Based on these studies, as well as our observation that TRIP13 inhibition combined with irradiation largely reduces in vitro survival, we suggest that the role of overexpressed TRIP13 in cancer may result in the recombination phenotype, similar to its physiological role during the prophase of meiosis I. As TRIP13 expression is not strictly germ cell (or cancer) specific, this recombination-promoting phenotype would thus be a germ cell/cancer specific manifestation of TRIP13 overexpression.</p>", "<p id=\"Par39\">In our experiments, TRIP13 is generally highly expressed in GC_high cell lines and lowly expressed in in GC_low cell lines. However, H1437 is a GC_low cell line that has a much higher TRIP13 expression than the other GC_low cell lines. From the clonogenic assay it indeed appears that H1437 is more radioresistant than the other 2 GC_low cell lines, and its survival curve follows the curve of GC_high cell lines. Inhibition of TRIP13 largely impaired the proliferation of the TRIP13-high cell line H1437, while leaving the proliferation rates of TRIP13-low cell lines H1563 and H2122 unaffected. In addition, when TRIP13 is inhibited, H1437 shows the second largest reduction in the ability to form colonies. Together, these experiments lead us to conclude that TRIP13 expression alone in this cell line causes a phenotype that is similar to the GC_high cell lines. Interestingly, in contrast to DSB-marker γH2AX, the cell line H1437 (low GC gene score but high TRIP13) did not follow the RAD51 pattern (marking HR) of the GC_high cell lines, suggesting that the TRIP13 dependent increase in HR may interact with expression of other (germ line specific) genes. Nevertheless, we suggest that TRIP13 inhibition may be an effective strategy in the treatment of tumors that express TRIP13. This is supported by our result showing a decrease in RAD51 levels, but not the NHEJ proteins KU70 and Ligase IV, in all six LUAD cell lines upon treatment with DCZ0415. We found that the effect of TRIP13 inhibition during IR treatment may be independent from the initial level of <italic>TRIP13</italic> RNA expression, suggesting that combining TRIP13 inhibition with irradiation may be effective regardless of the initial TRIP13 expression levels.</p>", "<p id=\"Par40\">GC genes have been proposed as ideal candidate targets in cancer treatment for two major reasons. First, because GC genes are responsible for germline-specific processes, solely targeting these processes should not harm other cells and thus lead to limited side-effects. Side effects may affect development, fertility, or none at all, depending on the expression profile of the target(s). Second, GC genes are hypothesized to contribute to the known hallmarks of cancer [##REF##36300921##26##]. As a cancer is dependent on these features, targeting these oncogenic processes is more likely to effectively cripple a cancer, rather than inducing resistance through the selection of cancer cells following a treatment. TRIP13 appeared as a GC gene in our previous analyses due to high expression in primordial germ cells and throughout spermatogenesis [##REF##29907769##6##, ##REF##33348709##7##]. Its dual involvement in both the spindle assembly checkpoint and DNA repair makes it an appealing anticancer target. Despite a high RNA expression in the germline and many types of cancer, and low RNA expression in normal somatic tissues, TRIP13 is not strictly specific to cancer and the germline as it is also involved in the mitotic spindle assembly checkpoint. Therefore, it may not be an appropriate target in CAR T-cell therapies. However, inhibiting TRIP13 directly, especially when combined with radiotherapy or other DNA damaging agents such as cisplatin [##REF##35041460##37##, ##REF##31396344##48##, ##REF##34521823##49##], could be a viable treatment modality to result in a higher mutational burden or lead to mitotic catastrophe. The clinical safety and efficacy of a TRIP13-targeted treatment remains to be investigated in future studies. Similar to the differential expression of TRIP13, there are many more (GC) genes that share a similar germline/cancer expression profile. Further investigation could focus on the role of GC genes in the human germline and soma, as targeting germline-specific processes such as meiosis in cancer treatment has the potential to severely limit side effects.</p>" ]

[]

[ "<p id=\"Par1\">In principle, germline cells possess the capability to transmit a nearly unaltered set of genetic material to infinite future generations, whereas somatic cells are limited by strict growth constraints necessary to assure an organism’s physical structure and eventual mortality. As the potential to replicate indefinitely is a key feature of cancer, we hypothesized that the activation of a “germline program” in somatic cells can contribute to oncogenesis. Our group recently described over one thousand germline specific genes that can be ectopically expressed in cancer, yet how germline specific processes contribute to the malignant properties of cancer is poorly understood. We here show that the expression of germ cell/cancer (GC) genes correlates with malignancy in lung adenocarcinoma (LUAD). We found that LUAD cells expressing more GC genes can repair DNA double strand breaks more rapidly, show higher rates of proliferation and are more resistant to ionizing radiation, compared to LUAD cells that express fewer GC genes. In particular, we identified the HORMA domain protein regulator TRIP13 to be predominantly responsible for this malignant phenotype, and that TRIP13 inhibition or expression levels affect the response to ionizing radiation and subsequent DNA repair. Our results demonstrate that GC genes are viable targets in oncology, as they induce increased radiation resistance and increased propagation in cancer cells. Because their expression is normally restricted to germline cells, we anticipate that GC gene directed therapeutic options will effectively target cancer, with limited side effects besides (temporary) infertility.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41419-024-06433-y.</p>", "<title>Acknowledgements</title>", "<p>This work has been supported by the Amsterdam Reproduction &amp; Development Research Institute and the China Scholarship Counsel (grant number 202006300005 to WL).</p>", "<title>Author contributions</title>", "<p>WL, JWB and GH conceived and designed the experiments. WL and JWB performed the experiments. WL, JWB, JK and GH analyzed the data. WL, QL and GH conceived and designed the knockout cell lines experiments. JWB, WL and GH wrote the manuscript. JK and AvP critically read the manuscript.</p>", "<title>Data availability</title>", "<p>All data generated or analyzed during this study are included in this published article [and its supplementary information files].</p>", "<title>Competing interests</title>", "<p id=\"Par41\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>GC-signature scores of 44 lung adenocarcinoma (LUAD) cell lines.</title><p>Every dot represents one cancer cell line. Red dots represent cell lines that we included in our analysis in order to compare the phenotype between high- versus low expression of GC-genes. H2085 and H1573 did not survive the standardized culture conditions and were not included for further analysis.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>GC_high cell lines are more radioresistant than GC_low cell lines.</title><p><bold>a</bold> Survival curves of 6 LUAD cell lines in response to irradiation. <bold>b</bold> Mean survival curves of LUAD cell lines in response to irradiation grouped by GC_high cell lines (<italic>n</italic> = 3) and GC_low cell lines (<italic>n</italic> = 3). <bold>c</bold> Survival curves of 6 LUAD cell lines in response to cisplatin. <bold>d</bold> Mean survival curves of LUAD cell lines in response to cisplatin grouped by GC_high cell lines (<italic>n</italic> = 3) and GC_low cell lines (<italic>n</italic> = 3). *<italic>p</italic> &lt; 0.05. **<italic>p</italic> &lt; 0.01.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>GC_high cell lines repair double-stranded breaks more efficiently than GC_low cell lines.</title><p><bold>a</bold> γ-H2AX foci after 1 Gy of irradiation at several time points in 6 LUAD cell lines. <bold>b</bold> γ-H2AX foci after 1 Gy of irradiation in 6 LUAD cell lines, relative to 30 min after exposure, averaged by GC gene category. <bold>c</bold> γ-H2AX foci after 1 Gy of irradiation in GC_high (red) and GC_low cell lines (blue), relative to 30 min after exposure. <bold>d</bold> RAD51 foci after 1 Gy of irradiation at several time points in 6 LUAD cell lines. <bold>e</bold> RAD51 foci after 1 Gy of irradiation in 6 LUAD cell lines, relative to 30 min after exposure, averaged by GC gene category. <bold>f</bold> RAD51 foci after 1 Gy of irradiation in GC_high (red) and GC_low cell lines (blue), relative to 30 min after exposure. *<italic>p</italic> &lt; 0.05. **<italic>p</italic> &lt; 0.01.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>GC_high cell lines maintain a higher rate of proliferation following irradiation.</title><p><bold>a</bold> Percentage of 5-ethynyl-2’-deoxyuridine (EdU) positive cells of each LUAD cell line before and after 1 Gy of irradiation, shown in triplicate. <bold>b</bold> After irradiation (1 Gy), GC_high cell lines show a larger reduction in EdU absorption, compared to GC_low cell lines. NS not significant, *<italic>p</italic> &lt; 0.05. **<italic>p</italic> &lt; 0.01. ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>TRIP13 is most differentially expressed between GC_high and GC_low cell lines.</title><p><bold>a</bold> Heat map based on the RNA expression (transcripts per million) of 9 genes involved in meiosis and DSB repair in 6 LUAD cell lines. <bold>b</bold> High TRIP13 RNA expression in 515 LUAD patient samples correlates with poor prognosis (median, <italic>p</italic> = 0.001). <bold>c</bold> Western blot gel showing TRIP13 and GAPDH protein expression. <bold>d</bold> Protein quantification expressed as relative to GAPDH in 6 LUAD cell lines. *<italic>p</italic> &lt; 0.05.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Inhibiting TRIP13 strongly impairs colony formation and proliferation.</title><p><bold>a</bold> Inhibiting TRIP13 with 10 µM DCZ0415 significantly reduces the surviving fraction in all cell lines (64%, CI_95% 55–73%), where 100% is defined as the average of three replicates not exposed to any treatment. <bold>b</bold> TRIP13 expression (Log₂ (transcripts per million)) is strongly correlated with a reduced surviving fraction after treatment with 10 µM DCZ0415 (R² = 0.94, <italic>p</italic> = 0.001). <bold>c</bold> TRIP13 expression is strongly correlated with an improved surviving fraction following 1 Gy of IR (R² = 0.98, <italic>p</italic> &lt; 0.001). <bold>d</bold> The addition of 10 µM DCZ0415 and 1 Gy of IR significantly decreased surviving fraction in all cell lines (81%, CI_95% 77–84%), where 100% is defined as the average of three replicates exposed to 1 Gy of IR alone. <bold>e</bold> Treatment with 1 Gy irradiation and 10 µM DCZ0415 strongly impairs the surviving fraction of all LUAD cell lines, independent of TRIP13 expression (R² = 0.003, <italic>p</italic> = 0.92). <bold>f</bold> EdU absorption after treatment with 10 µM DCZ0415 was significantly reduced in all GC_high cell lines and in H1437, where 100% is defined as the average of three replicates not exposed to any treatment. <bold>g</bold> EdU absorption after treatment with 10 µM DCZ0415 and 1 Gy irradiation was significantly reduced in all GC_high cell lines, where 100% is defined as the average of three replicates exposed to 1 Gy of IR alone. NS not significant, *<italic>p</italic> &lt; 0.05. **<italic>p</italic> &lt; 0.01. ***<italic>p</italic> &lt; 0.001.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Included LUAD cell lines and characteristics.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>GC category</th><th>Cell line</th><th>ATCC ID</th><th>Patient</th><th>FBS</th><th>Viability in cell culture</th><th>Protein-altering mutations in KRAS, NRAS, EGFR or TP53</th></tr></thead><tbody><tr><td rowspan=\"4\">Low</td><td>NCI-H1563</td><td>CRL-5875</td><td>Male, non-smoker, age unknown</td><td>10% FBS</td><td>Viable</td><td>–</td></tr><tr><td>NCI-H2122</td><td>CRL-5985</td><td>46 y/o Caucasian female, 30 PY</td><td>10% FBS</td><td>Viable</td><td><p>KRAS: G12C</p><p>TP53: C176F</p><p>TP53: Q16L</p></td></tr><tr><td>NCI-H1573</td><td>CRL-5877</td><td>35 y/o Caucasian female, 15 PY</td><td>5% FBS</td><td>Not viable</td><td><p>KRAS: G12A</p><p>TP53: R248L</p></td></tr><tr><td>NCI-H1437</td><td>CRL-5872</td><td>60 y/o Caucasian male, 70 PY</td><td>10% FBS</td><td>Viable</td><td>TP53: R267P</td></tr><tr><td rowspan=\"4\">High</td><td>NCI-H2347</td><td>CRL-5942</td><td>54 y/o Caucasian female, non-smoker</td><td>10% FBS</td><td>Viable</td><td><p>KRAS: L19F</p><p>NRAS: Q71R</p><p>TP53: T125T</p></td></tr><tr><td>NCI-H2085</td><td>CRL-5921</td><td>45 y/o male, smoking status unknown</td><td>10% FBS</td><td>Not viable</td><td>TP53: Y220C</td></tr><tr><td>NCI-H1703</td><td>CRL-5889</td><td>54 y/o Caucasian male, 50 PY</td><td>10% FBS</td><td>Viable</td><td>–</td></tr><tr><td>NCI-H1693</td><td>CRL-5887</td><td>55 y/o Caucasian female, 80 PY</td><td>5% FBS</td><td>Viable</td><td>–</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>" ]

[ "<table-wrap-foot><p><italic>FBS</italic> foetal bovine serum, <italic>ATCC</italic> American Type Culture Collection, <italic>PY</italic> pack years.</p></table-wrap-foot>", "<fn-group><fn><p>Edited by Massimiliano Agostini</p></fn><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Wenqing Liu, Jan Willem Bruggeman.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41419_2024_6433_Fig1_HTML\" id=\"d32e329\"/>", "<graphic xlink:href=\"41419_2024_6433_Fig2_HTML\" id=\"d32e661\"/>", "<graphic xlink:href=\"41419_2024_6433_Fig3_HTML\" id=\"d32e742\"/>", "<graphic xlink:href=\"41419_2024_6433_Fig4_HTML\" id=\"d32e852\"/>", "<graphic xlink:href=\"41419_2024_6433_Fig5_HTML\" id=\"d32e959\"/>", "<graphic xlink:href=\"41419_2024_6433_Fig6_HTML\" id=\"d32e1046\"/>" ]

[ "<media xlink:href=\"41419_2024_6433_MOESM1_ESM.xlsx\"><caption><p>Supplementary data 1</p></caption></media>", "<media xlink:href=\"41419_2024_6433_MOESM2_ESM.pdf\"><caption><p>Supplementary table and figures</p></caption></media>", "<media xlink:href=\"41419_2024_6433_MOESM3_ESM.pdf\"><caption><p>Checklist</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Since 1860, when the very first plastic was invented^{##UREF##0##1##}, about 8.3 billion tonnes of plastic has been manufactured worldwide and 6.3 billion tonnes of it is waste^{##UREF##1##2##,##UREF##2##3##}. As far as recycling of plastic waste is concerned only 8.7% of this waste has been recycled so far. Plastic imparts uncountable ecological as well as biological impacts^{##UREF##3##4##} on the living and non living components of our ecosystems^{##UREF##4##5##,##UREF##5##6##}. Considering these deleterious effects of plastics newer biodegradable alternatives are sought and therefore varied biological waste or other renewable raw materials are being explored to produce plastic alternatives. Biodegradable polyesters, polylactic acid, polysaccharides and proteins from plants or animal sources are few of the materials being explored to produce plastic alternates^{##UREF##6##7##–##UREF##11##14##}. Researchers around the globe are continuously thriving to improve the performance and properties of these bio-based plastics to maximize their applications in packaging and manufacturing of disposable items/ medical devices.</p>", "<p id=\"Par3\">Various proteins from plant and animal sources have gained heightened interest in past few years for the production of bioplastics. The interactions of protein molecules because of the range of functional groups present in amino acid side chains give them additional benefit over other biomolecules. The protein bioplastics have the properties of safety, biocompatibility and biodegradability^{##REF##37021675##15##}. The isolated proteins from various sources have demonstrated the property of denaturing and again renaturing under laboratory condition which allow them to be plasticized and obtain films with suitable properties. Collagen, Milk Proteins (casein and whey), Myofibrillar proteins, keratin and gelatin includes the animal proteins being studied for the synthesis of bioplastics^{##UREF##12##16##–##UREF##16##20##}. Keratin bioplastic films from sources such as chicken feather, duck feather and sheep wool and there characterization have also been reported^{##REF##29320725##21##–##REF##8836838##24##}.</p>", "<p id=\"Par4\">Human hair is made up of up to 80% of hard keratins. Amino acid Cystein (Cys) is present in large amount in hair keratins that gives them strength and stiffness as result of disulphide linkages^{##REF##22215855##25##,##UREF##19##26##}. For the extraction of human hair keratin different approaches could be applied including oxidation and reduction procedures^{##REF##31002909##27##}. The oxidized form of keratin is known as keratose and the reduced form is known as kerateine^{##REF##21835462##28##}. Extracted keratin from human hair has been reported to be used for the synthesis of films, fibers, sponges, Hydrogels and composites for various applications. Poly(ε‐caprolactone)—keratin fibers have been reported to possess structural integrity in the ratio 70:30^{##UREF##20##29##}. Human hair keratin films with 1% glycerol as plasticizers have also been reported but the effect of varied concentration of glycerol have not been reported so far^{##UREF##21##30##,##UREF##22##31##}. Application of ohmic heating has been reported to produce keratin films and it was found that the films formed with conventional heating had better surface morphology^{##REF##32061691##32##}.</p>", "<p id=\"Par5\">In the present research keratin protein derived from waste human hair is being utilized to produce the bioplastic film. We would like to coin the term “kertics” for all the keratin based bioplastics. The present research aimed at studying the effect of different concentrations of glycerol as plasticizer on the properties of human hair keratin film. Also, ethanediol (ED), diethylene glycol (DEG), triethylene glycol (TEG) are being reported as the novel plasticizers for keratin film in this research for the first time. Method of solution casting in silicon moulds was adopted to obtain the final stable films after curing procedures. Silicon moulds were adopted in place of polyethylene plate to cast the films owing to flexibility and ease of film removal, non-sticky surface as well as reusability. Characterization of the bioplastic film produced was done by various analytical techniques including field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD) and Fourier-transform infrared spectroscopy (FTIR). Biodegradability of the films was also studied by keratinophilic fungal isolate <italic>A. oryzae</italic> obtained from soil by hair baiting technique. The outcomes of the present study shall contribute to the understanding of effect of various plasticizers and their concentration on the film properties as well as their suitability for packaging and other applications.</p>" ]

[ "<title>Methods</title>", "<title>Collection of hair samples</title>", "<p id=\"Par39\">Hair samples were collected from volunteers with prior informed consent from the salons in Agra, Kamla Nagar and Dayalbagh region. The collected hair samples were cleaned by removing the coarse dust particles by hand and thereafter stored in sterile bags for further analysis. All experiments were performed in accordance with relevant guidelines and regulations. All the methods adopted in the present study were reviewed and approved by Dayalbagh Educational Institute, Dayalbagh, Agra, India.</p>", "<title>Methods for film formation</title>", "<title>Hair delipidization</title>", "<p id=\"Par40\">The collected hair samples was washed in doubled distilled water followed by mild soap and dried in oven overnight at 40 °C. The cleaned and dried hair samples were then soaked in chloroform and methanol in the ratio 2:1 for 48 h at room temperature in order to remove the lipids. After delipidization, the solvents were drained off and the hair samples were again washed twice with chloroform and methanol solution to completely remove the sticking lipid globules if any, thereafter the hair were again washed with ddH₂O, dried and used for protein extraction.</p>", "<title>Extraction of hair keratin</title>", "<p id=\"Par41\">The delipidized hair samples were cut into small fragments (1–2 mm) with the help of scissors. 20 g hair samples were then incubated with extraction buffer composed of trisHCl (25 mM, pH 8.5), thiourea (2.6 M), urea (5 M) and mercaptoethanol (5%) at 50 °C, 75 rpm^{##UREF##11##14##}. The extraction was done in shaker incubator for 3 to 6 days. The protein extract was retrieved by sieving through medical gauge, filtration and centrifugation at 4500 rpm for 20 min.</p>", "<title>Dialysis of protein extract</title>", "<p id=\"Par42\">The obtained protein extract was to completely remove the extraction buffer components. The dialysis was carried out with the Spectra Por S/P Dialysis Membrane, with MWCO 6000–8000 Da for 3 days against ddH₂0. The water was changed after every 12 h of interval. The dialyzed protein extract was stored at −90 °C and thawed before further processing.</p>", "<title>Quantification of protein</title>", "<p id=\"Par43\">Quantification of protein in the dialyzed protein extract was carried out by Bradford assay using Himedia HiGenoMB Bradford Reagent (ML106) and HiMedia bovine serum albumin (BSA) (MB083) as a standard.</p>", "<title>Lyophilization of dialyzed extract</title>", "<p id=\"Par44\">The dialyzed protein extract was freeze dried or lyophilized by freezing the extract and reducing the surrounding pressure to directly sublime the water from solid to gas phase. The lyophilization of the protein samples was done by Lyophilizer-FD 5.</p>", "<title>SDS-PAGE analysis</title>", "<p id=\"Par45\">For the analysis of molecular weight composition of the protein extract sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) was utilized. The protein samples were in the gel (10 × 10 cm). Separation was carried out on Analytical single moulded vertical electrophoretic system using standard protein ladder of 245 to 11 kDa. Coomassie brilliant blue dye was used for staining and the gel was thereafter de-stained using de-staining solution comprising of methanol, acetic acid and water in the ratio 5:1:4. Protein bands were then visualized.</p>", "<title>Solution casting for film formation</title>", "<p id=\"Par46\">10 mg of keratin powder was redissolved in ddH₂O and was then mixed with 100, 500, 1000 and 1500 µl of 1% glycerol solution in first set of trials. The resulting mixtures of glycerol and keratin solution was conditioned for 4 h at 50 °C under shaking conditions and then casted in silicon moulds. The films were kept for drying at 50 °C using dry heat. In the next set of trials 100 µl of 1% solutions of ethanediol (ED), diethylene glycol (DEG) and tri-ethylene glycol (TEG) were used to form the protein bioplastic films, rest of the procedures were kept same.</p>", "<title>Curing of the bioplastic films</title>", "<p id=\"Par47\">The preliminary films obtained after solution casting were then subjected to curing temperature of 110 °C for 3 h. Post curing, the films were then subjected to reduced temperatures (approximately 4 °C). The resultant hard films were then taken up for characterization studies.</p>", "<title>Methods for characterization</title>", "<title>Morphological characterization by FESEM</title>", "<p id=\"Par48\">Field Emission Scanning Electron Microscope was utilized to analyze the surface morphology of the hair fragments at various stages of the studies. Morphological characteristics of the bioplastic films obtained with different plasticizers were also revealed by using FESEM analysis. Before analysis the samples were platinum coated with the help of JEOL, JEC-3000FC auto fine platinum coater. Analysis was made FESEM-JEOL 7610F PLUS at magnifications ranging from ×300 to ×3000 in both lower electron imaging (LEI) and secondary electron imaging (SEI) mode as suitable depending on the sample in study.</p>", "<title>Characterization by XRD</title>", "<p id=\"Par49\">X-ray diffraction is utilized in order to analyze the crystalline structure of the polymeric substances. The analysis of Bragg peaks scattered to wide angles is made during this study. The analysis of Bragg peaks scattering caused by nanometer and sub-nanometer sized structures is done. The percentage crystallinity of the sample could be determined using this technique. The scattering intensity is plotted as a function of 2θ angle and the analysis of the same is made. This is a non destructive method of characterization. In a crystalline solid, the distance between the imaginary planes in which the atoms are regularly spaced is known as d-spacing. This d-spacing is specific to every material. The structure of keratin bioplastic membranes in the present study was analyzed by D8 ADVANCE X-Ray Diffractometer.</p>", "<title>Characterization by FTIR</title>", "<p id=\"Par50\">Fourier-Transform Infrared Spectroscopy provides the information about infrared spectrum of absorption or emission of a solid, liquid or gas samples. The information of these patterns could be exploited to identify the functional groups present in the samples. This may also help to analyze the changes, addition or removal of functional groups as a result of the processing of protein in the formation of bioplastic films. Films prepared with glycerol, ED, DEG and TEG were analyzed by FTIR NICOLET-IS-50 over a range of 400 to 4000 cm⁻¹. Sample preparation was done by mixing with KBr in ratio 1:100 (w/w) and grinding vigorously thereafter making pellet by using a press for analysis.</p>", "<title>Dimensions and water solubility of bioplastic films</title>", "<p id=\"Par51\">Film thickness was measured with the help of micrometer. Measurement of the radius was done by ruler and used for the calculating the area of the bioplastic samples.</p>", "<title>Biodegradation test by <italic>A. oryzae</italic></title>", "<p id=\"Par52\">The isolation of keratinophilic fungi was done from soil by To-ka-Va hair bating technique^{##UREF##36##55##}. Molecular identification of the isolate was done by ITSrRNA gene sequencing, conducted at NCIM Pune, India. For the degradation studies, the bioplastic substrates were incubated with fungal cultures and 10 ml basal solution in petri plates. Observations were made at the interval of 3, 5 and 7 days under optical microscope.</p>" ]

[ "<title>Results</title>", "<p id=\"Par6\">The keratin from delipidized human hair samples was isolated by Shindai Method^{##UREF##23##33##} and quantified by Bradford method^{##REF##942051##34##}. Protein concentration after 3 days of extraction at 50 °C was around 2.9 mg/ml and that after 6 days of extraction period was about 9.8 mg/ml. The extracted protein solution was dialyzed and lyophilized to obtain the keratin protein powder. Lyophilization of protein solution gave a yield of 28 ± 2%. The lyophilized protein was subjected to SDS PAGE analysis to determine the molecular weight composition of the isolated protein sample. The isolated protein gave two bands, first at 35–48 kDa representing the microfibril component and second at 10–20 kDa corresponding to matrix proteins. The isolated protein was then utilized to prepare the bioplastic film by solution casting in silicon moulds and final curing (Fig. ##FIG##0##1##). Various plasticizers viz. glycerol, ethanediol, diethylene glycol and triethylene glycol were used to form the bioplastic film and were characterized by FESEM, FTIR and XRD techniques.</p>", "<title>Morphological characteristics of the keratin bioplastic</title>", "<p id=\"Par7\">Field emission scanning electron microscopy (FESEM) was utilized to analyze the morphological characteristics of the bioplastic films formed with various plasticizers. Also the virgin hair delipidized hair and hair fragments after protein extraction were analyzed to access the changes during the extraction procedures. Imaging of virgin hair at X3000 showed the presence of lipid depositions between the cuticle scales (Fig. ##FIG##1##2##a). The analysis of hair fragments after lipid removal showed the absence of lipid depositions and depicted smoother appearance (Fig. ##FIG##1##2##b), that after extraction showed the distorted morphology of the hair scales and scales were broken and disrupted as a results of the action of reducing and denaturing agents from the extraction buffer (Fig. ##FIG##1##2##c).</p>", "<p id=\"Par8\">In order to access the suitability of glycerol as plasticizer and optimize the concentration required for the formation of stable bioplastic film varied amount of 1% glycerol were first utilized for solution casting and film formation. Films with 100, 500, 1000 and 1500 µl of 1% glycerol with 10 mg of keratin powder were formed and analyzed. FESEM images of films at about ×20,000 of G100, G500, G1000 and G1500 are shown in Fig. ##FIG##1##2##d–g respectively and that at about ×4000 are shown in Fig. ##FIG##1##2##h–k.</p>", "<p id=\"Par9\">The surface of G100 films at lower magnifications of ×300 was observed to be continuous with certain ups and downs (Supplementary Fig ##SUPPL##0##F1##a) with these lower magnifications no holes or pits were visible. Upon further increasing the magnification at ×5000 (Supplementary Fig. ##SUPPL##0##F1##a) just one or two pits were seen with an approximate size of 0.1 µm recorded at ×20,000 (Fig. ##FIG##1##2##d), 2 kV. These pits were not holes or tunnels and were formed as a result of discontinuous intermolecular interactions between the keratin molecules in the upper layers only and the layers underneath appeared to be continuous.</p>", "<p id=\"Par10\">The analysis of G500 films at ×800 depicted smooth and continuous surface (Supplementary Fig. ##SUPPL##0##F1##b). At ×4000, the morphology of the film was found to be irregular with certain bumps and bulges but no pits or holes were seen (Fig. ##FIG##1##2##i). At higher magnification (×15,000), Fig. ##FIG##1##2##e, the film displayed wrinkled appearance nevertheless no holes or pits were visible. These films were found to be sensitive to higher voltages and the specimen showed ruptures at further higher magnifications (Supplementary Fig. ##SUPPL##0##F1##b).</p>", "<p id=\"Par11\">Further increasing the concentration of glycerol deteriorated the surface morphology of the bioplastic films, hence G1000 and G1500 displayed non-uniform surface even at ×400 (Supplementary Fig. ##SUPPL##0##F1##c). Imaging at ×4000 revealed continuous surface in the films along with certain filamentous depositions (Fig. ##FIG##1##2##j). Observations at ×12,000 (Supplementary Fig. ##SUPPL##0##F1##c) and ×25,000 (Fig. ##FIG##1##2##f) displayed tiled appearance with no holes or pits. G1000 films were found insensitive to operating voltages of up to 5.0 kV.</p>", "<p id=\"Par12\">The surface structures of G1500 films appeared to be extremely discontinuous at ×23,000 (Fig. ##FIG##1##2##g), with the uppermost layer being non uniform and the inner layers seems to be continuous. At lower magnifications at around ×8000, these films showed granular appearance (Supplementary Fig. ##SUPPL##0##F1##d). Larger pits of about 1.8 µm were observed (Supplementary Fig. ##SUPPL##0##F1##d) and the discontinuous and granular appearance of these films could be attributed to the accumulation of excess glycerol.</p>", "<p id=\"Par13\">From the comparative analysis of all these glycerol films, it was concluded that the G100 films displayed the best morphological characteristics and hence same concentration of other plasticizers were taken up for further studies. In the next set of trials films were formed with 100 µl 1% solution of ED, DEG and TEG to yield ED100, DEG100 AND TEG100 films with the same protocol as applied for glycerol films.</p>", "<p id=\"Par14\">ED100 films displayed distinct surface morphology as observed in SEI and LEI mode. At lower magnifications, ED100 films showed similar surface morphology as G100 films (Supplementary Fig. ##SUPPL##0##F1##e). Pit of size 0.75 µm was recorded at ×8000 (Fig. ##FIG##1##2##l, m) and at the similar magnifications, under SEI imaging the films appeared to have wrinkled appearance (Supplementary Fig. ##SUPPL##0##F1##f). At further higher magnification of around ×20,000, the surface appeared to be wrinkled in LEI mode (Supplementary Fig. ##SUPPL##0##F1##g).</p>", "<p id=\"Par15\">As seen under varied magnifications, the surface structures of the DEG100 and TEG100 films were found to be smooth (Fig. ##FIG##1##2##n–o). No pits, holes, bulges or wrinkles were visible in DEG100 and TEG100 films at around ×100,000 and above magnifications. Overall comparison in all the films suggested that DEG100 and TEG100 films have the most uniform surface morphology followed by G100 and ED100.</p>", "<title>XRD diffractogram depicted the crystalline characteristics of the keratin films</title>", "<p id=\"Par16\">The X-ray diffractograms were obtained for all the keratin films in the 2θ range of 15° to 85° (Fig. ##FIG##2##3##a–d). Firstly the XRD analysis was conducted for all the glycerol films viz. G100, G500, G1000 and G1500. In all these films, the characteristic peak of keratin was observed at around 19.5°. In G100 and G500 and G1500 films the peak was observed at 19.5° and in G1000 films it was observed at 19.45°. In addition to this characteristic peak, additional less intense peaks were also observed at different 2θ values. In G100, the minor peak was observed at 29.2° and in other glycerol films it was observed at 29.1°. As intense peak was observed in all the glycerol films, at around 2θ values of 19.5°, this could be attributed to the crystalline behavior of these films. By applying the Bragg’s law the inter atomic spacing or d value for these films were found to be 0.455 nm for G100, G500 and G1500 films and 0.457 nm for G100 films respectively. Overall d value of glycerol films was found to be significantly similar with a difference in value of about 0.002 nm.</p>", "<p id=\"Par17\">The comparative diffractogram for all the glycerol films with different concentration of plasticizer (Fig. ##FIG##2##3##h) shows a clear distinction between G100 and other films. Most intense peak was observed in G100 films at 485.6 a.u followed by G1500, G500 and G1000 at 234.51, 209.59 and 177.51 a.u respectively. The highest peak intensity in G100 films could be attributed to their most crystalline nature among all the glycerol plasticized keratin films.</p>", "<p id=\"Par18\">In the later stages of study, the films formed with other plasticizers were also analyzed and X ray diffractogram for these films were recorded in the range of 15° to 85° (Fig. ##FIG##2##3##e–g). Use of ED, DEG and TEG as plasticizers in human hair keratin film is being reported for the first time in present study. Depicting the similar behavior as the glycerol plasticized keratin films, ED100, DEG100 and TEG100 films showed the characteristic peak for keratin at 19.5° as well. The minor peaks were recorded at 25.1° and 25.3° in ED100 and DEG100 films. In TEG100 films, additional sharp peaks were recorded at 30.5°, 35.45°, 51° and 60.6° that could be attributed to increased crystalline behavior in these films as a result of additional interactions between TEG and the amino acid side chains of the keratin molecules.</p>", "<p id=\"Par19\">The d spacing value in ED100, DEG100 and TEG100 films was found to be 0.455 nm which is same as that of glycerol films. The comparative analysis of all the films depicts the most intense peak in G100 films, followed by DEG100, TEG100 and ED100 being the least (Fig. ##FIG##2##3##i). Glycerol films displayed the most crystalline nature among all the films.</p>", "<title>FTIR showed the changes in amide peaks with different plasticizers</title>", "<p id=\"Par20\">FTIR analysis was utilized to analyze the functional groups and their behavior in the keratin films formed with different plasticizers. Lyophilized keratin powder was also analyzed by FTIR studies and the absorption and transmittance plots of the same were also compared with that of the films to analyze the change in bond stretching and amide peaks while the film formation. The peaks corresponding to Amide A, Amide I, Amide II and Amide III were located in all the samples and changes in them were analyzed.</p>", "<p id=\"Par21\">The absorbance spectra of lyophilized keratin are given in Fig. ##FIG##3##4##e and that of G100, G500, G1000 and G1500 are shown in Fig. ##FIG##3##4##a–d respectively. ED100, DEG100 and TEG100 absorbance spectra are given in Fig. ##FIG##3##4##f–h respectively. The comparative absorption spectrum of all glycerol films is given in Fig. ##FIG##3##4##i and that of films with all the plasticizers and lyophilized keratin is shown in Fig. ##FIG##3##4##j.The analysis of comparative spectra of glycerol films suggests that these films show the absorption peaks at similar wavenumbers. Most intense peak was observed in G1000 films that could be attributed to their increased moisture content relative to films with lower concentrations of glycerol.</p>", "<p id=\"Par22\">Similarly while observing the other films comparative absorption spectra with that of lyophilized protein, most intense peak was observed in lyophilized keratin and the least was observed in DEG100 films that could be again be due to difference in their moisture contents. Transmittance plots of G100, G500, G1000 and G1500 films are given in Fig. ##FIG##4##5##a–d and that of lyophilized keratin, ED100, DEG100, TEG100 films are given in Fig. ##FIG##4##5##e–h. Transmission peaks observed in all the films are given in Table ##TAB##0##1##.</p>", "<p id=\"Par23\">In lyophilized protein the Amide A broad peak was seen at 3424.04 cm⁻¹ with peak intensity 55.35 a.u. Amide I, Amide II and Amide III peaks were recorded at 1654.24, 1546.49, 1242.76 cm⁻¹ respectively. G100 films showed two characteristic peaks, one broad peak for Amide A at 3417.75 cm⁻¹ and for Amide I at 1654.32 cm⁻¹. The minor peak for Amide II was recorded at 1546.99 cm⁻¹ but that for Amide III was not observed. Transmission peaks observed in G500 are at 3417.86, 1654.15 and 1546.69 cm⁻¹ for Amide A, Amide I and Amide II respectively. The positions for amide peaks were found to similar in both G100 and G500 films.</p>", "<p id=\"Par24\">Multiple peaks were observed in G1000 and G1500 films in addition to the characteristics peak of keratin. The characteristic peaks for Amide A, Amide I, Amide II and Amide III were found to be at 3408.05, 1656.37, 1544.68 and 1241.28 cm⁻¹ in G1000 film. Along with these, the peaks at 1045.11 cm⁻¹ and 1406.50 cm⁻¹ could be attributed to phosphate and ammonium ion contributions from the amino acid side chains. Similarly the peak at 2934.31 cm⁻¹ represented the increased C–H stretch at methylene in side chains in protein chain^{##UREF##24##35##–##REF##3541539##37##}.</p>", "<p id=\"Par25\">The characteristics peaks observed in ED100 films transmittance plots were at 3435.71, 1636.95 and 1223.53 cm⁻¹ for Amide A, Amide I and Amide III respectively. Additional peak observed at 1712.00 cm⁻¹ could be attributed to carboxyl group from amino acid side chain. The characteristic peaks observed in the transmittance plots of DEG100 films were at 3427.73, 1636.76 and 1566.97 cm⁻¹ for Amide A, Amide I and Amide II respectively. Peaks at 1411.27 cm⁻¹ and 2924.81 cm⁻¹ correspond to C–H stretching in the side chains along the polypeptide chain. TEG100 transmission peaks for Amide A, Amide I, Amide II and Amide III were recorded at 3424.11, 1637.58, 1565.93 and 1223.08 cm⁻¹ respectively along with additional peaks present at 1364.25 and 1714.49 cm⁻¹ which may be due to additional interactions among proteins side chains and plasticizer molecules. Comparative transmittance plots of all the glycerol films and that of other plasticizers are given in Fig. ##FIG##4##5##i, j respectively.</p>", "<p id=\"Par26\">The position of Amide I peak suggests the global secondary structure present in the protein. The interpretation of Amide I peaks in all the films and the respective predicted secondary structures are given in Table ##TAB##1##2##. It was recorded that, the native alpha helix conformations were somewhat preserved in glycerol films although there might be some distortions. Whereas it was observed that the Amide I peak for ED100, DEG100 and TEG100 falls in the region of beta sheets suggesting a conformational change in the native protein structure during the film formation due to interactions with the plasticizers. This analysis suggested that the molecular characteristics of the films prepared with glycerol are different from that prepared with other plasticizers.</p>", "<title>Dimensions and water solubility of bioplastic film</title>", "<p id=\"Par27\">The film prepared were of the thickness 190–220 µm with the area of about 4.54 ± 0.2 cm². Water uptake by G100, ED100, DEG100 and TEG100 films was recorded to be 4.8, 6.2, 4.9 and 6.3% respectively. Maximum water uptake was recorded by TEG100 films and least by G100 films.</p>", "<title>Biodegradation by <italic>A. oryzae</italic></title>", "<p id=\"Par28\">Degradation of G100, ED100, DEG100 and TEG100 films (Fig. ##FIG##5##6##a–d) were studied by using keratinophilic isolate of <italic>A. oryzae</italic>. The films when incubated with <italic>A.oryzae</italic> depicted degradation to about 80% after 7 days. The fungus was observed to maintain good association on the surface of the film and was able to degrade it on the surface as well as penetrated and degraded the internal portions (Fig. ##FIG##5##6##e).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par29\">The exponential increase in the demands of synthetic plastics in each and every sector of human society coupled with unconscious and unjust disposal in majority of scenarios have made it indispensible to produce more environmental friendly plastics that are biodegradable and are derived from renewable resources. Animal proteins like Collagen, Milk proteins, Myofibrillar proteins, Keratin and Gelatin have been utilized for the production of bioplastics^{##REF##27596411##38##–##UREF##29##43##}. Some of the plant proteins utilized for the same purpose includes gluten, soy protein and zein^{##REF##27379431##44##–##UREF##32##48##}. Also, others include bio-waste and co- products like co-products from starch, bio-ethanol and seed oil, microalgae from sewage and agricultural farming waste^{##REF##33947093##49##}.</p>", "<p id=\"Par30\">With this aim, in present study we explored the use of keratin from human hair waste to analyze its potential as a candidate to produce bioplastic films. Keratin from human hair was utilized to form the bioplastic films by solution casting in silicon moulds. Effect of different plasticizers like glycerol, ED, DEG and TEG were analyzed. Glycerol has been shown to be useful in the formation of keratin film from human hair and poultry waste. Glycerol as plasticizer act by reducing the intermolecular interactions between the protein chains and allows free movement in them. Glycerol also improves the resistance to breaking and cracking in the bioplastic film and improves the physical characteristics of films.</p>", "<p id=\"Par31\">We have demonstrated the effect of various concentrations of glycerol on the properties of the film. By using 1% solution of glycerol, it was found that the G100 films depicted the most uniform surface morphology and by increasing the concentration of the plasticizers the time for drying of the film increased from about 48 h to almost 15–20 days, moreover the film surface showed excessive depositions and granular appearance. The increase in the drying time of the films with increased concentrations of glycerol could be attributed to the fact that excess glycerol makes the bioplastic material more susceptible to absorbing water and prolonged the water removal from the film surface. Moreover, the changed surface morphology with excess depositions emphasizes the importance of the right amount of glycerol to be added in order to achieve desirable film surface properties. It could also be noted that excessive glycerol can lead to weaker intermolecular interactions, resulting in films that are more susceptible to breaking. The data for human hair keratin film with varied concentration of glycerol is unavailable alas; studies are available showing good morphology under SEM with no holes in chicken feather keratin films with 2% glycerol^{##REF##29320725##21##}. Similarly chicken feather keratin film and microcrystalline cellulose with no holes or cavities in the SEM studies have been reported^{##UREF##33##50##}.</p>", "<p id=\"Par32\">Keratin films with porous structure and pore size 0.1–0.2 µm prepared in Teflon rings and siliconized base, films with 1% glycerol in petri plates having a non-homogenous morphology have been reportedpreviously^{##UREF##21##30##,##REF##32429167##51##}. Therefore our adopted method of using silicon moulds to prepare films was found to be better than previously reported methods as it yielded films with continuous and homogenous morphology with fewer and smaller pits.</p>", "<p id=\"Par33\">ED100 films also showed similar surface morphology as G100 films with minor pits of average size 0.75 µm. DEG100 and TEG100 films also possessed smooth surface with no pits or holes. The better surface characteristics with DEG100 and TEG100 films could be due to enhanced amino acid chain mobility leading to improved distribution of the proteins during processing. Also, the surface defects in the protein films arise because of internal stresses^{##UREF##34##52##}, DEG and TEG tends to reduce this stress owing to better chain alignment and reducing molecular entanglements. As a result, the surface of the film becomes smoother and more uniform with these plasticizers in comparison to ED and glycerol.</p>", "<p id=\"Par34\">Noting the crystalline nature of these films as recorded by XRD analysis, the d-spacing value was 0.455  ± 0.002 nm irrespective of the plasticizer used and G100 and DEG100 films showed the most crystalline behavior and ED100 possessed least crystalline nature as compared to all the other films. Nevertheless, the characteristic peak of keratin was observed at around 19.5° in all the films. Moreover, additional peaks were recorded in the TEG100 films, owing to the increased interactions between the polypeptide side chain and the plasticizer molecules. Lattice spacing of lyophilized keratin extracted by similar method is also 4.5 Å^{##UREF##28##42##}. According to previous reports, human hair keratin film with 1% glycerol possessed diffraction peak at 19.9°, chicken feather keratin film at 19°, 23° and 41° and keratin cellulose films at 19°, 32°, 41°, 45°and 66° ^{##UREF##33##50##,##REF##32429167##51##}.</p>", "<p id=\"Par35\">The FTIR analysis of the films showed presence of various Amide peaks in the transmittance plots. Moreover, the peak intensity for Amide A and amide I reduced with increased concentration of the glycerol and the highest peak intensity were observed in DEG100 films followed by TEG100 films. Thissuggested the presence of increased H bonded peptides in TEG100 and DEG100 films. The peak of Amide A for human hair keratin isolated by urea have been reported at 3276 cm⁻¹ and Amide I, Amide II and Amide III at 1640, 1517 and 1234 cm⁻¹ respectively^{##REF##31002909##27##}. Scaffolds prepared with keratin-PVA with alginate dialdehyde as cross-linking reagent recorded peaks at 3422.06, 1642.84, 1460.81 cm⁻¹\n^{##REF##34451878##53##}. Similar peaks in IR spectrum are shown by the regenerated keratin and films prepared from chicken feather keratin^{##REF##29320725##21##,##UREF##21##30##,##UREF##33##50##}. All the keratin films showed water uptake in water solubility test which was recorded to be highest in TEG100 films displaying its hydrophilic nature, owing to increased probability of forming hydrogen bonding. Nevertheless, all the films showed partial solubility in water that could be of importance in specific applications.</p>", "<p id=\"Par36\">In the present research, degradation by <italic>A. oryzae</italic> of human hair keratin films is being studied for the first time, nevertheless, the growth of <italic>Trichophyton rubrum </italic>on the human hair keratin film have shown that the fungus could grow on the surface and also penetrated these films^{##REF##32429167##51##}.</p>", "<p id=\"Par37\">In biodegradation studies using keratinophilic fungi (<italic>A. oryzae</italic>), the keratin films showed significant level of degradation of about 80% after seven days of incubation. The keratinases enzymes produced by the fungi, helped it in the penetration and further degradation of the keratin films^{##UREF##35##54##}. The biodegradability of these films is of significant importance as far as their future applications in packaging or other industry is concerned.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par38\">The present study involved the preparation and characterization of the keratin films or ‘kertics’ from human hair waste and exploring the potential of novel plasticizers. The addition of DEG and TEG as plasticizer in the keratin films improved their morphological properties. The characteristics and behavior of these films could be modulated by employing different plasticizers and by modulating the quantity of these plasticizers for specific applications. Moreover the keratin films were found to be biodegradable that makes them suitable to be utilized as a sustainable material in future applications as an alternate to conventional plastics. Kertics could be utilized for packaging application and also for the generation of materials suitable for various biomedical uses. The outcomes of the present study shall contribute in the better understanding of the human hair based keratin films and help in exploring more opportunities for their use. The mechanical properties of kertics, such as tensile strength, elongation at break and E-modulus could be analyzed in future studies to assess the strength and suitability of these films for various applications.</p>" ]

[ "<p id=\"Par1\">Since their invention, conventional plastics have contributed in the betterment of the society in numerous ways, nevertheless their deleterious impacts on the natural ecosystems and living creatures is irrefutable. The management of plastic waste generated is a concern worldwide and therefore quest for the plastic alternates or bioplastics is imminent. Here, we explore the suitability of keratin from human hair waste as the candidate for the production of bioplastic films. Keratin extracted from hair was used to form the films or ‘kertics’ by solution casting and curing. Ethanediol, di-ethylene glycol and tri-ethylene glycol were used as novel plasticizers along with glycerol in the keratin film formation. The film prepared were of the thickness 190–220 µm with the area of about 4.54 ± 0.2 cm². Water uptake by G100, ED100, DEG100 and TEG100 films was recorded to be 4.8, 6.2, 4.9 and 6.3% respectively. FESEM analysis revealed that the films with 100 µl of 1% glycerol (G100) had continuous surface morphology except few pits of 0.1 µm, also DEG100 and TEG100 films have the most uniform surface morphology with no evident pits, holes or bulges. X-ray diffractogram showed characteristic peak of keratin at 19.5° and the d-spacing value observed was 0.45 nm. The FTIR studies suggested that the films retained keratin in non degraded form, and possessed the characteristic Amide peaks. The films were also found to be biodegradable in studies involving keratinophilic fungal strain of <italic>A. oryzae.</italic> These films could found potential applications in packaging industry, disposable items manufacturing and biomaterial generation.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-44905-x.</p>", "<title>Acknowledgements</title>", "<p>We would like to thank the Dayalbagh Educational for providing necessary infrastructure and facilities to conduct the research work. We would like to extend our deepest appreciation to the Central Library, DEI for their valuable assistance in providing us with access to the necessary literature and resources.</p>", "<title>Author contributions</title>", "<p>A.S. conducted the research and wrote the main manuscript, prepared Figs. ##FIG##0##1##, ##FIG##1##2##, ##FIG##2##3##, ##FIG##3##4##, ##FIG##4##5## and ##FIG##5##6## and Tables ##TAB##0##1## and ##TAB##1##2##. G.S. and L.A. guided and supervised the research. All authors reviewed the manuscript.</p>", "<title>Data availability</title>", "<p>The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par53\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Overview of bioplastic production. Clean hair samples were delipidized in chloroform and methanol followed by the incubation with extraction buffer to extract keratin. Extraction buffer composed of urea, thiourea, betamercaptoethanol and tris–HCl. The obtained protein extract was dialyzed and lyophilized to obtain the protein powder which was further utilized to obtain bioplastic film by solution casting with various plasticizers. See text for details.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Surface morphology of bioplastic films. (<bold>a–c</bold>) FESEM images of virgin hair, delipidized hair and hair after extraction respectively. (<bold>d–g</bold>) FESEM images of G100, G500, G1000 and G1500 at ×20,000–×25,000 respectively-G100 shows a pit with size 0.1 µm, G500 shows wrinkled appearance, G1000 displayed tiled appearance and G1500 showed larger pits of about 1.4 µm. (<bold>h–k</bold>) FESEM images of G100, G500, G1000 and G1500 at ×4000 to ×5000 respectively. (<bold>l,m</bold>) FESEM images of ED100 at ×4500 and ×8000 respectively. (<bold>n,o</bold>) FESEM images of DEG100 and TEG100 respectively.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>XRD diffractogram of bioplastic films. (<bold>a–d</bold>) Diffractogram of G100, G500, G1000 and G15000 films. (<bold>e–g</bold>) Diffractogram of D100, DEG100 and TEG100 films. (<bold>h</bold>) Comparative diffractogram of glycerol films, G100 films showing the most intense peak at 19.5°. (<bold>i</bold>) Comparative diffractogram of G100, ED100, DEG100 and TEG100 films.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>FTIR absorbance spectra. (<bold>a–d</bold>) Infrared absorbance spectra of G100, G500, G1000 and G1500 respectively. (<bold>e</bold>) IR absorbance spectra of lyophilized keratin. (<bold>f–h</bold>) IR absorbance spectra of ED100, DEG100 and TEG100. (<bold>i</bold>) Comparative absorbance spectra of glycerol films at various concentrations. (<bold>j</bold>) Comparative absorbance spectra of lyophilized keratin, G100, ED100, DEG100 and TEG100 films.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>FTIR transmittance spectra. (<bold>a–d</bold>) Infrared transmittance spectra of G100, G500, G1000 and G1500 respectively. (<bold>e</bold>) IR transmittance spectra of lyophilized keratin. (<bold>f–h</bold>) IR transmittance spectra of ED100, DEG100 and TEG100. (<bold>i</bold>) Comparative transmittance spectra of glycerol films at various concentrations. (<bold>j</bold>) Comparative transmittance spectra of G100, ED100, DEG100 and TEG100 films.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Bioplastic films. (<bold>a–d</bold>) G100, ED100, DEG100 and TEG100 respectively. (<bold>e</bold>) Microscopic images of film degradation by <italic>A. oryzae</italic> after different time intervals (3, 5 and 7 days).</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>IR Transmission peaks for keratin bioplastic films.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Sample</th><th align=\"left\">Amide I</th><th align=\"left\">Amide II</th><th align=\"left\">Amide III</th><th align=\"left\">Amide A</th><th align=\"left\">Others</th></tr></thead><tbody><tr><td align=\"left\">Lyophilized keratin</td><td char=\".\" align=\"char\">1654.24</td><td char=\".\" align=\"char\">1546.49</td><td char=\".\" align=\"char\">1242.76</td><td char=\".\" align=\"char\">3424.04</td><td align=\"left\">–</td></tr><tr><td align=\"left\">G100</td><td char=\".\" align=\"char\">1654.32</td><td char=\".\" align=\"char\">1546.99</td><td char=\".\" align=\"char\">–</td><td char=\".\" align=\"char\">3417.75</td><td align=\"left\">–</td></tr><tr><td align=\"left\">G500</td><td char=\".\" align=\"char\">1654.15</td><td char=\".\" align=\"char\">1546.69</td><td char=\".\" align=\"char\">–</td><td char=\".\" align=\"char\">3417.86</td><td align=\"left\">–</td></tr><tr><td align=\"left\">G1000</td><td char=\".\" align=\"char\">1656.37</td><td char=\".\" align=\"char\">1544.68</td><td char=\".\" align=\"char\">1241.28</td><td char=\".\" align=\"char\">3408.05</td><td align=\"left\">2934.31 (C–H stretch, methylene), 1406.50 (ammonium ion), 1045.11 (phosphate ion)</td></tr><tr><td align=\"left\">G1500</td><td char=\".\" align=\"char\">1655.31</td><td char=\".\" align=\"char\">1547.05</td><td char=\".\" align=\"char\">–</td><td char=\".\" align=\"char\">3408.07</td><td align=\"left\">1046.69 (phosphate ion), 1408.55 (ammonium ion), 2970.67 (CH stretch, methyl)</td></tr><tr><td align=\"left\">ED100</td><td char=\".\" align=\"char\">1636.95</td><td char=\".\" align=\"char\">–</td><td char=\".\" align=\"char\">1223.53</td><td char=\".\" align=\"char\">3435.71</td><td align=\"left\">1365.3 (dimethyl/trimethyl), 1712.00 (carboxylic acid, ketone)</td></tr><tr><td align=\"left\">DEG100</td><td char=\".\" align=\"char\">1636.76</td><td char=\".\" align=\"char\">1566.97</td><td char=\".\" align=\"char\">–</td><td char=\".\" align=\"char\">3427.73</td><td align=\"left\">1411.27 (methyl: C–H bend), 2924.81 (methylene; C–H stretch),</td></tr><tr><td align=\"left\">TEG100</td><td char=\".\" align=\"char\">1637.58</td><td char=\".\" align=\"char\">1565.93</td><td char=\".\" align=\"char\">1223.08</td><td char=\".\" align=\"char\">3424.11</td><td align=\"left\">1364.25 (di-methy), 1714.49 (carboxyl)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Predicted secondary structures of keratin in bio-plastic films.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Film</th><th align=\"left\">Amide I peak (cm⁻¹)</th><th align=\"left\">Global secondary structure</th></tr></thead><tbody><tr><td align=\"left\">G100</td><td char=\".\" align=\"char\">1654.32</td><td align=\"left\">Alpha helix</td></tr><tr><td align=\"left\">G500</td><td char=\".\" align=\"char\">1654.15</td><td align=\"left\">Alpha helix</td></tr><tr><td align=\"left\">G1000</td><td char=\".\" align=\"char\">1656.37</td><td align=\"left\">Alpha helix</td></tr><tr><td align=\"left\">G1500</td><td char=\".\" align=\"char\">1655.31</td><td align=\"left\">Alpha helix</td></tr><tr><td align=\"left\">ED100</td><td char=\".\" align=\"char\">1636.95</td><td align=\"left\">Beta sheet</td></tr><tr><td align=\"left\">DEG100</td><td char=\".\" align=\"char\">1636.76</td><td align=\"left\">Beta sheet</td></tr><tr><td align=\"left\">TEG100</td><td char=\".\" align=\"char\">1637.58</td><td align=\"left\">Beta sheet</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

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[ "<media xlink:href=\"41598_2023_44905_MOESM1_ESM.pdf\"><caption><p>Supplementary Figure 1.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par3\">Glioblastoma (GBM) is the most common and aggressive malignant tumor in the central nervous system with an incidence of approximately three cases per 100,000 population in the United States (US)^{##REF##29927955##1##,##UREF##0##2##}. GBM patients have a dismal prognosis with a scarcity of active agents. With a median survival from diagnosis of 14–18 months^{##REF##24101040##3##–##UREF##1##5##} and median survival from recurrence of only 6–8 months^{##REF##29159777##6##–##REF##10561324##9##}, there is an urgent need for novel therapies for this disease.</p>", "<p id=\"Par4\">Despite initial promise, immunotherapy efforts in GBM treatment have failed to demonstrate consistent clinical activity to date with several negative phase III trials including ACT-IV, Checkmate-143, Checkmate-498, and CheckMate-548^{##REF##32437507##10##–##UREF##2##13##}. Oncolytic viruses as a novel immunotherapy treatment modality are gaining interest in the clinical community due to promising level of antitumor activity and the observation that they are not subject to the same resistance mechanisms that limit the use of chemotherapy and targeted agents^{##UREF##3##14##,##REF##34771615##15##}. Attenuated measles virus strains represent attractive options as oncolytic agents as evidence suggests they carry minimal safety risk to the patient and population^{##REF##23289598##16##,##REF##28129716##17##}. MV-based virotherapy offers tumor selectivity, a potent bystander-killing effect, amenability to genetic engineering and retargeting, and excellent safety^{##REF##23289598##16##,##REF##28228086##18##}. Strains of the Edmonston measles virus (MV) vaccine lineage have shown significant antitumor effects in preclinical patient derived GBM models^{##REF##18194077##19##–##REF##12750267##21##}. In phase 1 clinical trials of patients with recurrent or refractory ovarian cancer or multiple myeloma, administration of oncolytic MV strains engineered to express either the carcinoembryonic antigen (MV-CEA) or the sodium iodide symporter (MV-NIS) was associated with the development of tumor-specific immune responses and significant antitumor effects;^{##REF##28439108##22##,##REF##20103634##23##} treatment was well tolerated. Clinical trials are currently ongoing across a range of solid tumors^{##REF##28228086##18##}.</p>", "<p id=\"Par5\">Enhanced efficacy of virotherapy may be achievable using a pharmacogenomics approach to identify gene variants and expression signatures to preselect patients who are likely to respond to treatment. Preliminary data of a phase 1 study analyzing predictors for replication of oncolytic MV showed that constitutive activation of the interferon (IFN) pathway was a key determinant for MV replication, resulting in reduced infection of patient-derived GBM xenografts^{##REF##29788332##24##}. Using a diagonal linear discriminant analysis (DLDA) algorithm to predict permissiveness to viral replication, we observed that inhibition of JAK1/2, a critical component of IFN-stimulated gene (ISG) signaling, sensitized virus-resistant cells to MV infection. In ten consecutive patients with GBM who were treated by stereotactic injection of MV-CEA, elevated ISG expression was inversely correlated with MV replication^{##REF##29788332##24##}.</p>", "<p id=\"Par6\">Herein, we present the final analysis of a phase 1 trial (NCT00390299) that evaluated the maximum tolerated dose (MTD), safety and toxicity, as well as the preliminary efficacy of MV-CEA when administered intratumorally and into the resection cavity of patients with recurrent GBM. In addition, a 790-gene custom Nanostring panel based on microdissected tumor specimens at baseline and following one treatment dose was used to investigate tumor molecular signatures predictive of viral replication and the effect of viral treatment on tumor expression profiling of patients with GBM treated with MV-CEA. Here we show that treatment with repeat intratumoral administration of MV-CEA is safe without dose-limiting toxicity up to the maximum feasible dose and it results in proinflammatory tumor remodeling. An ISG-based DLDA algorithm predicts viral replication and can provide the basis for treatment personalization.</p>" ]

[ "<title>Methods</title>", "<p id=\"Par27\">The study (<ext-link ext-link-type=\"uri\" xlink:href=\"https://clinicaltrials.gov/study/NCT00390299\">https://clinicaltrials.gov/study/NCT00390299</ext-link>, registration date 10/19/2006) was designed and conducted in accordance with the provisions of the Declaration of Helsinki and Good Clinical Practice Guidelines. The Mayo Clinic Institutional Review Board Committee approved the protocol, which was conducted under the oversight of the Mayo Clinic Cancer Center Data and Safety Monitoring Board.</p>", "<title>Patients</title>", "<p id=\"Par28\">Eligible patients were aged ≥18 years with recurrent Grade 3 or 4 glioma, including astrocytoma, oligodendroglioma or mixed glioma with histologic confirmation at initial diagnosis or recurrence, who were candidates for gross total or subtotal resection. Patients were required to have an Eastern Cooperative Oncology Group (ECOG) performance status of 0–2, anti-measles virus immunity as demonstrated by immunoglobulin G (IgG) anti-measles antibody levels of ≥1.1 EU/mL by ELISA, normal serum CEA levels (&lt; 3 ng/mL), and adequate hematologic, hepatic and renal function. Ineligible patients included those with an active infection ≤5 days prior to enrollment; history of tuberculosis or a positive skin test; who had received noncytotoxic antitumor drugs ≤2 weeks, or chemotherapy, immunotherapy or biologic therapy ≤4 weeks, or radiation therapy ≤6 weeks, or bevacizumab treatment ≤12 weeks prior to enrollment, or any viral or gene therapy prior to enrollment; who had failed to fully recover from acute, reversible effects of prior chemotherapy; with New York Heart Association class III or IV heart failure; with exposure to household contacts ≤15 months old or household contact with immunodeficiency, or had allergy to measles vaccine or history of severe reaction to prior measles vaccination; who were HIV-positive or history of other immunodeficiency. Written informed consent was obtained from all patients and no patient received compensation for study participation.</p>", "<title>Study design</title>", "<p id=\"Par29\">This single-arm, phase I/II trial enrolled patients in two treatment regimens in a standard 3 + 3 cohort design, with additional patients enrolled in a maximum tolerated dose (MTD) expansion cohort. Cohorts of three patients were enrolled in Group A until the MTD of MV-CEA was determined following single-dose administration. Subsequently, cohorts of 3 patients were enrolled in Group B for further evaluation of the MTD following administration of two viral doses. Additional patients were then enrolled in the Group B MTD expansion cohort. The first study patient (Group A) was enrolled on 10/23/2006 and the last patient (Group B) was enrolled on 11/30/2019. The study schema is summarized in Supplementary Fig. ##SUPPL##0##6##, and the protocol is included as Supplementary Note in the Supplementary Information file. In Group A, patients underwent <italic>en bloc</italic> tumor resection on Day 1, followed by administration of MV-CEA into the resection cavity at viral tissue culture infectious doses 50% (TCID50) of 10⁵–10⁷. The viral dose was diluted in 1 mL of saline and delivered via a 20-gauge blunt tip needle injected 1–2 cm into the brain parenchyma at ten injection sites. The starting dose of 10⁵ TCID50 (dose level 1 [DL1]) was increased to 10⁶ TCID50 (DL2) and 10⁷ TCID50 (DL3) if ≤1 dose-limiting toxicity (DLT) was observed at the previous dose level. In Group B, recurrent GBM patients had a silastic ventricular catheter placed using stereotactic equipment, with computed tomography/magnetic resonance imaging employed to secure catheter placement. On Day 1, patients received an intratumoral injection of MV-CEA at viral doses of 2 × 10⁶–2 × 10⁷ TCID50, with the dose administered as a single 1 mL bolus diluted in saline and injected into the tumor at 0.1 mL per minute via the catheter. The catheter was secured to the dura and left in place to mark the injection site. On Day 5, patients underwent en bloc tumor resection before receiving a second injection of MV-CEA into the resection cavity, which was similarly diluted in 1 mL of NS and administered via a 20-gauge blunt tip needle in multiple sites of the resection cavity wall. Supportive care was given to all patients, including blood products, anticonvulsants, perioperative steroids, antibiotic therapy, and treatment of other newly diagnosed or concurrent medical conditions. The study protocol was approved by the Mayo Clinic Institutional Review Board.</p>", "<title>Safety and efficacy assessments</title>", "<p id=\"Par30\">Assessment of safety and toxicity with determination of MTD was the study’s primary endpoint. Secondary endpoints included progression-free survival and correlative analysis, including assessment of viral replication in tumor, viremia, and shedding. All adverse events (AEs) were evaluated per the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE). Patients were assessed at 4 weeks following day 1 viral administration for toxicity including DLT, then followed up every 2 months for disease progression and survival. DLTs were defined as those AEs definitely, probably or possibly attributed to the study treatment that met the following toxicity criteria: hematologic, defined as Grade ≥3 except Grade 3 neutropenia lasting &lt;72 h; nonhematologic, defined as Grade ≥3 (Grade ≥3 nausea, vomiting, or diarrhea was considered dose-limiting only if the patient is receiving the maximum supportive care regimen described in the protocol; alopecia will not be considered a DLT); neurologic, defined as Grade ≥2; allergic reaction, defined as Grade 2 asymptomatic bronchospasm and/or urticaria, and Grade ≥3 allergic reactions; or viremia lasting ≥6 weeks from last viral administration. The MTD was defined as the dose level below the lowest dose that induced DLT in at least two of six patients.</p>", "<p id=\"Par31\">Patients were evaluated for treatment response at 4 weeks after tumor resection and every 2 months until disease progression. Progression-free survival (PFS) was defined as the time from registration to documentation of disease progression. Patients who died without documentation of progression were considered to have had tumor progression at the time of death unless there was documented evidence that no progression occurred before death. Response assessment was performed according to the RANO criteria^{##REF##28640707##41##}.</p>", "<title>GBM patient sample preparation and analyses</title>", "<p id=\"Par32\">Formalin-fixed paraffin-embedded tumor tissue samples collected during the primary and recurrence surgery were used for histological staining immunohistochemical (IHC) analysis and NanoString analysis (custom-modified nCounter Pan-Cancer Immune Profiling Panel). RNA isolated from fresh/frozen tumor tissue was tested with qRT-PCR in order to detect virus replication. Tumor tissue removed en bloc with the catheter tip in place was measured and photographed in our pathology laboratory (Supplementary Fig. ##SUPPL##0##7##). The catheter was subsequently removed and fresh tissue was prepared into serial sections 2–3 mm in thickness, perpendicular to the catheter. Sections for formalin-fixing and freezing were photographed to establish subsequent correlations between the tissue and relationship to the catheter. Frozen tissue was stored at −80 °C.</p>", "<title>Immunohistochemistry of pre- and posttreatment samples for assessment of immune cell subpopulations</title>", "<p id=\"Par33\">All histological sections were reviewed, and 4-µm sections were obtained from the most representative formalin-fixed paraffin-embedded (FFPE) tissue blocks. Immunohistochemical stains (IHC) were performed utilizing antibodies directed against CD3 (clone LN10, dilution 1/250, Leica Biosystems, UK), CD4 (clone SP35, Ready to Use Predilute Antibody, Ventana, USA), CD8 (clone C8, dilution 1/250, Dako, Denmark), CD20 (clone L26, dilution 1/300, Dako, Denmark), and CD68 (clone KP1, dilution 1/1500, Dako, Denmark) utilizing clinically validated protocols. Slides were scanned at ×40 magnification on the Aperio GT450 brightfield instrument (Leica Biosystems). The resolution of the images was 0.26 µm/pixel at ×40. The images were 24-bit contiguous standard pyramid tiled TIFFs compressed via JPEG with a quality setting of 91. A board-certified neuropathologist selected and annotated regions for analysis using Aperio ImageScope Software (Leica Biosystems). The annotated regions of each stained slide were analyzed using proprietary nuclear and cytoplasmic algorithms. Cells within each region of interest were graded based on intensity of staining (0, 1 + , 2+ or 3 + ). Cells with an intensity of 1+ or higher were considered positive for immunostaining markers. Immunohistochemistry (IHC) scores were expressed as a percentage of positive cells (0 to 100) within the region of interest.</p>", "<title>Peripheral immune response, CEA levels, and viremia assessment</title>", "<p id=\"Par34\">MV-specific immunity was assessed by ELISA to measure anti-MV-specific IgG levels at baseline, 28 days after study entry and every 2 months until progression. Peripheral blood CEA levels were assessed at the Mayo Clinic Central Clinical Lab using the Bayer Diagnostics Advia Centaur Immunoassay system (Bayer Healthcare Diagnostics). Viremia and viral shedding were assessed by qRT-PCR from patient peripheral blood mononuclear cells, throat gargle specimens, and urine samples. The schedule for the correlative laboratory analysis is summarized in Supplementary Fig. ##SUPPL##0##8##.</p>", "<title>Quantitative qRT-PCR for the detection of virus replication</title>", "<p id=\"Par35\">The qRT-PCR assay was optimized for primers, probe, and magnesium concentration with TaqMan RNA to CT 1-step kit (Thermo Scientific). A 50-μL qRT-PCR reaction volume was used to amplify the MV-N genomic RNA target, in the presence of 0.3 mmol/L each of forward (5′-GGG TGT GCC GGT TGG A-3’) and reverse (5′-AGA AGC CAG GGA GAG CTA CAG A-3’) -primers, 0.2 mmol/L Black Hole Quencher–labeled probe (5′-/56-FAM/TGG GCA GCT CTC GCA TCA CTT GC/ 3BHQ_1/-3′), 4 mmol/L MgCl, and 1 mcg or a maximum total volume of 5 mcl of the RNA isolate. One cycle of reverse transcriptase reaction (15 min at 48 °C) was applied, followed by a denaturation step (10 min at 95 °C) and 40 cycles of amplification (15 s 95 °C and 1 min 60 °C), with fluorescence measured during the extension. A standard curve of tenfold dilutions containing 10⁷ to 10 MV-N gene copies/mL was generated using a manufactured RNA oligo (IDT, San Jose, CA) Quantification and subsequent calculation of copy number was done using the standard curve and the ROCHE480 Quantitative PCR System software. Total RNA from frozen tumor tissue and primary GBM lines was extracted using the RNeasy kit (Qiagen). On the first step of the reaction, cDNA was made using 25 ng of the RNA extracts and One-Step RT-PCR master mix reagents and TaqMan Probe-Based Gene Expression assays (Life Technologies). The assays were run on a Roche 480 Light Cycler instrument (Roche). The relative quantification was performed using human eukaryotic 18 S rRNA as a reference. Expression was calculated in fold change of expression as compared to corresponding normal tissue control using the comparative Ct method^{##REF##11846609##42##}.</p>", "<title>Nanostring analysis</title>", "<p id=\"Par36\">Patient tumor samples obtained at the time of primary surgery and recurrent tumor resection were examined by a pathologist to identify regions of ≥90% tumor involvement, which were subsequently scraped, and the RNA harvested. The RNA (100 ng) was hybridized with NanoString probes according to the manufacturer’s protocol and using the nCounter Pan-Cancer Immune Profiling Panel (NanoString Technologies, Seattle, WA) that was custom-modified in our laboratory with the addition of 30 gene probes (Supplementary Data ##SUPPL##4##2##). The resulting custom NanoString was used to determine the expression of 790 genes in individual patient tumor samples. Samples were analyzed using the nCounter Digital Analyzer. NanoString results were analyzed and values normalized to housekeeping genes.</p>", "<title>Diagonal linear discriminant analysis (DLDA)</title>", "<p id=\"Par37\">The DLDA scoring system, a method of classifying prospective tumors into known categories based on gene expression signatures^{##REF##12184810##43##,##REF##16896004##44##}, was used to generate an algorithm for predicting MV permissiveness in GBM. This unique system relies on a weighted gene voting scheme to influence the classification of a prospective sample. A 22 ISG gene panel identified in an earlier pathway enrichment analysis^{##REF##29788332##24##} and standardized to all 790 genes of the custom NanoString was utilized as the gene signature for MV permissiveness in this study. The weighting of each gene was determined according to a training data set using the permissive cell lines, GBM43 and GBM64, and the resistant cell lines, GBM150, GBM6, and GBM39. The training set DLDA model yields coefficients and a constant that can be used with other similarly standardized expression data to predict if a sample is MV-resistant or MV-permissive. A validation data set consisted of 35 GBM patient-derived xenografts^{##REF##29788332##24##}. Gene expression profiles of prospective tumor samples from patients with GBM were normalized and entered into the algorithm to calculate a DLDA score. A score above 150 is associated with no detectable virus indicating MV-resistance, with scores below −250 associated with the highest level of virus recovered from the tumor (MV-permissive). Intermediate values are associated with viral permissiveness at an ~2-log lower level than that associated with higher permissiveness.</p>", "<title>Pathway enrichment analysis</title>", "<p id=\"Par38\">We used GeneCodis online resource (<ext-link ext-link-type=\"uri\" xlink:href=\"http://qenecodis.cnb.csic.es/\">http://qenecodis.cnb.csic.es/</ext-link>) to perform gene/protein enrichment analysis of gene expression data obtained by NanoString analysis of tumor samples obtained pre-treatment and post treatment following one dose of the virus in group B patients^{##REF##19465387##45##,##REF##22573175##46##}. In total, 19,835 genes were used as an input into GeneCodis and we selected genes with changes between sample groups of at least 1.5- or 2.0-fold and <italic>P</italic> value &lt; 0.05. GeneCodis outputs a listing of functional groups (GO biological process, GO molecular function, KEGG) with gene/protein IDs assigned to each group. We used a custom script in R programming language to combine fold change values and <italic>P</italic> values with a functional group of proteins^{##UREF##8##47##}.</p>", "<title>Statistical analyses</title>", "<p id=\"Par39\">Standard cohorts of three design was applied for this phase I trial^{##REF##2790129##48##}. Evaluable patients were those who gave their informed consent and received MV-CEA treatment.</p>", "<p id=\"Par40\">MTD was defined as the dose level below the lowest dose that induces dose-limiting toxicity (DLT) in at least one-third of patients graded according to NCI Common Terminology Criteria for Adverse Events (CTCAE) version 3.0. Dose-limiting toxicities include hematologic events grade 3 or higher (except grade 3 ANC lasting &lt;72 h), nonhematologic events graded 3 or higher (except grade 3 nausea, vomiting, or diarrhea were to be considered DLT only if patient was receiving the max supportive care and alopecia was not considered dose-limiting), neurologic toxicity grade 2 or higher, grade 2 allergic reactions asymptomatic bronchospasm and/or urticarial, grade 3 or higher allergic reactions, viremia lasting for 6 weeks or more from last viral administration deemed at least possibly related to treatment.</p>", "<p id=\"Par41\">The percentage of patients who are progression-free at 3 and 6 months (PFS3 and PFS6) was summarized descriptively. Progression-free survival was defined as the length of time from the date of registration to (a) date of progression or death due to any cause or (b) last follow-up.</p>", "<p id=\"Par42\">Kaplan–Meier survival curves and log-rank tests were used to obtain median PFS and OS times. The distribution of PFS and OS was estimated for groups A and B separately before combining using the Kaplan–Meier method. Descriptive statistics and simple scatterplots were employed to present the CEA, CD4, CD8, MV antibody immunoglobulin data, as well as data on viremia and shedding. The relationship between viral replication and DLDA score was assessed using Pearson correlation.</p>", "<p id=\"Par43\">For the 790-gene custom NanoString analyses, to allow analysis on a common scale the gene expression values for each sample were transformed by adding 1.0 to each gene expression value then transforming each value by log² to a standardized mean of 0.0 and standard deviation of 1.0. Differences in gene expression among tumor samples were evaluated using unequal-variance <italic>t</italic> tests. <italic>P</italic> &lt; 0.05 were considered statistically significant. All statistical tests were two-sided.</p>", "<p id=\"Par44\">Trends in immune filtration were summarized and evaluated in relation to time as well as DLDA score and were graphically assessed using line plots. Pre- vs. posttreatment marker level changes were quantified and were analyzed using paired analyses as well as fold changes for percent-positive cells from pre-treatment vs. day 5 of treatment, where a standard log2 transformation was used. Univariate modeling was used as well as scatterplots and Spearman rank correlation tests to assess the relationships between DLDA score and both baseline marker levels and log2 fold change in percent-positive cells. Given the limited number of patients with paired sample data available, multivariable or more complex modeling was not employed.</p>", "<title>Reporting summary</title>", "<p id=\"Par45\">Further information on research design is available in the ##SUPPL##5##Nature Portfolio Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<title>Baseline demographics</title>", "<p id=\"Par7\">In total, 23 patients were enrolled: 10 patients (9 evaluable, 1 patient withdrew prior to receiving treatment) in Group A and 13 patients in Group B. One patient enrolled in Group A did not receive study treatment, so was unevaluable. The 13 patients in Group B were enrolled following the determination of the MTD in Group A. The baseline demographics and clinical characteristics are summarized in Table ##TAB##0##1##. The median age was 53.5 years (range 37–69), 86% patients had an ECOG performance status of 0 or 1, and 91% had received ≤2 previous chemotherapy regimens; bevacizumab was received prior to the trial in 23% of patients. IDH and MGMT status for group A and B patients are included in Supplementary Table ##SUPPL##0##1##.</p>", "<title>Safety</title>", "<p id=\"Par8\">No DLTs were observed at any of the three dose levels for Group A and the MTD for MV-CEA was determined to be 10⁷ TCID50. Subsequently, 13 patients were enrolled in Group B, with 10 patients dosed at the MTD. No DLTs were observed for any patient and 2 × 10⁷ TCID50 was established as the maximum tolerated Group B MV-CEA dose. In total, 14 patients (63.6%; Group A: 7 patients [77.7%); Group B: 7 patients [53.8%]) reported a treatment-related adverse event (TRAE). Overall, 4 patients reported a Grade 2 TRAE: fatigue was reported by 2 patients [(1 patient each in Group A (10⁷ TCID50) and B (2 × 10⁶ TCID50)], 1 patient had anemia [Group A (10⁷ TCID50)] and 1 patient [Group B (2 × 10⁶ TCID50)] reported both lymphopenia and speech impairment (Fig. ##FIG##0##1##). There were no occurrences of any Grade ≥3 TRAEs (Supplementary Fig. ##SUPPL##0##1A##, B and Supplementary Table ##SUPPL##0##2##).</p>", "<title>CEA levels</title>", "<p id=\"Par9\">There was a slight increase in CEA levels from pre- to post treatment: 0.127 ng/ml (95% CI: −0.093, 0.348), but this did not reach statistical significance (paired <italic>t</italic> test <italic>P</italic> = 0.244). CEA elevation in the peripheral blood following treatment above the 3 ng/ml upper limit of normal was observed in one patient treated with 2 × 10⁷ TCID50.</p>", "<title>Peripheral blood CD4, CD8, and complement immunoglobulin levels</title>", "<p id=\"Par10\">No significant difference as compared to baseline was observed following study treatment.</p>", "<title>Assessment of viral biodistribution and shedding</title>", "<p id=\"Par11\">There was no evidence of shedding as tested by qRT-PCR in mouth gargle and urine specimens for any of the study patients at the prespecified time points, and no detection of viral genomes in peripheral blood.</p>", "<title>Assessment of immune response to MV</title>", "<p id=\"Par12\">Figure ##FIG##1##2## depicts mean serum anti-measles antibody levels in the serum at baseline and post treatment (4 weeks from study entry) according to patient group. As per study eligibility, all patients were measles-immune at baseline. There was no significant change in the measles antibody titers in blood during the course of the trial, as compared with baseline. In arm A there was a mean change of −6.7 units (95% CI: −17.2 to 3.9; paired <italic>t</italic> test <italic>P</italic> value = 0.178). In arm B, the difference was −2.7 units (95% CI: −6.1 to 0.76; paired <italic>t</italic> test <italic>P</italic> value = 0.112).</p>", "<title>Molecular profiling of tumors in MV-treated patients</title>", "<p id=\"Par13\">Based on analysis performed on 35 patient-derived GBM xenografts and clinical patient samples we have developed a weighted gene signature, diagonal linear discriminate analysis (DLDA) classification algorithm, comprised of 22 interferon-stimulated genes (ISG). We have previously demonstrated that baseline levels of IFN response activation in the tumor were inversely correlated with virus replication^{##REF##29788332##24##} and we now present updated results on all 13 patients of Group B (Supplementary Data ##SUPPL##3##1##). Updated results confirm the initial observations; the baseline ISG DLDA score was strongly (<italic>P</italic> = 0.04) and inversely (<italic>R</italic> = −0.6) correlated with MV replication and predictive of viral infection in the patient tumors (Table ##TAB##1##2## and Fig. ##FIG##2##3##); this analysis was limited to Group B patients because in this group tumors were resected five days following the first viral administration, which allowed correlation of the DLDA score at baseline with viral replication post treatment in resected tumor material. Because the DLDA score was developed during the conduct of the trial, the analysis was not prespecified in the clinical protocol and as such is viewed as exploratory. As shown in Fig. ##FIG##2##3## and Table ##TAB##1##2##, patients with elevated baseline ISG expression, as reflected in a high DLDA score, had significantly lower levels of virus replication. Corticosteroid use at baseline did not impact viral replication (<italic>P</italic> = 0.876, Supplementary Fig. ##SUPPL##0##2A##). In contrast, expression levels of the three known MV entry receptors, CD46, SLAM, and Nectin-4, were comparable among Group B patients (Fig. ##FIG##3##4##) indicating that the observed differences in viral replication did not result from differences in viral entry.</p>", "<p id=\"Par14\">To identify gene expression changes following MV therapy, we analyzed post treatment (day 5) tumor samples in all Group B patients with the same 790-gene custom-made NanoString panel and performed hierarchical clustering and gene enrichment analysis. We selected genes, whose expression was at least twofold different (up- or downregulated) with a <italic>P</italic> value 0.05 or less in the group of replication permissive tumors versus their expression in the group of resistant tumors. We then performed hierarchical clustering of all samples on expression values of this set of genes. We observed that samples from patients with the most permissive tumors formed one cluster (left side of heat map in Fig. ##FIG##4##5A##, underlined with the black bar) while samples from patients with the least permissive (resistant) tumors formed a cluster on the opposite branch of the hierarchical tree (right side of heat map in Fig. ##FIG##4##5A##, underlined with the magenta bar). Samples from patients with intermediate permissiveness formed clusters were located between these two extreme groups (Fig. ##FIG##4##5A##, underlined with the green bar). Next, we performed gene enrichment analysis of this set of genes, which demonstrated that multiple biological processes involved in the immune response are differentially enriched. The biological processes associated with the 14 smallest (most significant) adjusted p values for the enrichment are plotted alongside the heat map in Fig. ##FIG##4##5B##: as Fig. ##FIG##4##5##A, ##FIG##4##B## illustrate, differences in viral permissiveness result in differential expression of genes associated with immune and inflammatory responses, chemotaxis and chemokine mediated signaling in posttreatment tumor samples.</p>", "<title>Assessment of immune cell subpopulations in tumor specimens</title>", "<p id=\"Par15\">The pre- and posttreatment gene expression and pathway analysis results indicate that differences in viral permissiveness translate in differences in expression levels of genes mediating immune and inflammatory responses. We then sought to evaluate if this would translate in differences in the development of posttreatment immune infiltrates and tumor microenvironment remodeling. Eleven out of 13 patients in Group B had matched pre- and posttreatment (day 5) samples available for IHC analysis of immune infiltrates. There was a significant increase in CD8+ and CD68 + T-cell infiltration from baseline tumor samples to day 5 of treatment (CD8: Wilcoxon signed-rank test V = 57, <italic>P</italic> = 0.032, <italic>n</italic> = 11, Fig. ##FIG##5##6##A, ##FIG##5##B##, CD68: Wilcoxon signed-rank test V = 56, <italic>P</italic> = 0.042, <italic>n</italic> = 11), but not of CD4+ cells (Supplementary Fig. ##SUPPL##0##3A##). There was a moderate negative correlation between lower DLDA score (i.e., increased permissiveness to viral replication) and a greater increase in CD4+ and CD8 + T cells following treatment (CD4: Spearman’s rho = −0.52, S = 334, <italic>P</italic> = 0.11; CD8: Spearman’s rho = -0.46, S = 322, <italic>P</italic> = 0.154, Fig. ##FIG##5##6C## and Supplementary Fig. ##SUPPL##0##3B##). A greater change in posttreatment CD4 + , CD8+ and CD20+ cell percentage was observed in patients who were not on corticosteroids at study entry (Wilcoxon rank-sum test CD4+ <italic>P</italic> = 0.042, CD8+ <italic>P</italic> = 0.024, CD20+ <italic>P</italic> = 0.042; Supplementary Fig. ##SUPPL##0##2B##).</p>", "<p id=\"Par16\">Five of the 11 patients had additional surgeries performed at 1.3, 1.8, 4, 7.3, and 8 mo from study entry In 4 of 5 patients, lymphocytic infiltration had returned at or below baseline levels at the time of subsequent surgery, while in one patient the lymphocytic infiltration increased over time (Fig. ##FIG##5##6D##).</p>", "<title>Efficacy</title>", "<p id=\"Par17\">Comparable median PFS was observed between the two treatment arms: Group A, 3.0 months (95% confidence intervals [CI]: 3.0–NA); Group B, 3.4 months (95% CI: 2.3, NA; HR: 0.97 (95% CI: 0.41, 2.3), <italic>P</italic> = 0.95). Median PFS for all study patients was 3.4 mo (95% CI: 2.9, 4.9) (Fig. ##FIG##6##7A##). Median OS was also similar between the two arms: Group A, 11.8 months (95% CI: 4.4; NA); Group B, 11.4 (4.3; NA); HR = 1.66 (95% CI: 0.67; 4.11), <italic>P</italic> = 0.28 (Fig. ##FIG##6##7B##). Median OS for all study patients was 11.6 mo (95% CI: 6.4; 17.8). Overall PFS rates at 3 and 6 months were 59.1% (95% CI: 41.7%, 83.7%) and 22.7% (95% CI: 10.5%, 49.1%), respectively. Overall OS rates at 6 and 12 months were 68.2% (95% CI: 51.3, 90.7) and 45.5% (95% CI: 28.8%, 71.8%), respectively. Only two study patients (both in group A) were IDH mutant. Median PFS in the study was not significantly impacted by IDH status: IDH wild-type patients had a median PFS of 3.4 months (95% CI: 3.0, 5.0) versus 4.8 months in IDH mutant patients (95% CI: 3.0, NA; log-rank <italic>P</italic> = 0.650). As expected, IDH mutant patients lived longer as compared to IDH wild-type patients: IDH wild-type patients had a median overall survival of 11 months (95% CI: 4.4, 16) versus 30 months in IDH mutant patients (95% CI: 22, NA; log-rank <italic>P</italic> = 0.031) (Supplementary Fig. ##SUPPL##0##4A, B##). All study patients had surgery as per trial design: the best objective response was stable disease and observed in 8 (88.9%) and 12 (92.3%) of the patients in Groups A and B, respectively. One patient in each arm had progressive disease. Supplementary Fig. ##SUPPL##0##5## includes a characteristic example in a Group B patient, highlighting the evolution of imaging changes post treatment.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par18\">This manuscript reports on first-in-human testing of an engineered oncolytic measles virus strain administered intratumorally in the CNS for the treatment of recurrent GBM. We evaluated two different dosing strategies of this oncolytic MV strain expressing the human carcinoembryonic antigen (MV-CEA), with the aim of determining the MTD and assessing the safety and preliminary efficacy of this agent. In group A, patients had resection of their recurrent tumor followed by virus administration into the resection cavity; the MTD was established as 10⁷ TCID50. Patients in group B first received an intratumoral injection of the MV-CEA followed by resection 5 days later; the MTD was determined to be 2 × 10⁷ TCID50, which represented the maximum planned dose given viral titers and limitations regarding feasible CNS injection volume.</p>", "<p id=\"Par19\">Both strategies were safe with no DLT observed in either group at levels up to 2 × 10⁷ TCID50. There were no reports of Grade ≥3 toxicity, while 4/22 patients (18%) had grade 2 AEs at least possibly related to the virus. Immunosuppression has been observed following wild-type MV infection and can be associated with suppression of delayed-type hypersensitivity response (DTH), bacterial infections, and reactivation of tuberculosis^{##UREF##4##25##}. It is, however, infrequent and transient following measles vaccination^{##REF##11448026##26##}. In this study, no treatment-induced immunosuppression as assessed by DTH, CD4, CD8, immunoglobulin, and complement levels was observed, an important consideration, given the immunosuppression frequently observed in glioblastoma patients, both due to their disease and treatment^{##REF##29643471##27##}. Moreover, no viremia or virus shedding was observed, which confirms that MV strains exhibit high level of environmental safety.</p>", "<p id=\"Par20\">Although efficacy was a secondary endpoint in the trial, preliminary evidence indicates that intratumoral injection with MV-CEA alone is associated with biologic activity despite the fact that 41% of the study patients had received more than 1 chemotherapy regimens and 23% had failed bevacizumab. Stable disease was observed in 88% of patients in Group A and 92.3% of patients in Group B, respectively. Observed median OS was 11.5 mo; these outcomes are favorable versus other contemporary studies in the recurrent GBM population. For example, in the contemporary Alliance A071101 trial patients with recurrent GBM at first recurrence were treated with gross total resection followed by two different combinations of heat shock protein vaccine with bevacizumab versus bevacizumab: a median survival of 6–8.5 mo was observed^{##UREF##5##28##}. Other contemporary randomized data demonstrate that in bevacizumab pretreated patients, the expected median OS is dismal and in the range of 3–4 mo^{##REF##26130744##29##}. In addition, the OS12 rate compares favorably with the 25% OS12 observed in contemporary recurrent GBM trials, including patients at first recurrence^{##UREF##6##30##,##REF##31290996##31##}. Although these findings cannot be viewed as definitive given the small sample size in the trial, they support prospective validation of measles-based immunovirotherapy strategies in this patient population.</p>", "<p id=\"Par21\">Analysis of posttreatment samples, obtained on day 5 after viral administration, confirmed detection of viral genomes to an extent that depended on baseline expression of interferon-stimulated genes in these tumors. We have previously developed a predictive algorithm, a weighted gene signature (DLDA score) based on 22 interferon-stimulated genes, that can predict viral permissiveness following MV infection in patients with GBM and ovarian cancer^{##REF##29788332##24##}. Applying this algorithm in all 13 Group B patients, we found that the DLDA score was also predictive of MV replication. Those patients who had lower ISG scores tended to have tumors that were more permissive to the virus and had higher levels of virus replication. Thus, patients who are more likely to potentially benefit from the MV therapy can be pre-selected by assessing the level of ISG expression. Of importance, there was a strong trend supporting a reverse correlation between DLDA score and CD8 lymphocytic infiltration in posttreatment samples suggesting that viral replication plays an important role in the observed posttreatment remodeling of tumor microenvironment.</p>", "<p id=\"Par22\">It is of note that 2 of the 13 patients in group B (15%) had a low DLDA score and were very permissive to viral replication despite the fact that one of these patients was treated in the lower dose level (2 × 10⁶ TCID50). Given the importance of interferon response pathway in controlling the replication of most other oncolytic viruses, this data suggests that approximately one out of five GBM patients would have tumors exhibiting the degree of permissiveness that results in optimal viral replication. This hypothesis is corroborated by clinical observations with several other viruses including Delta-24-RGD^{##REF##29432077##32##}, poliovirus^{##REF##29943666##33##}, and Toca-511^{##UREF##7##34##} where response rates ranging from 9–13% were observed. It also highlights one of the possible challenges in the field of oncolytic virotherapy in GBM: if the benefit of single-agent therapy is expected to be confined to &lt;20% of patients who have a suppressed baseline response against interferon, phase III trials in unselected patients would have a very high likelihood of being negative by diluting the virotherapy responsive patient population^{##REF##33119048##35##}.</p>", "<p id=\"Par23\">Viral treatment resulted in tumor microenvironment remodeling with significant increase in CD8+ cell infiltrates on day 5 posttreatment samples. Of note, our data illustrates that those patients with moderate DLDA score ( &lt; 150 and &gt; −250) can still accomplish intermediate levels of viral replication which is adequate to allow them to benefit from the immunostimulatory effect of even limited viral replication on tumor microenvironment; upregulation of proinflammatory mediators and lymphocytic infiltration on day 5 biopsy was observed. Viral infection was found to induce increases in proinflammatory cytokines and chemokines (Fig. ##FIG##4##5##A, ##FIG##4##B##) that have previously been shown to be involved in creating an immunogenic environment^{##REF##28648866##36##} and stimulate immunologic response^{##REF##28555670##37##}. This type of localized inflammation has the potential to augment the effector functions of infiltrating immune cells, facilitate the generation of antitumor immunity, and counteract tumor-induced immunosuppression^{##REF##11244031##38##}. It is also possible that repeat (beyond two doses) administration of our MV oncolytic strain could have the potential to further enhance this effect and maintain the proinflammatory remodeling of the tumor microenvironment, that otherwise may reverse. Although the impact of multiple dosing cannot be addressed by our study, data generated with repeat administration of the herpes virus strain G47Δ in Japanese patients appear to support this approach^{##REF##35864254##39##}.</p>", "<p id=\"Par24\">Overall, our data indicates that intratumoral administration of measles virus strains can act as a form of in situ vaccination inducing microenvironment changes that can facilitate tumor-immune recognition and help reverse resistance to other immunotherapies such as immune checkpoint inhibitors. Indeed, in parallel preclinical work in the GL261 and CT2A models, we have demonstrated that combination of oncolytic measles virus strains with murine anti-PD1 resulted in synergy with 60–80% of animals being cured^{##REF##27663389##20##,##REF##34196308##40##}. In addition, the development of tumor-specific immunologic memory was observed as demonstrated by the fact that 100% of the surviving animals remained disease-free when rechallenged with the autologous glioblastoma lines, but not when rechallenged with different tumor (melanoma) line^{##REF##34196308##40##}. Thus, patients with intermediate DLDA scores, although not benefiting from single-agent virotherapy as much as patients with low DLDA scores, could still be excellent candidates for combinatorial strategies, for example, with immune checkpoint inhibitors or agents that block activation of the interferon response pathway. We have also demonstrated that even low levels of oncolytic viral replication are adequate for the synergistic effect of virotherapy with anti-PD1 inhibition to materialize, and that increasing viral replication with the use of JAK/STAT inhibitors, which block the interferon response pathway, can further enhance this effect^{##REF##27663389##20##,##REF##34196308##40##}.</p>", "<p id=\"Par25\">Despite promising clinical data in this area, as with any new agent, further studies are required to fully assess the translation and clinical applicability of this agent, and other MV strains. In this first-in-human study in glioblastoma the Edmonston measles oncolytic platform demonstrated safety, ability to replicate in the tumor and resulted in promising survival outcomes. Despite the fact that all patients were immune to the virus per study design and FDA mandate in order to increase safety, systemic pre-existing immunity did not block replication in the tumor, following intratumoral administration. Our data also demonstrate that variability in viral permissiveness needs to be considered, emphasizing the importance of patient selection. The DLDA-weighted gene signature we have developed along those lines could help individualize treatment and allow us to select patients that may derive optimal benefit from single-agent virotherapy versus combinatorial strategies^{##REF##29788332##24##}. Furthermore, in order to further enhance the immunostimulatory potential of oncolytic cell death, we have engineered measles strains to express the Helicobacter pylori neutrophil-activating protein (NAP), a potent TLR2 agonist. We have demonstrated a significant increase in activity in immunocompetent GBM models, enhancement of immunostimulatory response with increased secretion of damage-associated molecular patterns such as HMBG1 and calreticulin, and synergy with immune checkpoint inhibitors^{##REF##34196308##40##}.</p>", "<p id=\"Par26\">In conclusion, these data of oncolytic measles virus strains in recurrent GBM patients create an important foundation that supports subsequent testing of MV strains with immunostimulatory payloads as well as strategies for treatment individualization.</p>" ]

[]

[ "<p id=\"Par1\">Measles virus (MV) vaccine strains have shown significant preclinical antitumor activity against glioblastoma (GBM), the most lethal glioma histology. In this first in human trial (NCT00390299), a carcinoembryonic antigen-expressing oncolytic measles virus derivative (MV-CEA), was administered in recurrent GBM patients either at the resection cavity (Group A), or, intratumorally on day 1, followed by a second dose administered in the resection cavity after tumor resection on day 5 (Group B). A total of 22 patients received study treatment, 9 in Group A and 13 in Group B. Primary endpoint was safety and toxicity: treatment was well tolerated with no dose-limiting toxicity being observed up to the maximum feasible dose (2×10⁷ TCID50). Median OS, a secondary endpoint, was 11.6 mo and one year survival was 45.5% comparing favorably with contemporary controls. Other secondary endpoints included assessment of viremia, MV replication and shedding, humoral and cellular immune response to the injected virus. A 22 interferon stimulated gene (ISG) diagonal linear discriminate analysis (DLDA) classification algorithm in a post-hoc analysis was found to be inversely (R = −0.6, p = 0.04) correlated with viral replication and tumor microenvironment remodeling including proinflammatory changes and CD8 + T cell infiltration in post treatment samples. This data supports that oncolytic MV derivatives warrant further clinical investigation and that an ISG-based DLDA algorithm can provide the basis for treatment personalization.</p>", "<p id=\"Par2\">Oncolytic measles virus (MV) vaccine strains have shown preclinical antitumor activity against glioblastoma (GBM). Here the authors report the results of a phase 1 trial of intratumoral administration of a MV strain engineered to express the carcinoembryonic antigen in patients with recurrent GBM including assessment of viral replication and proinflammatory remodeling of the treated tumors.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n\n\n</p>", "<title>Source data</title>", "<p>\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41467-023-43076-7.</p>", "<title>Acknowledgements</title>", "<p>This work was supported in part by NIH grants R01CA258239, P50CA 108961, R21CA 123839, and The Ben &amp; Catherine Ivy Foundation. The authors would like to express their gratitude to patients and their families. They would also like to thank Mrs. Susan Steinmetz for her support in coordinating patient care, Marie R. Passow, SCT (ASCP) who in conjunction with Dr. Aditya Raghunathan optimized the digital image analysis algorithms, and Mrs. Raquel Ostby for help with manuscript preparation.</p>", "<title>Author contributions</title>", "<p>Conceptualization: E.G. Data curation: E.G., S.K.A., X.W.C., and I.A. Formal analysis: E.G., S.K.A., C.B.K., X.W.C., and I.A. Funding acquisition: E.G. Investigation: E.G., C.B.K., I.A., J.H.U., J.E.H., R.S.M., S.I.R., D.R.J., T.J.K., J.C.B., K.E.D., D.H.L., T.C.B., C.G., A.R., and I.F.P. Methodology: E.G., M.J.F., A.A.L., I.A., K.B.V., C.G., A.R., I.D.I., and I.F.P. Writing— original draft: E.G. and S.K.A. Writing—review and editing: E.G., S.K.A., C.B.K., X.W.C., J.H.U., M.J.F., A.A.L., K.B.V., J.E.H., R.S.M., S.I.R., D.R.J., T.J.K., J.C.B., K.E.D., D.H.L., T.C.B., C.G., A.R., I.D.I., and I.F.P.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par46\"><italic>Nature Communications</italic> thanks E.Antonio Chiocca, Minoru Tanaka and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.</p>", "<title>Data availability</title>", "<p>All requests for raw and analyzed data will be reviewed by the Mayo Clinic (MC) Institutional Review Board (IRB). Patient-related data not included in the manuscript were generated as part of a clinical trial and are subject to patient confidentiality. Any data and materials (e.g., tissue samples or imaging data) that can be shared will need approval from the MC IRB and a material transfer agreement in place; this process requires an average of 6 months. All data shared will be de-identified and will be available for 1 year after access is granted. Any requests for clinical data should be addressed to the corresponding author Evanthia Galanis ([email protected]). The study protocol is available as a Supplementary Note in the Supplementary Information file. The remaining data are available within the Article, Supplementary Information or Source Data file. <xref ref-type=\"sec\" rid=\"Sec27\">Source data</xref> are provided with this paper.</p>", "<title>Competing interests</title>", "<p id=\"Par47\">The authors declare no competing interests or other interests that might be perceived to influence the interpretation of the article. Outside of this submission, EG has received honoraria for advisory board participation from Kiyatec, Inc. (personal compensation) and Karyopharm Therapeutics, Inc. for Data Safety and Monitoring Board participation (compensation to the employer). Her institution has received grant funding from Servier Pharmaceuticals LLC (formerly Agios Pharmaceuticals, Inc.), Celgene, MedImmune, Inc. and Tracon Pharmaceuticals. The remaining authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Treatment-related adverse events.</title><p>Treatment was well tolerated with only grade 1 and 2 toxicity being observed (<italic>n</italic> = 22 evaluable patients).</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Baseline and posttreatment anti-measles virus (MV) antibody levels.</title><p>Error bars represent the standard error of the mean (SEM) <bold>A</bold> pre-treatment: <italic>n</italic> = 9 patients, mean =104.7 + /−13.0 SEM; <bold>A</bold> post treatment: <italic>n</italic> = 8 patients, mean=95.9 + /−14.6 SEM; <bold>B</bold> pre-treatment: <italic>n</italic> = 13 patients, mean=30.9 + /−10.4 SEM; <bold>B</bold> post treatment: <italic>n</italic> = 10 patients, mean=21.2 + /−10.2 SEM). Source data are provided as Source Data file.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>DLDA score correlation with viral replication in treated tumors.</title><p>DLDA scores calculated for all Group B patients were correlated with virus replication in the treated tumors (<italic>n</italic> = 12 patients with available virus replication data). Pearson’s correlation coefficient (<italic>r</italic>), 95% CI and two-sided <italic>P</italic> value based on a t-distribution with <italic>n</italic>-2 degrees of freedom. Source data are provided as Source Data file.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Measles virus (MV) receptor expression in study patients.</title><p>Gene expression levels of the three known MV receptors CD46, SLAM and Nectin-4 were assessed in Group B patients (<italic>n</italic> = 13) and found to be comparable. Source data are provided as Source Data file.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Differential gene expression in posttreatment samples of viral replication resistant versus permissive tumors (<italic>N</italic> = 13 patients).</title><p><bold>A</bold> RNA was isolated from tumor biopsies before and after MV therapy, expression was analyzed by Nanostring and differentially expressed genes were used to determine differentially activated pathways. The heatmap shows gene expression intensity across samples (right panel) and biological processes enriched by each gene (left panel). Permissive tumors (<italic>N</italic> = 3 patients) are underlined with a black bar, intermediate permissiveness (<italic>N</italic> = 9 patients) with a green bar and resistant tumors (<italic>N</italic> = 1 patient) with a magenta bar at the bottom of the heat map. Expression of the genes presented in this plot was at least twofold different (up- or downregulated) with <italic>P</italic> value 0.05 or lower in the group of good responders vs poor responders after the treatment. <bold>B</bold> Bar plot depiction of adjusted <italic>P</italic> values corresponding to biological processes (BP) of the Gene Ontology (<ext-link ext-link-type=\"uri\" xlink:href=\"http://geneontology.org/\">http://geneontology.org/</ext-link>): The 14 processes that are most differentially enriched post treatment in patients with replication permissive versus resistant tumors are shown here.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Pre- versus posttreatment CD8 + T-cell infiltration and correlation with baseline DLDA scores in group B patients.</title><p><bold>A</bold> There was a significant increase in CD8 + T-cell infiltration from baseline tumor samples to day 5 of treatment (CD8: Wilcoxon signed-rank test V = 57, <italic>P</italic> = 0.032, <italic>n</italic> = 11). <bold>B</bold> Development of CD8 + T-cell predominant lymphocytic infiltrates was observed in study patients following one dose of MV treatment, including patients with intermediate DLDA scores. Representative examples of two study patients are shown. <bold>C</bold> Correlation between DLDA score and CD8 + T-cell increase following treatment. Spearman’s rho = −0.46 (95% CI: −0.83 to 0.19, two-sided <italic>P</italic> value, <italic>P</italic> = 0.154, <italic>n</italic> = 11 patients with available log2 fold change CD8 data). <bold>D</bold> Lymphocytic cell infiltration was evaluated in tumor specimens obtained in subsequent surgeries following study completion in a subset of study patients; evolution of the percentage of CD8-positive cells is depicted. Source data are provided as Source Data file.</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><title>Progression-free survival and overall survival outcomes in study patients.</title><p><bold>A</bold> Progression-free survival in Group A and Group B patients. <bold>B</bold> Overall survival in Group A and Group B patients. Source data are provided as Source Data file.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Patient demographics and baseline characteristics of treated patients</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Characteristic</th><th>Patients (<italic>n</italic> = 22)</th></tr></thead><tbody><tr><td>Age, median (min, max), years</td><td>53.5 (37.0, 69.0)</td></tr><tr><td colspan=\"2\"><bold>Gender</bold></td></tr><tr><td>Female</td><td>11 (50.0)</td></tr><tr><td>Male</td><td>11 (50.0)</td></tr><tr><td colspan=\"2\"><bold>ECOG performance status score,</bold>\n<bold><italic>n</italic></bold>\n<bold>(%)</bold></td></tr><tr><td>0</td><td>6 (27.3)</td></tr><tr><td>1</td><td>13 (59.1)</td></tr><tr><td>2</td><td>3 (13.6)</td></tr><tr><td colspan=\"2\"><bold>Corticosteroid therapy at study entry,</bold>\n<bold><italic>n</italic></bold>\n<bold>(%)</bold></td></tr><tr><td>Yes</td><td>12 (54.5)</td></tr><tr><td>No</td><td>10 (45.5)</td></tr><tr><td colspan=\"2\"><bold>Prior chemotherapy regimens,</bold>\n<bold><italic>n</italic></bold>\n<bold>(%)</bold></td></tr><tr><td>1</td><td>13 (59.1)</td></tr><tr><td>2</td><td>7 (31.8)</td></tr><tr><td>3</td><td>2 (9.1)</td></tr><tr><td colspan=\"2\"><bold>Prior bevacizumab treatment</bold></td></tr><tr><td>Yes</td><td>5 (22.7)</td></tr><tr><td>No</td><td>17 (77.3)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Measles virus detection in tumors by qRT-PCR on day 5 following viral administration</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Patient</th><th>Dose TCID₅₀</th><th>Genome copies/µg RNA</th></tr></thead><tbody><tr><td>Pt 1</td><td>2 × 10⁶</td><td>6 × 10⁷</td></tr><tr><td>Pt 2</td><td>2  × 10⁶</td><td>Not available</td></tr><tr><td>Pt 3</td><td>2  × 10⁶</td><td>3.8 × 10⁴</td></tr><tr><td>Pt 4</td><td>2  × 10⁷</td><td>4.1 × 10⁴</td></tr><tr><td>Pt 5</td><td>2 × 10⁷</td><td>1.3 × 10⁵</td></tr><tr><td>Pt 6</td><td>2 × 10⁷</td><td>1.7 × 10⁵</td></tr><tr><td>Pt 7</td><td>2 × 10⁷</td><td>1.3 × 10³</td></tr><tr><td>Pt 8</td><td>2 × 10⁷</td><td>6.8 × 10⁶</td></tr><tr><td>Pt 9</td><td>2 × 10⁷</td><td>1.2 × 10⁴</td></tr><tr><td>Pt 10</td><td>2 × 10⁷</td><td>0</td></tr><tr><td>Pt 11</td><td>2 × 10⁷</td><td>2.6 × 10³</td></tr><tr><td>Pt 12</td><td>2 × 10⁷</td><td>1.6 × 10³</td></tr><tr><td>Pt 13</td><td>2 × 10⁷</td><td>1.2 × 10⁴</td></tr></tbody></table></table-wrap>" ]

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[ "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>Deceased: Ileana Aderca.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41467_2023_43076_MOESM1_ESM.pdf\"><caption><p>Supplementary Information</p></caption></media>", "<media xlink:href=\"41467_2023_43076_MOESM2_ESM.pdf\"><caption><p>Peer Review File</p></caption></media>", "<media xlink:href=\"41467_2023_43076_MOESM3_ESM.pdf\"><caption><p>Description of Additional Supplementary Files</p></caption></media>", "<media xlink:href=\"41467_2023_43076_MOESM4_ESM.csv\"><caption><p>Supplementary Data 1</p></caption></media>", "<media xlink:href=\"41467_2023_43076_MOESM5_ESM.xlsx\"><caption><p>Supplementary Data 2</p></caption></media>", "<media xlink:href=\"41467_2023_43076_MOESM6_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>", "<media xlink:href=\"41467_2023_43076_MOESM7_ESM.zip\"><caption><p>Source Data</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Background &amp; Summary</title>", "<p id=\"Par2\">Many vital industries, including petroleum and chemical production, processing, refining, and transport, rely on short-term storage in above-ground storage tanks (ASTs)^{##UREF##0##1##}. For example, in the United States, the total petroleum storage capacity at sites that commonly use ASTs exceeds two billion barrels^{##UREF##1##2##}. Typical types of ASTs include closed roof, external floating roof, and spherical pressure tanks, the choice of which depends on the characteristics of the stored material, including the specific gravity, volatility, and flash point^{##UREF##2##3##,##UREF##3##4##}.</p>", "<p id=\"Par3\">ASTs are vulnerable to various hazards, both natural and anthropogenic^{##UREF##4##5##}. For example, during Hurricanes Katrina^{##UREF##5##6##}, Isaac^{##UREF##6##7##}, and Harvey, thousands of barrels of petroleum were released from storage tanks and spread by floodwaters into the environment^{##UREF##7##8##–##UREF##9##10##}, threatening ecosystems, economies, and human health^{##UREF##10##11##–##UREF##12##13##}. Internationally, oil depots have been targeted during civil unrest and military conflict, demonstrating the possibility for ASTs to become targets^{##UREF##13##14##,##UREF##14##15##}. In 2020, as a result of the covid-19 pandemic and the Russia-Saudi Arabia price war, the crude oil market experienced decreased demand and increased inventory, straining storage capacity^{##REF##34898736##16##}. Despite these widespread risks, consolidated data suitable for assessing system vulnerabilities and failures, estimating current production and capacity, and evaluating the state of energy and other infrastructure are not readily available to researchers, regulators, and other decision-makers.</p>", "<p id=\"Par4\">The Environmental Protection Agency (EPA) collects information on facilities that process petroleum and hazardous materials through the Facility Registry System (FRS) and Toxic Release Inventory (TRI); however, these datasets do not contain specific tank locations, sizes, or contents^{##REF##20345576##17##}. The Emergency Planning and Community Right-to-Know Act (EPCRA) requires that industrial sites make chemical inventory data available to community members via material safety data sheets (MSDS)^{##UREF##15##18##}; however, these data are not available outside of one’s immediate locale.</p>", "<p id=\"Par5\">Remotely sensed imagery has been utilized in some cases to develop AST datasets for specialized purposes. The Oil and Gas Storage Tank (OGST) dataset, for example, identifies tanks located inside the footprint of well pads across Alberta, Canada, in 760 images with resolutions varying from 0.3 to 1.2 meters^{##UREF##16##19##}. The Oil Storage Tank (OST) dataset of external floating roof tanks was developed to estimate capacity and contains 1,595 annotated images taken from Google Earth^{##UREF##17##20##}. A dataset of over 4,500 storage tanks along the Houston Ship Channel (HSC), includes tank location and indication of contaminant barriers, as well as estimates of diameter, height, shell thickness, and content characteristics^{##UREF##18##21##}. Finally, the DOTA dataset includes over 10,000 annotated storage tanks from aerial imagery at various resolutions and locations worldwide^{##UREF##19##22##}. While these datasets all provide useful data in certain contexts, they are generally limited by too few annotations, missing location data, lack of geographic coverage in the United States, simplified classifications, and limited availability.</p>", "<p id=\"Par6\">Recognizing the value of comprehensive, publicly available data for community health and safety risk assessment, petroleum market research, and other analyses, we have developed an original dataset of ASTs from high-resolution aerial imagery across the contiguous United States. It contains geospatial coordinates, border vertices, and orthorectified imagery for over 130,000 spherical pressure, closed roof, external floating roof, sedimentation tanks, and water towers. This dataset was developed for two primary purposes: (1) as training and testing data for subsequent object detection algorithms, and (2) as geospatial data for AST risk assessments. Additionally, the dataset will benefit researchers interested in:<list list-type=\"bullet\"><list-item><p id=\"Par7\">Petroleum storage working and net capacity estimates;</p></list-item><list-item><p id=\"Par8\">Petrochemical market evaluation and economic assessment; and</p></list-item><list-item><p id=\"Par9\">Machine learning or computer vision tasks, particularly those that require extensive training datasets.</p></list-item></list></p>" ]

[ "<title>Methods</title>", "<p id=\"Par10\">We constructed this dataset to contain the imagery, location, bounding boxes, and classifications for various ASTs across the contiguous United States. As illustrated in Fig. ##FIG##0##1##, our process involved: (1) selecting aerial imagery data, (2) manually annotating and classifying storage tanks, water towers, and sedimentation tanks, (3) validating and correcting when necessary, the bounding boxes and classifications, (4) obtaining geospatial information for each tank, image, and tile, and (5) developing tile level annotations and compiling the full dataset. Each step will be described in the subsections that follow.</p>", "<title>Selecting aerial imagery</title>", "<p id=\"Par11\">The United States Department of Agriculture (USDA) Farm Service Agency’s (FSA) National Agriculture Imagery Program (NAIP) collects high-resolution, remotely-sensed aerial imagery of the continental U.S. during the agricultural growing seasons^{##UREF##20##23##}. We selected NAIP tiles based on two criteria: (1) presence of relevant infrastructure and (2) objects being clearly identifiable. The first criterion was evaluated using existing point datasets of natural gas and petroleum processing plants, reserves, terminals, and ports from the U.S. Department of Homeland Security, Energy Information Administration (EIA), and National Oceanic and Atmospheric Administration (NOAA)^{##UREF##21##24##–##UREF##27##30##}. As objects of interest range from 3 to 69 meters in diameter, to meet the second criterion only NAIP tiles collected after 2018 were included, guaranteeing a minimum 60 cm ground sampling distance (GSD) so that objects are represented by multiple pixels^{##UREF##20##23##,##UREF##28##31##}.</p>", "<p id=\"Par12\">A total of 2132 NAIP tiles from 48 states were acquired for annotation from the Microsoft Planetary Computer Data Catalog repository^{##UREF##29##32##}. Each NAIP tile includes four bands (red, green, blue, and near-infrared) over a 3.75-minute longitude by 3.75-minute latitude quarter quadrangle with an additional 300-meter buffer, thereby covering between 12 and 18 square miles^{##UREF##20##23##}. The large size, high-resolution, and high concentration of objects require meticulous annotation^{##UREF##30##33##}. To ensure adequate visual inspection, each NAIP tile was broken into smaller 512-by-512-pixel images, representing approximately 23 acres (0.094 square kilometers) (Fig. ##FIG##1##2##).</p>", "<p id=\"Par13\">File names for tiles utilize the USDA’s original file naming convention separating the USGS quadrangle identifier corresponding to a 7.5-minute × 7.5-minute area; quarter-quad two-character ordinal direction identifying a given quarter section within a quadrangle; two-digit Universal Transverse Mercator (UTM) zone; image resolution; and capture date in year-month-day, each separated by underscores. 512-by-512-pixel images and image-level annotations utilize the same naming convention and include the row and column index corresponding to the position of the image within the tile (Fig. ##FIG##2##3##).</p>", "<title>Annotating storage tanks</title>", "<p id=\"Par14\">To accurately and efficiently review and annotate the large number of images identified, we adapted the large-scale annotation procedure developed to create ImageNet^{##UREF##31##34##,##UREF##32##35##}. Using the NAIP imagery, research assistants manually annotated images using LabelImg, an annotation tool with a graphical user interface (GUI) written in Python^{##UREF##33##36##}. LabelImg allows the researcher to view and identify positive images, or images containing objects of interest, and manually draw rectangular bounding boxes. Annotations and images were further inspected using the zoom in/out function, adjusted using a sidebar with annotation details, or deleted if created in error.</p>", "<p id=\"Par15\">Research assistants annotated tanks into one of five categories (Fig. ##FIG##3##4##). <italic>External floating roof tanks</italic> are cylindrical shells outfitted with a roof that floats on the surface of the stored liquid, rising and falling with the liquid level, and are suitable for liquids with high vapor pressure. By contrast, <italic>closed-roof tanks</italic> have coned, domed, or flat roofs permanently affixed to the tank shell, and generally contain products with lower vapor pressures. Closed roof tanks may also have an internal floating roof. To allow versatility for end users, closed roof tanks less than or equal to 9 meters in diameter are classified as <italic>narrow closed roof tanks</italic>. <italic>Spherical pressure tanks</italic>, also known as Horton spheres, are designed to contain gases or liquids at pressures significantly different than the external environment and to withstand significant internal pressures. Although of less interest for our purposes, <italic>water towers</italic> and <italic>sedimentation tanks</italic> were annotated due to their visual similarity, and in some cases proximity, to ASTs of primary interest. Water towers are tanks elevated to provide pressure for water distribution, while sedimentation tanks are generally used in water and wastewater treatment.</p>", "<p id=\"Par16\">To maintain consistency, research assistants were provided with training on the visual differences between object classes, the LabelImg software, and image annotation protocol. To prevent worker fatigue, research assistants were allocated subsets of the images to annotate on a weekly basis. Due to the low ratio of positive-to-negative images, research assistants reviewed only the positive images and annotations in each subset. The annotation and validation required 22 research assistants to review 22,815 images over 2,300 hours.</p>", "<title>Estimating object characteristics: geographic coordinates and tank diameter</title>", "<p id=\"Par17\">Using the orthorectified NAIP tiles, longitude and latitude coordinates were identified for the northwest and southeast vertices for images and objects. A mesh overlay of the Universal Transverse Mercator (UTM) coordinates was linearly interpolated using the northwest and southeast tile vertices and then transformed into longitude and latitudes using the tile datum. The tile pixel coordinates were then used to obtain each object’s northwest and southwest longitude and latitude coordinates.</p>", "<p id=\"Par18\">Annotated images themselves provide valuable data for a variety of contexts; however, some analyses, particularly infrastructure risk assessment, require data compiled at larger spatial scales and the estimation of additional characteristics, such as location and diameter. Tile level annotations were created to provide this information by translating the image’s pixel coordinates, as well as the row and column position within the tile, to tile pixel coordinates^{##UREF##34##37##}. Approximately 20 percent of the objects in the image level annotations are truncated objects or objects that partially lie outside of the image. Within each tile, truncated objects were merged if they belonged to the same class, separated by a maximum of three meters, and did not intersect. The diameter of each object was calculated as the minimum width or height of each object’s bounding box. Additionally, the capture date is included to allow for longitudinal analyses when multiple tank annotations may exist over time.</p>", "<title>Assembling data</title>", "<p id=\"Par19\">The individual 512 by 512-pixel images and corresponding annotations were compiled into a nationwide dataset along with metadata^{##UREF##34##37##,##UREF##35##38##}. The annotated dataset includes 142,107 objects distributed across seven classes. Due to the image sampling methods or natural object frequencies, the validated dataset is imbalanced in favour of closed roof and narrow closed roof tanks, which comprise 51% and 35% of the dataset, respectively (Table ##TAB##0##1##).</p>", "<p id=\"Par20\">Figure ##FIG##4##5## depicts the distribution of annotated objects across the contiguous United States in comparison to active terminals and refineries reported to the Internal Revenue Service^{##UREF##36##39##,##UREF##37##40##}. This figure illustrates that the spatial coverage of the above-ground storage tank dataset is generally consistent with existing petroleum datasets that were not used to develop our dataset.</p>" ]

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[ "<p id=\"Par1\">Remotely sensed imagery has increased dramatically in quantity and public availability. However, automated, large-scale analysis of such imagery is hindered by a lack of the annotations necessary to train and test machine learning algorithms. In this study, we address this shortcoming with respect to above-ground storage tanks (ASTs) that are used in a wide variety of industries. We annotated available high-resolution, remotely sensed imagery to develop an original, publicly available multi-class dataset of ASTs. This dataset includes geospatial coordinates, border vertices, diameters, and orthorectified imagery for over 130,000 ASTs from five labeled classes (external floating roof tanks, closed roof tanks, spherical pressure tanks, sedimentation tanks, and water towers) across the contiguous United States. This dataset can be used directly or to train machine learning algorithms for large-scale risk and hazard assessment, production and capacity estimation, and infrastructure evaluation.</p>", "<title>Subject terms</title>" ]

[ "<title>Data Records</title>", "<p id=\"Par21\">Separate data products, including the aerial imagery dataset^{##UREF##35##38##}, above-ground storage tank inventory^{##UREF##34##37##}, and image and tile characteristics^{##UREF##38##41##,##UREF##39##42##}, totaling 2.3 GB in size, are available in a Figshare repository^{##UREF##40##43##}. Each component is detailed below.</p>", "<p id=\"Par22\">The above-ground storage tank aerial imagery dataset provides a ready-to-use training dataset for deep learning models. This dataset is comprised of two folders which contain 27639 512-by-512-pixel images from 2132 tiles stored in jpg format (“images” folder) and the corresponding annotations in PASCAL Visual Object Classes (VOC) 2007 format as Extensible Markup Language (XML) files (“xmls” folder).</p>", "<p id=\"Par23\">The above-ground storage tank inventory dataset provides cleaned geospatial data and storage tank characteristics for tanks across CONUS. The table is accessible in JSON, GeoJSON, and ESRI shapefile formats to allow for accessibility across applications and software. This dataset is accompanied by a description of the variables included in the inventory dataset.</p>", "<p id=\"Par24\">Metadata relating to the images and tiles are provided by two data records accessible in CSV file format. The image characteristics metadata provides the name of each image and the N.W. and S.E. latitude and longitude coordinates. Additionally, each image can be related to the corresponding parent NAIP tile using the tile name, the image’s row and column index within the tile, and the N.W. and S.E. pixel coordinates respective to the tile. The tile characteristics data record provides the tile name, latitude, and longitude extent of the tile. The image and tile characteristics data records are supplemented with a description of their contents, including the field name, description, data type and units.</p>", "<title>Technical Validation</title>", "<p id=\"Par25\">The development of a high-value, large-scale, multi-class dataset through manual annotation can be laborious and expensive. To efficiently and cost-effectively ensure data quality, we implemented a validation procedure originally developed and described in further detail by Su, 2012^{##UREF##31##34##}. In this validation procedure, we controlled for three potential sources of error: (1) missed objects; (2) poorly drawn bounding boxes; and (3) misclassified objects.<list list-type=\"order\"><list-item><p id=\"Par26\"><italic>Missed objects</italic>. Relying on human annotators requires that annotators label every object in every image. This is made difficult by potential changes in the appearance of objects due to imagery characteristics such as sensor aperture, cloud characteristics, and time of day when collected.</p></list-item><list-item><p id=\"Par27\"><italic>Poorly drawn bounding boxes</italic>. Rectangular bounding boxes provide the spatial location for an object of interest in an image. When a bounding box is too large, excess pixels are incorrectly noted as part of an object, most commonly occurring with smaller objects. Alternatively, when a bounding box is too small, pixels representing an object of interest are incorrectly excluded (i.e., the legs of water towers or the walls of tanks).</p></list-item><list-item><p id=\"Par28\"><italic>Misclassified objects</italic>. Annotators may confuse: (1) objects of interest for one another, such as external floating roof tanks and sedimentation tanks, or (2) objects of interest with other objects in the image, such as circular buildings, concrete pads, or above-ground pools. In addition, annotators may neglect to indicate when objects are truncated by the edge of the image.</p></list-item></list></p>", "<p id=\"Par29\">Several procedures were implemented to minimize the effect of these errors and ensure that quality was maintained across all classes and annotators.</p>", "<title>Hiring</title>", "<p id=\"Par30\">Sorokin and Forsyth note that worker compensation may affect the quality of the data annotations, where low wages workers may lose motivation, and high wages would waste resources and attract inefficient workers^{##UREF##41##44##}. Therefore, we controlled the quality of our data set by hiring student research assistants (RAs), allowing our team to carefully screen applicants and employ highly skilled workers who are jointly incentivized by wages and obtained experience.</p>", "<title>Training and feedback</title>", "<p id=\"Par31\">RAs were given extensive training to learn the purpose of the project, use LabelImg, properly annotate images, and understand and distinguish between the object classes. During the training, RAs were instructed to label every object of interest, including those truncated by the edge of an image. To prevent false negatives or mislabeled annotations, annotators were instructed to label ambiguous objects of interest as <italic>undefined objects</italic> so they may be further reviewed during validation. After the completion of the first subset of images and periodically during the annotation phase, RAs were provided with additional training and feedback on their annotations and opportunities to make corrections to minimize the propagation of systematic errors. Additionally, RAs had access to a Slack channel where they could ask for clarification on the annotation procedure, receive feedback on a specific image, and learn from guidance provided to other RAs.</p>", "<title>Annotation validation</title>", "<p id=\"Par32\">All images and corresponding annotations were reviewed by a set of three RAs using a simple workflow illustrated in Fig. ##FIG##0##1##. The first RA ensured that every object instance in an image has a corresponding bounding box. This ensures that objects in an image that may have been missed are annotated, particularly small objects, images truncated by the edge of an image, or those outside a cluster of objects. Additionally, they removed bounding boxes drawn in error. The next RA reviewed the quality of each bounding box and adjusted it where necessary to ensure the tightest possible bounding box around every object in each image. The final RA confirmed each annotation was correctly classified, reclassified undefined objects if possible, and checked that truncated objects were correctly marked.</p>", "<title>Evaluation of validation procedure</title>", "<p id=\"Par33\">Since consistency across annotators is a positive characteristic of a dataset, we used multiple metrics to evaluate the changes resulting from the validation procedure. To assess the coverage validation, the number of bounding boxes added and removed during validation was calculated (as illustrated in Fig. ##FIG##5##6##). The pre- and post-validation datasets contain 128,127 and 142,091 objects, respectively, and it was determined that during the coverage validation process, 0.8 percent (1,067 objects total) of the pre-validation and 10.6 percent (15,032) of the post-validation annotations were removed and added, respectively, as shown in Table ##TAB##1##2##. To evaluate the quality validation procedure, the number of pre- and post-validation bounding box agreements and exact matches were determined. Of the objects in the post-validation dataset, 89.4 percent (127,050) of the bounding boxes were in agreement and 78.6 percent (111,694) matched exactly with the pre-validation boxes (Table ##TAB##1##2##). Thus, the difference between bounding boxes in agreement and that exactly match, 10.8 percent (15,356) of the post-validation bounding boxes, required minor adjustments.</p>", "<p id=\"Par34\">In analysing the bounding box agreement of the annotations, we did not consider the class labels (tank types). Looking at both the agreement of bounding boxes and the assignment of class labels, 93.8 percent (133,303) are in agreement with the pre-validation bounding boxes and have the same class label, while 73.4 percent (104,344) of bounding boxes exactly match <italic>and</italic> have the same class with respect to the post-validation bounding boxes. To assess the number of changes made to class labels during the class validation phase, the joint frequency of the pre- and post-validation classes for bounding boxes in agreement were tabulated as shown in Table ##TAB##2##3##. The values on the diagonal of the table indicate the percent of class labels matching pre- and post-validation. The sum of the diagonals, 93.1 percent of the bounding boxes in agreement, indicates that the vast majority of class labels matched before and after validation. The largest share of those that changed class were between closed roof tanks and narrow closed roof tanks. Seven percent of the tanks believed to be closed roof pre-validation were converted to narrowed closed roof tanks, and 5.2 percent were changed vice versa. Given the similarity between these two classes, these changes are not surprising.</p>", "<title>Evaluation of data reliability</title>", "<p id=\"Par35\">Further evaluation of the efficacy of the large-scale validation procedure was conducted on a subset of the data. One percent of the compiled dataset, or 276 images, were randomly selected to be judged according to what we are calling a ground truth dataset. The lead author, with expertise in AST risk assessment, corrected and reviewed each image. To ensure that objects in each image were correctly attributed to the right class, the expert utilized their knowledge, Google Maps, and Google Street View to locate and classify each tank as accurately as possible. This process of checking multiple sources for each tank was far more time-consuming and so is not scalable. However, it provided another assay of the quality of the annotation and validation procedure.</p>", "<p id=\"Par36\">Results from comparing the ground truth data to the results of the validation process revealed an average precision of 0.99 and recall of 0.952 across tank classes. These indicate that the bounding boxes were correctly associated with objects of interest, and fewer than 5 percent of objects were missed. Further inspection offered insight into the causes of missed objects. Of the bounding boxes that were missed, 71.9 percent had a pixel area less than 16² (i.e., an area less than 92.2 square meters) and 93 percent had a pixel area less than 32² (i.e., an area less than 368.64 square meters), indicating that smaller tanks were harder to identify.</p>" ]

[ "<title>Acknowledgements</title>", "<p>Student research assistants performed the manual annotation of storage tanks, sedimentation tanks, and water towers using the LabelImg GUI. In particular, we thank the diligent efforts of Qianyu Zhao, Sunny Li, Jackson Harwood, Joshua Kang, Jaewon Jong, Dominic Van Cleave-Schottland, Ryan Feinberg, and Chunxin Tang who served for months as manual annotators and/or validators for this work. This work was supported in part by the Alfred P. Sloan Foundation grant number G-2020-13922 and in part by Environmental Protection Agency (EPA) STAR grant number R840041. The content is solely the responsibility of the authors and does not necessarily represent the official views of the Alfred P. Sloan Foundation or the EPA.</p>", "<title>Author contributions</title>", "<p>C.R. led this research, created the original idea for the AST detection project, developed the algorithm to merge polygon annotations, developed validation procedure, led the student research team management from Summer 2021 to Spring 2022, was involved in all stages of data collection, assembly, and management, and wrote most of the manuscript. M.B. provided intellectual guidance and edited the manuscript. K.B. provided intellectual leadership on the project, georeferencing, and edited the manuscript.</p>", "<title>Code availability</title>", "<p>The raw aerial imagery and annotation tools used in this study are publicly accessible^{##UREF##33##36##,##UREF##42##45##}. The source code developed by the authors to process the imagery and develop the tank inventory dataset are available on GitHub (<ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/celinerobi/ast-data-pipeline\">https://github.com/celinerobi/ast-data-pipeline</ext-link>).</p>", "<title>Competing interests</title>", "<p id=\"Par37\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Schematic of the data development and validation process.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Example of tile (m_4107341_sw_18_060_20190917) split into 512 by 512-pixel images with row and column indices.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Interpretation of NAIP tile and image file naming convention.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Data samples of each tank type category in the dataset.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Fishnet grid of the density of annotated tanks in comparison to CONUS and IRS reported active terminals and refineries.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Illustration of the coverage and quality assessment criteria. On the left, pre-validation annotations are shown on top and the post-validation annotations are shown below. Bounding boxes were determined to be in agreement through a multi-step process. For each post-validation bounding box, the intersection-over-union (IoU) was calculated with respect to each of the pre-validation bounding boxes. The highest IoU for a post- and pre-validation bounding box pair was identified. (<bold>a.1</bold>) If the IoU exceeded or equalled 0.5, the post- and pre- validation bounding box pair was determined to be <bold>in agreement</bold>. (<bold>a.2</bold>) Furthermore, if the IoU was 1.0, the bounding box pair was regarded as an <bold>exact match</bold>. (<bold>b</bold>) If the highest IoU for a bounding box was less than 0.5 and the bounding box was present only in the pre-validation or post-validation annotations, we determined that it was <bold>removed</bold> or <bold>added</bold>, respectively, during the validation process.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Distribution of objects across classes.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Object Class</th><th>Number of Annotations</th><th>Percent of Annotations</th></tr></thead><tbody><tr><td>Closed roof tank</td><td>71,990</td><td>50.7</td></tr><tr><td>Narrow closed roof tank</td><td>50,202</td><td>35.3</td></tr><tr><td>External floating roof tank</td><td>10,312</td><td>7.3</td></tr><tr><td>Sedimentation Tank</td><td>5,664</td><td>4.0</td></tr><tr><td>Water Tower</td><td>1,332</td><td>0.9</td></tr><tr><td>Spherical Tank</td><td>1,687</td><td>1.2</td></tr><tr><td>Undefined Object</td><td>904</td><td>0.6</td></tr><tr><td>Total</td><td>142,091</td><td>100</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Summary of annotation validation assessment, including the number and relative percentage of the post-validation (i.e., compiled) annotations impacted.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Validation Phase</th><th>Assessment</th><th>Number of Observations</th><th>Percent of post-validation annotations</th></tr></thead><tbody><tr><td rowspan=\"2\">Coverage</td><td>Bounding boxes added</td><td>15,032</td><td>10.6</td></tr><tr><td>Bounding boxes removed</td><td>1,067</td><td>0.8</td></tr><tr><td rowspan=\"3\">Quality</td><td>Bounding boxes in agreement</td><td>127,050</td><td>89.4</td></tr><tr><td>Bounding boxes with exact matches</td><td>111,694</td><td>78.6</td></tr><tr><td>Bounding boxes requiring minor adjustment</td><td>15,356</td><td>10.8</td></tr><tr><td>Class</td><td>Bounding boxes with object class corrected</td><td>8,789</td><td>6.2</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Two-way relative frequency table, expressed as a percent of post-validation objects reporting the object class before and after validation for bounding boxes in agreement.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"2\" colspan=\"2\"/><th colspan=\"8\">Tank type after validation (percent)</th></tr><tr><th>Closed roof tank</th><th>Narrow closed roof tank</th><th>External floating roof tank</th><th>Sedimentation tank</th><th>Water tower</th><th>Spherical tank</th><th>Undefined object</th><th>Total</th></tr></thead><tbody><tr><td rowspan=\"8\">Tank type before validation (percent)</td><td>Closed roof tank</td><td>51.20</td><td>3.81</td><td>0.09</td><td>0.03</td><td>0.01</td><td>0.04</td><td>0.02</td><td>55.2</td></tr><tr><td>Narrow closed roof tank</td><td>1.52</td><td>27.43</td><td>0.01</td><td>&lt;0.01</td><td>&lt;0.01</td><td>0.01</td><td>&lt;0.01</td><td>28.97</td></tr><tr><td>External floating roof tank</td><td>0.06</td><td>&lt;0.01</td><td>7.59</td><td>0.07</td><td>0</td><td>0</td><td>0.01</td><td>7.72</td></tr><tr><td>Sedimentation tank</td><td>0.04</td><td>0.01</td><td>0.11</td><td>4.07</td><td>&lt;0.01</td><td>0</td><td>0.02</td><td>4.25</td></tr><tr><td>Water tower</td><td>0.03</td><td>≤0.01</td><td>0</td><td>&lt;0.01</td><td>0.99</td><td>0.02</td><td>&lt;0.01</td><td>1.05</td></tr><tr><td>Spherical tank</td><td>0.20</td><td>0.02</td><td>&lt;0.01</td><td>0</td><td>0.01</td><td>1.21</td><td>0.02</td><td>1.46</td></tr><tr><td>Undefined object</td><td>0.37</td><td>0.29</td><td>0.04</td><td>0.05</td><td>0.01</td><td>0.01</td><td>0.59</td><td>1.35</td></tr><tr><td>Total</td><td>53.41</td><td>31.57</td><td>7.84</td><td>4.22</td><td>1.02</td><td>1.28</td><td>0.66</td><td>100</td></tr></tbody></table></table-wrap>" ]

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[ "<title>Introduction</title>", "<p id=\"Par7\">Strokes are the leading cause of death worldwide. Cortical microinfarcts (CMIs) are frequently observed in older individuals. Approximately 48% of people over the age of 65 worldwide suffer from microinfarct [##REF##31130428##1##]. The impact of CMIs on the brain is not limited to their specific locations but instead extends to a significant number of areas with a widespread distribution. It has been reported that patients who have experienced microinfarcts are at a heightened risk of suffering from additional strokes (15–42% over 5 years) [##REF##32811382##2##]. Epidemiologically, recurrent strokes account for up to 40% of all strokes and are associated with high mortality and poor functional recovery [##REF##21691873##3##]. Moreover, CMIs have been associated with worse outcomes in patients with acute ischemic stroke, including cognitive and motor function impairments [##REF##30890075##4##]. However, the exact mechanism underlying this relationship is still unclear.</p>", "<p id=\"Par8\">Inflammation and immune mediators play a critical role in stroke pathogenesis [##REF##21511199##5##]. The inflammatory response in the brain is mainly mediated by microglia, which are highly plastic and phenotypically diverse cells that adapt to their microenvironment through different signaling pathways [##REF##25582288##6##]. Recently, microglia have been reported to play a key role in the development of trained immunity in the brain through histone modifications after inflammatory stimulation [##REF##29643512##7##]. Enhanced H3K4me1/3 modification can open the chromatin, resulting in easier transcription of the modified inflammatory gene, such as IL1β and TNF-α [##REF##24962734##8##]. Trained microglia can exhibit more severe inflammatory responses and produce excessive pro-inflammatory cytokines once a secondary inflammatory stimulus occurs [##REF##30833177##9##]. The deleterious role of trained immunity has been implicated in a mouse model of central nervous system (CNS) diseases, such as Alzheimer’s disease and stroke since a single dose of inflammatory stimulus can activate trained immunity [##REF##32132681##10##]. These long-lasting (at least 6 months) trained microglia promote the deposition of amyloid β and aggravate stroke outcome over long time periods. Therefore, trained immunity in the CNS needs to be properly investigated.</p>", "<p id=\"Par9\">The NLRP3 inflammasome is a multi-protein complex that is heavily involved in brain inflammation [##REF##30206330##11##] as it mediates the cleavage of pro-inflammatory cytokines (e.g., IL-1β). High NLRP3 level has been observed in the ischemic brain of stroke animals, and NLRP3 inhibitor has been reported to alleviate ischemic brain damage in various stroke models [##REF##33307174##12##, ##REF##32251636##13##]. However, whether NLRP3 is involved in the development of trained immunity remains largely uninvestigated.</p>", "<p id=\"Par10\">The present study explored whether CMIs can induce trained immunity and influence subsequent recurrent strokes. We also examined the role of NLRP3 in mediating CMI-induced trained immunity by promoting epigenetic reprogramming of MLL1 complex and subsequently increased H3K4 methylation. This revealed a novel therapeutic aspect to mitigate recurrent stroke consequences by targeting the NLRP3-MLL1 interaction.</p>" ]

[ "<title>Materials and Methods</title>", "<title>Animals</title>", "<p id=\"Par11\">C57BL/6J male mice (12-month-old, 20–25 g) were provided by the Sun Yat-sen University Medical Experimental Animal Center (Guangzhou, China). Animals were kept in a temperature- and humidity-controlled specific pathogen-free laboratory with a 12/12 h light/dark cycle. Animal experimental procedures were performed following the guidelines set by the Sun Yat-sen University Committee on the Care and Use of Animals.</p>", "<p id=\"Par12\">Tamoxifen (T-143, Sigma-Aldrich, USA) was used to induce NLRP3 deletion in CX3CR1^CreER × NLRP3^fl/fl mice or CreER activation in <italic>Cxc3r1</italic>^CreER mice following a standard protocol [##REF##24360280##14##]. Briefly, tamoxifen was first dissolved in corn oil at a concentration of 20 mg/mL by shaking overnight at 37 °C. It was then stored at 4 °C for the duration of injections. Tamoxifen was administered to animals via intraperitoneal injections once a day for five consecutive days at a dose of 75 mg/kg.</p>", "<p id=\"Par13\">The genotype identification of <italic>Cxc3r1</italic>^CreER and mice was performed as previously described [##REF##24360280##14##] (Fig. ##SUPPL##0##S7##). Briefly, mice tail was sampled, and DNA purification was performed using TIANamp Genomic DNA kit (DP304, Tiangen, China) according to the manufacture’s guide. And collected DNA sample was subjected to PCR analysis using TaKaRa Ex Taq® kit (RR001A, TaKaRa, Japan). The primer for <italic>Cxc3r1</italic>^CreER mice were listed as below: common: 5’-CCGCCAGACGCCCAGACTA; WT forward: 5’-AGCCGGAAGCCCAAGAGCATC; mutant forward: 5’-TGCTGCTGCCCGACAACCAC. The primer for mice were listed as belows: FW: 5’-GAAGCTCCACAGGTCTCCCTT; RV: 5’-GGTTAGCCTGGGCTACACGAA.</p>", "<p id=\"Par14\">And the PCR product were separated on 1-2.5% agarose gels and detected by Red Nucleic Acid Gel Stain (HY-K1007, MCE, USA).</p>", "<title>Microinfarct model</title>", "<p id=\"Par15\">The microinfarct model was generated as previously described [##REF##26187758##15##]. Briefly, mice were anesthetized with a combination of ketamine (0.12 mg/g, i.p.) and xylazine (0.01 mg/g, i.p.) and fixed on the stage of a two-photon microscope (Leica, DM6000, Wetzlar, Germany). Then, 0.1 mL of 0.3% 2000 KD FITC-dextran (FD20, Sigma-Aldrich, USA) was injected into the tail vein. A ROI measuring 15–20 µm in diameter and 10 µm/ms in velocity was selected as the target vessel for occlusion under 25× magnification water-immersion. Bleach mode with maximum laser power was used to damage the endothelium and bleach points located within the vessel lumen. Irradiation was initiated with an 800-nm laser and continued until a clot became apparent and red blood cell motion was stalled. Observation lasting for 1 h was required to evaluate the redistribution and stabilization of the downstream flow. Irradiation was repeated if any recanalization occurred. Mice models with hemorrhage or diffuse burns were discarded. MM102 (15 mg/kg, S7265, Selleck, USA) was intravenously injected immediately after microinfarction.</p>", "<title>MLL1-shRNA, NLRP3 mutant construction and rAAV/MG 1.2 construction and administration</title>", "<p id=\"Par16\">In this study, shRNA targeting MLL1 (AATTATGGTCAAGTGAAGGCG) was used. To determine the role of different domains of NLRP3 in the interaction with MLL1, three truncated versions of NLRP3 including NLRP3 lacking LRR domain (NLRP3ΔLRR), NACHT (NLRP3ΔNACHT) and PYD (NLRP3ΔPYD) were amplified from genomic DNA by PCR and cloned into the pMXs-IRES-GFP by NEBuilder HiFi DNA Assembly Cloning kit (New England Biolabs, Ipswich, MA).</p>", "<p id=\"Par17\">We further packaged these MLL1-shRNA and NLRP3 mutant plasmid into rAAV/MG1.2, created by Minmin Luo et al. [##REF##35879607##16##]. This synthesis was constructed by GeneChem, Shanghai, China. Then, the rAAVs were stereoscopically injected into lateral ventricles of <italic>Cxc3r1</italic>^CreER mice.</p>", "<p id=\"Par18\">Briefly, mice were anesthetized using 4% isoflurane and maintained on 2% isoflurane by a mask. Then, mice were placed on a stereotaxic injection instrument (68805, RWD, China). rAAVs were injected into the lateral ventricle (AP, −0.2 mm; ML, +1.5 mm; DV, −2.3 mm from bregma). 2 × 10¹¹ genome copies were infused at a rate of 1 μl/min, after which the needle was left in place for 10 min to prevent backflow before withdrawal.</p>", "<title>Photothrombotic stroke model</title>", "<p id=\"Par19\">After administering anesthesia using a combination of ketamine (0.12 mg/g, i.p.) and xylazine (0.01 mg/g, i.p.), mouse skulls were exposed by making a 2-mm incision 4 mm posterior and 3 mm left of the bregma for further investigation. Rose bengal dye (10 mg/mL, dissolved in saline) was injected into the tail vein at a dose of 0.03 mg/g body weight. The skull was then exposed to two-photon illumination with blue Hg light (450–500 nm) for 10 min focusing on the aperture incision. The skin was then sutured, and mice were kept on a warm heating pad to recover.</p>", "<title>Microglial isolation</title>", "<p id=\"Par20\">The isolation of microglia was performed as previously described [##UREF##0##17##]. Briefly, mice were anesthetized with a combination of ketamine (0.12 mg/g, i.p.) and xylazine (0.01 mg/g, i.p.), and brains were placed in ice-cold phosphate-buffered saline (PBS) as quickly as possible. Brains were carefully minced into small fragments and digested with trypsin at 37 °C for 20 min. The digested tissue was then triturated and centrifuged at 400 g for 5 min. Centrifuged cells were collected and resuspended in 37% Percoll. The resuspended tissue was placed into 30% Percoll and 70% Percoll was added as the top layer. The tube was then centrifuged once more (700g) for 10 min. The cells between the 30 and 70% Percoll were collected and resuspended in Dulbecco’s Phosphate-Buffered Saline (DPBS)(~2 × 10⁷/mL). Cd11b⁺-positive magnetic isolation was then performed with a STEMCELL Easysep isolation kit (18970, EasySep™ Mouse CD11b Positive Selection Kit II, STEMCELL, Canada). Isolated cells were lysed in Radio Immunoprecipitation Assay (RIPA) buffer and subjected to western blot analysis.</p>", "<title>Nuclear and cytoplasmic protein extraction</title>", "<p id=\"Par21\">Isolated Cd11b⁺ microglia were further processed to extract nuclear and cytoplasmic proteins. The isolation protocol was performed using NE-PER Nuclear and Cytoplasmic Extraction Reagents according to the manufacturer’s instructions (78833, ThermoFisher Scientific Inc., USA). Briefly, cells were resuspended in 50 μL of lysis buffer and incubated for 30 min on ice. Digested cells were lysed via ten strokes through a 26-gage needle and centrifuged for 10 min at 1000 <italic>g</italic>. The supernatant then contained the cytoplasm and mitochondria, while the pellet contained the nuclei.</p>", "<title>ChIP-qPCR</title>", "<p id=\"Par22\">Chromatin precipitation was performed as previously described [##UREF##1##18##]. Briefly, isolated microglia were fixed in 0.75% formaldehyde for 10 min and quenched using glycine. Chromatin was then sonicated for four cycles of 10X (30 s ON, 30 s OFF) at 10% maximum power. Chromatin precipitation was performed using a rabbit anti-mouse H3K4me3 IgG Ab (5326, Cell Signaling Technology, USA). DNA was then quantified using qPCR with the following primer pairs: GAPDH, FW 59-ATCCAAGCGTGTAAGGGTCC-39, RV-59-ACTGAGATTGGCCCGATGG-39; IL6, FW 59-AGCTCTATCTCCCCTCCAGG-39; RV-59-ACAC-CCCTCCCTCACACAG-39; TNF-α, FW 59-CAGGCAGGTTCTCTTCCTCT-39, RV59-GCTTTCAGTGCTCATGGTGT-39.IL1b, FW-59-TGTGTGTCTTCCACTTTGTCCCAC-39; RV-59 CCTGACAATCGTTGTGCAGTTGATG-39; IL-10, FW 59- GGCGCTGTCATCGATTTCTC-39; RV-59- GCTCCACTGCCTTGCTCTTATTT-39. For all ChIP experiments, qPCR values were normalized as the percentage recovery of the input DNA.</p>", "<title>Western blot analysis</title>", "<p id=\"Par23\">Mice were euthanized and perfused with ice-cold saline. The ischemic cortex was sampled and homogenized using ultrasonication in RIPA buffer. Western blot analysis was performed on protein samples of equal mass quantified using a Bicinchoninic Acid Assay (BCA) assay.</p>", "<p id=\"Par24\">The following primary antibodies were used: anti-β-actin (1:1000, 4970, Cell Signaling Technology, USA), anti-IL-1β (1:1000, 31202, Cell Signaling Technology, USA), anti-IL-6 (1:1000, 12912, Cell Signaling Technology, USA), anti-H3K4me3 (1:1000; cell-signaling technology, USA), anti-H3K4me1 (1:1000, 5326, Cell Signaling Technology, USA), and anti-H3 (1:1000, 4499, Cell Signaling Technology, USA). Goat anti-rabbit HRP-linked antibody (1:1000, 7074, Cell Signaling Technology, USA) served as the secondary antibody.</p>", "<title>Immunofluorescence and in situ proximity ligation assay</title>", "<p id=\"Par25\">Mice were euthanized, perfused with ice-cold saline, and fixed using 4% formaldehyde. After dehydration with 30% sucrose, coronal brain slices (20 µm thick) from the right parietal cortices were sectioned using a frozen microtome (CM1950, Leica, Germany) at 200-µm intervals.</p>", "<p id=\"Par26\">For immunofluorescence experiments, slices were first permeabilized with 0.1% Triton X-100 in PBS for 15 min and then blocked with PBS containing 5% Bovine Serum Albumin (BSA) for 1 h. Primary antibodies diluted in blocking buffer were added to the sections and incubated at 4 °C overnight. The sections were then washed three times with PBS and incubated for 30 min at room temperature with the secondary antibody, then washed three more times with PBS. Next, the sections were mounted using DAPI mounting medium (F6057, Sigma-Aldrich, USA) for subsequent observations.</p>", "<p id=\"Par27\">For proximity ligation assay experiments, cells were incubated for 1 h at 37 °C with the appropriate probes after primary antibodies were washed out and washed twice with PBS. Probes were then ligated for 30 min at 37 °C and washed twice in buffer A, then amplified for 100 min at 37 °C in the dark with polymerase (DUO92101, Sigma-Aldrich, USA).</p>", "<p id=\"Par28\">The following primary antibodies were used in the experiment: anti-iba1 (1:500, ab5076, abcam, USA), anti-NLRP3 (1:200, MA5-16274, ThermoFisher Scientific Inc., USA), and anti-MLL1 (1:100, 14197, Cell-Signaling Technology, USA). The following secondary antibodies were used: donkey anti-rabbit IgG H&amp;L (Alexa Fluor® 568) (1:1000; ab175470, abcam, USA), donkey anti-mouse IgG H&amp;L (Alexa Fluor® 488) (1:1000; ab150105, abcam, USA), and donkey anti-goat IgG H&amp;L (Alexa Fluor® 488) (1:1000; ab150129, abcam, USA).</p>", "<title>Nissl staining</title>", "<p id=\"Par29\">Nissl staining was performed using serial frozen coronal sections 10 μm in thickness at 200-μm intervals from Posterior Parietal Cortex (PPC). The sections were hydrated in 1% toluidine blue at 37 °C overnight and washed using double distilled water. After soaking in dimethylbenzene for 5 s, sections were sealed in permount covered by a coverslip. Infarct volume (mm³) was used to measure the infarct size with Image J software (version 2.0.0-rc-68/1.52e).</p>", "<title>ELISA</title>", "<p id=\"Par30\">Blood serum was obtained from the heart ventricle and sampled into coagulating mouse blood collection tubes (Vacutainer 367843, BD, USA) for 10 min at room temperature The blood was then centrifuged at 2000 g for 10 min to isolate the serum. Prior to cytokine measurements, the serum samples were diluted 1:2. After the blood collection, mice were perfused with ice-cold PBS and brain cortex was sampled in cell lysis buffer (EPX-99999-000, Invitrogen, USA), sonicated, and centrifuged at 25,000 g for 10 min. The supernatants were then collected for subsequent analysis.</p>", "<p id=\"Par31\">The blood serum and brain homogenate samples were assayed using ELISA for IL-6 (M6000B, R&amp;D Systems Inc., USA), IL-1β (MLB00C, R&amp;D Systems Inc., USA), and TNF-α (MTA00B, R&amp;D Systems Inc., USA) according to the manufacturer’s instructions.</p>", "<title>Sequence Alignment Assay</title>", "<p id=\"Par32\">The protein structure of MLL1 (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.uniprot.org/uniprot/Q03164\">https://www.uniprot.org/uniprot/Q03164</ext-link>) was predicted using the open-source server trRosetta (<ext-link ext-link-type=\"uri\" xlink:href=\"https://yanglab.nankai.edu.cn/trRosetta/\">https://yanglab.nankai.edu.cn/trRosetta/</ext-link>). The confidence score of the predicted structure model is: TM-score = 0.134. The protein structure of NLRP3 was based on PDB database (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.rcsb.org/structure/6NPY\">https://www.rcsb.org/structure/6NPY</ext-link>).</p>", "<p id=\"Par33\">All the computational work were completed using the Rosetta 2020 program (Cambridge, USA). The docking method used was global docking, which allows the program to freely select the docking site. Parameters were set to default values unless otherwise specified.</p>", "<p id=\"Par34\">The proteins to be docked were combined using Pymol and then subjected to global docking, generating 50,000 conformations for each protein complex. All generated conformations were evaluated using the InterfaceAnalyzer module in the Rosetta2020 program. Conformations with packstate ≥ 0.65 and dG_separated / dSASAx100 ≤ –1.5 were selected. (packstate: the degree of packing between protein interfaces (0 = no packing, 1 = perfect packing)). (dG_separated / dSASAx100: binding free energy per unit area). Finally, the conformation with the optimal binding free energy was analyzed as a potential protein binding mode. All docking results and scores are included in output_files.zip and pack_input_score.</p>", "<title>Statistical analysis</title>", "<p id=\"Par35\">Data were analyzed using Graphpad Prism 9.5.0 and presented as mean ± standard deviation (SD). Experimental groups were randomized and investigators blinded to treatment conditions and mouse types for all outcome analyses. Randomization occurred pre-surgically using Graphpad’s random number generator. Sample sizes (<italic>n</italic>) are indicated in figure legends. One-way, two-way, or three-way ANOVA tests were utilized for data analyses based on the number of factors per group, with Tukey’s multiple comparisons to assess differences between individual groups. Significance was defined as <italic>p</italic> &lt; 0.05. Regardless of test, results were equivalent in magnitude and statistically significant. Sample sizes were calculated to provide 95% power and α = 0.05.</p>" ]

[ "<title>Results</title>", "<title>CMI aggravates secondary stroke</title>", "<p id=\"Par36\">To investigate the influence of microinfarct on recurrent stroke, we first established a microinfarct mouse model using a two-photon microscope (Fig. ##FIG##0##1A##). The perforating artery with a diameter of 40 μm was lased and photothrombotic stroke was induced four weeks later (Fig. ##FIG##0##1B##). Acute and chronic pathologies of recurrent photothrombotic stroke were investigated. As the results showed, there was increased production of pro-inflammatory cytokines, including TNF-α, IL-6, and IL-1β, in the CMI+PT group compared to the PT group on the first day after ischemic stroke. However, no significant differences were observed in infarct volume, microglia activation, or astroglia activation between the CMI+PT and PT groups during this time period. (Fig. ##FIG##0##1C–I##, Fig. ##SUPPL##0##S1A–C##). In the 7^th day post-stroke, the CMI+PT group displayed enhanced microglial activation characterized by shorter filament lengths and increased filament volumes compared to the PT group. (Fig. ##FIG##0##1J, M##). The increased activation of GFAP-positive astrocytes were also observed in CMI+PT group (Fig. ##SUPPL##0##S1D–F##). As a result, the infarct volume is larger in the CMI+PT group (Fig. ##FIG##0##1J–L##). Inflammation was evident in the acute stage following stroke; however, brain edema was the primary factor affecting infarct size. In the chronic stage after stroke, the modulation of inflammatory responses was evident in mice with preceding CMI treatment and resulted in increased infarct volume. These findings suggest that microglia undergo long-term modification following CMI, resulting in exacerbated inflammatory responses and worsened stroke pathology during the secondary stroke event.</p>", "<title>CMI initiated microglial trained immunity in the contralateral cortex</title>", "<p id=\"Par37\">The increased inflammatory responses and deteriorated pathology of PT stroke following CMI indicated that trained immunity might be involved. To investigate this, we first examined the morphology of microglia and astrocytes in the contralateral cortex after CMI (Fig. ##FIG##1##2A##). Microglial morphology was significantly changed, as evidenced by the decreased microglial filament length and increased filament volume (Fig. ##FIG##1##2B–D##). Additionally, the number of GFAP-positive astrocytes was robustly increased in the first 2 weeks post CMI (Fig. ##FIG##1##2A, E##). This activation of glial cells gradually returned to normal levels four weeks later (Fig. ##FIG##1##2B–E##), suggesting the activation of glial cells in the contralateral cortex after CMI and we speculated that this activation might prime the trained immunity in the microglia and influenced the subsequent stroke event.</p>", "<p id=\"Par38\">Trained immunity in the brain is driven by epigenetic changes in microglia though H3 methylation. Since the activation of microglia was prominent one week post CMI, we isolated CD11b-positive microglia in the contralateral CMI side and performed ChIP-seq analysis (Fig. ##FIG##1##2F##). The gene ontology (GO) analysis revealed a significant enrichment of biological processes related to external stimulation, while Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis showed a significant enrichment of pathways associated with inflammatory responses, such as HIF-α, which is typically increased in LPS-induced trained immunity [##REF##29643512##7##] (Fig. ##FIG##1##2G, H##). Moreover, the expression levels of H3K4me1 and H3K4me3 increased after exposure to CMI and remained elevated for a duration of four weeks (Fig. ##SUPPL##0##S1G–I##). Therefore, we also examined the H3K4me3 modification on the promoters of TNF-α, IL-6, IL-1β, and IL-10 and found a significant increase in TNF-α, IL-6, IL-1β following CMI. Notably, this H3K4me3 modification persisted for at least four weeks, indicating that microglia were epigenetically modified following CMI and retained their altered state at least for four weeks (Fig. ##FIG##1##2I–L##).</p>", "<title>H3 methylation inhibition abolished the detrimental effect of CMI on recurrent PT stroke</title>", "<p id=\"Par39\">The increased H3 methylation and its binding on the promoter of pro-inflammatory cytokines after CMI suggested the participation of trained immunity in the exacerbation of recurrent stroke. To verify that trained immunity was involved, we knocked down the MLL1, a crucial protein for MLL1 complex to induce H3 methylation [##REF##36068197##19##], using MLL1-shRNA which was packed into AAV-MG1.2. And we injected the rAAVs into the lateral ventricle of the <italic>Cxc3r1</italic>^CreER mice. Utilizing this specialized method, pioneered by Minmin Luo et al., we achieved precise transduction of microglia in vivo [##REF##35879607##16##] (Fig. ##SUPPL##0##S2A##). Microglial MLL1 was inhibited by rAAVs injection when CMI was induced (Fig. ##FIG##2##3A## and Fig. ##SUPPL##0##S2B, C##). Interestingly, microglial H3K4me1 and H3K4me3 levels were significantly inhibited by MLL1-shRNA in CMI mice (Fig. ##FIG##2##3B–D##), which were accompanied by the abolished H3K4me3 modification on TNF-α, IL-6, IL-1β, and IL-10 promoters (Fig. ##FIG##2##3E–H##).</p>", "<p id=\"Par40\">Since trained immunity promoted the increased inflammatory response, TNF-α, IL-6, IL-1β, and IL-10 expression levels after CMI were detected. The results showed that CMI significantly increased TNF-α, IL-6 and IL-1β production 6 h after recurrent PT stroke, whereas MLL1 knockdown abolished this increase (Fig. ##FIG##2##3I–M##). Accordingly, the infarct size and microglial number around the infarct region were also inhibited by MLL1 knockdown seven days post PT stroke (Fig. ##FIG##2##3N, O, and Q##). And the microglia exhibited increased filament length, alleviated filament volume by MLL1 knockdown (Fig. ##FIG##2##3P, R##). The infarct size and number of microglia around the para infarct region one day post PT stroke did not show significant differences (Fig. ##SUPPL##0##S3A, B##). TNF-α, IL-6, IL-1β, and IL-10 were also measured in peripheral blood samples to examine the possible effect of peripheral inflammatory response on the recurrent stroke. The results showed that PT stroke with preceding CMI did not influence the peripheral inflammatory cytokine production and H3 methylation inhibition did not alter the inflammatory status in the peripheral (Fig. ##SUPPL##0##S3C–F##). Similar results were also validated by MM102 administration, which was a high affinity peptidomimetic inhibitor of the WDR5/MLL1 complex (Figs. ##SUPPL##0##S4##, ##SUPPL##0##S5##).</p>", "<title>CMI primes the microglial-trained immunity through NLRP3 in contralateral cortex</title>", "<p id=\"Par41\">NLRP3, which is critical in mediating the cleavage of the IL-1β, has recently been reported to mediate trained immunity [##REF##30967658##20##]. To investigate the effect of NLRP3 in trained immunity on recurrent stroke, the expression of NLRP3 was first measured in microglia isolated from the cortex contralateral to the CMI. The NLRP3 expression robustly increased within the first 2 weeks and gradually returned to the baseline level over the next 2 weeks (Fig. ##FIG##3##4A## and Fig. ##SUPPL##0##S6A–C##). However, IL-1β production and other proinflammatory cytokines remained at the baseline level (Fig. ##FIG##3##4B–E##), indicating that NLRP3 functioned in an inflammasome-independent manner. The localization of NLRP3 in isolated microglia was therefore examined. The results showed that NLRP3 expression was significantly higher in the nuclei within the first two weeks after CMI, whereas its expression in the cytoplasm remained unchanged (Fig. ##FIG##3##4A##). The nuclear localization of NLRP3 was further confirmed by immunofluorescent staining in the contralateral cortex in mice 1 week post CMI (Fig. ##FIG##3##4F##). H3 was majorly methylated by the MLL1 complex, which is important in initiating trained immunity. Therefore, the interaction between NLRP3 and MLL1 was examined using immunoprecipitation on microglia isolated from the non-ischemic cortex one week after CMI. The results indicated that NLRP3 interacted with MLL1 in the microglia of CMI mice one week after the surgery while not in the sham group (Fig. ##FIG##3##4G##). The interaction was further confirmed in microglial nuclei using a proximity ligation assay (Fig. ##FIG##3##4H##). The ChIP-seq analysis further verified that the MLL1 peak found in the il1b showed a significant increased overlap with NLRP3 peak after CMI treatment (Fig. ##FIG##3##4I##).</p>", "<p id=\"Par42\">To identify potential interaction sites between MLL1 and NLRP3, sequence alignment analysis was first performed (Fig. ##FIG##3##4J##). The NACHT domain of NLRP3, specifically Cys277-Pro281 residues, emerged as an ideal docking site based on a favorable binding free energy of -9.884 kcal/mol. Therefore, we constructed mutant NLRP3 with deletion of one of the structural domains (LRR, NACHT, or PYD), packaged into AAV-MG1.2, and transduced into microglia though stereotactic injection into lateral ventricle of mice. One week after CMI, mice were sacrificed and subjected to immunoprecipitation assay. The result showed that the NACHT domain of NLRP3 was required for interacting with MLL1 (Fig. ##FIG##3##4K##). More importantly, the NACHT-deleted NLRP3 variant failed to induce the H3 modification on inflammatory genes (Fig. ##FIG##3##4L–O##). This underscores the importance of the NACHT domain for NLRP3 to interact with MLL1 and promote H3 modifications on inflammatory genes.</p>", "<p id=\"Par43\">Collectively, contralateral nuclear NLRP3 in the microglia was elevated in the chronic stage of microinfarct and interacted with MLL1, which mediate the activation of trained immunity.</p>", "<title>Microglial knockout of NLRP3 mitigated H3 methylation and attenuated CMI-induced detrimental effects on recurrent stroke</title>", "<p id=\"Par44\">To further determine the role of NLRP3 in the development of trained immunity following CMI, we used microglial conditional NLRP3 knockout mice (CX3CR1^CreER × NLRP3^fl/fl mice). The depletion of microglial NLRP3 was induced by tamoxifen administration after microinfarction (Fig. ##FIG##4##5A, B## and Fig. ##SUPPL##0##S6D–F##). Interestingly, the elevated H3K4me1 and H3K4me3 expression levels by CMI were abolished in mice (Fig. ##FIG##4##5C## and Fig. ##SUPPL##0##S6G, H##). And microglial NLRP3 knockout abolished H3K4me3 modification on TNF-α and IL-1β promoters (Fig. ##FIG##4##5D–G##).</p>", "<p id=\"Par45\">Most importantly, CMI-increased infarct size was mitigated in mice seven days post PT stroke (Fig. ##FIG##4##5H, I## and Fig. ##SUPPL##0##S6I, J##), while the microglia also showed mitigated activation, indicating by the reduced number and filament length. (Fig. ##FIG##4##5J–L##).</p>", "<title>Propagation of inflammatory cytokines after CMI initiates trained immunity in photothrombotic stroke cortex</title>", "<p id=\"Par46\">Although we verified that CMI could potentiate the detrimental effect of recurrent stroke through trained immunity in NLRP3-dependent manner, it is still unclear how CMI influenced the PT stroke in the contralateral side. Classically, trained immunity is induced by vaccinations and inflammatory stimulators, such as LPS [##REF##29328910##21##]. Therefore, pro-inflammatory cytokines, such as TNF-α and IL-1β, in the acute stage of CMI might mediate the activation of trained immunity. The inflammatory responses after CMI were determined. The inflammatory cytokine TNF-α, IL-6, IL-1β, and IL-10 levels were elevated and peaked 6 h after microinfarct in both ipsilateral and contralateral cortexes, whereas serum cytokines did not show significant changes (Fig. ##FIG##5##6A–E##). Interestingly, milder inflammatory responses were observed on the contralateral side at the same time (Fig. ##FIG##5##6D–E##), indicating that CMI was able to propagate whole-cortex inflammatory responses and these inflammatory cytokines might be the trigger to initiate the trained immunity in the contralateral cortex.</p>", "<p id=\"Par47\">Using mice, we further investigated the cellular sources of these inflammatory cytokines. The microglial knockout of NLRP3 significantly abolished the elevation of IL-1β in both ipsilateral and contralateral cortexes (Fig. ##FIG##5##6F–J##). Similarly, there was no alteration in serum cytokines observed, either with CMI or in the case of microglia NLRP3 knockout. As we previously found that microglial knockout of NLRP3 could abolish the trained effect on the contralateral cortex (Fig. ##FIG##4##5C–H##), it was reasonable to speculate that the activation of trained immunity on the contralateral cortex after CMIs was primed by the microglial inflammation from the ipsilateral cortex which was at least induced by the release of IL-1β.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par48\">The present study found that CMI increases the neuropathology of recurrent ischemic stroke via NLRP3-dependent trained immunity. CMI induced MLL1-dependent H3K4 methylation, increased the inflammatory responses, and exacerbated the outcome of subsequent PT stroke. The interaction between nuclear NLRP3 and MLL1 is critical in CMI-induced trained immunity as the knockout of microglial NLRP3 inhibits trained immunity and attenuates recurrent stroke. The study results also highlighted the influence of trained immunity on recurrent stroke and provided a novel insight on the influence of NLRP3 in this innate immunity memory formation.</p>", "<p id=\"Par49\">It is common for elderly individuals to experience CMIs [##REF##27664944##22##]. However, recurrent stroke risk is difficult to predict, as most CMIs cannot be detected via magnetic resonance imaging. It has been recently reported that diffusion-weighted imaging can detect and monitor acute CMIs for 2 weeks, which may provide a better intervention window [##REF##28716371##23##]. The present study found that a single CMI can induce epigenetic alterations (H3K4me1 and H3K4me3) in the contralateral cortex, suggesting that a single CMI may have a substantial impact on the brain at the epigenetic level. This impact is significant as it induces trained immunity, which leads to excessive immune activation and aggravates the consequences of subsequent strokes.</p>", "<p id=\"Par50\">It is not clear how CMIs induce trained immunity. Traditionally, it is triggered by vaccinations and inflammatory stimulators, such as LPS [##REF##29328910##21##]. However, endogenous alarm signals associated with tissue damage and sterile inflammation can also induce trained immunity through the epigenetic regulation of histone modifications, such as inflammatory cytokines, damage‐associated molecular patterns (DAMPs), Oxidized Low-density Lipoprotein (oxLDL), and High-density Lipoprotein HDL [##REF##26970440##24##]. It has been reported that DAMPs activate TLR2 to epigenetically modify histone methylation, while peripheral low-dose TNF-α can activate trained immunity in the brain [##REF##29230022##25##]. Consistently, the present study results demonstrated that TNF-α, IL-6, and IL-1β levels were elevated in the contralateral cortex in a similar but milder pattern to that in the ipsilateral CMI cortex, which indicated that CMI-induced trained immunity was based on the release of inflammatory cytokines. Alternatively, released inflammatory cytokines from CMIs might reach the contralateral cortex through cerebrospinal fluid, as evidenced by the fact that peripheral serum inflammatory cytokine levels did not elevate after CMI. The epigenetic modification caused by this damage signal further worsens the outcome of subsequent strokes.</p>", "<p id=\"Par51\">Ischemic preconditioning (IPC) demonstrates an impressive capacity to protect against future strokes [##REF##28110083##26##]. IPC could be induced not only by transient cerebral ischemic event (TIA) but also by ischemia. In addition to trigger an elevation in HIF-1a expression in both neurons and astrocytes, IPC is also reported to reduce H3K4 methylation [##REF##27785755##27##, ##REF##34694864##28##]. In contrast, CMI can increase the H3K4 methylation and promote the epigenetic modification in proinflammatory-related gene, indicating completely different signaling pathways underlying these two conditions [##REF##23868468##29##].</p>", "<p id=\"Par52\">Histone modifications with chromatin reconfiguration are a central process in trained immunity [##REF##34320411##30##]. As a super-enhancer, H3K4me1/3 modifications unfold the chromatin, enabling easier transcription of the modified gene sequences. This deposition of H3K4 methylation is mainly accomplished by MLL family histone methyltransferases, particularly MLL1 [##REF##17957188##31##]. In the present study, CMI induced the interaction between MLL1 and NLRP3 in microglial nuclei. Interestingly, the interaction did not lead to the activation of the NLRP3 inflammasome. The IL-1β production remained unchanged in microglia after a single CMI. Instead, the interaction was related to an increase in H3K4me1 and H3K4me3 expression. Furthermore, a knockout of microglial NLRP3 significantly inhibited MLL1 elevation, suggesting that NLRP3 mediated CMI-induced trained immunity through the interaction with MLL1 independently of inflammasomes. Indeed, NLRP3 has been reported to have several inflammasome-independent functions in immunity, although IL-1β and IL-18 secretion from activated NLRP3 inflammasomes is important for various innate and adaptive immune responses. For example, NLRP3 can interact with both DNA and transcription factor IRF4 to mediate the differentiation of Th2 cells [##REF##26098997##32##].</p>", "<p id=\"Par53\">NLRP3 has been a therapeutic target in the treatment of cerebrovascular diseases [##REF##35680186##33##]. However, it is debated whether NLRP3 inhibition can reduce infarct volume in experimental ischemic stroke [##REF##31009361##34##]. Previously, our group found that NLRP3 could aggravate the recurrent ischemic strokes following a single infarction in an inflammasome-dependent manner [##REF##33051464##35##]. The data from this study further revealed that NLRP3 had an inflammasome-independent role in exacerbating subsequent stroke. Therefore, NLPR3 is a critical candidate to influence the recurrent ischemic strokes and proper therapeutic intervention is needed to rectify this abnormal immune activation.</p>", "<p id=\"Par54\">There are some limitations in the present study. Although we found that IL-1β could induce the trained immunity in the contralateral cortex after CMI, whether the release of other inflammatory cytokines, such as IL-6, TNF-α, could promote the formation of trained immunity worth further study. Besides, further research is required to address the function of caspase-1 and ASC in microglial nuclei. Researchers should also investigate other functional roles of NLRP3 in the nuclei of inflammatory cells. Moreover, microinfarcts are just one type of vascular disease and the influence of other small vascular diseases (SVDs) on recurrent stroke requires more research.</p>", "<p id=\"Par55\">The present study is the first to reveal the epigenetic regulation role of NLRP3 in innate immune memory, as it increases H3K4me1 and H3K4me3 levels through its interaction with the MLL1 complex. This innate immune memory formation influences the pathology of recurrent stroke in mice with CMI. Therefore, NLRP3 may provide an alternative therapeutic target to mitigate the detrimental effect of CMI and subsequent stroke.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par56\">The present study confirmed that a single CMI event can significantly exacerbate the outcome of subsequent stroke. This relationship was likely present because the microinfarct triggered the formation of innate immunity memory in microglia in a NLRP3-dependent manner, which epigenetically primes the inflammatory genes ready for transcription after the microinfarct. Our results highlighted the clinical relevance of microinfarct on subsequent stroke and pointed out the importance of NLRP3 as a potential therapeutic target to mitigate recurrent stroke in CMI patients.</p>" ]

[ "<p id=\"Par1\">Microinfarcts are common among the elderly and patients with microinfarcts are more vulnerable to another stroke. However, the impact of microinfarcts on recurrent stroke has yet to be fully understood. The purpose of this study was to explore the negative effects of microinfarcts on recurrent stroke. To achieve this, two-photon laser was used to induce microinfarcts, while photothrombotic stroke was induced on the opposite side. The results showed that microinfarcts led to trained immunity in microglia, which worsened the pro-inflammatory response and ischemic injury in the secondary photothrombotic stroke. Additionally, the study clarified the role of NLRP3 in microglial nuclei, indicating that it interacts with the MLL1 complex through NACHT domain and increases H3K4 methylation, which suggests that NLRP3 is critical in the formation of innate immune memory caused by microinfarcts. Furthermore, the knockout of NLRP3 in microglia alleviated the trained immunity and reduced the harmful effects of microinfarcts on recurrent stroke. This study emphasizes the detrimental effect of trained immunity on recurrent stroke and highlights the critical role of NLRP3 in mediating the formation of this memory, which may offer a potential therapeutic target for mitigating recurrent strokes.</p>", "<title>Subject terms</title>" ]

[ "<title>Facts</title>", "<p id=\"Par2\">\n<list list-type=\"bullet\"><list-item><p id=\"Par3\">Single microinfarct could worsen the subsequent stroke event through the long-term activation of trained immunity in microglia.</p></list-item><list-item><p id=\"Par4\">H3K4 methylation by MLL1 is critical in initiating the microinfarct-induced trained immunity.</p></list-item><list-item><p id=\"Par5\">NLRP3 is elevated in the microglial nuclei following microinfarct and subsequently activates trained immunity through MLL1-mediated methylation of H3K4.</p></list-item><list-item><p id=\"Par6\">Knockout out of NLRP3 substantially alleviates the trained immunity and protects secondary stroke event.</p></list-item></list>\n</p>", "<title>Supplementary information</title>", "<p>\n\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41419-023-06414-7.</p>", "<title>Author contributions</title>", "<p>YF and LL designed the experiments. YF, TW, YF, and GL performed the experiments. YG and SL provided technical support. YZ, GX, and ZP provided financial support. YF and ZP drafted the manuscript.</p>", "<title>Funding</title>", "<p>This study was supported by grants from the National Natural Science Foundation of China (No.82071255, No.82271266, No.82201468, No. 81873751, No. 82101330, No. 82072548, No. 82272588), the Guangdong Provincial Key Laboratory of Diagnosis and Treatment of Major Neurological Diseases (2020B1212060017), Guangdong Provincial Clinical Research Center for Neurological Diseases (2020B1111170002), Southern China International Joint Research Center for Early Intervention and Functional Rehabilitation of Neurological Diseases (2015B050501003 and 2020A0505020004), Guangdong Provincial Engineering Center for Major Neurological Disease Treatment, Guangdong Provincial Translational Medicine Innovation Platform for Diagnosis and Treatment of Major Neurological Disease, Guangzhou Clinical Research and Translational Center for Major Neurological Diseases (201604020010).</p>", "<title>Data availability</title>", "<p>The datasets generated and/or analyzed during the current study are available in the supplementary material.</p>", "<title>Competing interests</title>", "<p id=\"Par57\">The authors declare no competing interests.</p>", "<title>Ethics approval and consent to participate</title>", "<p id=\"Par58\">All protocols were performed according to the Guide for the Care and Use of Laboratory Animals of Sun Yat-sen University (Guangzhou, China) Committee.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>CMI initiates trained immunity and exacerbates secondary stroke in contralateral cortex.</title><p><bold>A</bold> Representative three-dimensional two-photon images showing CMI induction. Scale bar, 1 mm. <bold>B</bold> Representative Nissl staining showing the ischemic location and pathologies of CMI and PT. Scale bar, 2 mm. <bold>C</bold>–<bold>E</bold> Representative Nissl and Iba1 IHC staining and quantitative analysis of infarct size and microglial activation after one-day post-PT stroke. Scale bar, 200 μm for Nissl staining and 50 μm for Iba1 staining, <italic>n</italic> = 12 mice per group. One-way ANOVA <italic>F</italic>_{2, 33} = 468.2, <italic>p</italic> &lt; 0.0001. PT vs. CMI+PT: <italic>p</italic> = 0.7213. (<bold>D</bold>) and <italic>F</italic>_{2, 33} = 7.497, <italic>p</italic> = 0.0021. PT vs. CMI+PT: <italic>p</italic> = 0.7471 (<bold>E</bold>) with Turkey’s correction. <bold>F-I</bold> Quantitative ELISA analysis of TNF-α (<bold>F</bold>), IL-6 (<bold>G</bold>), IL-1β (<bold>H</bold>), and IL-10 (<bold>I</bold>) expression in contralateral cortex 6 h after CMI. One-way ANOVA <italic>F</italic>_{2, 33} = 97.44, <italic>p</italic> &lt; 0.0001. PT vs CMI+PT: <italic>p</italic> = 0.0013 (<bold>F</bold>); <italic>F</italic>_{2, 33} = 76.13, <italic>p</italic> &lt; 0.0001. PT vs CMI+PT: <italic>p</italic> = 0.0511 (<bold>G</bold>); <italic>F</italic>_{2, 33} = 16.58, <italic>p</italic> &lt; 0.0001. PT vs. CMI+PT: <italic>p</italic> = 0.0214 (<bold>H</bold>); <italic>F</italic>_{2, 33} = 28.71, <italic>p</italic> &lt; 0.0001. PT vs. CMI+PT: <italic>p</italic> = 0.0020 (<bold>I</bold>). <bold>J</bold>–<bold>M</bold> Representative Nissl and Iba1 IHC staining and quantitative analysis of infarct size and microglial activation after seven-day post-PT stroke. Scale bar, 200 μm for Nissl staining and 50 μm for Iba1 staining, <italic>n</italic> = 12 mice per group. One-way ANOVA <italic>F</italic>_{2, 33} = 314.8, <italic>p</italic> &lt; 0.0001. PT vs. CMI+PT: <italic>p</italic> = 0.0009 (<bold>K</bold>) and <italic>F</italic>_{2, 33} = 50.87, <italic>p</italic> &lt; 0.0001. PT vs. CMI+PT: <italic>p</italic> = 0.0331 (<bold>L</bold>). Data are presented as mean ± standard deviation (SD), n.s., non-significant, *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, and ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>CMI initiated microglial trained immunity in the contralateral cortex.</title><p>Representative GFAP and Iba1 IHC staining (<bold>A</bold>) and quantitative analysis for Iba-1 (<bold>B–D</bold>) and GFAP- (<bold>E</bold>) positive astrocytes around the contralateral cortex following CMI, <italic>n</italic> = 12 mice per group. One-way ANOVA <italic>F</italic>_{4, 55} = 2.808, <italic>p</italic> = 0.0342. Sham vs. 1w: <italic>p</italic> = 0.2748; Sham vs. 2w: <italic>p</italic> = 0.8075; Sham vs. 3w: <italic>p</italic> = 0.9621; Sham vs. 4w: <italic>p</italic> = 0.9515 (<bold>B</bold>); <italic>F</italic>_{4, 55} = 34.01, <italic>p</italic> &lt; 0.0001; Sham vs. 1w: <italic>p</italic> &lt; 0.001; Sham vs. 2w: <italic>p</italic> &lt; 0.001; Sham vs. 3w: <italic>p</italic> = 0.0142; Sham vs. 4w: <italic>p</italic> = 0.9215 (<bold>C</bold>); and <italic>F</italic>_{4, 55} = 9.049, <italic>p</italic> &lt; 0.0001; Sham vs. 1w: <italic>p</italic> = 0.0008; Sham vs. 2w: <italic>p</italic> = 0.0017; Sham vs. 3w: <italic>p</italic> = 0.0540; Sham vs 4w: <italic>p</italic> = 0.9999 (<bold>E</bold>) with Tukey’s correction. Scale bars, 25 μm. <bold>F</bold> Schematic diagram of experimental design. <bold>G</bold> Top 10 Gene Ontology (GO) enrichment terms from H3K4me3 ChIP-seq in contralateral microglia one week after CMI induction. <bold>H</bold> Top 10 Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment components from H3K4me3 ChIP-seq in contralateral microglia one week after CMI induction. Quantitative analysis of H3K4me3 ChIP-qPCR on TNF-α (<bold>I</bold>), IL-6 (<bold>J</bold>), IL-1β (<bold>K</bold>), and IL-10 (<bold>L</bold>) promoters in contralateral microglia after CMI induction, <italic>n</italic> = 12 mice per group. One-way ANOVA. <italic>F</italic>_{4, 55} = 7.884, <italic>p</italic> &lt; 0.0001; Sham vs CMI1w: <italic>p</italic> = 0.0434; Sham vs. CMI 2w: <italic>p</italic> &lt; 0.0001; Sham vs. CMI 3w: <italic>p</italic> = 0.0218; Sham vs. CMI 4w: <italic>p</italic> = 0.0256 (<bold>I</bold>); <italic>F</italic>_{4, 55} = 5.031, <italic>p</italic> = 0.0016; Sham vs. CMI1w: <italic>p</italic> = 0.0091; Sham vs. CMI 2w: <italic>p</italic> = 0.9744; Sham vs. CMI 3w: <italic>p</italic> = 0.9477; Sham vs. CMI 4w: <italic>p</italic> = 0.9488 (<bold>J</bold>); <italic>F</italic>_{4, 55} = 11.98, <italic>p</italic> &lt; 0.0001; Sham vs. CMI1w: <italic>p</italic> &lt; 0.0001; Sham vs. CMI 2w: <italic>p</italic> = 0.0037; Sham vs. CMI 3w: <italic>p</italic> = 0.7670; Sham vs. CMI 4w: <italic>p</italic> = 0.0183 (<bold>K</bold>); and <italic>F</italic>_{4, 55} = 1.38, <italic>p</italic> = 0.253; Sham vs CMI1w: <italic>p</italic> = 0.6866; Sham vs. CMI 2w: <italic>p</italic> = 0.5709; Sham vs CMI 3w: <italic>p</italic> = 0.2671; Sham vs. CMI 4w: <italic>p</italic> = 0.2671 (<bold>L</bold>) with Tukey’s correction. Data are presented as mean ± standard deviation (SD), n.s., non-significant, *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, and ***<italic>p</italic> &lt; 0.001.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Inhibition of H3 methylation abolished the detrimental effect of CMI on recurrent PT stroke.</title><p><bold>A</bold> Schematic diagram of experimental design. <bold>B</bold>–<bold>D</bold> Immunoblots and quantitative analysis of H3K4me1/3 showing microglial H3K4me1/3 expression in contralateral mouse cortex subjected to CMI and MLL1-shRNA treatment, <italic>n</italic> = 12 mice per group. Two-way ANOVA, for interaction: <italic>p</italic> &lt; 0.0001. So, t-tests were used to detect the difference between groups. Sham vs. CMI: <italic>p</italic> &lt; 0.0001; CMI vs. CMI+ MLL1-shRNA: <italic>p</italic> &lt; 0.0001 (<bold>C</bold>) For interaction: <italic>p</italic> = 0.0774. For MLL1-shRNA factor: <italic>p</italic> &lt; 0.0001. For CMI factor: <italic>p</italic> &lt; 0.0001. Sham vs. CMI: <italic>p</italic> &lt; 0.0001; CMI vs. CMI+ MLL1-shRNA: <italic>p</italic> &lt; 0.0001 (<bold>D</bold>) with Turkey’s correction. Quantitative analysis of H3K4me3 ChIP-qPCR on TNF-α (<bold>E</bold>), IL-6 (<bold>F</bold>), IL-1β (<bold>G</bold>), and IL-10 (<bold>H</bold>) promoters in contralateral microglia 4 weeks after CMI and MLL1-shRNA treatment, <italic>n</italic> = 12 mice per group. Two-way ANOVA, for interaction <italic>p</italic> = 0.8532. For MLL1-shRNA factor, <italic>p</italic> &lt; 0.0001. CMI vs. CMI+ MLL1-shRNA: <italic>p</italic> = 0.0129 (<bold>E</bold>); For interaction <italic>p</italic> = 0.3404. For MLL1-shRNA factor, <italic>p</italic> &lt; 0.0001. CMI vs. CMI+MLL1-shRNA: <italic>p</italic> = 0.0238 (<bold>F</bold>); For interaction <italic>p</italic> = 0.7885. For MLL1-shRNA factor, <italic>p</italic> = 0.0002. CMI vs. CMI+ MLL1-shRNA: <italic>p</italic> = 0.0165 (<bold>G</bold>); For interaction <italic>p</italic> = 0.2121. For MLL1-shRNA factor, <italic>p</italic> = 0.0645. CMI vs. CMI+MLL1-shRNA: <italic>p</italic> = 0.9701 (<bold>H</bold>) with Tukey’s correction. <bold>I</bold>–<bold>M</bold> Immunoblots and quantitative analysis of TNF-α (<bold>J</bold>), IL-6 (<bold>K</bold>), IL-1β (<bold>L</bold>), and IL-10 (<bold>M</bold>) showing pro-inflammatory cytokine expression in peri-infarct region 12 h after PT stroke, <italic>n</italic> = 12 mice per group. Three-way ANOVA. For interaction, <italic>p</italic> &lt; 0.0001. So, t-tests were used to detect the difference between groups. PT vs. CMI+PT: <italic>p</italic> &lt; 0.0001; CMI+PT vs. CMI+PT+MLL1-shRNA: <italic>p</italic> &lt; 0.0001 (<bold>J</bold>); For interaction, <italic>p</italic> = 0.0026. So, t-tests were used to detect the difference between groups. PT vs. CMI+PT: <italic>p</italic> = 0.0056; CMI+PT vs. CMI+PT+MLL1-shRNA: <italic>p</italic> = 0.8656 (<bold>K</bold>); For interaction, <italic>p</italic> &lt; 0.0001. So, t-tests were used to detect the difference between groups. PT vs. CMI+PT: <italic>p</italic> &lt; 0.0001; CMI+PT vs. CMI+PT+MLL1-shRNA: <italic>p</italic> &lt; 0.0001 (<bold>L)</bold> For interaction, <italic>p</italic> = 0.7475. PT vs. CMI+PT: <italic>p</italic> = 0.7733; CMI+PT vs. CMI+PT+MLL1-shRNA: <italic>p</italic> = 0.0188 (<bold>M</bold>) with Tukey’s correction. Representative Nissl and Iba1 IHC staining (<bold>N</bold>) and quantitative analysis of infarct size and microglial activation (<bold>O</bold>–<bold>R</bold>) showing PT stroke exacerbated by CMI was potentially mitigated by H3 methylation inhibition, <italic>n</italic> = 12 mice per group. Two-way ANOVA. For interaction, <italic>p</italic> = 0.0205. So, t-tests were used to detect the difference between groups. CMI+PT vs. CMI+PT+MLL1-shRNA: <italic>p</italic> = 0.0046 (<bold>O</bold>); For interaction, <italic>p</italic> = 0.2487. CMI+PT vs. CMI+PT+ MLL1-shRNA: <italic>p</italic> = 0.0228 (<bold>Q</bold>); For interaction, <italic>p</italic> &lt; 0.0001. So, t-tests were used to detect the difference between groups. CMI+PT vs. CMI+PT++ MLL1-shRNA: <italic>p</italic> = 0.0001 (<bold>R</bold>) with Tukey’s correction. Scale bar, 200 μm for Nissl staining and 50 μm for Iba1 staining. Data are presented as mean ± standard deviation (SD), *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, ***<italic>p</italic> &lt; 0.001, n.s., non-significant.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>CMI-induced interaction of NLRP3 with MLL1 in contralateral cortex.</title><p><bold>A</bold> Immunoblots of NLRP3 expression in microglial whole-cell, cytoplasmic, and nuclear lysis after CMI, <italic>n</italic> = 12 mice per group. Quantitative ELISA analysis of TNF-α (<bold>B</bold>), IL-6 (<bold>C</bold>), IL-1β (<bold>D</bold>) and IL-10 (<bold>E</bold>) expression in the contralateral side of CMI showing that CMI did not influence the inflammatory cytokines expression in the chronic phase of CMI. (<italic>n</italic> = 12 mice per group). One-way ANOVA <italic>F</italic>\n_{4, 55} = 8.251, <italic>p</italic> &lt; 0.0001. Sham vs. CMI1w: <italic>p</italic> = 0.0867; Sham vs. CMI 2w: <italic>p</italic> = 0.9064; Sham vs. CMI 3w: <italic>p</italic> &lt; 0.0001; Sham vs. CMI 4w: <italic>p</italic> = 0.0331 (<bold>B</bold>); F _{4, 55} = 3.113, <italic>p</italic> = 0.0222. Sham vs. CMI1w: <italic>p</italic> = 0.9992; Sham vs. CMI 2w: <italic>p</italic> = 0.9211; Sham vs. CMI 3w: <italic>p</italic> = 0.0390; Sham vs. CMI 4w: <italic>p</italic> = 0.9554 (<bold>C</bold>); F_{4, 55} = 10.62, <italic>p</italic> &lt; 0.0001. Sham vs. CMI1w: <italic>p</italic> = 0.2167; Sham vs. CMI 2w: <italic>p</italic> = 0.5763; Sham vs. CMI 3w: <italic>p</italic> = 0.9177; Sham vs. CMI 4w: <italic>p</italic> = 0.0027 (<bold>D</bold>); F_{4, 55} = 4.098, <italic>p</italic> = 0.0056. Sham vs. CMI1w: <italic>p</italic> = 0.4233; Sham vs. CMI 2w: <italic>p</italic> &gt; 0.9999; Sham vs. CMI 3w: <italic>p</italic> = 0.0266; Sham vs. CMI 4w: <italic>p</italic> = 0.9984 (<bold>E</bold>) with Tukey’s correction. <bold>F</bold> Representative immunofluorescence images of NLRP3 (red) expression in microglia (iba1, green) one week after CMI. Scale bars, 20 μm. <bold>G</bold> Immunoprecipitation and immunoblot analysis of MLL1 and NLRP3 in microglial lysates from mice subjected to sham and CMI. Lysates were immunoprecipitated by anti-MLL1 (IP) or immunoglobulin control (IgG) or directly subjected to immunoblot (Input), <italic>n</italic> = 3 mice per group. <bold>H</bold> Proximity ligation assay of microglial (iba1, green) NLRP3 and MLL1 (red dots) in sham and one-week post-CMI mice. Scale bars, 20 μm. <bold>I</bold> ChIP-seq analysis of NLRP3 and MLL1 binding to IL-1β in one-week post-CMI mice. <bold>J</bold> Representative images of sequence alignments showing interaction of NLRP3 (blue) with MLL1 (green). <bold>K</bold> Immunprecipitation and immunoblot analysis of MLL1 and Flag in microglial lysates from Cxc3r1^CreER mice transfected with 3xFlag-NLRP3 or truncated mutants (ΔPYD, ΔNACHT, ΔLRR) and subjected to CMI surgery. Lysates were immunoprecipitated by anti-MLL1 (IP) or immunoglobulin control (IgG) or directly subjected to immunoblot (Input), <italic>n</italic> = 3 mice per group. Quantitative analysis of H3K4me3 ChIP-qPCR on TNF-α (<bold>L</bold>), IL-6 (<bold>M</bold>), IL-1β (<bold>N</bold>), and IL-10 (<bold>O</bold>) promoters in contralateral microglia one week after CMI. Cxc3r1^CreER mice transfected with 3xFlag-NLRP3 or truncated mutants (ΔPYD, ΔNACHT, ΔLRR) and subjected to CMI surgery. One-way ANOVA, <italic>F</italic>\n_{4, 55} = 42.25, <italic>p</italic> &lt; 0.0001;Empty vs Full Length, <italic>p</italic> &lt; 0.0001; Full Length vs ΔPYD: <italic>p</italic> = 0.7675; Full length vs ΔNACHT, <italic>p</italic> &lt; 0.0001; Full Length vs ΔLRR: <italic>p</italic> = 0.1030 (<bold>L</bold>); <italic>F</italic>\n_{4, 55} = 8.732, <italic>p</italic> &lt; 0.0001; Empty vs. Full Length, <italic>p</italic> = 0.0077; Full Length vs ΔPYD: <italic>p</italic> = 0.9998; Full length vs ΔNACHT, <italic>p</italic> = 0.0001; Full Length vs. ΔLRR: <italic>p</italic> = 0.3921(<bold>M</bold>); <italic>F</italic>\n_{4, 55} = 122.5, <italic>p</italic> &lt; 0.0001;Empty vs. Full Length, <italic>p</italic> &lt; 0.0001; Full Length vs ΔPYD: <italic>p</italic> = 0.9868; Full length vs. ΔNACHT, <italic>p</italic> &lt; 0.0001; Full Length vs. ΔLRR: <italic>p</italic> = 0.2638 (<bold>N</bold>); <italic>F</italic>\n_{4, 55} = 2.246, <italic>p</italic> = 0.0758; Empty vs Full Length, <italic>p</italic> &gt; 0.9999; Full Length vs ΔPYD: <italic>p</italic> = 0.9988; Full length vs ΔNACHT, <italic>p</italic> = 0.5413; Full Length vs. ΔLRR: <italic>p</italic> = 0.6035(<bold>O</bold>). <italic>n</italic> = 12 mice per group. Data are presented as mean ± standard deviation (SD). *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, ***<italic>p</italic> &lt; 0.001, n.s., non-significant.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Knockout of microglial NLRP3 mitigated MLL1, reduced H3 methylation, and attenuated CMI-induced detrimental effects on recurrent stroke.</title><p><bold>A</bold> Schematic diagram of experimental design. <bold>B</bold> Immunoblot of microglial NLRP3 expression in WT and mice four weeks after CMI induction, <italic>n</italic> = 12 mice per group. <bold>C</bold> Immunoblot of microglial H3K4me1/3 expression in WT and mice four weeks after CMI induction, <italic>n</italic> = 12 mice per group. Quantitative analysis of H3K4me3 ChIP-qPCR on TNF-α (<bold>D</bold>), IL-6 (<bold>E</bold>), IL-1β (<bold>F</bold>), and IL-10 (<bold>G</bold>) promoters among contralateral microglia four weeks after CMI induction in WT and mice, <italic>n</italic> = 12 mice per group. Two-way ANOVA, for interaction: <italic>p</italic> = 0.0110. So, t-tests were used to detect the difference between groups. CMI vs. CMI+: <italic>p</italic> = 0.0053 (<bold>D</bold>); For interaction: <italic>p</italic> = 0.7059. CMI vs. CMI+: <italic>p</italic> = 0.9965 (<bold>E</bold>); For interaction: <italic>p</italic> = 0.0106. So, t-tests were used to detect the difference between groups. CMI vs. CMI+: <italic>p</italic> = 0.0341 (<bold>F</bold>); For interaction: <italic>p</italic> = 0.0003. So, t-tests were used to detect the difference between groups. CMI vs. CMI+: <italic>p</italic> = 0.6246 (<bold>G</bold>) with Tukey’s correction. Representative Nissl and Iba1 IHC staining (<bold>H</bold>) and quantitative analysis of infarct size and microglial activation (<bold>I</bold>–<bold>L</bold>) showing that NLRP3 blockade in microglia after CMI abolished the exacerbated infarct size and microglial activation by CMI, <italic>n</italic> = 12 mice per group. Two-way ANOVA, for interaction: <italic>p</italic> = 0.6293. CMI vs. CMI+: <italic>p</italic> = 0.0231 (<bold>I</bold>), for interaction: <italic>p</italic> = 0.2277. CMI vs CMI+: <italic>p</italic> = 0.0034 (<bold>K</bold>), for interaction: <italic>p</italic> = 0.0617. CMI vs. CMI+: <italic>p</italic> = 0.0229 (<bold>L</bold>) with Tukey’s correction. Data are presented as mean ± standard deviation (SD), *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, ***<italic>p</italic> &lt; 0.001, n.s. non-significant.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Propagation of inflammatory cytokines after CMI initiates trained immunity in photothrombotic stroke cortex.</title><p><bold>A</bold> Schematic diagram of experimental design. Quantitative ELISA analysis of TNF-α (<bold>B</bold>), IL-6 (<bold>C</bold>), IL-1β (<bold>D</bold>), and IL-10 (<bold>E</bold>) expression in ipsilateral cortex, contralateral cortex, and peripheral serum after PT stroke, <italic>n</italic> = 12 mice per group. One-way ANOVA was used to analyze the data. For TNF-α analysis, ipsilateral cytokines: <italic>F</italic>_{4, 55} = 70.40, <italic>p</italic> &lt; 0.0001; Sham vs. CMI 6h: <italic>p</italic> &lt; 0.0001; Contralateral cytokines: <italic>F</italic>_{4, 55} = 147.1, <italic>p</italic> &lt; 0.0001; Sham vs. CMI 6h: <italic>p</italic> &lt; 0.0001. Serum cytokines: <italic>F</italic>_{4, 55} = 2.047, <italic>p</italic> = 0.1004; Sham vs. CMI 3h: <italic>p</italic> = 0.6059 (<bold>B</bold>). For IL-6 analysis, ipsilateral cytokines: <italic>F</italic>_{4, 55} = 56.01, <italic>p</italic> &lt; 0.0001; Sham vs. CMI 6h: <italic>p</italic> &lt; 0.0001. Contralateral cytokines: <italic>F</italic>_{4, 55} = 23.23, <italic>p</italic> &lt; 0.0001; Sham vs. CMI 6h: <italic>p</italic> &lt; 0.0001. Serum cytokines: <italic>F</italic>_{4, 55} = 4.546, <italic>p</italic> = 0.0030; Sham vs. CMI 6h: <italic>p</italic> = 0.7525 (<bold>C</bold>). For IL-1βanalysis, ipsilateral cytokines: <italic>F</italic>_{4, 55} = 7.952, <italic>p</italic> &lt; 0.0001; Sham vs. CMI 6h: <italic>p</italic> = 0.0004. Contralateral cytokines: <italic>F</italic>_{4, 55} = 34.73, <italic>p</italic> &lt; 0.0001; Sham vs. CMI 6h: <italic>p</italic> &lt; 0.0001. Serum cytokines: <italic>F</italic>_{4, 55} = 3.635, <italic>p</italic> = 0.0107; Sham vs. CMI 6h: <italic>p</italic> = 0.0207 (<bold>D</bold>). For IL-10 analysis, ipsilateral cytokines: <italic>F</italic>_{4, 55} = 35.99, <italic>p</italic> &lt; 0.001; Sham vs. CMI 6h: <italic>p</italic> &lt; 0.0001. Contralateral cytokines: <italic>F</italic>_{4, 55} = 11.86, <italic>p</italic> &lt; 0.0001; Sham vs. CMI 6h: <italic>p</italic> &lt; 0.0001. Serum cytokines: <italic>F</italic>_{4, 55} = 5.919, <italic>p</italic> = 0.0005; Sham vs. CMI 6h: <italic>p</italic> = 0.0047 (<bold>E</bold>) with Tukey’s correction. <bold>F</bold> Schematic diagram of experimental design. Quantitative ELISA analysis of TNF-α (<bold>G</bold>), IL-6 (<bold>H</bold>), IL-1β (<bold>I</bold>), and IL-10 (<bold>J</bold>) expression in ipsilateral cortex, contralateral cortex, and peripheral serum after PT stroke in WT and mice. <italic>n</italic> = 12 mice per group. Two-way ANOVA for analysis. Ipsilateral cytokines: for interaction: <italic>p</italic> = 0.0166. So t-tests was used to detect the difference between groups. CMI vs CMI+: <italic>p</italic> = 0.0233. Contralateral cytokines: for interaction: <italic>p</italic> = 0.0489. CMI vs. CMI+: <italic>p</italic> &lt; 0.0001. Serum cytokine: for interaction: <italic>p</italic> = 0.2285. CMI vs. CMI+: <italic>p</italic> = 0.8071 (<bold>G</bold>); For IL-6 analysis, ipsilateral cytokines: for interaction: <italic>p</italic> = 0.0052. CMI vs. CMI+: <italic>p</italic> = 0.0100. Contralateral cytokines: for interaction: <italic>p</italic> = 0.0544. CMI vs. CMI+: <italic>p</italic> = 0.0317. Serum cytokine: for interaction: <italic>p</italic> = 0.1273. CMI vs. CMI+: <italic>p</italic> = 0.3334 (<bold>H</bold>); For IL-1βanalysis, ipsilateral cytokines: for interaction: <italic>p</italic> = 0.0040. CMI vs. CMI+: <italic>p</italic> = 0.0031. Contralateral cytokines: for interaction: <italic>p</italic> &lt; 0.0001. CMI vs. CMI+: <italic>p</italic> &lt; 0.0001. Serum cytokine: for interaction: <italic>p</italic> = 0.0774. CMI vs. CMI+: <italic>p</italic> = 0.6185 (<bold>I</bold>); For IL-10 analysis, ipsilateral cytokines: for interaction: <italic>p</italic> = 0.9477. CMI vs. CMI+: <italic>p</italic> = 0.9222. Contralateral cytokines: for interaction: <italic>p</italic> = 0.6117. CMI vs. CMI+: <italic>p</italic> = 0.9997. Serum cytokine: for interaction: <italic>p</italic> = 0.3239. CMI vs. CMI+: <italic>p</italic> = 0.9192 (<bold>J</bold>) with Turkey’s corrections. Data are presented as mean ± standard deviation (SD), *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.01, ***<italic>p</italic> &lt; 0.001, n.s. non-significant.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM4\"></supplementary-material>" ]

[ "<fn-group><fn><p>Edited by Dr. Akira Sawa</p></fn><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Yiwei Feng, Lishan Lin.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41419_2023_6414_MOESM1_ESM.docx\"><caption><p>Supplementary information</p></caption></media>", "<media xlink:href=\"41419_2023_6414_MOESM2_ESM.pdf\"><caption><p>aj-checklist</p></caption></media>", "<media xlink:href=\"41419_2023_6414_MOESM3_ESM.pdf\"><caption><p>Suplemantery material---WB</p></caption></media>", "<media xlink:href=\"41419_2023_6414_MOESM4_ESM.xlsx\"><caption><p>Original Data File</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Social distancing and isolation are among the most effective methods to mitigate the spread of viral outbreaks. Especially early in a pandemic when little is known and other interventions are unavailable, preventing physical proximity between susceptible individuals can reduce virus transmissions and protect vulnerable populations^{##REF##32213647##1##–##REF##32213329##3##}. At the start of the COVID-19 pandemic in the United States, public health officials requested that the public avoid large gatherings and limit contact with others as part of a social distancing initiative^{##UREF##1##4##}. Subsequent research demonstrated the effectiveness of these social distancing guidelines^{##UREF##2##5##–##REF##32305155##7##}. However, mixed compliance with these recommendations limited their effectiveness. A number of factors may negatively affect social distancing, including financial factors, the housing environment, and distrust of public officials^{##REF##33727410##8##–##REF##31913322##11##}. Furthermore, experiences during the pandemic have motivated calls for research into models that include the likelihood of compliance related to social factors in pandemic forecasting models^{##REF##33388037##12##–##REF##32836442##15##}. Understanding who adheres to social distancing and what factors influence these practices may be critical to ensuring the effectiveness of these practices.</p>", "<p id=\"Par3\">One way we can measure compliance is through online mobility data, a quantitative measure of travel patterns^{##REF##32205458##16##}. Near real-time measures of mobility from, for example, GPS-enabled mobile phones, offer a massive, detailed indicator of mobility patterns, and have thus been used during the COVID-19 pandemic^{##UREF##5##17##–##UREF##7##19##}. In contrast, traditional survey data can be time-consuming to collect and suffers from response bias^{##REF##10435838##20##}. However, a drawback of these data compared to surveys is that they are only available in aggregated form, and thus cannot associate mobility with other factors. Critically, we cannot answer who has reduced their mobility, and what factors are related to this decision.</p>", "<p id=\"Par4\">Following research that uses social media data for public health^{##UREF##8##21##–##UREF##11##25##}, work during the COVID-19 pandemic (and in previous epidemics^{##UREF##12##26##}) has turned to Twitter as an alternative source of mobility data^{##UREF##13##27##,##REF##33170889##28##}. At the time the study was conducted, public tweets could be collected on an ongoing basis in real-time through Twitter’s publicly available Application Programming Interface (API) for free. Twitter changed such access to paid service in 2023. Important for our purposes, Twitter allows for geotagging tweets, which then includes location information in the tweet metadata. Additionally, numerous studies have explored automatic Twitter geolocation^{##UREF##14##29##–##UREF##17##32##}, including work on patterns and trends in Twitter geotagged data^{##UREF##18##33##}. In this study, we rely on public Twitter posts that contain user-provided location data.</p>", "<title>Social distancing and demographics</title>", "<p id=\"Par5\"> An advantage to Twitter data is that we can observe other information about the user who posted the tweet, which allows us to study how mobility changes correlate with individual characteristics related to health behaviors, such as age^{##REF##32275075##34##–##REF##32915884##36##}, income^{##REF##32727905##37##,##UREF##20##38##}, race^{##UREF##21##39##}, and political affiliation^{##UREF##4##9##,##REF##33139897##10##,##UREF##22##40##}. For example, partisanship is more strongly associated with physical distancing than other factors in the United States^{##REF##33139897##10##}. Prior work has demonstrated how to infer relevant characteristics from Twitter data^{##UREF##23##41##–##UREF##26##44##}, including gender^{##UREF##27##45##–##UREF##29##47##}, race/ethnicity^{##UREF##30##48##,##UREF##31##49##}, age^{##UREF##32##50##}, and political affiliation^{##UREF##33##51##,##UREF##34##52##}. Demographic factors (gender, age, race/ethnicity, political party) help predict intent to adhere to social distancing but are relatively poor predictors compared with individual attitudes and media diets^{##REF##32836442##15##}. Similarly, cellular mobility data at the county level can be used to reveal patterns in social distancing correlated with partisanship, media consumption, and racial and ethnic composition, as well as to measure the effectiveness of interventions that promote social distancing^{##UREF##35##53##}. Twitter data provides a complement to these data sources, allowing for confirmation of population-level trends as well as more fine-grained analysis.</p>", "<title>Mask usage</title>", "<p id=\"Par6\"> Face masks have been another critical intervention adopted during the pandemic. The adoption of mask requirements and compliance have varied dramatically by location and jurisdiction^{##REF##32203710##54##}. Chernozhukov et al. causally evaluate the impact of various policies of U.S. states and social distancing behavior measured by Google Mobility Reports on the spread of COVID-19 cases, demonstrating that nationally mandating face masks for employees early in the pandemic could have largely reduced the growth rate of cases and deaths^{##REF##33100476##55##}. Similarly, Eikenberry et al. studied mask effectiveness in New York State and Washington State^{##REF##32355904##56##}. Others have concluded that mandatory mask policies increase mask usage as compared to voluntary policies^{##REF##32820078##57##}.</p>", "<title>Contribution</title>", "<p id=\"Par7\"> We use data from the Twitter Social Mobility Index^{##UREF##13##27##} (Fig. ##FIG##0##1##) to study how demographic characteristics and political affiliation correlate with changes in mobility patterns, revealing insights into social distancing practices. We use demographic inference techniques, combined with user-level mobility data, to examine how different groups responded to the COVID-19 pandemic in the United States. We describe in detail the Twitter Social Mobility Index data and demographic characteristics in the Methods. Our findings can inform public health messaging and identify communities at higher risk from the virus.</p>" ]

[ "<title>Methods</title>", "<title>Data collection</title>", "<p id=\"Par31\">We use data collected as part of the Twitter Social Mobility Index Project^{##UREF##37##59##} This data includes public geotagged tweets from the United States from January 1, 2019 to June 21, 2020. The index is computed by aggregating geotagged data for a user and measuring the standard deviation across locations within each week. A high standard deviation in a week means high mobility. Changes in mobility behavior are measured over time by comparing mean mobility week to week. See Xu et al. for more details on data and computing mobility^{##UREF##13##27##}.</p>", "<p id=\"Par32\">We select March 16, 2020 as the start of social distancing in the United States, since the national “Slow the Spread” guidelines announced on that date had the largest effect on mobility^{##UREF##13##27##}. Furthermore, Badr et al. showed mobility changes in many US counties following this announcement, even before individual state-level policies were implemented^{##UREF##7##19##}. We compare the time period before (January 1, 2019 - March 15, 2020) and after (March 16, 2020 - June 21, 2020) this date as “before” and “after” the start of the pandemic. Our analysis relies on inferring demographics and analyzing the content of tweets. Therefore, we download the 3,200 most recent tweets for each of the 505,589 Twitter users in the collection who are present both before and after the start of the pandemic. We exclude 51,447 users identified as organizations by either of the existing individual vs. organizational account systems^{##UREF##32##50##,##UREF##38##60##}, leading to a total of 454,142 Twitter users. Our user-level dataset contains one entry for each user, including the mobility index, number of weekly geotagged tweets, and mean mobility index before and after the start of the pandemic. On average, the users in the dataset have 14.25 geotagged tweets weekly.</p>", "<p id=\"Par33\">We augment each user in the dataset with demographic information as follows.</p>", "<title>Location</title>", "<p id=\"Par34\"> The user’s home city and state are computed from the centroid of all of their geotagged tweets. In our analysis, we use the home location to categorize a user as living in a high or low population density state, with a threshold set as the median US state population density^{##UREF##39##61##}.</p>", "<title>Age and gender</title>", "<p id=\"Par35\"> Age and gender are inferred using M3^{##UREF##32##50##}, which uses both image (profile image) and text (name, username, user self-description) features. We use the text-based model when the profile image is unavailable. For gender, the full model achieves 0.918 macro-F1 and the text-only model 0.907 when evaluated on heuristically-labeled self-report data. For age, the full model achieves a 0.522 macro-F1 score. M3 produces age categories of 18 and under, 19-29, 30-39, and over 39. In our ANOVA analysis, we simplify this to be over/under 30. The macro-F1 score for simplified categories is 0.700.</p>", "<title>Race/ethnicity</title>", "<p id=\"Par36\"> We include categorical race/ethnicity based on the model using DistilBERT^{##UREF##40##62##} to embed the latest 200 tweets of each user into a fixed-length representation, which is then passed through a logistic regression with l2 regularization^{##UREF##31##49##}. The model achieves 0.513 macro-F1 and accuracy on a balanced dataset of self-reported race/ethnicity labels^{##UREF##30##48##}. Both the model and evaluation dataset provide the following race/ethnicity labels: White people, Black people, Asians, and Latinxs. We note that there are other racial groups in the US. The current categorizations are limited by the inference tool and evaluation data available. We provide the confusion matrices for age, gender, and race/ethnicity inference models in Supplementary Tables ##SUPPL##0##S1##, ##SUPPL##0##S2##, ##SUPPL##0##S3## and ##SUPPL##0##S4##.</p>", "<title>Political affiliation</title>", "<p id=\"Par37\"> We identify political affiliation in the United States (Democrat or Republican) using a strategy similar to Preotiuc-Pietro et al^{##UREF##33##51##}. We use three methods and include each in the dataset. (1) A user is assigned a label if they follow a member of congressional leadership from <italic>either</italic> the Democrats – Nancy Pelosi (@SpeakerPelosi) or Chuck Schumer (@SenSchumer) – or the Republicans – Kevin McCarthy (@GOPLeader) or Mitch McConnell (@senatemajldr). Otherwise, they are assigned the label unknown. (2) We apply the same approach but consider all members of Congress in 2020^{##UREF##41##63##}. We use the labels produced by this approach in our ANOVA analysis. (3) We also assign political affiliation labels based on the home state’s vote in the 2016 US presidential election^{##UREF##42##64##}. We excluded former President Trump’s account from this method since it is very popular and widely followed. Instead, we indicate if a user follows the former US President as a separate field, which may be useful as some studies have found that Trump supporters are less likely to accept a future COVID-19 vaccine^{##UREF##36##58##}.</p>", "<p id=\"Par38\">We include two characteristics that reflect tweeted content.</p>", "<title>COVID-19 hashtags</title>", "<p id=\"Par39\"> We indicate if this user tweeted or retweeted a COVID-19 hashtag in their most recent 3200 tweets. We collected hashtag usage from of all the active users since 2020 March in^{##UREF##13##27##}, which is 1,103,749 users. We then manually identified COVID-19 hashtags by examining the 427 most popular hashtags whose total usage is above 30,000 tweets.</p>", "<title>Social-distancing hashtags</title>", "<p id=\"Par40\"> We repeat the same process to identify social distancing hashtags. The hashtags for COVID-19 and social distancing are listed in Supplementary Table ##SUPPL##0##S5##.</p>", "<title>ANOVA tests</title>", "<p id=\"Par41\">We run ANOVA tests to determine whether the differences in mobility reduction among the demographic groups are significant. For all ANOVA tests in this study, we use the difference in mobility (reduction) as the dependent variable. We select age, gender, race/ethnicity, and political affiliation considering all current members of Congress, and state population density as independent variables for our major ANOVA test. We show the summary statistics of these five variables in Table ##TAB##0##1##, and significant interactions and mean mobility difference in Supplementary Table ##SUPPL##0##S9##. We run three other separate ANOVA tests where we replace political affiliation with indicators of whether a user mentions COVID-19, or social distancing-related hashtags, and whether a user follows former U.S. president Trump. The summary statistics are shown in Supplementary Tables ##SUPPL##0##S10##, ##SUPPL##0##S11## and ##SUPPL##0##S12## respectively. For the major ANOVA test, we also conduct post-hoc analysis by running a pairwise t-test to compare the groups in each significant interaction cell. We use Bonferroni correction to reduce the likelihood of committing Type I Error. The mean mobility difference and corrected p-values for post-hoc analysis are shown in Supplementary Table ##SUPPL##0##S8##.</p>", "<title>Regression analysis</title>", "<p id=\"Par42\">We run a linear regression to test our hypothesis that social distancing behavior is associated with trust in government and perceived risk. We further augment each user in our dataset with trust-in-government measures based on age and race/ethnicity, and perceived risk based on state. We obtain trust measures for race/ethnicity and age from the Pew Research Center. We used the datapoint on 8/2/2020 which covers 4 race/ethnicity groups considered in our analysis. Original age trust measure data covers 5 generations. We used a weighted average by population from the US Census Bureau to generate trust measures for those below (born after 1981) and above 30 (born before 1980). The generated trust measures are 19.0 and 20.3 accordingly. We measure perceived risk using the cumulative confirmed cases for each state on 6/21/2020 which is the end of our mobility dataset. We note that the trust-in-government measures are aggregated numbers and we do not include them in the proposed user-level dataset. We use these aggregated numbers that link to users’ race and age groups to test the related hypothesis. We leave building a reliable trust-in-government inference model on Twitter for future works.</p>", "<p id=\"Par43\">We first include perceived risk and categorical demographics predictors, i.e. age, gender, political affiliation, and race/ethnicity, as independent variables. We then replace age and race with trust in government measures, controlling for perceived risk. To tease apart rural from trust-related variables, we also control for the state population density. We use the exact density values in this analysis. Considering that the dependent variable, users’ mobility reduction, is not normally distributed as shown in Supplementary Fig. ##SUPPL##0##S1##, we split the users into two groups based on whether their mobility reduction is over or below 0. Users with 0 mobility both before and after March 16, 2020 are removed from the analysis. The log-transformed mobility reduction distribution plots for these two groups are shown in Supplementary Fig. ##SUPPL##0##S2##. We run a linear regression on users who have mobility reduction over 0 with the above-mentioned experiments. We then log-transform the reduction with and repeat the linear regression analysis. Finally, we run a logistic regression comparing users who have a mobility reduction over 0 to those who have a reduction of 0 or less in the same settings. When using dummy encoding for categorical variables, the reference group is the largest one except for political affiliation’s reference group is Democrats where the largest group is unknown. Min-max normalization is applied for each numerical dependent variable. The results are in Supplementary Tables ##SUPPL##0##S15##, ##SUPPL##0##S16## and ##SUPPL##0##S17##.</p>", "<title>Data limitation</title>", "<p id=\"Par44\">A responsible analysis must contextualize our results with the known, and potentially unknown, limitations of our data and methods. We enumerate some of these issues.</p>", "<p id=\"Par45\">Twitter is a biased source of data on a population. It reflects a non-random sample of the underlying population, and users choose to share different types of information and use the platform in different ways^{##UREF##43##65##}. For example, different demographic groups do not use geotagging with the same prevalence^{##UREF##44##66##}. Demographics like age and gender introduce bias that interacts with geographic inference and how geotagging may be used on Twitter^{##UREF##17##32##}. Similar demographic bias is also found in mobility data from cell phones, i.e. older and non-White users are less likely to be captured^{##UREF##45##67##}. While Twitter has yielded numerous insights into population health^{##UREF##8##21##}, we must remain cautious about this source of bias as we explore each new issue. We note that at the time of data collection for this study, Twitter provided free access to its data for academic purposes. However, the recent policy change regarding access to Twitter data has introduced greater challenges in utilizing it as a data source for research.</p>", "<p id=\"Par46\">Furthermore, our methods for inferring demographic information, including gender, age, and race/ethnicity are far from perfect. We report the accuracies of our selected systems in the body of the paper. Beyond raw accuracy, these systems all have biases in how they make demographic inference decisions. They mostly capture perceived demographics, which may not be consistent with an individual’s self-identified demographics. Furthermore, prior work has shown that different demographic groups may use Twitter differently, a factor that is not captured by demographic inference systems or our own analysis^{##UREF##44##66##}. The demographic inference models we use are limited in that they do not cover all groups within a demographic characteristic. For example, we combine race and ethnicity into 4 groups supported by the data and models but exclude other groups in the United States. Similarly, our gender models reflect only cisgender labels and exclude gender minorities. These limitations in data and available systems must be considered when drawing conclusions from our analysis.</p>", "<p id=\"Par47\">Despite the massive size of our dataset, there are many gaps. We have only a few geotagged tweets from each user each week, and we do not have enough data to produce county-level analyses for most locations in the United States. Therefore, these results should be compared to those from other data sources, and further work should more fully explore specific conclusions of the analysis.</p>", "<title>Ethics</title>", "<p id=\"Par48\">We must consider issues of ethics and privacy when mining social media data, even when it is data publicly posted online. There are different ethics and privacy issues to be considered when using Twitter data versus other mobility data, such as from mobile phone use. While mobile phone data are private and potentially very sensitive, they are not widely available, nor do they contain message content. In contrast, our Twitter data is (potentially) less sensitive and publicly available, but contains the text of messages. We must be sensitive to unintentional privacy violations that occur when analyzing aggregated data from a single user. More generally, when addressing issues related to health, attention to privacy is critical^{##UREF##46##68##}.</p>", "<p id=\"Par49\">In our work, we aggregated all mobility metrics to produce population-level analyses. None of our work considers the identity of individual users, and we removed identifiable user information from the distributed data aggregations. Furthermore, we caution others who pursue work similar to ours to consider privacy ramifications for users when collecting new data and conducting similar analyses. Finally, this research is conducted under an IRB-approved exemption under 45 CFR 46 category 4.</p>" ]

[ "<title>Results</title>", "<p id=\"Par8\">Overall we found the following groups in the United States exhibited larger reductions in mobility as compared to counterpart groups based on analysis of variance (ANOVA) tests: males, Asian and Latinx individuals, older individuals, Democrats, and people from higher population density states. The conclusions on characteristics with multiple groups, i.e. race/ethnicity and political affiliation, are supported by Tukey’s test (see Supplementary Tables ##SUPPL##0##S6## and ##SUPPL##0##S7## online). In the following section, we explain each of these findings in detail and ground them in the literature.</p>", "<title>Political affiliation</title>", "<title>Hypothesis</title>", "<p id=\"Par9\"> (1) Democrats reduced mobility more than Republicans, and (2) political affiliation acts as the main effect in interactions with other variables such as population density, race/ethnicity, and age.</p>", "<title>Background</title>", "<p id=\"Par10\"> In the United States, political affiliation has been identified as a significant factor in determining COVID-19 behaviors. After a government order, residents in Democratic counties are more likely to stay home relative to those in Republican counties, based on geolocation data from SafeGraph^{##UREF##4##9##}. Similar results were found using smartphone location data^{##REF##33139897##10##,##UREF##22##40##}. Additionally, population density confounds political affiliation as Democrats are more likely to live in dense, urban areas and thus be subject to stricter policies^{##UREF##22##40##}. Nevertheless, Allcott et al. and Gollwitzer et al. controlled for population density and still found that people from areas with more Democrats reduced mobility more^{##REF##33139897##10##,##UREF##22##40##}. Gollwitzer et al also found partisanship is more strongly associated with physical distancing than numerous other factors, including counties’ COVID-19 cases, population density, median income, and racial and age demographics^{##REF##33139897##10##}.</p>", "<p id=\"Par11\">Another breakdown can examine support for US President Donald Trump, who was president during the start of the COVID-19 pandemic. Recent work suggests Trump supporters are less likely to accept COVID-19 vaccines^{##UREF##36##58##}. Painter et al. studied the effect of Trump’s initial message which downplayed the severity of the coronavirus pandemic^{##UREF##4##9##} as the press suggested that Republicans may not take social distancing seriously. They found Democratic counties with Republican governors have lower responses relative to the aligned Democratic counties and there were no significant differences among Republican counties.</p>", "<title>Result</title>", "<p id=\"Par12\"> From Table ##TAB##0##1## and Supplementary Table ##SUPPL##0##S7##, we observe that Democrats have a significantly larger mobility reduction than Republicans. Regarding the interactions between political affiliation and other variables, we follow the interaction analysis from our major ANOVA test in Supplementary Table ##SUPPL##0##S9## and the post-hoc analysis in Supplementary Table ##SUPPL##0##S8##. We find that Democrats have a larger mobility reduction than Republicans, regardless of whether they are in high or low-population-density states. Furthermore, political affiliation has a larger impact than gender. All Democrats have larger mobility reductions regardless of gender. We also observe a significant interaction with three variables, i.e. gender, age, and political affiliation. After ignoring groups with unknown political affiliations, we find 12/28 significant comparisons. 9/12 out of these comparisons are between Democrat groups and Republican groups. For each of these comparisons, the Democrat group has a significantly larger mobility reduction compared to the Republican group, demonstrating the strong impact of political affiliation. Finally, Supplementary Table ##SUPPL##0##S12## implies that users who follow Trump on Twitter have a larger mobility reduction, although the difference is small.</p>", "<title>Race/ethnicity</title>", "<title>Hypothesis</title>", "<p id=\"Par13\"> we believe that (1) Black and Latinx groups show smaller mobility reduction while Asian group shows the opposite. As many studies control for population density^{##REF##33139897##10##,##UREF##22##40##}, we expect (2) there are significant differences in the interaction of race/ethnicity and population density.</p>", "<title>Background</title>", "<p id=\"Par14\"> Gollwitzer et al. found counties with higher Black or Latinx populations were less likely to reduce general mobility and non-essential visits, while Asian populations were in favor of these reductions^{##REF##33139897##10##}. Census data combined with COVID-19 tests show that individuals from poor and immigrant neighborhoods and areas with predominantly Black populations in New York City are more likely to test positive^{##UREF##21##39##}.</p>", "<title>Result</title>", "<p id=\"Par15\"> The results partly support our hypothesis. From Supplementary Tables ##SUPPL##0##S6## and ##SUPPL##0##S8##, we find that Asian and Latinx groups have a larger mobility reduction compared to Black and White groups. Furthermore, state population density has little impact when interacting with race/ethnicity as shown in Supplementary Table ##SUPPL##0##S8##. The significant differences between the groups mostly follow the trends for race. For all race/ethnicity groups, there is no significant difference between people from high and low-population-density states in this interaction.</p>", "<title>Age</title>", "<title>Hypothesis</title>", "<p id=\"Par16\"> (1) Older individuals have a larger mobility reduction. (2) However, we expect significant interactions between multiple demographics, namely between age and race/ethnicity.</p>", "<title>Background</title>", "<p id=\"Par17\"> Previous studies found people born before 1965 are more likely to practice social distancing than people born between 1981 and 1996 using an online survey^{##REF##32915884##36##}. Counties with higher median ages showed larger reductions in movement^{##REF##33139897##10##}.</p>", "<title>Result</title>", "<p id=\"Par18\"> Table ##TAB##0##1## confirms our hypothesis on older individuals. The results are more mixed for the age and race interaction in Supplementary Table ##SUPPL##0##S8##. Older people reduce their mobility more when compared with other younger groups regardless of race/ethnicity except for the comparisons involving Black people over 30. Black individuals have the smallest mobility reduction among all combinations for people over 30 in this interaction. They have a significantly smaller reduction when compared to Asian people below 30, and have no significant differences when compared to Latinx and White people below 30. For each of the four race/ethnicity groups included in our study, older people have significantly larger mobility reductions, showing age is the main effect when interacted with race/ethnicity.</p>", "<title>Gender</title>", "<title>Background</title>", "<p id=\"Par19\"> Allcott et al. found that there were no statistically significant differences in social distancing behaviors by gender^{##UREF##22##40##}. Similarly, we do not expect to detect any significant difference between males and females.</p>", "<title>Result</title>", "<p id=\"Par20\"> Looking at the interaction between gender and age from Supplementary Table ##SUPPL##0##S8##, we find that age has a larger impact on mobility; younger people have a smaller reduction when compared with other older groups regardless of gender. The differences between gender and other variables only exist for certain groups. For males and females in the same age range, we observe that males have a significantly larger mobility reduction (, ) than females do when over 30. Male Republicans have () larger mobility reduction than female Republicans, but we cannot conclude a significant difference between Democrat males and females.</p>", "<title>Content analysis</title>", "<p id=\"Par21\">We also include Twitter content characteristics, i.e. mentioning of COVID-19 and social-distancing hashtags, in separate analyses to validate our method, shown in Supplementary Tables ##SUPPL##0##S10## and ##SUPPL##0##S11##. People who tweeted COVID-19 related hashtags have a larger reduction in mobility. We cannot conclude the same for people tweeting about social-distancing hashtags due to the relatively small sample size for the five-way ANOVA analysis. However, for the one-way ANOVA that includes all the above-mentioned characteristics, Supplementary Table ##SUPPL##0##S13## confirms the intuitions that people tweeted COVID-19 and social distancing related hashtags reduce more mobility, and it also supports our previous conclusions on the other characteristics.</p>", "<title>Mobility index distribution</title>", "<p id=\"Par22\">Figure ##FIG##1##2## shows changes in mobility from before and after the start of social distancing for each characteristic in our dataset. Each sub-group displays a reduction in mobility, consistent with the ANOVA tests. We can also see differences by attributes: we observe larger reductions for older individuals, people from high-density states, and Democrats. We note that high-density areas may have seen a larger drop because individuals can find services in a smaller geographic area.</p>", "<title>Regression analysis</title>", "<p id=\"Par23\">Beyond reductions correlated with different demographic groups, we hypothesize that trust in government and perceived risk are associated with social distancing behavior. Our regression analysis, described in the \"<xref rid=\"Sec11\" ref-type=\"sec\">Methods</xref>\" Section with results in Supplementary Tables ##SUPPL##0##S15##, ##SUPPL##0##S16## and ##SUPPL##0##S17##, shows that trust in the government predicts social distancing behavior even after controlling for perceived risk and population density at the state level.</p>", "<p id=\"Par24\">\n\n</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par25\">Our analysis concludes that male users, Asian and Latinx users, older users, Democrats, and people from higher population density states showed larger reductions in mobility. For race/ethnicity, the observations of Asian and Black populations confirm previous work^{##REF##33139897##10##}. However, in our analysis, Latinx people are more likely to reduce movement. This might be due to the relatively poor performance of the race/ethnicity inference model on Latinxs (See Supplementary Tables ##SUPPL##0##S3## and ##SUPPL##0##S4## online). We are surprised to observe a significant gender difference which might be caused by the imbalanced age distribution in our dataset, i.e. the sample sizes between males and females are close when under 30 while there are many more male users relative to females over 30. In general, a consistent picture emerges across multiple data sources and analyses that indicates that some groups practice less social distancing, and thus may be at a higher risk of infection.</p>", "<p id=\"Par26\">Moreover, our study provides meaningful insights into the interactions between different groups. For example, political affiliation shows a stronger impact when interacting with gender and age, which is similar to the findings from smartphone data^{##REF##33139897##10##}. Age is another strong factor since older people have a larger mobility reduction regardless of gender, as we expected. However, when it interacts with race/ethnicity, we find an exception for Black people as older Black people show smaller mobility reduction than some of the younger people from other race/ethnicity groups.</p>", "<p id=\"Par27\">We emphasize that our results do not indicate willingness or attitudes towards social distancing or mobility reduction of certain groups. We are measuring actual behaviors, which may not align with attitudes for a variety of reasons. For example, individuals may agree with the importance of social distancing but may still need to travel for economic reasons. Weill et al. showed wealthy areas reduced mobility more during the pandemic^{##REF##32727905##37##}. Population density has less impact when interacting with other demographics, which contradicts our hypothesis, which may be due to the fact that our population density labels are at the state, and not individual, level. There are dense, urban areas in states with low population density and vice versa.</p>", "<p id=\"Par28\">A major advantage of Twitter data over other mobility data sources is the ability to link to comments and other behaviors of the users. We utilize this ability to show that increased trust in government correlates with greater mobility reductions across age and race/ethnicity. Public health communication strategies should consider how to best reach this at-risk group.</p>", "<p id=\"Par29\">Our results demonstrate the utility of data from the Twitter Social Mobility Index. Future work on social distancing and health behaviors during epidemics can utilize similar public Twitter data to measure the effectiveness of public health policies. Still, future analyses must recognize the limitations of this data source, which we discuss in the \"<xref rid=\"Sec11\" ref-type=\"sec\">Methods</xref>\" section. Critically, our analysis considers individual characteristics rather than a holistic analysis that may illuminate other issues. For example, Democrats may be more likely to reduce their mobility because they live in dense urban areas. Additional unavailable variables may form critical parts of the story, but we lack this information. For example, we do not have access to socioeconomic information, but these factors may be confounding variables that explain why some groups have smaller reductions in mobility. Additionally, following other studies, we measure social distancing as reflected through social mobility. While there is significant evidence to support this association, the correlation is not perfect. Individuals may have increased mobility but stayed away from others (e.g. travel to rural areas), decreased mobility but increased social interactions (in-person gatherings in their neighborhood), or increased mobility but adopted other precautions (6 feet distancing, masking.) We cannot measure the difference between mobility and other precautions using our data. Furthermore, the dramatic social changes from the pandemic may have influenced how users geotagged their data, perhaps leading to changes in the social mobility measure. While the large drop in social mobility at the start of the pandemic strongly suggests a causal link between the pandemic and mobility, we cannot rule out other unobserved factors.</p>", "<p id=\"Par30\">Overall, our analysis illustrates the value of geolocated Twitter data in understanding public health behaviors during a pandemic.</p>" ]

[]

[ "<p id=\"Par1\">The COVID-19 pandemic demonstrated the importance of social distancing practices to stem the spread of the virus. However, compliance with public health guidelines was mixed. Understanding what factors are associated with differences in compliance can improve public health messaging since messages could be targeted and tailored to different population segments. We utilize Twitter data on social mobility during COVID-19 to reveal which populations practiced social distancing and what factors correlated with this practice. We analyze correlations between demographic and political affiliation with reductions in physical mobility measured by public geolocation tweets. We find significant differences in mobility reduction between these groups in the United States. We observe that males, Asian and Latinx individuals, older individuals, Democrats, and people from higher population density states exhibited larger reductions in movement. Furthermore, our study also unveils meaningful insights into the interactions between different groups. We hope these findings will provide evidence to support public health policy-making.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51555-0.</p>", "<title>Acknowledgements</title>", "<p>This work was supported in part by the John S. and James L. Knight Foundation to the GW Institute for Data, Democracy, and Politics, and by the National Science Foundation under Grant DEB-2034008.</p>", "<title>Author contributions</title>", "<p>All authors conceived the experiments, analyzed the results, and reviewed the manuscript. P.X. conducted the experiments.</p>", "<title>Data availability</title>", "<p>Our data are public tweets containing user-provided geolocation information. To protect user privacy we remove all content and only use the information described in our analysis. The data that support the findings of this study are available from the corresponding author upon reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par50\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Visualization of Twitter Social Mobility Index. A Twitter user’s trajectories for Week 1 (blue) and Week 2 (red) are shown on the map of Chicago while the detailed location information is shown on the left. Each point on the map represents a coordinate derived from the user’s check-in Tweet. The number by the point is the order in which the tweet occurred. Each circle is centered at the centroid location for that week, and the radius of the gyration shows the distance traveled. The Twitter Social Mobility index is computed by the standard deviation of distance traveled across locations within each week.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Mobility index distributions of each characteristic before (blue) and after (red) the start of the COVID-19 pandemic.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Summary statistics of ANOVA tests and mean mobility differences. F statistic, DF (degrees of freedom), and p value are shown for each variable.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Variable</th><th align=\"left\">F statistic</th><th align=\"left\">DF</th><th align=\"left\">P-value</th><th align=\"left\">Group</th><th align=\"left\">Mean mobility difference</th><th align=\"left\">Sample size</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"2\">Gender</td><td align=\"left\" rowspan=\"2\">6.80</td><td align=\"left\" rowspan=\"2\">1.0</td><td align=\"left\" rowspan=\"2\"></td><td align=\"left\">Female</td><td align=\"left\">32.48</td><td align=\"left\">194414</td></tr><tr><td align=\"left\">Male</td><td align=\"left\">36.40</td><td align=\"left\">258625</td></tr><tr><td align=\"left\" rowspan=\"4\">Race/ethnicity</td><td align=\"left\" rowspan=\"4\">24.50</td><td align=\"left\" rowspan=\"4\">3.0</td><td align=\"left\" rowspan=\"4\"></td><td align=\"left\">White people</td><td align=\"left\">35.65</td><td align=\"left\">184654</td></tr><tr><td align=\"left\">Asians</td><td align=\"left\">47.11</td><td align=\"left\">40193</td></tr><tr><td align=\"left\">Latinxs</td><td align=\"left\">42.70</td><td align=\"left\">81509</td></tr><tr><td align=\"left\">Black people</td><td align=\"left\">25.72</td><td align=\"left\">146683</td></tr><tr><td align=\"left\" rowspan=\"2\">Age</td><td align=\"left\" rowspan=\"2\">22.85</td><td align=\"left\" rowspan=\"2\">1.0</td><td align=\"left\" rowspan=\"2\"></td><td align=\"left\"></td><td align=\"left\">28.40</td><td align=\"left\">245202</td></tr><tr><td align=\"left\"></td><td align=\"left\">42.18</td><td align=\"left\">207837</td></tr><tr><td align=\"left\" rowspan=\"3\">Political affiliation</td><td align=\"left\" rowspan=\"3\">8.05</td><td align=\"left\" rowspan=\"3\">2.0</td><td align=\"left\" rowspan=\"3\"></td><td align=\"left\">Unknown</td><td align=\"left\">32.70</td><td align=\"left\">363927</td></tr><tr><td align=\"left\">Democrats</td><td align=\"left\">45.53</td><td align=\"left\">63955</td></tr><tr><td align=\"left\">Republicans</td><td align=\"left\">36.44</td><td align=\"left\">25157</td></tr><tr><td align=\"left\" rowspan=\"2\">State population density category</td><td align=\"left\" rowspan=\"2\">10.50</td><td align=\"left\" rowspan=\"2\">1.0</td><td align=\"left\" rowspan=\"2\"></td><td align=\"left\">High</td><td align=\"left\">35.69</td><td align=\"left\">295719</td></tr><tr><td align=\"left\">Low</td><td align=\"left\">32.90</td><td align=\"left\">157320</td></tr></tbody></table></table-wrap>" ]

[ "<inline-formula id=\"IEq1\"><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$11.3\\%$$\\end{document}</tex-math><mml:math id=\"M2\"><mml:mrow><mml:mn>11.3</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq2\"><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p&lt;0.001$$\\end{document}</tex-math><mml:math id=\"M4\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.001</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq3\"><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$18.5\\%$$\\end{document}</tex-math><mml:math id=\"M6\"><mml:mrow><mml:mn>18.5</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq4\"><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p&lt;0.05$$\\end{document}</tex-math><mml:math id=\"M8\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.05</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq5\"><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$9.13\\times 10^{-03}$$\\end{document}</tex-math><mml:math id=\"M10\"><mml:mrow><mml:mn>9.13</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>03</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq6\"><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$7.60\\times 10^{-16}$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mrow><mml:mn>7.60</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq7\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.75\\times 10^{-06}$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:mrow><mml:mn>1.75</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>06</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq8\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$&lt; 30$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn>30</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq9\"><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\ge 30$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:mrow><mml:mo>≥</mml:mo><mml:mn>30</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3.18\\times 10^{-04}$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mrow><mml:mn>3.18</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>04</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.19\\times 10^{-03}$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:mrow><mml:mn>1.19</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>03</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$52.6\\%$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mrow><mml:mn>52.6</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$81.1\\%$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:mrow><mml:mn>81.1</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$log(x+1)$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">When a magnetic field is applied perpendicular to the plane of type-II superconductors, magnetic flux quanta called vortices are generated^{##UREF##0##1##}. By applying a current above the depinning threshold, the vortices pinned by the quenched disorder start to flow due to the Lorentz-like force exerted from the current and their motion causes energy dissipation. Therefore, understanding the depinning and vortex dynamics is of practical importance. Fundamentally, the dynamics of vortices have been intensively studied because they exhibit rich nonequilibrium phases and phase transitions^{##REF##10053608##2##–##REF##35091669##14##}, which are generic to many-particle assemblies driven over random substrates^{##REF##27997373##15##}. When the driving force is increased and the interaction between the vortices and pinning centers is reduced, the flow structure of the vortices is considered to show dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow^{##REF##10062043##16##–##UREF##9##20##}.</p>", "<p id=\"Par3\">One of the long-standing questions is whether the current-induced dynamical ordering from the plastic flow to the smectic flow actually takes place. However, this question has not been answered experimentally because from conventional transport measurements, it is difficult to detect the moving smectic phase with long-range order in the direction transverse to the driving force^{##REF##10062043##16##–##UREF##10##21##}. Recently, we have overcome this problem by using two-step measurements of transient voltage in response to mutually perpendicular driving currents^{##UREF##11##22##}. We found dynamical ordering from the plastic flow to the anisotropic smectic flow as a function of the current. Convincing evidence of the moving smectic phase was obtained from the first transverse mode locking with signals larger than those of longitudinal mode locking, indicating the higher transverse order than the longitudinal one. However, the central issue of whether the current-induced dynamical ordering is a phase transition or a crossover still remains elusive. If it turns out to be a true phase transition, it is also of interest to examine whether it shows a critical behavior.</p>", "<p id=\"Par4\">In this work, we resolve the issue by studying the critical scaling for the dynamical ordering transition. The scaling approach is generally employed to demonstrate second-order phase transitions and critical phenomena^{##UREF##12##23##–##UREF##14##25##}. Here, we measure the response of vortex flow to the <italic>transverse</italic> driving force using a cross-shaped amorphous MoGe film. From transverse current-voltage (i.e., force-velocity) characteristics under various longitudinal currents superimposed with the transverse current, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear behavior with nonzero transverse depinning current to a linear behavior with zero transverse depinning current at a well-defined longitudinal current that marks the dynamical ordering from the plastic to smectic flow. We also find a scaling collapse of the transverse current-voltage curves to a universal scaling function, providing firm evidence of the second-order transition for the dynamical ordering transition.</p>" ]

[ "<title>Methods</title>", "<title>Sample preparation</title>", "<p id=\"Par16\">The 280-nm-thick cross-shaped amorphous MoGe () film with weak random pinning was deposited using rf sputtering onto a Si substrate held at room temperature^{##UREF##11##22##}. Current () and voltage () electrodes are arranged as schematically shown in Fig. ##FIG##0##1##a. is measured using voltage electrodes arranged in the <italic>x</italic> direction. The size of the central intersection of the sample is mm and the distance between voltage electrodes is 1.95 mm. The critical temperature K is independent of the directions, indicating the uniformity of the film. The sample was directly immersed in liquid He to reduce possible heating.</p>", "<title>Transport measurements</title>", "<p id=\"Par17\">We conducted standard four-probe measurements at 3.6 K and 1.0 T, corresponding to the Bragg-glass phase at equilibrium^{##UREF##30##48##}. We confirmed that the depinning current densities A/m in the <italic>x</italic> and <italic>y</italic> directions are identical to each other. For the measurements, we measured and for each . As a result, we safely subtracted the background signal, including the small component of coming from the possible misalignment of voltage electrodes, and obtained reliable values of the transverse voltage . Compared with the conventional strip-shaped film, some current may leak in a wider central zone in our cross-shaped film. We believe that this may lead to a slight overestimation of the absolute value of currents but does not influence the discussion, in particular, the scaling analysis. Further measurements, such as using samples with the voltage contacts placed closer to the cross center, would prove it clearly.</p>" ]

[ "<title>Results and discussion</title>", "<p id=\"Par5\">To study the transverse response of flowing vortices, we used a cross-shaped film of amorphous MoGe (see “Methods”), in which we can apply the driving current in <italic>x</italic> and <italic>y</italic> directions simultaneously. The schematic of experimental setup is shown in Fig. ##FIG##0##1##a. The magnetic field of 1.0 T was applied perpendicular to the plane of the film at 3.6 K to generate the vortices.</p>", "<p id=\"Par6\">We first apply the current (driving force) in the minus <italic>x</italic> direction (<italic>y</italic> direction) with a given current density and then examine the response to the transverse driving force applied in the <italic>x</italic> direction by measuring the transverse current-voltage characteristics in the <italic>y</italic> direction as shown with red color in Fig. ##FIG##0##1##a. Here, is the control parameter that changes the flow structure of vortices, while the transverse characteristics are used to probe the transverse vortex response, where and are the current density and electric field in the <italic>y</italic> direction, respectively. Figure ##FIG##0##1##b displays curves in a double logarithmic scale measured under various . For smaller , the curves have a negative curvature and rapidly drops below the voltage resolution of V upon reducing . At around A/m (), the curve exhibits a power-law behavior as shown by a dashed straight line. For , the curves have a positive curvature and cross over to a low-current linear behavior upon reducing .</p>", "<p id=\"Par7\">From Fig. ##FIG##0##1##b, we extract the depinning current density using a V criterion and plot it against in Fig. ##FIG##1##2##a. It is found that there are three qualitatively different regimes, which are separated by the ordinary depinning current density and , as shown by vertical dotted lines. In the region with (region I), the vortices are initially pinned before applying since is smaller than the depinning current density . With an increase in , the depinning occurs when , as shown by a quadrant line. This indicates the ordinary depinning in the oblique direction by the combined currents of and . In the region where (region II), the vortices initially flow in the longitudinal (<italic>y</italic>) direction due to the Lorentz-like force by . Nevertheless, is nonzero, indicating the occurrence of the nontrivial depinning in the transverse (<italic>x</italic>) direction, which we call a transverse depinning^{##UREF##15##26##,##UREF##16##27##}. For (region III), is zero and the vortices can flow freely in the transverse (<italic>x</italic>) direction by infinitesimal .</p>", "<p id=\"Par8\">The disappearance of the transverse depinning at implies the presence of the dynamical transition of the longitudinal vortex flows (in the <italic>y</italic> direction) at , where the transverse response changes from a nonlinear behavior with to a linear behavior with . We have found recently in the same sample that the transition or crossover from the plastic flow to the smectic flow takes place at A/m^{##UREF##11##22##}. Since this value is close to the value of A/m obtained here, the change of the flow state at is considered to correspond to the dynamical ordering transition from the plastic flow in the region II to the smectic flow in the region III. This view, together with the second-order nature of the transition, is justified by the scaling analysis described below.</p>", "<p id=\"Par9\">As schematically illustrated in Fig. ##FIG##1##2##b, the plastic flow initially generated by is a disordered flow dominated by random pinning and shows riverlike features, where a small number of vortices flow around regions of pinned vortices shaded by red color^{##UREF##17##28##,##UREF##18##29##}. Once such flow patterns are formed in the <italic>y</italic> direction, it is difficult even for the flowing vortices to flow in the transverse (<italic>x</italic>) direction when the small driving force (driving current ) is applied in the <italic>x</italic> direction (<italic>y</italic> direction). This accounts for the nonzero in the region II.</p>", "<p id=\"Par10\">In contrast, when larger than is applied initially, the effects of pinning are much more suppressed and the smectic flow is generated, as schematically shown in Fig. ##FIG##1##2##c. In the smectic flow, the vortices form one-dimensional channels along the longitudinal (<italic>y</italic>) direction with long-range transverse order in the <italic>x</italic> direction^{##REF##10062043##16##–##UREF##10##21##}. The areas of pinned vortices (shaded by red color) shrink and instead the pin-free regions (shaded by blue) grow, percolating in the transverse (<italic>x</italic>) direction. As a result, the vortices no longer feel transverse barriers and flow freely in the <italic>x</italic> direction by the infinitesimal driving force (), which explains the absence of the transverse depinning in the region III.</p>", "<p id=\"Par11\">The current-voltage () characteristics in Fig. ##FIG##0##1##b with a sign change of curvature at is reminiscent of the isotherms near the critical point for gases^{##UREF##19##30##}, Ising ferromagnets^{##UREF##14##25##}, and vortex glasses^{##REF##10040591##31##–##REF##12935101##40##}, and the flow curves for yielding and jamming transitions^{##REF##17995371##41##–##REF##23863014##43##}, where the critical scaling associated with the second-order phase transition has been well established. We perform the scaling analysis for the characteristics shown in Fig. ##FIG##2##3##, which are converted from the data in Fig. ##FIG##0##1##b, to test whether the dynamical transition at is the second-order phase transition, where . If the threshold current is a critical point for the second-order transition, the resistivity as functions of and should obey the following scaling equation^{##UREF##14##25##,##UREF##27##44##}:where and are scaling exponents, is the scaling variable, and and are the two branches of the scaling function for and , respectively. For , the scaling function takes an asymptotic form . This gives a power law relation at , which satisfies scale invariance,For , the two branches are expected to be and , which gives the power-law scaling of a linear resistivity for ,A dashed line in Fig. ##FIG##2##3## represents the power law of Eq. (##FORMU##131##2##) with . The inset of Fig. ##FIG##2##3## displays the log-log plot of as a function of the dimensionless distance from the critical point, , where open squares are for A/m extracted from in the main panel. Solid circles are the resistivity for small currents, \n\n and A/m, measured with changing continuously. The collapse of all data indicates the linear behavior and is found to be scaled in the form of Eq. (##FORMU##137##3##) with , as shown with a solid straight line. From the values of and obtained here, the exponent is determined to be .</p>", "<p id=\"Par12\">In Fig. ##FIG##3##4##, we replot the data shown with solid circles in Fig. ##FIG##2##3## with respect to the scaled variables of Eq. (##FORMU##119##1##), versus , where A/m, , and are used. A good scaling collapse to universal branches is found, in agreement with Eq. (##FORMU##119##1##). A dashed straight line represents the asymptotic behavior for , . The results provide convincing evidence that the dynamical ordering transition from the plastic flow to the smectic flow, which occurs at , is indeed the second-order phase transition. Recent simulation studying the Kibble-Zurek mechanism for dynamical ordering also predicted the continuous phase transition^{##UREF##28##45##}, which was indirectly supported by our experiment in the vortex system^{##REF##36493453##46##}, consistent with the present results. In these studies, the dynamical ordering transition is considered to be an absorbing phase transition in dimensional directed percolation universality class^{##UREF##28##45##–##UREF##29##47##}.</p>", "<p id=\"Par13\">In the scaling analysis, the probe current up to about 50% of the drive current is used. Unless is sufficiently smaller than , the probe may affect the flow state formed by the drive . We have confirmed that the possible interference effect of the probe current does not seriously affect our discussion (See ##SUPPL##0##Supplementary Material## for discussion of the possible interference effect of the probe current on the drive current).</p>", "<p id=\"Par14\">We have shown that with an increase in , the transverse response of vortex flow changes from the nonlinear behavior associated with the transverse depinning () to the linear one without the transverse depinning (). The result together with the scaling collapse indicates that the dynamical ordering transition from the plastic flow to the smectic flow is of second order. The disappearance of the transverse depinning for results from the reduced effective pinning due to increased . As mentioned above, the present finding is analogous to the vortex-glass transition^{##REF##10040591##31##–##REF##12935101##40##}, where the vortex phase below the transition temperature is the vortex-glass phase dominated by pinning, while the high-temperature phase is the vortex-liquid phase, where the pinning is ineffective due to thermal fluctuations. The role of the current in the dynamical ordering transition corresponds to that of the temperature in the vortex-glass transition, both of which play a similar role in weakening the pinning effects.</p>", "<p id=\"Par15\">The scaling exponents and obtained in this work are slightly smaller than those of the vortex-glass transition, –8 and –4^{##REF##10040591##31##,##UREF##21##33##}. This discrepancy is not surprising because the two transitions are rather different: The dynamical ordering is the nonequilibrium phase transition and the effect of the current is anisotropic while the vortex-glass transition is the equilibrium phase transition and the effect of the temperature is isotropic.</p>" ]

[ "<title>Results and discussion</title>", "<p id=\"Par5\">To study the transverse response of flowing vortices, we used a cross-shaped film of amorphous MoGe (see “Methods”), in which we can apply the driving current in <italic>x</italic> and <italic>y</italic> directions simultaneously. The schematic of experimental setup is shown in Fig. ##FIG##0##1##a. The magnetic field of 1.0 T was applied perpendicular to the plane of the film at 3.6 K to generate the vortices.</p>", "<p id=\"Par6\">We first apply the current (driving force) in the minus <italic>x</italic> direction (<italic>y</italic> direction) with a given current density and then examine the response to the transverse driving force applied in the <italic>x</italic> direction by measuring the transverse current-voltage characteristics in the <italic>y</italic> direction as shown with red color in Fig. ##FIG##0##1##a. Here, is the control parameter that changes the flow structure of vortices, while the transverse characteristics are used to probe the transverse vortex response, where and are the current density and electric field in the <italic>y</italic> direction, respectively. Figure ##FIG##0##1##b displays curves in a double logarithmic scale measured under various . For smaller , the curves have a negative curvature and rapidly drops below the voltage resolution of V upon reducing . At around A/m (), the curve exhibits a power-law behavior as shown by a dashed straight line. For , the curves have a positive curvature and cross over to a low-current linear behavior upon reducing .</p>", "<p id=\"Par7\">From Fig. ##FIG##0##1##b, we extract the depinning current density using a V criterion and plot it against in Fig. ##FIG##1##2##a. It is found that there are three qualitatively different regimes, which are separated by the ordinary depinning current density and , as shown by vertical dotted lines. In the region with (region I), the vortices are initially pinned before applying since is smaller than the depinning current density . With an increase in , the depinning occurs when , as shown by a quadrant line. This indicates the ordinary depinning in the oblique direction by the combined currents of and . In the region where (region II), the vortices initially flow in the longitudinal (<italic>y</italic>) direction due to the Lorentz-like force by . Nevertheless, is nonzero, indicating the occurrence of the nontrivial depinning in the transverse (<italic>x</italic>) direction, which we call a transverse depinning^{##UREF##15##26##,##UREF##16##27##}. For (region III), is zero and the vortices can flow freely in the transverse (<italic>x</italic>) direction by infinitesimal .</p>", "<p id=\"Par8\">The disappearance of the transverse depinning at implies the presence of the dynamical transition of the longitudinal vortex flows (in the <italic>y</italic> direction) at , where the transverse response changes from a nonlinear behavior with to a linear behavior with . We have found recently in the same sample that the transition or crossover from the plastic flow to the smectic flow takes place at A/m^{##UREF##11##22##}. Since this value is close to the value of A/m obtained here, the change of the flow state at is considered to correspond to the dynamical ordering transition from the plastic flow in the region II to the smectic flow in the region III. This view, together with the second-order nature of the transition, is justified by the scaling analysis described below.</p>", "<p id=\"Par9\">As schematically illustrated in Fig. ##FIG##1##2##b, the plastic flow initially generated by is a disordered flow dominated by random pinning and shows riverlike features, where a small number of vortices flow around regions of pinned vortices shaded by red color^{##UREF##17##28##,##UREF##18##29##}. Once such flow patterns are formed in the <italic>y</italic> direction, it is difficult even for the flowing vortices to flow in the transverse (<italic>x</italic>) direction when the small driving force (driving current ) is applied in the <italic>x</italic> direction (<italic>y</italic> direction). This accounts for the nonzero in the region II.</p>", "<p id=\"Par10\">In contrast, when larger than is applied initially, the effects of pinning are much more suppressed and the smectic flow is generated, as schematically shown in Fig. ##FIG##1##2##c. In the smectic flow, the vortices form one-dimensional channels along the longitudinal (<italic>y</italic>) direction with long-range transverse order in the <italic>x</italic> direction^{##REF##10062043##16##–##UREF##10##21##}. The areas of pinned vortices (shaded by red color) shrink and instead the pin-free regions (shaded by blue) grow, percolating in the transverse (<italic>x</italic>) direction. As a result, the vortices no longer feel transverse barriers and flow freely in the <italic>x</italic> direction by the infinitesimal driving force (), which explains the absence of the transverse depinning in the region III.</p>", "<p id=\"Par11\">The current-voltage () characteristics in Fig. ##FIG##0##1##b with a sign change of curvature at is reminiscent of the isotherms near the critical point for gases^{##UREF##19##30##}, Ising ferromagnets^{##UREF##14##25##}, and vortex glasses^{##REF##10040591##31##–##REF##12935101##40##}, and the flow curves for yielding and jamming transitions^{##REF##17995371##41##–##REF##23863014##43##}, where the critical scaling associated with the second-order phase transition has been well established. We perform the scaling analysis for the characteristics shown in Fig. ##FIG##2##3##, which are converted from the data in Fig. ##FIG##0##1##b, to test whether the dynamical transition at is the second-order phase transition, where . If the threshold current is a critical point for the second-order transition, the resistivity as functions of and should obey the following scaling equation^{##UREF##14##25##,##UREF##27##44##}:where and are scaling exponents, is the scaling variable, and and are the two branches of the scaling function for and , respectively. For , the scaling function takes an asymptotic form . This gives a power law relation at , which satisfies scale invariance,For , the two branches are expected to be and , which gives the power-law scaling of a linear resistivity for ,A dashed line in Fig. ##FIG##2##3## represents the power law of Eq. (##FORMU##131##2##) with . The inset of Fig. ##FIG##2##3## displays the log-log plot of as a function of the dimensionless distance from the critical point, , where open squares are for A/m extracted from in the main panel. Solid circles are the resistivity for small currents, \n\n and A/m, measured with changing continuously. The collapse of all data indicates the linear behavior and is found to be scaled in the form of Eq. (##FORMU##137##3##) with , as shown with a solid straight line. From the values of and obtained here, the exponent is determined to be .</p>", "<p id=\"Par12\">In Fig. ##FIG##3##4##, we replot the data shown with solid circles in Fig. ##FIG##2##3## with respect to the scaled variables of Eq. (##FORMU##119##1##), versus , where A/m, , and are used. A good scaling collapse to universal branches is found, in agreement with Eq. (##FORMU##119##1##). A dashed straight line represents the asymptotic behavior for , . The results provide convincing evidence that the dynamical ordering transition from the plastic flow to the smectic flow, which occurs at , is indeed the second-order phase transition. Recent simulation studying the Kibble-Zurek mechanism for dynamical ordering also predicted the continuous phase transition^{##UREF##28##45##}, which was indirectly supported by our experiment in the vortex system^{##REF##36493453##46##}, consistent with the present results. In these studies, the dynamical ordering transition is considered to be an absorbing phase transition in dimensional directed percolation universality class^{##UREF##28##45##–##UREF##29##47##}.</p>", "<p id=\"Par13\">In the scaling analysis, the probe current up to about 50% of the drive current is used. Unless is sufficiently smaller than , the probe may affect the flow state formed by the drive . We have confirmed that the possible interference effect of the probe current does not seriously affect our discussion (See ##SUPPL##0##Supplementary Material## for discussion of the possible interference effect of the probe current on the drive current).</p>", "<p id=\"Par14\">We have shown that with an increase in , the transverse response of vortex flow changes from the nonlinear behavior associated with the transverse depinning () to the linear one without the transverse depinning (). The result together with the scaling collapse indicates that the dynamical ordering transition from the plastic flow to the smectic flow is of second order. The disappearance of the transverse depinning for results from the reduced effective pinning due to increased . As mentioned above, the present finding is analogous to the vortex-glass transition^{##REF##10040591##31##–##REF##12935101##40##}, where the vortex phase below the transition temperature is the vortex-glass phase dominated by pinning, while the high-temperature phase is the vortex-liquid phase, where the pinning is ineffective due to thermal fluctuations. The role of the current in the dynamical ordering transition corresponds to that of the temperature in the vortex-glass transition, both of which play a similar role in weakening the pinning effects.</p>", "<p id=\"Par15\">The scaling exponents and obtained in this work are slightly smaller than those of the vortex-glass transition, –8 and –4^{##REF##10040591##31##,##UREF##21##33##}. This discrepancy is not surprising because the two transitions are rather different: The dynamical ordering is the nonequilibrium phase transition and the effect of the current is anisotropic while the vortex-glass transition is the equilibrium phase transition and the effect of the temperature is isotropic.</p>" ]

[]

[ "<p id=\"Par1\">Dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow induced by a dc force has been studied in various many-particle systems, including vortices in type-II superconductors. However, it remains unclear whether the dynamical ordering is a true phase transition because of lack of suitable experimental methods. Here, we study the response of vortex flow to the <italic>transverse</italic> force using a cross-shaped amorphous MoGe film. From transverse current-voltage (force-velocity) characteristics under various longitudinal currents, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear to linear behavior at a well-defined longitudinal current that marks the dynamical ordering transition. We also find the scaling collapse of the transverse current-voltage curves to a universal scaling function, providing evidence of the second-order transition for the dynamical ordering transition.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51534-5.</p>", "<title>Acknowledgements</title>", "<p>This work was supported by a Grant-in-Aid for Scientific Research (B) (KAKENHI Grant No. 22H01165), on Innovative Areas (KAKENHI Grant No. 20H05266), and JSPS Fellows (KAKENHI Grant No. 20J21425) from the Japan Society for the Promotion of Science.</p>", "<title>Author contributions</title>", "<p>S.M. conceived the experiments in discussion with K.I. and S.O. S.M. fabricated the sample, conducted most of the measurements, and analyzed the data with input from K.I. and S.O. Manuscript was written by S.M. under the supervision of S.O. S.O. supervised the project. All authors discussed the results and commented on the manuscript.</p>", "<title>Data availability</title>", "<p>The data that support the findings of this study are available from the corresponding author upon reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par18\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>(<bold>a</bold>) Schematics of the experimental setup of the cross-shaped amorphous MoGe film on the Si substrate. The magnetic field <italic>B</italic> is applied perpendicular to the film surface. (<bold>b</bold>) characteristics measured under fixed listed on the right-hand side. The right axis indicates the voltage in the <italic>y</italic> direction. Solid circles represent the points used for the scaling analysis in Fig. ##FIG##3##4##. A dashed line labeled shows the power-law behavior.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>(<bold>a</bold>) deduced from the curves in Fig. ##FIG##0##1##b using a V criterion plotted against . The right axis indicates the depinning current in the <italic>y</italic> direction. Vertical dotted lines mark the isotropic depinning current density and the threshold current density , separating the regions I and II and regions II and III, respectively. In region I, all the vortices are pinned initially and then undergo depinning obliquely, when exceeds . A solid quadrant line represents . In region II, the vortices initially flowing in the longitudinal (<italic>y</italic>) direction undergo the transverse depinning for . In region III, the transverse depinning does not occur (). (<bold>b</bold>,<bold>c</bold>) Schematics of initial vortex flow generated by . (b) The plastic flow in region II. (<bold>c</bold>) The smectic flow in region III. The areas shaded by red and blue represent the regions with strong and weak effective pinning, respectively.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Log-log plots of the data converted from the data in Fig. ##FIG##0##1##b. A dashed line labeled A/m) indicates the power law of Eq. (##FORMU##131##2##), with . Inset: Log-log plots of the linear resistivity as a function of . Solid circles represent the data from measured by using small currents, \n\n and A/m, with changing continuously. Open squares are the data collected from at A/m in the main panel. A solid straight line indicates the fit to Eq. (##FORMU##137##3##), with .</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>The scaling plot of the transverse data shown with solid circles in Fig. ##FIG##2##3## using Eq. (##FORMU##119##1##): versus . A good collapse of the data to the universal branches is obtained with A/m, , and . A dashed straight line represents the asymptotic behavior for , . Inset: Schematics of the plastic flow () and the smectic flow ().</p></caption></fig>" ]

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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$V_{y}$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:msub><mml:mi>V</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}=J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10^{-8}$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_{y,\\text{d}}$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_\\text{d}$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq18\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(J_{y}^2 + J_{x}^2)^{1/2}$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq19\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_\\text{d}$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq20\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(J_{y,\\text{d}}^2 + J_{x}^2)^{1/2} = J_\\text{d}$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq21\"><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}&gt;J_{y,\\text{d}}$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq22\"><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}=0$$\\end{document}</tex-math><mml:math id=\"M44\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq23\"><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M46\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq24\"><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$_{x}$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:msub><mml:mrow/><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq25\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$_{1-x}$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:msub><mml:mrow/><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq26\"><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M52\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq27\"><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M54\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq28\"><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M56\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq29\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq30\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$E_{y}$$\\end{document}</tex-math><mml:math id=\"M60\"><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq31\"><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M62\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq32\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq33\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq34\"><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq35\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$E_{y}$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq36\"><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10^{-8}$$\\end{document}</tex-math><mml:math id=\"M72\"><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq37\"><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M74\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq38\"><alternatives><tex-math id=\"M75\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x} \\approx 1.38\\times 10^7$$\\end{document}</tex-math><mml:math id=\"M76\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>≈</mml:mo><mml:mn>1.38</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq39\"><alternatives><tex-math id=\"M77\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M78\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M79\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\equiv J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M80\"><mml:mrow><mml:mo>≡</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M81\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M82\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq42\"><alternatives><tex-math id=\"M83\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&gt; J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M84\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq43\"><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M86\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq44\"><alternatives><tex-math id=\"M87\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M88\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq45\"><alternatives><tex-math id=\"M89\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}$$\\end{document}</tex-math><mml:math id=\"M90\"><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq46\"><alternatives><tex-math id=\"M91\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10^{-8}$$\\end{document}</tex-math><mml:math id=\"M92\"><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq47\"><alternatives><tex-math id=\"M93\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M94\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq48\"><alternatives><tex-math id=\"M95\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_\\text{d}$$\\end{document}</tex-math><mml:math id=\"M96\"><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq49\"><alternatives><tex-math id=\"M97\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M98\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq50\"><alternatives><tex-math id=\"M99\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x} &lt; J_\\text{d}$$\\end{document}</tex-math><mml:math id=\"M100\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq51\"><alternatives><tex-math id=\"M101\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M102\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq52\"><alternatives><tex-math id=\"M103\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M104\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq53\"><alternatives><tex-math id=\"M105\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_\\text{d}$$\\end{document}</tex-math><mml:math id=\"M106\"><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq54\"><alternatives><tex-math id=\"M107\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M108\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq55\"><alternatives><tex-math id=\"M109\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y} = \\sqrt{J_\\text{d}^{2} - J_{x}^{2}}$$\\end{document}</tex-math><mml:math id=\"M110\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msubsup><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq56\"><alternatives><tex-math id=\"M111\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M112\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq57\"><alternatives><tex-math id=\"M113\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M114\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq58\"><alternatives><tex-math id=\"M115\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_\\text{d}&lt; J_{x} &lt; J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M116\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq59\"><alternatives><tex-math id=\"M117\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M118\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq60\"><alternatives><tex-math id=\"M119\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}$$\\end{document}</tex-math><mml:math id=\"M120\"><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq61\"><alternatives><tex-math id=\"M121\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x} &gt; J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M122\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq62\"><alternatives><tex-math id=\"M123\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}$$\\end{document}</tex-math><mml:math id=\"M124\"><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq63\"><alternatives><tex-math id=\"M125\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M126\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq64\"><alternatives><tex-math id=\"M127\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}\\ge J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M128\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>≥</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq65\"><alternatives><tex-math id=\"M129\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M130\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq66\"><alternatives><tex-math id=\"M131\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}&gt;0$$\\end{document}</tex-math><mml:math id=\"M132\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq67\"><alternatives><tex-math id=\"M133\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}=0$$\\end{document}</tex-math><mml:math id=\"M134\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq68\"><alternatives><tex-math id=\"M135\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}\\approx 1.5\\times 10^7$$\\end{document}</tex-math><mml:math id=\"M136\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>≈</mml:mo><mml:mn>1.5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq69\"><alternatives><tex-math id=\"M137\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M138\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq70\"><alternatives><tex-math id=\"M139\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*} \\approx 1.38\\times 10^7$$\\end{document}</tex-math><mml:math id=\"M140\"><mml:mrow><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo>≈</mml:mo><mml:mn>1.38</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq71\"><alternatives><tex-math id=\"M141\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M142\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq72\"><alternatives><tex-math id=\"M143\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M144\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq73\"><alternatives><tex-math id=\"M145\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x} (&lt;J_{x}^{*})$$\\end{document}</tex-math><mml:math id=\"M146\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>&lt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq74\"><alternatives><tex-math id=\"M147\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M148\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq75\"><alternatives><tex-math id=\"M149\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y,\\text{d}}$$\\end{document}</tex-math><mml:math id=\"M150\"><mml:msub><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>d</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq76\"><alternatives><tex-math id=\"M151\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M152\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq77\"><alternatives><tex-math id=\"M153\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M154\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq78\"><alternatives><tex-math id=\"M155\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M156\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq79\"><alternatives><tex-math id=\"M157\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-\\rho _{y}$$\\end{document}</tex-math><mml:math id=\"M158\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq80\"><alternatives><tex-math id=\"M159\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M160\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq81\"><alternatives><tex-math id=\"M161\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}=J_{x}^{*} (\\approx 1.38\\times 10^7$$\\end{document}</tex-math><mml:math id=\"M162\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>≈</mml:mo><mml:mn>1.38</mml:mn><mml:mo>×</mml:mo></mml:mrow><mml:msup><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq82\"><alternatives><tex-math id=\"M163\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M164\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq83\"><alternatives><tex-math id=\"M165\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y} \\propto J_{y}^{\\beta /\\Delta }$$\\end{document}</tex-math><mml:math id=\"M166\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>∝</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq84\"><alternatives><tex-math id=\"M167\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta /\\Delta = 2.2\\pm 0.3$$\\end{document}</tex-math><mml:math id=\"M168\"><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>=</mml:mo><mml:mn>2.2</mml:mn><mml:mo>±</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq85\"><alternatives><tex-math id=\"M169\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y,\\text{lin}}$$\\end{document}</tex-math><mml:math id=\"M170\"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>lin</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq86\"><alternatives><tex-math id=\"M171\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$|1 - J_{x}/J_{x}^{*}|$$\\end{document}</tex-math><mml:math id=\"M172\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo></mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq87\"><alternatives><tex-math id=\"M173\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}(J_{x}, J_{y})$$\\end{document}</tex-math><mml:math id=\"M174\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq88\"><alternatives><tex-math id=\"M175\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_y = 1.79\\times 10^4,$$\\end{document}</tex-math><mml:math id=\"M176\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.79</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq89\"><alternatives><tex-math id=\"M177\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$5.36\\times 10^4,$$\\end{document}</tex-math><mml:math id=\"M178\"><mml:mrow><mml:mn>5.36</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq90\"><alternatives><tex-math id=\"M179\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8.93\\times 10^4,$$\\end{document}</tex-math><mml:math id=\"M180\"><mml:mrow><mml:mn>8.93</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq91\"><alternatives><tex-math id=\"M181\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.25\\times 10^5$$\\end{document}</tex-math><mml:math id=\"M182\"><mml:mrow><mml:mn>1.25</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>5</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq92\"><alternatives><tex-math id=\"M183\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M184\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq93\"><alternatives><tex-math id=\"M185\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M186\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq94\"><alternatives><tex-math id=\"M187\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}(J_{x},J_{y})$$\\end{document}</tex-math><mml:math id=\"M188\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq95\"><alternatives><tex-math id=\"M189\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_y = 1.79\\times 10^4$$\\end{document}</tex-math><mml:math id=\"M190\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.79</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq96\"><alternatives><tex-math id=\"M191\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M192\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq97\"><alternatives><tex-math id=\"M193\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y,\\text{lin}} \\propto |1 - J_{x}/J_{x}^{*}|^{\\beta }$$\\end{document}</tex-math><mml:math id=\"M194\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>lin</mml:mtext></mml:mrow></mml:msub><mml:mo>∝</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq98\"><alternatives><tex-math id=\"M195\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta = 2.65 \\pm 0.3$$\\end{document}</tex-math><mml:math id=\"M196\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mn>2.65</mml:mn><mml:mo>±</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq99\"><alternatives><tex-math id=\"M197\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-\\rho _{y}$$\\end{document}</tex-math><mml:math id=\"M198\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq100\"><alternatives><tex-math id=\"M199\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}(J_{x}, J_{y}) / |1 - J_{x}/J_{x}^{*}|^{\\beta }$$\\end{document}</tex-math><mml:math id=\"M200\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">/</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq101\"><alternatives><tex-math id=\"M201\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w(= J_{y}/|1 - J_{x}/J_{x}^{*}|^\\Delta )$$\\end{document}</tex-math><mml:math id=\"M202\"><mml:mrow><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mo stretchy=\"false\">|</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq102\"><alternatives><tex-math id=\"M203\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*} = 1.378\\times 10^7$$\\end{document}</tex-math><mml:math id=\"M204\"><mml:mrow><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>1.378</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq103\"><alternatives><tex-math id=\"M205\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M206\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq104\"><alternatives><tex-math id=\"M207\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta = 2.65$$\\end{document}</tex-math><mml:math id=\"M208\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mn>2.65</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq105\"><alternatives><tex-math id=\"M209\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta = 1.2$$\\end{document}</tex-math><mml:math id=\"M210\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>=</mml:mo><mml:mn>1.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq106\"><alternatives><tex-math id=\"M211\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w\\rightarrow \\infty$$\\end{document}</tex-math><mml:math id=\"M212\"><mml:mrow><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq107\"><alternatives><tex-math id=\"M213\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y} / |1 - J_{x}/J_{x}^{*}|^{\\beta }\\propto w^{\\beta /\\Delta }$$\\end{document}</tex-math><mml:math id=\"M214\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup><mml:mo>∝</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq108\"><alternatives><tex-math id=\"M215\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&lt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M216\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq109\"><alternatives><tex-math id=\"M217\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&gt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M218\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq110\"><alternatives><tex-math id=\"M219\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M220\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq111\"><alternatives><tex-math id=\"M221\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M222\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq112\"><alternatives><tex-math id=\"M223\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-\\rho _{y}$$\\end{document}</tex-math><mml:math id=\"M224\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq113\"><alternatives><tex-math id=\"M225\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M226\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq114\"><alternatives><tex-math id=\"M227\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M228\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq115\"><alternatives><tex-math id=\"M229\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}\\equiv E_{y}/J_{y}$$\\end{document}</tex-math><mml:math id=\"M230\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>≡</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq116\"><alternatives><tex-math id=\"M231\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M232\"><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq117\"><alternatives><tex-math id=\"M233\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}(J_{x}, J_{y})$$\\end{document}</tex-math><mml:math id=\"M234\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq118\"><alternatives><tex-math id=\"M235\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M236\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq119\"><alternatives><tex-math id=\"M237\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M238\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M239\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\rho _{y}(J_{x}, J_{y}) = |1 - J_{x}/J_{x}^{*}|^{\\beta } f_{\\pm }\\left( \\frac{J_{y}}{|1 - J_{x}/J_{x}^{*}|^{\\Delta }}\\right) , \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M240\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup><mml:msub><mml:mi>f</mml:mi><mml:mo>±</mml:mo></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo></mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq120\"><alternatives><tex-math id=\"M241\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta$$\\end{document}</tex-math><mml:math id=\"M242\"><mml:mi>β</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq121\"><alternatives><tex-math id=\"M243\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta$$\\end{document}</tex-math><mml:math id=\"M244\"><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq122\"><alternatives><tex-math id=\"M245\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w \\equiv J_{y}/|1 - J_{x}/J_{x}^{*}|^\\Delta$$\\end{document}</tex-math><mml:math id=\"M246\"><mml:mrow><mml:mi>w</mml:mi><mml:mo>≡</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq123\"><alternatives><tex-math id=\"M247\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f_{+}(w)$$\\end{document}</tex-math><mml:math id=\"M248\"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>+</mml:mo></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq124\"><alternatives><tex-math id=\"M249\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f_{-}(w)$$\\end{document}</tex-math><mml:math id=\"M250\"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>-</mml:mo></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq125\"><alternatives><tex-math id=\"M251\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&gt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M252\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq126\"><alternatives><tex-math id=\"M253\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&lt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M254\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq127\"><alternatives><tex-math id=\"M255\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w\\rightarrow \\infty$$\\end{document}</tex-math><mml:math id=\"M256\"><mml:mrow><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq128\"><alternatives><tex-math id=\"M257\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f_{\\pm }(w) \\approx w^{\\beta /\\Delta }$$\\end{document}</tex-math><mml:math id=\"M258\"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>±</mml:mo></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>≈</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq129\"><alternatives><tex-math id=\"M259\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-\\rho _{y}$$\\end{document}</tex-math><mml:math id=\"M260\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq130\"><alternatives><tex-math id=\"M261\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x} = J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M262\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M263\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\rho _{y}(J_{x} = J_{x}^{*}) \\propto J_{y}^{\\beta /\\Delta }. \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M264\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>∝</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow></mml:msubsup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq131\"><alternatives><tex-math id=\"M265\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w\\rightarrow 0$$\\end{document}</tex-math><mml:math id=\"M266\"><mml:mrow><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq132\"><alternatives><tex-math id=\"M267\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f_{-}(w) =0$$\\end{document}</tex-math><mml:math id=\"M268\"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>-</mml:mo></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq133\"><alternatives><tex-math id=\"M269\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f_{+}(w) =\\mathrm {const.}$$\\end{document}</tex-math><mml:math id=\"M270\"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>+</mml:mo></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant=\"normal\">const</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq134\"><alternatives><tex-math id=\"M271\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y,\\text{lin}}$$\\end{document}</tex-math><mml:math id=\"M272\"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>lin</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq135\"><alternatives><tex-math id=\"M273\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&gt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M274\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M275\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\rho _{y,\\text{lin}} \\propto |1 - J_{x}/J_{x}^{*}|^{\\beta }. \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M276\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>lin</mml:mtext></mml:mrow></mml:msub><mml:mo>∝</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq136\"><alternatives><tex-math id=\"M277\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta /\\Delta = 2.2\\pm 0.3$$\\end{document}</tex-math><mml:math id=\"M278\"><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>=</mml:mo><mml:mn>2.2</mml:mn><mml:mo>±</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq137\"><alternatives><tex-math id=\"M279\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y,\\text{lin}}$$\\end{document}</tex-math><mml:math id=\"M280\"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>lin</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq138\"><alternatives><tex-math id=\"M281\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$|1- J_{x}/J_{x}^{*}|$$\\end{document}</tex-math><mml:math id=\"M282\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo></mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq139\"><alternatives><tex-math id=\"M283\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y,\\text{lin}}$$\\end{document}</tex-math><mml:math id=\"M284\"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>lin</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq140\"><alternatives><tex-math id=\"M285\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_y = 1.79\\times 10^4$$\\end{document}</tex-math><mml:math id=\"M286\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.79</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq141\"><alternatives><tex-math id=\"M287\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M288\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq142\"><alternatives><tex-math id=\"M289\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}(J_{x},J_{y})$$\\end{document}</tex-math><mml:math id=\"M290\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq143\"><alternatives><tex-math id=\"M291\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}(J_{x},J_{y})$$\\end{document}</tex-math><mml:math id=\"M292\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq144\"><alternatives><tex-math id=\"M293\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_y = 1.79\\times 10^4,$$\\end{document}</tex-math><mml:math id=\"M294\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.79</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq145\"><alternatives><tex-math id=\"M295\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$5.36\\times 10^4,$$\\end{document}</tex-math><mml:math id=\"M296\"><mml:mrow><mml:mn>5.36</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq146\"><alternatives><tex-math id=\"M297\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8.93\\times 10^4,$$\\end{document}</tex-math><mml:math id=\"M298\"><mml:mrow><mml:mn>8.93</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq147\"><alternatives><tex-math id=\"M299\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.25\\times 10^5$$\\end{document}</tex-math><mml:math id=\"M300\"><mml:mrow><mml:mn>1.25</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>5</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq148\"><alternatives><tex-math id=\"M301\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M302\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq149\"><alternatives><tex-math id=\"M303\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M304\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq150\"><alternatives><tex-math id=\"M305\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y,\\text{lin}}$$\\end{document}</tex-math><mml:math id=\"M306\"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mtext>lin</mml:mtext></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq151\"><alternatives><tex-math id=\"M307\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta = 2.65\\pm 0.3$$\\end{document}</tex-math><mml:math id=\"M308\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mn>2.65</mml:mn><mml:mo>±</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq152\"><alternatives><tex-math id=\"M309\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta /\\Delta$$\\end{document}</tex-math><mml:math id=\"M310\"><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq153\"><alternatives><tex-math id=\"M311\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta$$\\end{document}</tex-math><mml:math id=\"M312\"><mml:mi>β</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq154\"><alternatives><tex-math id=\"M313\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta$$\\end{document}</tex-math><mml:math id=\"M314\"><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq155\"><alternatives><tex-math id=\"M315\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta = 1.2\\pm 0.2$$\\end{document}</tex-math><mml:math id=\"M316\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>=</mml:mo><mml:mn>1.2</mml:mn><mml:mo>±</mml:mo><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq156\"><alternatives><tex-math id=\"M317\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y}(J_{x}, J_{y}) / |1 - J_{x}/J_{x}^{*}|^{\\beta }$$\\end{document}</tex-math><mml:math id=\"M318\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">/</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq157\"><alternatives><tex-math id=\"M319\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w(= J_{y}/|1 - J_{x}/J_{x}^{*}|^\\Delta )$$\\end{document}</tex-math><mml:math id=\"M320\"><mml:mrow><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mo stretchy=\"false\">|</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq158\"><alternatives><tex-math id=\"M321\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}^{*} = 1.378\\times 10^7$$\\end{document}</tex-math><mml:math id=\"M322\"><mml:mrow><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>1.378</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq159\"><alternatives><tex-math id=\"M323\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M324\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq160\"><alternatives><tex-math id=\"M325\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta = 2.65$$\\end{document}</tex-math><mml:math id=\"M326\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mn>2.65</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq161\"><alternatives><tex-math id=\"M327\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta = 1.2$$\\end{document}</tex-math><mml:math id=\"M328\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>=</mml:mo><mml:mn>1.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq162\"><alternatives><tex-math id=\"M329\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w\\rightarrow \\infty$$\\end{document}</tex-math><mml:math id=\"M330\"><mml:mrow><mml:mi>w</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq163\"><alternatives><tex-math id=\"M331\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho _{y} / |1 - J_{x}/J_{x}^{*}|^{\\beta }\\propto w^{\\beta /\\Delta }$$\\end{document}</tex-math><mml:math id=\"M332\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>β</mml:mi></mml:msup><mml:mo>∝</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mrow><mml:mi>β</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq164\"><alternatives><tex-math id=\"M333\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}=J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M334\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq165\"><alternatives><tex-math id=\"M335\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1+1$$\\end{document}</tex-math><mml:math id=\"M336\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq166\"><alternatives><tex-math id=\"M337\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_y$$\\end{document}</tex-math><mml:math id=\"M338\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq167\"><alternatives><tex-math id=\"M339\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_x$$\\end{document}</tex-math><mml:math id=\"M340\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq168\"><alternatives><tex-math id=\"M341\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_y$$\\end{document}</tex-math><mml:math id=\"M342\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq169\"><alternatives><tex-math id=\"M343\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_x$$\\end{document}</tex-math><mml:math id=\"M344\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq170\"><alternatives><tex-math id=\"M345\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_y$$\\end{document}</tex-math><mml:math id=\"M346\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq171\"><alternatives><tex-math id=\"M347\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_x$$\\end{document}</tex-math><mml:math id=\"M348\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq172\"><alternatives><tex-math id=\"M349\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M350\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq173\"><alternatives><tex-math id=\"M351\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&lt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M352\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq174\"><alternatives><tex-math id=\"M353\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&gt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M354\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq175\"><alternatives><tex-math id=\"M355\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}&gt;J_{x}^{*}$$\\end{document}</tex-math><mml:math id=\"M356\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msubsup><mml:mi>J</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq176\"><alternatives><tex-math id=\"M357\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M358\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq177\"><alternatives><tex-math id=\"M359\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{x}$$\\end{document}</tex-math><mml:math id=\"M360\"><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq178\"><alternatives><tex-math id=\"M361\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta = 2.65\\pm 0.3$$\\end{document}</tex-math><mml:math id=\"M362\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mn>2.65</mml:mn><mml:mo>±</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq179\"><alternatives><tex-math id=\"M363\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta = 1.2\\pm 0.2$$\\end{document}</tex-math><mml:math id=\"M364\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>=</mml:mo><mml:mn>1.2</mml:mn><mml:mo>±</mml:mo><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq180\"><alternatives><tex-math id=\"M365\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta = 4$$\\end{document}</tex-math><mml:math id=\"M366\"><mml:mrow><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq181\"><alternatives><tex-math id=\"M367\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta = 2$$\\end{document}</tex-math><mml:math id=\"M368\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq182\"><alternatives><tex-math id=\"M369\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$_x$$\\end{document}</tex-math><mml:math id=\"M370\"><mml:msub><mml:mrow/><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq183\"><alternatives><tex-math id=\"M371\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$_{1-x}$$\\end{document}</tex-math><mml:math id=\"M372\"><mml:msub><mml:mrow/><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq184\"><alternatives><tex-math id=\"M373\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x\\approx 0.78$$\\end{document}</tex-math><mml:math id=\"M374\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>≈</mml:mo><mml:mn>0.78</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq185\"><alternatives><tex-math id=\"M375\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I_{x}, I_{y}$$\\end{document}</tex-math><mml:math id=\"M376\"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq186\"><alternatives><tex-math id=\"M377\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$V_{y}$$\\end{document}</tex-math><mml:math id=\"M378\"><mml:msub><mml:mi>V</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq187\"><alternatives><tex-math id=\"M379\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$V_{x}$$\\end{document}</tex-math><mml:math id=\"M380\"><mml:msub><mml:mi>V</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq188\"><alternatives><tex-math id=\"M381\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2\\times 2$$\\end{document}</tex-math><mml:math id=\"M382\"><mml:mrow><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq189\"><alternatives><tex-math id=\"M383\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M384\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq190\"><alternatives><tex-math id=\"M385\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$T_\\text{c} = 6.2$$\\end{document}</tex-math><mml:math id=\"M386\"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>c</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq191\"><alternatives><tex-math id=\"M387\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^4$$\\end{document}</tex-math><mml:math id=\"M388\"><mml:msup><mml:mrow/><mml:mn>4</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq192\"><alternatives><tex-math id=\"M389\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{\\text{d}}=0.86\\times 10^{7}$$\\end{document}</tex-math><mml:math id=\"M390\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mtext>d</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn>0.86</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq193\"><alternatives><tex-math id=\"M391\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^2$$\\end{document}</tex-math><mml:math id=\"M392\"><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq194\"><alternatives><tex-math id=\"M393\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}-E_{y}$$\\end{document}</tex-math><mml:math id=\"M394\"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq195\"><alternatives><tex-math id=\"M395\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$E_{y}(J_{x},J_{y})$$\\end{document}</tex-math><mml:math id=\"M396\"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq196\"><alternatives><tex-math id=\"M397\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$E_{y}(J_{x},J_{y}=0)$$\\end{document}</tex-math><mml:math id=\"M398\"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq197\"><alternatives><tex-math id=\"M399\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{y}$$\\end{document}</tex-math><mml:math id=\"M400\"><mml:msub><mml:mi>J</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq198\"><alternatives><tex-math id=\"M401\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$E_{x}$$\\end{document}</tex-math><mml:math id=\"M402\"><mml:msub><mml:mi>E</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq199\"><alternatives><tex-math id=\"M403\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$E_{y}$$\\end{document}</tex-math><mml:math id=\"M404\"><mml:msub><mml:mi>E</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41598_2024_51534_MOESM1_ESM.pdf\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par3\">The certified nurse specialist system aims to expand and improve the quality of nursing care by utilizing advanced nursing skills and knowledge in specific nursing fields and providing advanced nursing practice to individuals in need of care in all settings. A certified nurse has proficient skills and knowledge in a particular field of nursing and is certified by the Japanese Nursing Association^{##UREF##0##1##}. A certified perioperative nurse (CPN) has passed the certification examination after completing &gt; 800 h of the specialized perioperative curriculum at a designated educational institution in Japan. CPNs practice safety management to minimize physical and mental surgical stress, prevent secondary complications, and provide continuous nursing care in the perioperative period^{##UREF##0##1##}. They practice high-level nursing care for individuals, families, and groups based on high clinical reasoning ability and disease state judgment using nursing skills and knowledge and provide guidance and consultation to nursing professionals through nursing practice.</p>", "<p id=\"Par4\">Patients scheduled for elective surgery may experience various anxieties. In addition, patients may feel anxious and tense about the disease and its associated treatment^{##REF##35157656##2##}. This is because some patients find it difficult to understand and imagine a surgical procedure through explanations alone. It is crucial for patients to understand the changes that occur in their own body after surgery and receive explanations of the process from the preoperative period to postoperative discharge from the hospital. Through this, patients understand the necessity and methods of breathing techniques, pain control, and getting out of bed early and can take necessary actions to help in the recovery process. This is significantly critical as a prenursing intervention^{##UREF##1##3##}. There exist two distinct categories delineating the perioperative nurse's engagement with preoperative patients: \"preoperative outpatient care,\" initiating nursing intervention upon the patient's determination to pursue either outpatient or inpatient major surgical procedures, and \"preoperative nursing visits,\" commencing nursing intervention upon the patient's hospital admission for the surgical endeavor^{##REF##35970660##4##,##REF##31879076##5##}. Preoperative outpatient care is when a patient awaiting surgery goes to a hospital and is examined by a perioperative nurse before admission. Preoperative outpatient care is performed in the preoperative outpatient clinic. Nevertheless, not all hospitals in Japan possess preoperative outpatient clinics^{##UREF##2##6##}. Preoperative nursing visits are conducted in hospitals devoid of a dedicated preoperative outpatient clinic. Preoperative nursing visits are visits by perioperative nurses to a patient in a hospital waiting for surgery. In preoperative outpatient care and preoperative nursing visits, perioperative nurses obtain physical characteristics data, such as height and weight, and patient information, such as medical history, allergies, and medications required for surgery.</p>", "<p id=\"Par5\">The process, from entering the operating room to the end of surgery, and the state of the operating room are explained to the patients in advance^{##REF##36681844##7##}. Frequent causes for the sudden cessation of surgical interventions encompass \"anxiety or skepticism,\" \"acute illness,\" \"changes in treatment plans,\" and \"consent authorization \"^{##REF##19413817##8##–##REF##36374361##10##}. Perioperative nurses should ensure that patients undergoing surgery receive preoperative outpatient care and preoperative nursing visits. However, in Japan, preoperative intervention by perioperative nurses is not currently available for all patients undergoing surgery^{##UREF##3##11##}. It has been reported that the rate of preoperative assessment by perioperative nurses in Japan is about 75%, and in cases where no preoperative assessment has been performed by perioperative nurses, the current situation is that nursing interventions are conducted based only on the information obtained by outpatient nurses and ward nurses^{##UREF##3##11##}. CPNs often work in hospitals, and some roles include encouraging patients undergoing surgery to have a preoperative outpatient care or preoperative nursing visits and increasing the rate at which perioperative nurses perform preoperative assessments^{##UREF##0##1##}. However, to date, there have been no reports on the effects of CPN enrollment on prevalence of preoperative outpatient clinic and preoperative assessments. That is, facilities with CPNs may have higher rates of preoperative assessment, whereas those without CPNs may have lower rates. This is because the CPN has established, instructed, and managed systems for facilities and perioperative nurses to improve their preoperative assessment rates^{##UREF##0##1##}. Therefore, this study aimed to analyze the relationship between the presence or absence of CPN in the operating room and prevalence of preoperative outpatient clinic and the preoperative assessment rate. Furthermore, we elected to undertake a comparative analysis, employing the presence of CPN as the dependent variable. Concurrently, we considered variables such as hospital and operating room dimensions, staff qualifications, the existence of preoperative outpatient consultations, preoperative nursing consultations, the rate of preoperative evaluation implementation over a one-year span, and the incidence and rate of postoperative nursing consultations over the same duration, positing that such an approach would elucidate causal relationships. We hypothesized that the presence of CPNs is associated with an increase in the preoperative assessment rate and number of preoperative outpatient clinic. The expected influence of this study was that we will find CPNs to work effectively during the preoperative nursing visits and preoperative outpatient care and improve the quality of preoperative nursing interventions.</p>", "<title>Operational definitions</title>", "<p id=\"Par6\">In this study, a preoperative assessment was defined as preoperative outpatient care and preoperative nursing visits by the perioperative nurses to patients undergoing surgery.</p>" ]

[ "<title>Methods</title>", "<title>Study design and ethical considerations</title>", "<p id=\"Par17\">The study design was a multicenter retrospective cross-sectional study. This study was approved by the Ethics Committee of the Japan Perioperative Nursing Academy (no. 14). All methods were performed in accordance with relevant guidelines and regulations. This study was conducted in accordance with the ethical standards of the Declaration of Helsinki (1964) and its amendments. Informed consent was confirmed by completing a questionnaire, and the Ethics Committee of the Japan Perioperative Nursing Academy confirmed this method of consent. All observational protocols were approved by the institutional and licensing committees of the Japan Perioperative Nursing Academy. The study design adhered to the Strengthening the Reporting of Observational studies in Epidemiology guidelines^{##REF##27465839##21##}. In this study, the questions were entered anonymously so that the names of the individuals and institutions to which they belonged were not identified. Consent was provided by completing the questionnaire. In addition, the system of the questionnaire tool “Questant” (<ext-link ext-link-type=\"uri\" xlink:href=\"https://questant.jp\">https://questant.jp</ext-link>) used in the survey in this study was monitored 24 h a day, 365 days a year. \"Questant\" serves as a web-based instrument for questionnaire administration, encompassing both nominal and ratio scales.</p>", "<title>Study setting and population</title>", "<p id=\"Par18\">This multicenter, retrospective cross-sectional study was conducted between February 2021 and September 2022. The study was conducted at 865 hospitals in Japan that administered general anesthesia in &gt; 800 procedures annually to standardize the number of operations and other matters as facilities that provide comprehensive and advanced medical care, in accordance with the requirements of the additional comprehensive hospitalization system. Facilities accredited with in excess of 800 cases per annum of general anaesthesia were sourced from the database accessible on the Ministry of Health, Labour and Welfare website^{##UREF##6##22##}.</p>", "<title>Outcome and data collection</title>", "<p id=\"Par19\">Regarding the scale of hospitals and operating rooms, the number of hospital beds, operating rooms (all operating rooms), annual number of operations, and annual number of general anesthesia procedures were surveyed. In relation to the operating room staff, the number of perioperative nurses, number of years of experience, presence or absence of CPNs, and number of such nurses were registered. Institutions with CPNs were categorized into the enrollment group and institutions without CPNs into the nonenrolled group. We investigated the presence or absence of preoperative outpatient clinic and preoperative nursing visits, rate of preoperative assessments (1 year), presence or absence of postoperative nursing visits, and rate of implementation (1 year). The data covered the fiscal year 2020–2021. The primary endpoint was the preoperative assessment rate, including preoperative outpatient care and preoperative nursing visits. The secondary endpoints were the presence or absence of a preoperative outpatient clinic, presence or absence of a postoperative nursing visits, and rate of nursing visits. The data was collected using a questionnaire with answers input to Questant (<ext-link ext-link-type=\"uri\" xlink:href=\"https://questant.jp\">https://questant.jp</ext-link>), an application that allowed input via the Internet, and a quantitative survey was conducted. The questionnaire was created independently; all researchers confirmed that the content was in line with the study objectives, and it was used after the pretest.</p>", "<title>Data analysis procedures</title>", "<p id=\"Par20\">The scale of hospitals and operating rooms, in relation to the operating room staff and preoperative outpatient care, are presented as median (interquartile range). The sample size could not be calculated because there is no sample data for CPN. To analyze the factors affecting the rate of preoperative assessment by the primary endpoint of preoperative outpatient care and preoperative nursing visits, we performed multiple linear regression analysis by facility characteristics, personal backgrounds, and the presence or absence of CPNs. In addition, the CPN enrolled group was compared with the nonenrolled group using the Student’s t-test, and differences were considered significant at a significance level of 5%. Secondary endpoints were compared using the chi-squared test, Fisher's exact test, Mann‒Whitney U test, and Student’s t-test. Differences with a significance level of 5% were considered statistically significant. The statistical software JMP® 15 (SAS Institute Inc., Cary, NC, USA) was used in this study.</p>" ]

[ "<title>Results</title>", "<title>Participant demographics</title>", "<p id=\"Par7\">Of the 865 institutions included in this study, 252 responded (response rate, 29.1%). After an initial analysis, 5 hospitals with missing data were excluded, and data from 247 hospitals were finally analyzed (Fig. ##FIG##0##1##). The enrolled and nonenrolled groups had 130 (52.6%) and 117 (47.4%) CPNs, respectively.</p>", "<title>Facility characteristics</title>", "<p id=\"Par8\">The characteristics of the study facilities are shown in Table ##TAB##0##1##. Significant differences were found between the two groups regarding the number of intensive care units (ICU) (<italic>p</italic> &lt; 0.01), advanced treatment hospitals (<italic>p</italic> &lt; 0.01), licensed beds (<italic>p</italic> &lt; 0.01), total operating rooms (<italic>p</italic> &lt; 0.01), operations per year (<italic>p</italic> &lt; 0.01), and procedures involving general anesthesia (<italic>p</italic> &lt; 0.01).</p>", "<title>Perioperative nurse background</title>", "<p id=\"Par9\">The perioperative nurse background of the study facilities is shown in Table ##TAB##1##2##. The enrolled group had significantly more perioperative nurses than the nonenrolled group (<italic>p</italic> &lt; 0.01); however, no significant difference was noted in the number of perioperative nurses per operating room between the two groups (<italic>p</italic> = 0.13). Of the 130 facilities, 73.2% had 1 CPN.</p>", "<title>Preoperative assessment and preoperative and postoperative nursing visits</title>", "<p id=\"Par10\">The preoperative and postoperative relationships are shown in Table ##TAB##2##3##. Regarding the presence or absence of a preoperative outpatient clinic, patients from 68 (52.3%) and 41 (35.0%) institutions in the enrolled and nonenrolled groups. Respectively, underwent a preoperative assessment; the rate of preoperative assessments in the enrolled group was significantly higher than that in the nonenrolled group (<italic>p</italic> = 0.01). Regarding the preoperative assessment rate, the medians (quartile ranges) of the enrolled and nonenrolled groups were 90.0% (70.0–99.0%) and 75.0% (54.5–95.0%), respectively, indicating a significantly higher preoperative assessment rate in the enrolled group than in the nonenrolled group (<italic>p</italic> = 0.01). Regarding conducting postoperative nursing visits, the enrolled group was significantly more likely to conduct postoperative nursing visits than the nonenrolled group (<italic>p</italic> = 0.03). No significant difference was observed in the rate of postoperative nursing visits between the two groups.</p>", "<p id=\"Par11\">Multiple linear regression analysis of the factors influencing the preoperative assessment rate, including facility characteristics, personal background, and the presence or absence of CPNs, revealed a significant association with CPN presence (R² = 0.571, adjusted R² = 0.571) (B = 6.7, <italic>p</italic> &lt; 0.01) (Table ##TAB##3##4##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par12\">This study aimed to analyze the relationship between the presence or absence of CPN in the operating room and prevalence of preoperative outpatient clinic and the preoperative assessment rate. The results from this study demonstrated significant differences between the enrolled and nonenrolled CPN groups in all facility characteristics, except the location. Skilled professionals, such as certified and professional nurses, have different requirements depending on the hospital size. In addition, it suggest that CPNs tend to be placed in acute care hospitals in which patients may require surgery. That is, the CPNs were placed in an environment where they could intervene preoperatively with patients undergoing surgery.</p>", "<p id=\"Par13\">From the results of facility characteristics and medical staff backgrounds, it can be inferred that the size of facilities and staffing in the enrolled group were larger than those in the nonenrolled group. With an increase in the number of surgeries, appropriate staffing with operating room nurses is critical^{##REF##24616946##12##–##REF##15974387##14##}. We believed that the preoperative assessment rate would be high because there were several perioperative nurses, with the number of operations increasing according to the facility characteristics of the enrolled and nonenrolled groups. However, no significant difference was found in the number of patients per operating room between the enrolled and nonenrolled groups, suggesting that there may not be any additional personnel to perform preoperative assessments. Consequently, predicated on the outcomes of the multiple regression analysis, it appears plausible that the augmented preoperative consultation rate within the registration group does not solely emanate from an ample cadre of operating room personnel for preoperative assessments. Rather, the involvement of CPNs might exert influence on this elevated preoperative assessment frequency. For patients for whom surgery is decided, starting physical and psychological preparations before surgery is crucial to provide a safe and secure surgery^{##REF##35251804##15##}. For patients undergoing surgery, nurse-led preoperative outpatient visits have been introduced in various specialties to prevent cancellations before surgery^{##REF##26352856##16##–##UREF##4##18##}. In addition, there is no difference in costs between professional nurse- and physician-led preoperative outpatients when examined using economic models based on patient satisfaction with care and completeness^{##UREF##5##19##}. Therefore, setting up a preoperative outpatient clinic and intervening from an early stage may be beneficial for patients undergoing surgery and for medical professionals. The enrolled group had a significantly higher preoperative assessment rate than the nonenrolled group. An effective preoperative assessment improves patient outcomes by ensuring that patients are adequately prepared for anesthesia, surgery, and the postoperative period^{##REF##32362485##20##}. Moreover, it can improve hospital efficiency by shortening patient waiting time and allowing for an early discharge. Consequently, a preoperative assessment within a preoperative outpatient clinic, fortified by the presence of a CPN, may serve as an invaluable mechanism to uphold patient safety and facilitate a more structured hospital sojourn. In the operating rooms of Japanese hospitals, CPNs are not always deployed. Therefore, for the safety and security of patients undergoing surgery, hospital operating rooms should deploy CPNs and increase the rate of preoperative assessment.</p>", "<p id=\"Par14\">This study had a few limitations. Within our study, encompassing 865 facilities, a mere 247 provided responses, a circumstance that could be delineated as a potential limitation predisposing to bias. The 247 hospitals in this study were active in preoperative evaluation and may have had a latent tendency to incorporate CPNs or an inherent motivation to foster and acquire proficiency in CPN. In addition, whilst we discerned a potential causal nexus between CPNs and the preoperative outpatient clinic and rates of preoperative assessment, elucidating the precise activities and involvements of CPNs influencing these rates remained elusive within our analysis. In the future, we aim to conduct additional studies on CPNs, including quantitative and qualitative studies on the backgrounds of CPNs and the activities they performed in the affiliated facilities.</p>", "<p id=\"Par15\">This study suggests that CPN enrollment may contribute to the establishment of preoperative outpatient. We believe that the establishment of this preoperative outpatient clinic is closely related to an improvement in the preoperative assessment rates. Preoperative outpatients clinics are more efficient, as preoperative interviews do not require hospitalization. Therefore, we infer that the preoperative assessment rate was higher in the facilities with CPNs, which had preoperative outpatient clinics, because they could interview patients scheduled for surgery without failure. This is suggested by the results of the multivariate analysis of the preoperative assessment rates.</p>", "<p id=\"Par16\">Facilities with CPNs have a significantly higher prevalence of preoperative outpatient clinic and significantly higher rates of preoperative assessments than facilities without CPNs. Our investigation underscores the prospective efficacy of CPNs in enhancing preoperative outpatient care. Consequently, we posit that advocating for outpatient care will bolster preoperative evaluation rates and engender a holistic patient assessment.</p>" ]

[]

[ "<p id=\"Par1\">This study aimed to investigate the influence of certified perioperative nurses on preoperative outpatient clinic and preoperative assessments. The study was conducted from February 2021 to September 2022; data were collected and analyzed using a questionnaire at 247 hospitals in Japan. To analyze the factors affecting the rate of preoperative assessment with the primary endpoint of preoperative outpatient care and preoperative nursing visits, we performed multiple linear regression analysis of facility characteristics, perioperative nurse background, and the presence or absence of certified perioperative nurses. Regarding the presence or absence of a preoperative outpatient clinic, patients from 68 (52.3%) and 41 (35.0%) institutions in the enrolled and nonenrolled groups. Respectively, underwent a preoperative assessment; the rate of preoperative assessments in the enrolled group was significantly higher than that in the nonenrolled group. Multivariate analysis of factors influencing the preoperative assessment rate revealed a significant association with certified perioperative nurse attendance. Facilities with certified perioperative nurses have a significantly higher prevalence of preoperative outpatient clinic and significantly higher rates of preoperative assessments than facilities without certified perioperative nurses. Enrollment of certified perioperative nurses may lead to the improvement of the quality of preoperative nursing interventions.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-51043-x.</p>", "<title>Acknowledgements</title>", "<p>We gratefully acknowledge the work of the past and present members of our medical center. We would like to thank Wiley Editing Services (<ext-link ext-link-type=\"uri\" xlink:href=\"https://wileyeditingservices.com\">https://wileyeditingservices.com</ext-link>) for English language editing. The authors declare no competing interests and have not received any external financial support for this work. Support was provided solely by institutional and departmental sources. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.</p>", "<title>Author contributions</title>", "<p>K.H. was responsible for the organization and coordination of the study. K.H. was the chief investigator responsible for the data analysis. C.Y., S.M., K.O., and K.T. provided the study data. T.I. made critical revisions to incorporate the relevant information. All authors contributed to the writing of the final manuscript and have approved it.</p>", "<title>Data availability</title>", "<p>The questionnaire data for this study can be found in Kentaro, Hara (2023), “Certified Perioperative Nurses in the Establishment of Preoperative Outpatient Visits and Rate of Preoperative Assessment in Japan: A Cross-sectional Study,” Mendeley Data, V1, 10.17632/vkx6m3n57h.1. The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par21\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Trial STROBE diagram. Of the 865 institutions included in this study, 252 are shown to have responded. After an initial analysis, 5 hospitals with missing data are excluded, and 247 hospitals are finally analyzed.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Facility characteristics (n = 247).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Factors</th><th align=\"left\">Enrolled group (n = 130)</th><th align=\"left\">Nonenrolled group (n = 117)</th><th align=\"left\"><italic>p</italic>-value</th></tr></thead><tbody><tr><td align=\"left\" colspan=\"3\">Hospital location</td><td align=\"left\">0.58</td></tr><tr><td align=\"left\"> Ordinance-designated city</td><td align=\"left\">45 (34.6%)</td><td align=\"left\">36 (30.8%)</td><td align=\"left\"/></tr><tr><td align=\"left\"> Nonordinance-designated city</td><td align=\"left\">85 (65.4%)</td><td align=\"left\">81 (69.2%)</td><td align=\"left\"/></tr><tr><td align=\"left\" colspan=\"3\">Intensive care unit</td><td align=\"left\"> &lt; 0.01*</td></tr><tr><td align=\"left\"> Yes</td><td align=\"left\">116 (89.2%)</td><td align=\"left\">66 (56.4%)</td><td align=\"left\"/></tr><tr><td align=\"left\"> No</td><td align=\"left\">14 (10.8%)</td><td align=\"left\">51 (43.6%</td><td align=\"left\"/></tr><tr><td align=\"left\" colspan=\"3\">Advanced treatment hospital</td><td align=\"left\" rowspan=\"3\"> &lt; 0.01*</td></tr><tr><td align=\"left\"> Yes</td><td align=\"left\">58 (44.6%)</td><td align=\"left\">22 (18.8%)</td></tr><tr><td align=\"left\"> No</td><td align=\"left\">72 (55.4%)</td><td align=\"left\">95 (81.2%)</td></tr><tr><td align=\"left\" colspan=\"3\">Number of hospital beds</td><td align=\"left\" rowspan=\"5\"> &lt; 0.01*</td></tr><tr><td align=\"left\"> &lt; 200</td><td align=\"left\">4 (3.1%)</td><td align=\"left\">19 (16.2%)</td></tr><tr><td align=\"left\"> 200–399</td><td align=\"left\">29 (22.3%)</td><td align=\"left\">51 (43.6%)</td></tr><tr><td align=\"left\"> 400–599</td><td align=\"left\">41 (31.5%)</td><td align=\"left\">36 (30.8%)</td></tr><tr><td align=\"left\"> &gt; 600</td><td align=\"left\">56 (43.1%)</td><td align=\"left\">11 (9.4%)</td></tr><tr><td align=\"left\">Number of operating rooms</td><td align=\"left\">10 (3–26)</td><td align=\"left\">6 (1–23)</td><td align=\"left\"> &lt; 0.01*</td></tr><tr><td align=\"left\">Number of surgeries annually</td><td align=\"left\">4632 (1327–12,742)</td><td align=\"left\">2592 (200–9662)</td><td align=\"left\"> &lt; 0.01*</td></tr><tr><td align=\"left\">Number of general anesthesia cases annually</td><td align=\"left\">2913 (856–8800)</td><td align=\"left\">1603 (130–6361)</td><td align=\"left\"> &lt; 0.01*</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Perioperative nurse characteristics (n = 247).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Factors</th><th align=\"left\">Enrolled group (n = 130)</th><th align=\"left\">Nonenrolled group (n = 117)</th><th align=\"left\"><italic>p</italic>-value</th></tr></thead><tbody><tr><td align=\"left\">Number of perioperative nurses</td><td align=\"left\">34 (10–97)</td><td align=\"left\">21 (4–72)</td><td align=\"left\"> &lt; 0.01**</td></tr><tr><td align=\"left\">Number of perioperative nurses per operating room</td><td align=\"left\">3.6 (1.9–6.8)</td><td align=\"left\">3.3 (1.8–5.7)</td><td align=\"left\">0.13</td></tr><tr><td align=\"left\"> &lt; 3.0</td><td align=\"left\">22 (16.9%)</td><td align=\"left\">25 (21.6%)</td><td align=\"left\"/></tr><tr><td align=\"left\"> 3.0–3.4</td><td align=\"left\">20 (15.4%)</td><td align=\"left\">33 (28.5%)</td><td align=\"left\"/></tr><tr><td align=\"left\"> 3.5–3.9</td><td align=\"left\">40 (30.8%)</td><td align=\"left\">27 (23.3%)</td><td align=\"left\"/></tr><tr><td align=\"left\"> 4.0–4.4</td><td align=\"left\">24 (18.5%)</td><td align=\"left\">17 (14.7%)</td><td align=\"left\"/></tr><tr><td align=\"left\"> &gt; 4.5</td><td align=\"left\">24 (18.5%)</td><td align=\"left\">14 (12.1%)</td><td align=\"left\"/></tr><tr><td align=\"left\">Certified perioperative nurses (n)</td><td align=\"left\"/><td align=\"left\">–</td><td align=\"left\">–</td></tr><tr><td align=\"left\"> One</td><td align=\"left\">95 (73.2%)</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"> Two</td><td align=\"left\">31 (23.8%)</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"> Three</td><td align=\"left\">2 (1.5%)</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"> Four</td><td align=\"left\">2 (1.5%)</td><td align=\"left\"/><td align=\"left\"/></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Preoperative assessment and preoperative and postoperative visits (n = 247).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Factors</th><th align=\"left\">Enrolled group (n = 130)</th><th align=\"left\">Nonenrolled group (n = 117)</th><th align=\"left\"><italic>p</italic>-value</th></tr></thead><tbody><tr><td align=\"left\" colspan=\"3\">Preoperative outpatient care/ nursing visits</td><td align=\"left\" rowspan=\"5\">0.01*</td></tr><tr><td align=\"left\"> Preoperative outpatient care only</td><td align=\"left\">8 (6.2%)</td><td align=\"left\">4 (3.4%)</td></tr><tr><td align=\"left\"> Preoperative nursing visits only</td><td align=\"left\">62 (47.7%)</td><td align=\"left\">73 (62.4%)</td></tr><tr><td align=\"left\"> Both conducted</td><td align=\"left\">60 (46.1%)</td><td align=\"left\">37 (31.6%)</td></tr><tr><td align=\"left\"> Neither conducted</td><td align=\"left\">0 (0.0%)</td><td align=\"left\">3 (2.6%)</td></tr><tr><td align=\"left\">Preoperative assessment rate (%)</td><td align=\"left\">90.0 (70.0–99.0)</td><td align=\"left\">75.0 (54.5–95.0)</td><td align=\"left\">0.01*</td></tr><tr><td align=\"left\" colspan=\"3\">Postoperative nursing visits</td><td align=\"left\" rowspan=\"3\">0.03*</td></tr><tr><td align=\"left\"> Yes</td><td align=\"left\">112 (86.2%)</td><td align=\"left\">88 (75.2%)</td></tr><tr><td align=\"left\"> No</td><td align=\"left\">18 (13.8%)</td><td align=\"left\">29 (24.8%)</td></tr><tr><td align=\"left\">Postoperative nursing visits rate (%)</td><td align=\"left\">44.0 (11.5–80.0)</td><td align=\"left\">39.0 (14.3–80)</td><td align=\"left\">0.93</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Analysis of factors influencing the rate of preoperative assessment (n = 247).</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Factors</th><th align=\"left\">B</th><th align=\"left\">SE</th><th align=\"left\">t</th><th align=\"left\"><italic>p</italic>-value</th><th align=\"left\">95%CI</th></tr></thead><tbody><tr><td align=\"left\">Hospital Location (ordinance-designated city)</td><td char=\".\" align=\"char\">− 4.31</td><td char=\".\" align=\"char\">1.82</td><td char=\".\" align=\"char\">− 0.95</td><td char=\".\" align=\"char\">0.32</td><td align=\"left\">− 1.88 to 5.58</td></tr><tr><td align=\"left\">Intensive care unit (yes)</td><td char=\".\" align=\"char\">− 2.42</td><td char=\".\" align=\"char\">2.53</td><td char=\".\" align=\"char\">− 0.98</td><td char=\".\" align=\"char\">0.32</td><td align=\"left\">− 7.33 to 2.45</td></tr><tr><td align=\"left\">Advanced treatment hospital (yes)</td><td char=\".\" align=\"char\">− 4.48</td><td char=\".\" align=\"char\">2.37</td><td char=\".\" align=\"char\">− 1.93</td><td char=\".\" align=\"char\">0.05</td><td align=\"left\">− 1.88 to 5.58</td></tr><tr><td align=\"left\">Number of operating rooms</td><td char=\".\" align=\"char\">0.81</td><td char=\".\" align=\"char\">1.93</td><td char=\".\" align=\"char\">0.38</td><td char=\".\" align=\"char\">0.44</td><td align=\"left\">− 3.15 to 4.66</td></tr><tr><td align=\"left\">Number of surgeries annually</td><td char=\".\" align=\"char\">− 0.93</td><td char=\".\" align=\"char\">1.65</td><td char=\".\" align=\"char\">0.22</td><td char=\".\" align=\"char\">0.94</td><td align=\"left\">− 0.08 to 0.02</td></tr><tr><td align=\"left\">Number of general anesthesia cases annually</td><td char=\".\" align=\"char\">0.01</td><td char=\".\" align=\"char\">0.34</td><td char=\".\" align=\"char\">0.58</td><td char=\".\" align=\"char\">0.76</td><td align=\"left\">− 0.02 to 0.01</td></tr><tr><td align=\"left\">Number of perioperative nurses per operating room</td><td char=\".\" align=\"char\">0.45</td><td char=\".\" align=\"char\">2.60</td><td char=\".\" align=\"char\">0.17</td><td char=\".\" align=\"char\">0.86</td><td align=\"left\">− 4.68 to 5.58</td></tr><tr><td align=\"left\">Certified perioperative nurse (enrolled)</td><td char=\".\" align=\"char\">6.7</td><td char=\".\" align=\"char\">2.5</td><td char=\".\" align=\"char\">2.62</td><td char=\".\" align=\"char\"> &lt; 0.01**</td><td align=\"left\">1.46–11.57</td></tr><tr><td align=\"left\">Preoperative outpatient clinic (yes)</td><td char=\".\" align=\"char\">4.3</td><td char=\".\" align=\"char\">2.1</td><td char=\".\" align=\"char\">2.54</td><td char=\".\" align=\"char\">0.03*</td><td align=\"left\">1.01–5.97</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p>Values are presented as medians (interquartile ranges) or numbers (percentages). The Mann–Whitney U test was used for the comparison of ordinal data. Nominal data were compared using the chi-squared or Fisher’s exact test.</p><p>*Significant difference between groups.</p></table-wrap-foot>", "<table-wrap-foot><p>Values are presented as medians (interquartile ranges) or numbers (percentages). The Mann–Whitney U test was used for the comparison of ordinal data.</p><p>*Significant difference between groups.</p></table-wrap-foot>", "<table-wrap-foot><p>Values are presented as medians (interquartile ranges) or numbers (percentages). The Mann–Whitney U test was used for the comparison of ordinal data. Nominal data were compared using the chi-squared or Fisher’s exact test.</p><p>*Significant difference between groups.</p></table-wrap-foot>", "<table-wrap-foot><p>*Significant difference between groups.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"41598_2023_51043_Fig1_HTML\" id=\"MO1\"/>" ]

[ "<media xlink:href=\"41598_2023_51043_MOESM1_ESM.docx\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [ "CPN" ], "definition": [ "Certified perioperative nurse" ] }

[ "<title>Introduction</title>", "<p id=\"Par2\">No-take marine reserves are effective conservation tools for protecting marine resources within reserve borders^{##UREF##0##1##–##UREF##3##5##}. Protection from fishing often leads to the increased size^{##UREF##4##6##}, density^{##UREF##3##5##,##UREF##5##7##}, and spawning biomass^{##UREF##5##7##} of harvested species. The role marine reserves play in fishery management is less certain and widely debated. Controversy arises in part from the clear short-term costs to fishers associated with reserve implementation, which reduces the size of fishing grounds potentially leading to revenue loss, especially over the short term^{##REF##10348743##8##–##UREF##6##10##}. Other fishery effects of reserves include displacing and redistributing fishing effort, and influencing yield through the export, or spillover, of production from the reserve into fishable areas^{##UREF##7##11##}.</p>", "<p id=\"Par3\">Theory predicts that a network of marine reserves can stabilize or enhance fishery yield if large, old spawning individuals are protected, and the reserves are arranged in space so that unprotected areas open to fishing receive spillover from reserves^{##UREF##6##10##–##REF##20181570##13##}. Such spillover can be ecological (larvae, juveniles, and adults) or fishery (biomass that can be fished) in nature^{##UREF##8##14##}. Tests of spillover theory using spatial population modelling indicates that larval spillover from a reserve network can enhance yield for over-capitalized fisheries that have been depleted through excess fishing^{##UREF##9##15##,##UREF##10##16##}. Statistical analysis of marine reserve data also found that spillover of adult target species is a relatively common phenomenon^{##REF##25188380##17##}, but modelling of those data indicated that adult spillover was sufficient to sustain depleted fisheries in some cases^{##UREF##11##18##,##UREF##12##19##} and insufficient in other cases^{##REF##25188380##17##,##UREF##12##19##}. By contrast, results from field studies have shown that spillover of adults can enhance local catch in depleted fisheries^{##UREF##11##18##,##UREF##13##20##,##UREF##14##21##}, and at least in one case a sustainable, well-managed fishery^{##REF##33414495##22##–##UREF##16##24##}.</p>", "<p id=\"Par4\">Here we report the results of a Before-After Control-Impact Paired Series (BACIPS)^{##UREF##17##25##} analysis designed to test whether a large marine reserve network influenced the catch in a large, well-managed spiny lobster fishery in California, USA. Specifically, we tested the hypothesis that the establishment of a reserve network in California along the mainland coast increased total catch and catch-per-unit effort (CPUE) due to spillover of legal-sized lobsters from reserves to adjacent unprotected fishing grounds, where fishers adapted to fish near the reserve borders and intercept the emigrating lobsters. This hypothesis rested on our prediction that reserves would have no effect on total fishing effort. Our test relied on fishery-dependent catch and effort data collected by the State of California, as well as a fine-scale survey of lobster trapping effort near reserve borders.</p>", "<title>California’s marine reserve network</title>", "<p id=\"Par5\">Small coastal marine reserves have existed in California since the 1930s. In 2012, the California Marine Life Protection Act (MLPA) greatly expanded the area protected from fishing by establishing a network of 86 marine reserves along California’s 1350 km of coastline^{##UREF##18##26##}. Examination of the ecological effects of the MLPA reserve network revealed that recovery of exploited species of kelp forest fishes inside reserves was rapid, but highly variable in space^{##REF##26373803##27##}. Much less is known about the extent to which the MLPA network, or networks of marine reserves in general, have benefitted populations of fished species occurring outside of reserves.</p>", "<p id=\"Par6\">We evaluated the fishery benefits of the MLPA network along the mainland coast of southern California (Fig. ##FIG##0##1##), where the state’s most valuable reef-based fishery targets the California spiny lobster (<italic>Panulirus interruptus</italic>), in addition to many other commercial and recreational fisheries. Fourteen MLPA reserves established in this region in 2012 closed 10% of spiny lobster fishing grounds along the mainland coast through the protection of 137 km² of ocean space, much of which was composed of lobster-rich rocky reef habitat^{##UREF##19##28##}. Lobsters are also caught in shallow waters surrounding the offshore Channel Islands where other reserves established in 1974–2003 removed 17% of the fishable habitat at the islands^{##UREF##20##29##}. The first and only quantitative stock assessment of the spiny lobster fishery, conducted in 2011, concluded that the fishery was sustainable^{##UREF##16##24##}. The 2016 CA Spiny Lobster Fishery Management plan established an adaptive management process designed to guard against unsustainably increasing commercial and recreational fishing effort, and accounted for the MLPA marine reserves. The fishery is managed by the State of California, with no Federal or interstate councils or commissions involved.</p>" ]

[ "<title>Materials and methods</title>", "<title>Fishery-dependent data and analysis</title>", "<title>The fishery</title>", "<p id=\"Par16\">The commercial fishery for spiny lobster in California, USA extends from Morro Bay (35.3659°N 120.8500°W) south to the US–Mexico border and involves fishers using relatively small boats to deploy baited wire box-like traps set on the bottom in shallow reef habitats. Traps are set in water depths from 3 to 170 m. The fishing season is from October to March with approximately 80% of the annual catch landed within the first half of the season. It is assumed that most of lobsters landed by the fishery reached legal size (83 mm carapace length) during the previous year, but this has yet to be confirmed.</p>", "<title>Fishing blocks and recorded catch</title>", "<p id=\"Par17\">California (CA) fisheries are managed by the CA Department of Fish and Wildlife (CDFW), who has divided the entire coastline into rectangular fishing blocks (~ 140 km²), from which commercial lobster fishers, and other fisheries, are required to record and log all their landings and fishing effort (<ext-link ext-link-type=\"uri\" xlink:href=\"https://nrm.dfg.ca.gov/FileHandler.ashx?DocumentID=67449&amp;inline\">https://nrm.dfg.ca.gov/FileHandler.ashx?DocumentID=67449&amp;inline</ext-link>). Annual fishing block data of commercial lobster landings (wet pounds caught) and fishing effort (number of traps pulled) were obtained from CDFW for all fishing seasons for which data were recorded (1998–2020). We defined a fishing season by the year in which it started (e.g., the 2012 season extended from October 2012 through March 2013). Fishing block data are based on landings weighed at the dock by the processor, who records the data on a “fish ticket” that is submitted to the CDFW. Fishers are required to assign their landings to a specific fishing block (recorded in “fish ticket” data) and report the fishing effort (i.e., number of traps pulled; recorded in fisher logbooks) allocated to their catch. Although Catch-Per-Unit-Effort (CPUE) is defined by CDFW as the number of legal lobsters per trap pull, for our analyses we defined it as the weight of legal lobsters caught per traps pulled.</p>", "<title>Designation of fishing blocks</title>", "<p id=\"Par18\">The study region included commercial fishing blocks that extend along the mainland coast of California (Fig. ##FIG##0##1##). The southern California lobster fishing fleet is organized primarily around ports where fishing boats are moored and fishers land their catch. Through our ongoing collaborative research program, we learned that a majority of boats fishing within the northern section of the fishery utilized the four northern ports (Santa Barbara, Channel Islands, Ventura, and Hueneme) located in Ventura and Santa Barbara counties. Many lobster fishers using these ports were active members of the California Lobster and Trap Fishermen’s Association, a social organization with whom we shared information and developed research projects over the past two decades. Fishers from the southern region of fishery, who fished south of Pt. Dume to the US-Mexico Border, utilized mainly 10 ports (Marine del Rey, King, Los Angeles, Alamitos, Sunset-Huntington, Newport, Dana Point, Oceanside, Mission Bay, and San Diego) located in Los Angeles, Orange, and San Diego counties. We had very few interactions with fishers from these ports.</p>", "<p id=\"Par19\">Thirty-four fishing blocks located along the coastline where MLPA reserves were established in 2012 reported spiny lobster commercial fishing data to the CDFW (Block #s: 651, 652, 653, 654, 655, 656, 657, 664, 665, 666, 667, 680, 681, 682, 683, 702, 704, 718, 719, 720, 737, 738, 739, 740, 756, 757, 801, 802, 821, 822, 859, 860, 877, 878). Fourteen State Marine Reserves (SMR) or State Marine Conservation Areas (SMCA) that did not allow lobster fishing were established in 12 of those blocks in 2012 (Blocks #657—Point Conception SMR; 654—Naples/Campus Point SMCA; 681 and 704—Pt. Dume SMCA; 680—Pt. Dume SMR; 720—Pt. Vincente SMCA and Abalone Cove SMCA; 737—Laguna Beach SMCA/SMR; 821 and 822—Swami’s SMCA; 860—South La Jolla SMCA/SMR; 877—Tijuana River Mouth SMCA; and 878—Cabrillo SMR). Four of the no-lobster fishing blocks were in the northern region (654, 657, 681, and 704; Fig. ##FIG##0##1##); while 8 reserve blocks (680, 720, 737, 821, 822, 860, 877, and 878) were in the southern region. The remaining 22 blocks where lobster catch was recorded were control blocks without reserves, or were blocks with SMCAs that allowed lobster fishing (block 656 in the northern region with Kashtiyat SMCA; and blocks 738 and 757 in the southern region with Crystal Cove and Dana Point SMCAs). The distribution of control and reserve blocks in the different regions of the fishery are illustrated in Fig. ##FIG##0##1##.</p>", "<title>Statistical analysis</title>", "<p id=\"Par20\">The effects of fishing status (blocks with reserves versus blocks without reserves), and period (i.e., before versus after MLPA implementation) on annual catch, effort, and catch-per-unit-effort (CPUE) were evaluated using a Before-After, Control-Impact, Paired Series (BACIPS) design^{##UREF##17##25##} in which Delta values were calculated as the difference Reserve blocks—Control blocks, for each of the 14 annual fishing seasons “Before” MLPA implementation (1998–2011) and eight seasons ”After” implementation (2013–2020). We removed the 2012 season when reserves were first activated from our analyses because many fishers were forced to re-establish new fishing grounds in the first year after reserve establishment leading to overall less intensive fishing^{##UREF##20##29##}. A Delta value for each response variable was calculated for each season by subtracting the total value summed from the control blocks from the total sum from reserve blocks. The population of Deltas in the before period (N = 14) were then compared with that from the after period (N = 8) in a two-sample T-test with equal variances, as verified by a folded F-test. Separate BACIPS analyses were conducted for the entire fishery, the northern region of the fishery (Pt. Conception to Pt. Dume) and the southern region (Pt. Dume to the US-Mexico Border). Before the analyses, catch and effort data were log transformed to meet the assumptions of additivity in the BACIPS analysis. CPUE was calculated as the log catch/log effort. All statistical analyses were conducted in SAS software.</p>", "<title>Lobster fishing behavior</title>", "<p id=\"Par21\">Fishing behavior in the vicinity of the no-fishing zones was examined by counting lobster trap buoys at increasing increments of distance (0–100 m, 101–300 m, 301–500 m, 501–1000 m, and 1001–1500 m) away from reserve borders visually from land with a spotting scope. Each trap buoy is connected to one lobster trap. Buoys within 1 km of shore were counted from shore, in each distance increment. We reported as the number of traps within 1 km of shore because all reserve borders began at the shoreline. Three no-fishing zones in the northern region (Pt. Conception SMR, Campus Point SMCA, and Pt. Dume SMR/SMCA) and southern region (Pt. Vincente SMCA, Matlahuayl SMR, and South La Jolla SMR/SMCA) were surveyed for buoys in November 2021 over a 2-day period of excellent fishing conditions. We focused our observations on these six reserves because they were close enough to shore for us to accurately count traps. These reserves were considered representative of many other MLPA reserves because of their proximity to shore, size, and quantity of lobster habitat. We used a similar method in our previous study of the Campus Point SMCA^{##REF##33414495##22##}.</p>", "<title>Statistical analysis</title>", "<p id=\"Par22\">Mean differences in the number of traps among distance increments between the three reserves in the north and south regions were analyzed with a Two-Way Analysis of Variance (ANOVA), in which Region (north vs. south) and Distance interval were fixed factors, and Region × Distance was the interaction. The Tukey test was used for the post-hoc analysis. Data were log transformed prior to analysis to meet the assumptions of normality and homoscedasticity of ANOVA.</p>", "<title>Percentage of lobster fishing grounds inside versus outside of marine reserve</title>", "<p id=\"Par23\">The area of lobster fishing grounds removed within the no-fishing marine reserves reported in the text was calculated by overlaying the CDFW fishing blocks (<ext-link ext-link-type=\"uri\" xlink:href=\"https://wildlife.ca.gov/Conservation/Marine/GIS/Downloads\">https://wildlife.ca.gov/Conservation/Marine/GIS/Downloads</ext-link>) with no-take reserves and bathymetry data provided by GEBCO (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.gebco.net/data_and_products/gridded_bathymetry_data/\">https://www.gebco.net/data_and_products/gridded_bathymetry_data/</ext-link>). We calculated the total fishable area within each fishing block by first confining the blocks to the deepest depth at which a lobster trap was recorded being placed (79 m). There are records of traps being set in water as deep as 170 m, but the vast majority were set in &lt; 80 m depth. This layer was then overlaid with the boundaries of no-take reserves that were restricted to the same depth, and the restricted fishable area and the remaining area of fishing grounds were estimated. All spatial analysis was performed in R (R Core Team 2019) using the packages 'raster'^{##UREF##26##39##}, 'maptools'^{##UREF##27##40##}, and 'rgdal'^{##UREF##26##39##}. Those data are reported in the text.</p>" ]

[ "<title>Results and discussion</title>", "<title>Effects of reserves on fishing effort and yield</title>", "<p id=\"Par7\">We used data from jurisdictional fishing blocks where lobster fishing occurred and was reported from, including those with reserves, as only portions of reserve blocks were closed to fishing. Results of the BACIPS analysis showed the difference in catch (∆ = Reserve blocks—Control blocks) between fishing blocks with and without reserves was on average 13% lower in the period after reserves were established (2013–2020) than in the period before reserves were established (1998–2011; Figs. ##FIG##1##2##A, ##FIG##2##3##A). There was also a significant effect of reserves on fishing effort, effectively resulting in an average 43% decrease in the Delta log values for lobster traps set after reserves were established (Fig. ##FIG##1##2##B). Fishing effort declined overall across the entire fishery beginning in 2015 (Fig. ##FIG##2##3##B) when state fishery managers implemented a limit of 300 traps per fishing permit^{##UREF##16##24##}. The number of traps set per fishing permit was not limited prior to 2015. While the implementation of a trap limit caused an overall reduction in fishing effort, it did not account for the reduced effort observed in the reserve blocks relative to the control blocks in the after period (Fig. ##FIG##1##2##B), as trap limits applied equally to reserve and control blocks. There was no significant effect of reserves on lobster CPUE, which varied substantially over time in both the before and after periods (Fig. ##FIG##1##2##C).</p>", "<p id=\"Par8\">A closer examination of the data revealed dramatic regional differences in the effect of reserves on the fishery. In the northern region (Point Conception to Point Dume; Fig. ##FIG##0##1##) the Delta values for catch increased threefold after the establishment of reserves while effort and CPUE doubled (Fig. ##FIG##3##4##A–C). This pattern emerged even though effort in control blocks without reserves during the after period was as high or higher than that in the before period (Fig. ##SUPPL##0##S1##), indicating the positive effects of reserves on lobster catch and CPUE in this region. The switch from negative Delta values of CPUE in the before period to positive values in the after period (Fig. ##FIG##3##4##C) further signifies that reserves had a substantially positive overall effect on the fishery in the northern region. We reason that increased effort in reserve blocks in the after period benefited the fishery through increased catch because there were more lobsters to catch via spillover. We documented a similar pattern at a local level in prior work^{##REF##33414495##22##,##UREF##15##23##}.</p>", "<p id=\"Par9\">By contrast, in the southern region (Pt. Dume to Mexico) Delta values for catch, effort, and CPUE decreased significantly after the establishment of reserves (Fig. ##FIG##4##5##A–C), thus driving the negative effect of reserves at the entire fishery level (Fig. ##FIG##1##2##A). Overall effort in the southern region, and to a lesser extent catch, declined in both the reserve and control blocks after reserve establishment (Fig. ##SUPPL##0##S2##), and the negative effect of reserves on CPUE (Fig. ##FIG##4##5##C) reflects a greater decline in effort in reserve blocks relative to control blocks (Fig. ##SUPPL##0##S2##B). It should be noted that total lobster fishing effort and catch in the southern region is consistently three to four times higher than the northern region (Figs. ##SUPPL##0##S1##, ##SUPPL##0##S2##). These differences are due largely to the larger size of the southern region, which has approximately four times more fishable area and three times as many fishing ports, thus supporting about three times as many fishers compared to the northern region^{##UREF##16##24##}.</p>", "<title>Regional differences in fishing behavior</title>", "<p id=\"Par10\">Our prior work showed increases in spiny lobster abundance within two reserves located in one fishing block in the northern region, and the related spillover of legal-sized adult lobsters, as well as enhanced lobster catch and CPUE in that fishing block relative to nearby blocks without reserves^{##REF##33414495##22##}. Prior research also revealed that lobster fishers often concentrate their trapping effort near reserve borders^{##REF##33414495##22##,##UREF##21##30##,##REF##21265452##31##}, in part due to the fisher’s participation in collaborative research with scientists and awareness of its results^{##UREF##15##23##,##REF##22471093##32##}. We reasoned that differences in lobster yield between the north and south regions associated with the establishment of the MLPA reserves could be explained by differences in fishing behavior between the two regions, specifically the degree to which fishers in each region fished near reserve borders early in the fishing season (October–November) when landings are by far the highest. Evidence for this comes from our field observations of trapping effort in which we recorded a much higher average number of traps within 2 km of the borders reserves in the north than we did in the south (Fig. ##FIG##5##6##; <italic>F</italic>_5,35 = 12.29; <italic>P</italic> &lt; 0.002), despite a far greater number of traps set overall in the south (Fig. ##SUPPL##0##S2##B vs. Fig. ##SUPPL##0##S1##B). This result indicated that fishing reserve borders, relatively early in the season, is more prevalent and intensive in the north than the south.</p>", "<p id=\"Par11\">Of course, factors other than fishing behavior may help explain the spatial difference in catch in response to reserve establishment. For example, historical logbook catch data indicate that reserves in the south were placed in relatively more productive lobster fishing blocks than reserves in the north (see Figs. ##SUPPL##0##S1##A and ##SUPPL##0##S2##A), suggesting that the quality and carrying capacity of reef habitat may vary between the two regions. Such habitat differences could influence lobster movement out of reserves^{##REF##22471093##32##,##UREF##22##33##} and thus spillover^{##UREF##23##34##}.</p>", "<p id=\"Par12\">Our research team included a CA spiny lobster fisherman with three decades of fishing experience, a state resource manager, and scientists who began collaborating on research with the lobster fishery in 2002^{##UREF##15##23##,##REF##22471093##32##}. Our collective experience and conversations with fishers lead us to believe that regional differences in the effects of reserves were generated by interactions of fleet dynamics, fishing behavior, and the physical environment. We learned that, in response to reserve establishment in 2012, some of the most productive fishers who fished in reserve areas in the south moved their fishing effort to the northern region, where there are fewer fishers and less competition for space^{##UREF##19##28##,##UREF##20##29##}. This helps to explain the reduction of fishing effort in reserve blocks in the south (Fig. ##SUPPL##0##S2##B) and the increased effort in reserve blocks in the north (Fig. ##SUPPL##0##S1##B) following reserve establishment.</p>", "<p id=\"Par13\">In our collaborative research with lobster fishers^{##REF##22471093##32##} we discovered that baited traps are generally set in groups or lines located along edges of rocky reef habitat, where lobsters normally forage for food and find refuge from predators and physical disturbance caused ocean swell. Spiny lobsters’ attraction to the baited traps apparently increases when competition for food and refuge intensifies, for example, within or adjacent to reserves where population abundances are significantly higher due to protection^{##UREF##24##35##}. Lobsters also move from shallow rocky habitat to deeper water as wave intensity increases throughout the fishing season (October–March). Fishers in turn shift their traps from shallow to deep water to avoid trap loss or damage caused by swell, and to intercept lobsters that are migrating from shallow to deep water. This shift in fishing behavior typically involves placing lines of traps near rocky habitat located at increasing depths as the season progresses. For some fishers this includes shifting traps to areas with rocky habitat located near reserve borders. We also learned that fishers in the north generally move their traps into deeper water earlier in the season than those in the south because swell size increases earlier in the north than south (<italic>Personal Communication</italic> with fisher S. Escobar, who has fished both regions). Accordingly, northern fishers may move their traps to reserve borders earlier in the season, when lobster catch is relatively high, than fishers in the south. Other potential causes of shifts in fishing behavior, such as fishers exiting the fishery or changes in dockside value, are unlikely to have led to these shifts, based on discussions with fishers and resource managers (<italic>Personal communication</italic>).</p>", "<p id=\"Par14\">Regional differences in fishing behavior that altered the effectiveness of reserves on fishery yield may also reflect cultural differences in addition to environmental differences. Beginning in 2002, we developed a collaborative fishery research program, (<italic>CALobster</italic>) in the northern region of the fishery to assess the effects of marine reserves on lobster populations, spillover, and fishery yield^{##REF##33414495##22##,##UREF##15##23##,##REF##22471093##32##}. Our collaboration relied on research trapping campaigns with fishers as well as numerous formal and informal meetings with members of the California Lobster and Trap Fisherman’s Association (CLTFA) and the CA Department of Fish and Wildlife (CDFW), at which our results pertaining to the responses of lobster populations to reserve protection were discussed. This concerted and sustained effort to share information increased understanding among stakeholders about the predicted and actual effects of the MLPA reserves on lobsters and fishers^{##REF##22471093##32##}, and stimulated an increase in the propensity of the fleet to fish the border of reserves in the north (C. Voss, <italic>personal observations</italic>). Similar types of collaborations and interactions have enhanced the performance of fisheries in other regions in response to reserve establishment^{##REF##19906064##36##,##REF##33194393##37##}.</p>", "<p id=\"Par15\">Collectively, our results demonstrate that a reserve network can have an overall positive influence on lobster catch, even in a well-managed sustainable fishery, where fishers respond to spillover of target species from reserve borders. Understanding the primary factors determining population and behavioral responses of targeted species to reserve establishment remains difficult, but communicating research results on these responses can assist fishers to adapt to reserve establishment. Collaborative marine reserve research involving diverse stakeholders helps scientists to better understand conservation actions on human livelihoods, while also helping fishers to operate productively within seascapes that include large marine reserve networks^{##UREF##25##38##}. Our results suggests that the fishery benefits of marine reserves will be enhanced when collaborative research involving diverse stakeholders and Before-After assessments are incorporated into marine reserve design and implementation.</p>" ]

[ "<title>Results and discussion</title>", "<title>Effects of reserves on fishing effort and yield</title>", "<p id=\"Par7\">We used data from jurisdictional fishing blocks where lobster fishing occurred and was reported from, including those with reserves, as only portions of reserve blocks were closed to fishing. Results of the BACIPS analysis showed the difference in catch (∆ = Reserve blocks—Control blocks) between fishing blocks with and without reserves was on average 13% lower in the period after reserves were established (2013–2020) than in the period before reserves were established (1998–2011; Figs. ##FIG##1##2##A, ##FIG##2##3##A). There was also a significant effect of reserves on fishing effort, effectively resulting in an average 43% decrease in the Delta log values for lobster traps set after reserves were established (Fig. ##FIG##1##2##B). Fishing effort declined overall across the entire fishery beginning in 2015 (Fig. ##FIG##2##3##B) when state fishery managers implemented a limit of 300 traps per fishing permit^{##UREF##16##24##}. The number of traps set per fishing permit was not limited prior to 2015. While the implementation of a trap limit caused an overall reduction in fishing effort, it did not account for the reduced effort observed in the reserve blocks relative to the control blocks in the after period (Fig. ##FIG##1##2##B), as trap limits applied equally to reserve and control blocks. There was no significant effect of reserves on lobster CPUE, which varied substantially over time in both the before and after periods (Fig. ##FIG##1##2##C).</p>", "<p id=\"Par8\">A closer examination of the data revealed dramatic regional differences in the effect of reserves on the fishery. In the northern region (Point Conception to Point Dume; Fig. ##FIG##0##1##) the Delta values for catch increased threefold after the establishment of reserves while effort and CPUE doubled (Fig. ##FIG##3##4##A–C). This pattern emerged even though effort in control blocks without reserves during the after period was as high or higher than that in the before period (Fig. ##SUPPL##0##S1##), indicating the positive effects of reserves on lobster catch and CPUE in this region. The switch from negative Delta values of CPUE in the before period to positive values in the after period (Fig. ##FIG##3##4##C) further signifies that reserves had a substantially positive overall effect on the fishery in the northern region. We reason that increased effort in reserve blocks in the after period benefited the fishery through increased catch because there were more lobsters to catch via spillover. We documented a similar pattern at a local level in prior work^{##REF##33414495##22##,##UREF##15##23##}.</p>", "<p id=\"Par9\">By contrast, in the southern region (Pt. Dume to Mexico) Delta values for catch, effort, and CPUE decreased significantly after the establishment of reserves (Fig. ##FIG##4##5##A–C), thus driving the negative effect of reserves at the entire fishery level (Fig. ##FIG##1##2##A). Overall effort in the southern region, and to a lesser extent catch, declined in both the reserve and control blocks after reserve establishment (Fig. ##SUPPL##0##S2##), and the negative effect of reserves on CPUE (Fig. ##FIG##4##5##C) reflects a greater decline in effort in reserve blocks relative to control blocks (Fig. ##SUPPL##0##S2##B). It should be noted that total lobster fishing effort and catch in the southern region is consistently three to four times higher than the northern region (Figs. ##SUPPL##0##S1##, ##SUPPL##0##S2##). These differences are due largely to the larger size of the southern region, which has approximately four times more fishable area and three times as many fishing ports, thus supporting about three times as many fishers compared to the northern region^{##UREF##16##24##}.</p>", "<title>Regional differences in fishing behavior</title>", "<p id=\"Par10\">Our prior work showed increases in spiny lobster abundance within two reserves located in one fishing block in the northern region, and the related spillover of legal-sized adult lobsters, as well as enhanced lobster catch and CPUE in that fishing block relative to nearby blocks without reserves^{##REF##33414495##22##}. Prior research also revealed that lobster fishers often concentrate their trapping effort near reserve borders^{##REF##33414495##22##,##UREF##21##30##,##REF##21265452##31##}, in part due to the fisher’s participation in collaborative research with scientists and awareness of its results^{##UREF##15##23##,##REF##22471093##32##}. We reasoned that differences in lobster yield between the north and south regions associated with the establishment of the MLPA reserves could be explained by differences in fishing behavior between the two regions, specifically the degree to which fishers in each region fished near reserve borders early in the fishing season (October–November) when landings are by far the highest. Evidence for this comes from our field observations of trapping effort in which we recorded a much higher average number of traps within 2 km of the borders reserves in the north than we did in the south (Fig. ##FIG##5##6##; <italic>F</italic>_5,35 = 12.29; <italic>P</italic> &lt; 0.002), despite a far greater number of traps set overall in the south (Fig. ##SUPPL##0##S2##B vs. Fig. ##SUPPL##0##S1##B). This result indicated that fishing reserve borders, relatively early in the season, is more prevalent and intensive in the north than the south.</p>", "<p id=\"Par11\">Of course, factors other than fishing behavior may help explain the spatial difference in catch in response to reserve establishment. For example, historical logbook catch data indicate that reserves in the south were placed in relatively more productive lobster fishing blocks than reserves in the north (see Figs. ##SUPPL##0##S1##A and ##SUPPL##0##S2##A), suggesting that the quality and carrying capacity of reef habitat may vary between the two regions. Such habitat differences could influence lobster movement out of reserves^{##REF##22471093##32##,##UREF##22##33##} and thus spillover^{##UREF##23##34##}.</p>", "<p id=\"Par12\">Our research team included a CA spiny lobster fisherman with three decades of fishing experience, a state resource manager, and scientists who began collaborating on research with the lobster fishery in 2002^{##UREF##15##23##,##REF##22471093##32##}. Our collective experience and conversations with fishers lead us to believe that regional differences in the effects of reserves were generated by interactions of fleet dynamics, fishing behavior, and the physical environment. We learned that, in response to reserve establishment in 2012, some of the most productive fishers who fished in reserve areas in the south moved their fishing effort to the northern region, where there are fewer fishers and less competition for space^{##UREF##19##28##,##UREF##20##29##}. This helps to explain the reduction of fishing effort in reserve blocks in the south (Fig. ##SUPPL##0##S2##B) and the increased effort in reserve blocks in the north (Fig. ##SUPPL##0##S1##B) following reserve establishment.</p>", "<p id=\"Par13\">In our collaborative research with lobster fishers^{##REF##22471093##32##} we discovered that baited traps are generally set in groups or lines located along edges of rocky reef habitat, where lobsters normally forage for food and find refuge from predators and physical disturbance caused ocean swell. Spiny lobsters’ attraction to the baited traps apparently increases when competition for food and refuge intensifies, for example, within or adjacent to reserves where population abundances are significantly higher due to protection^{##UREF##24##35##}. Lobsters also move from shallow rocky habitat to deeper water as wave intensity increases throughout the fishing season (October–March). Fishers in turn shift their traps from shallow to deep water to avoid trap loss or damage caused by swell, and to intercept lobsters that are migrating from shallow to deep water. This shift in fishing behavior typically involves placing lines of traps near rocky habitat located at increasing depths as the season progresses. For some fishers this includes shifting traps to areas with rocky habitat located near reserve borders. We also learned that fishers in the north generally move their traps into deeper water earlier in the season than those in the south because swell size increases earlier in the north than south (<italic>Personal Communication</italic> with fisher S. Escobar, who has fished both regions). Accordingly, northern fishers may move their traps to reserve borders earlier in the season, when lobster catch is relatively high, than fishers in the south. Other potential causes of shifts in fishing behavior, such as fishers exiting the fishery or changes in dockside value, are unlikely to have led to these shifts, based on discussions with fishers and resource managers (<italic>Personal communication</italic>).</p>", "<p id=\"Par14\">Regional differences in fishing behavior that altered the effectiveness of reserves on fishery yield may also reflect cultural differences in addition to environmental differences. Beginning in 2002, we developed a collaborative fishery research program, (<italic>CALobster</italic>) in the northern region of the fishery to assess the effects of marine reserves on lobster populations, spillover, and fishery yield^{##REF##33414495##22##,##UREF##15##23##,##REF##22471093##32##}. Our collaboration relied on research trapping campaigns with fishers as well as numerous formal and informal meetings with members of the California Lobster and Trap Fisherman’s Association (CLTFA) and the CA Department of Fish and Wildlife (CDFW), at which our results pertaining to the responses of lobster populations to reserve protection were discussed. This concerted and sustained effort to share information increased understanding among stakeholders about the predicted and actual effects of the MLPA reserves on lobsters and fishers^{##REF##22471093##32##}, and stimulated an increase in the propensity of the fleet to fish the border of reserves in the north (C. Voss, <italic>personal observations</italic>). Similar types of collaborations and interactions have enhanced the performance of fisheries in other regions in response to reserve establishment^{##REF##19906064##36##,##REF##33194393##37##}.</p>", "<p id=\"Par15\">Collectively, our results demonstrate that a reserve network can have an overall positive influence on lobster catch, even in a well-managed sustainable fishery, where fishers respond to spillover of target species from reserve borders. Understanding the primary factors determining population and behavioral responses of targeted species to reserve establishment remains difficult, but communicating research results on these responses can assist fishers to adapt to reserve establishment. Collaborative marine reserve research involving diverse stakeholders helps scientists to better understand conservation actions on human livelihoods, while also helping fishers to operate productively within seascapes that include large marine reserve networks^{##UREF##25##38##}. Our results suggests that the fishery benefits of marine reserves will be enhanced when collaborative research involving diverse stakeholders and Before-After assessments are incorporated into marine reserve design and implementation.</p>" ]

[]

[ "<p id=\"Par1\">A network of marine reserves can enhance yield in depleted fisheries by protecting populations, particularly large, old spawners that supply larvae for interspersed fishing grounds. The ability of marine reserves to enhance sustainable fisheries is much less evident. We report empirical evidence of a marine reserve network improving yield regionally for a sustainable spiny lobster fishery, apparently through the spillover of adult lobsters and behavioral adaptation by the fishing fleet. Results of a Before-After, Control-Impact analysis found catch, effort, and Catch-Per-Unit Effort increased after the establishment of marine reserves in the northern region of the fishery where fishers responded by fishing intensively at reserve borders, but declined in the southern region where they vacated once productive fishing grounds. The adaptation of the northern region of the fishery may have been aided by a history of collaboration between fishers, scientists, and managers, highlighting the value of collaborative research and education programs for preparing fisheries to operate productively within a seascape that includes a large marine reserve network.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-024-51525-6.</p>", "<title>Acknowledgements</title>", "<p>We thank the CA Lobster and trap Fishermen’s Association (CLTFA) for sharing knowledge and expertise on lobster fishing and natural history, and for collaborating in science, especially S. Escobar, C. Miller, and S. Shrout. We also thank C. Barsky of the CA Department of Fish and Wildlife (CDFW), and J. Richards of the CA Sea Grant Extension, for encouraging and participating in collaborative fishery research. Thank you to M. C. Kay and S. Fitzgerald for collaborative scientific lobster trapping that quantified spillover from MLPA reserves and to S. C. Schroeter for a thoughtful discussion and review of the manuscript. Funding was provided by the US National Science Foundation in support of the Santa Barbara Coastal Long Term Ecological Research Program (Award no. OCE-1831937).</p>", "<title>Author contributions</title>", "<p>H.S.L. and D.C.R. conceived of the study; D.C.R and R.J.M. obtained funding for the study; J.K.K.H. provide fishery data from CDFW; C.V. provided fishery information; M.V. Collected field data; H.S.L., D.C.R., C.L., P.M., and J.P.G. conducted the analyses; H.S.L. and D.C.R. wrote the paper with assistance from R.J.M., M.V., and C.V. The manuscript reflects the contributions and ideas of all authors.</p>", "<title>Data availability</title>", "<p>The raw datasets, specifically of spiny lobster fishery Logbook data and Fish Ticket data, analyzed for this study are not publicly available due to legally mandated confidentially as specified by State of California Fish and Game code 8022. They are available from the California Department of Fish and Wildlife on reasonable request. Requests for the data should be made to the California Marine Region Office (Region 7) using email address <italic>[email protected]</italic>, or by calling the Region 7 office at 001-831-649-2870.</p>", "<title>Competing interests</title>", "<p id=\"Par24\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Location of the spiny lobster fishery in southern California (CA), USA. Displayed are the 12 jurisdictional fishing blocks with marine reserves (gray) and the 22 blocks without reserves (white) established in 2012. Block numbers are those used by the California Department of Fish and Wildlife to record fishery-dependent data, which for the spiny lobster fishery include the weight of lobster caught, and the number of traps pulled. Also shown are the 14 marine reserves (SMR) and State Marine Conservation Areas (SMCA) established along the coast where lobster fishing is prohibited, and the fishing ports (black stars) where fishers are based and land their catch. “North” refers to the northern region of the fishery, and “South” the southern region.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Response of the CA spiny lobster fishery to establishment of a marine reserve network along mainland coast of California, USA in 2012 (The area from Pt. Conception to the U.S.-Mexico Border in Fig. ##FIG##0##1##). Displayed are Delta values (∆ = sum of Reserve blocks − sum of Control blocks) for: (<bold>A</bold>) catch (kg of lobster caught per annual fishing season), (<bold>B</bold>) fishing effort (number of traps pulled per annual fishing season), and (<bold>C</bold>) the Catch-Per-Unit Effort (kg lobster caught per trap pulled per annual fishing season) for the entire fishery. Reserve blocks are jurisdictional fishing blocks with marine reserves and control blocks are fishing blocks without reserves. Fishing occurs in both block types. Horizontal lines represent the means (solid line), and the zero value (dotted line) represents no difference between the values of Reserve and Control blocks. Delta values above zero represent years when Reserve blocks had overall higher values than Control blocks. Also shown are upper and lower 95% confidence limits (grey shaded area) for the 14 years <italic>Before</italic>, and 8 years <italic>After</italic> reserves were implemented. The dashed vertical lines separate the <italic>Before</italic> and <italic>After</italic> periods, and include a transition year (2012) that was not included in the analysis (see “Methods”). Results (<italic>P</italic>-values) of two-sample <italic>t</italic>-tests comparing Delta values in the Before vs After period are shown. Data are log transformed catch, effort, and CPUE (Log Catch/Log Effort).</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Annual summed values of the commercial mainland spiny lobster fishery in California for: (<bold>A</bold>) lobster catch (kg) and (<bold>B</bold>) fishing effort (trap pulls) for reserve (solid circles) and control (open circles) fishing blocks. These data are for the entire fishery (north and south regions combined). Reserve blocks (n = 12) are jurisdictional fishing blocks with marine reserves and control blocks (n = 22) are fishing blocks without reserves. The vertical dotted lines designate when the reserves were established and include a transitional year (2012) not used in the calculations of the Delta values shown in Figs. ##FIG##1##2##, ##FIG##3##4##, and ##FIG##4##5##.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Response of the spiny lobster fishery to the establishment of a marine reserve network in the northern portion of the fishery (“North” in Fig. ##FIG##0##1##). Displayed are log transformed Delta values for (<bold>A</bold>) catch, (<bold>B</bold>) effort, and (<bold>C</bold>) CPUE (Log Catch/Log Effort). See Fig. ##FIG##1##2## for definitions of catch, effort, CPUE and the horizontal and vertical lines. Results (<italic>P</italic>-values) of two-sample <italic>t</italic>-tests comparing delta values in the Before vs After period are shown. Untransformed values for catch, effort and CPUE are displayed in Fig. ##SUPPL##0##S2##.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Response of the spiny lobster fishery to the establishment of a marine reserve network in the southern portion of the fishery (“South” in Fig. ##FIG##0##1##). Displayed are log transformed Delta values for (<bold>A</bold>) catch, (<bold>B</bold>) effort, and (<bold>C</bold>) CPUE (Log Catch/Log Effort). See Fig. ##FIG##1##2## for definitions of catch, effort, CPUE and the horizontal and vertical lines. Results (<italic>P</italic>-values) of two-sample <italic>t</italic>-tests comparing Delta values in the Before vs After period are shown. Untransformed values for catch, effort and CPUE are displayed in Fig. ##SUPPL##0##S3##. Please note the difference in the scale on the Y-axis between this Figure and Fig. ##FIG##3##4##.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>The mean number (± SE) of lobster traps placed at increasing distances from borders of three reserves in the northern portion of the fishery (Point Conception, Campus Point, and Point Dume) and three reserves in the southern region (Point Vincente SMCA, Matlahuay, and South La Jolla). There were more traps in the northern region (gray bars) than the southern region (black bars) (<italic>P</italic> &lt; 0.05) within 2 km of reserves, despite there being many more traps set in the south than north (See “Results and discussion” for details).</p></caption></fig>" ]

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[ "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">The last decade has seen significant technological progress in manufacturing hardware platform of quantum computers^{##UREF##0##1##}. The current pace of scale-up in quantum devices raises a hope that quantum processors with hundreds or thousands of physical qubits could be available within the next decade. These near-term quantum computers are referred to as noisy intermediate-scale quantum (NISQ) computers^{##UREF##1##2##} in that they are classically intractable, but still not sufficiently large to implement quantum error correction. As the NISQ era approaches, there have been an increasing number of researches that develop algorithms to efficiently leverage NISQ devices^{##UREF##2##3##–##UREF##4##5##}. They are designed to solve quantum many-body problems in chemistry and physics as well as classical problems in combinatorial optimization and machine learning. Most of these studies employ hybrid quantum-classical approaches, primarily variational quantum algorithms^{##REF##25055053##6##,##UREF##5##7##}. In these algorithms, variational quantum states are created via parametrized quantum circuits on a quantum computer, whereas the parameters are updated on a classical computer to optimize the objective function calculated with the measurement outcomes. Since variational quantum algorithms generally take a relatively low number of gate operations, they are considered as suitable to gain quantum advantage on NISQ computers.</p>", "<p id=\"Par3\">Quantum approximate optimization algorithm (QAOA)^{##UREF##6##8##}, a representative example of variational quantum algorithms, solves combinatorial optimization problems in a spirit analogous to adiabatic quantum annealing (QA)^{##UREF##7##9##–##REF##32235066##11##}. The variational state (ansatz) of QAOA can be deduced by applying the Trotter decomposition to the time evolution of QA and allowing the time step of each term to vary. Despite some numerical demonstrations of its efficacy in small-size problems^{##UREF##9##12##,##UREF##10##13##}, it has been a subject of discussions whether QAOA could practically outperform the best classical algorithms^{##UREF##11##14##,##REF##33449785##15##}. Several kinds of variants have been proposed to improve upon the original version of QAOA^{##UREF##12##16##–##UREF##18##22##}. To name a few, Farhi et al. proposed a variant of the ansatz by allowing different parameters for each rotation gate^{##UREF##12##16##}. Hadfield et al. extended the ansatz by generalizing mixer operations, which could be suitable to optimization problems with constraints^{##UREF##15##19##}.</p>", "<p id=\"Par4\">A promising variant that our work will focus on is the warm-start QAOA (WS-QAOA) proposed by Egger et al.^{##UREF##17##21##} and Tate et al.^{##UREF##18##22##}. The warm-start approach adjusts the distribution of bit strings in the initial state of the ansatz away from the equal superposition for standard QAOA to increase the amplitude of a classically-obtained approximate solution. Both of Refs.^{##UREF##17##21##} and^{##UREF##18##22##} showed enhancement of the solution quality relative to the original version of QAOA particularly for small depth. Egger et al. encode rounded/unrounded semidefinite programming solutions into the initial state as well as the mixer term in the ansatz^{##UREF##17##21##}. They numerically showed improvement in the optimized energy and fidelity compared to standard QAOA in portfolio optimization problems by warm-starting QAOA with classically-obtained continuous solutions. They also solved MAX-CUT problems by WS-QAOA with rounded solutions produced by the Goemans-Williamson algorithm and observed maximum cuts more often than standard QAOA in the recursive procedure developed in Ref.^{##REF##33449785##15##}. Tate et al. also encode semidefinite programming relaxations into the initial state, but not the unitary circuit^{##UREF##18##22##}. They observed improvement in the approximation ratio relative to standard QAOA for MAX-CUT problems on weighted and unweighted graphs by using WS-QAOA with relaxed solutions obtained by the Burer-Monteiro algorithm. We also mention that a similar warm-start approach has been independently studied in QA^{##REF##31633984##23##}. Meanwhile, it has been reported that WS-QAOA typically shows no improvement if the initial state is strictly a classical string^{##UREF##19##24##}.</p>", "<p id=\"Par5\">In this paper, we examine how the performance of WS-QAOA depends on quality of approximate solutions to make a deep understanding of its efficacy. In Refs.^{##UREF##17##21##,##UREF##18##22##}, the authors solved problems with WS-QAOA by acquiring approximate solutions by classical algorithms. Meanwhile, it remains unclear how accurate approximate solutions should be for WS-QAOA to outperform QAOA. Here we deduce the ansatz of WS-QAOA starting from QA with a bias field^{##REF##31633984##23##} and carefully study how the performance of WS-QAOA depends on the quality of approximate solutions by numerical simulations on the MAX-CUT problem. We find out that WS-QAOA shows higher fidelity and approximation ratio than QAOA as the Hamming distance of the approximate solutions to the exact ones becomes smaller. We also reveal that the observation could be partially attributed to the initial state of the ansatz. Finally, we solve the MAX-CUT problem with WS-QAOA after obtaining approximate solutions by QAOA and have higher fidelity and approximation ratio than QAOA especially when the circuit depth is small.</p>", "<p id=\"Par6\">The rest of the paper is organized as follows. In Sect. <xref rid=\"Sec2\" ref-type=\"sec\">2</xref>, we formulate WS-QAOA in the context of QA. Then, in Sect. <xref rid=\"Sec6\" ref-type=\"sec\">3</xref>, we numerically study the performance of WS-QAOA on the MAX-CUT problem for various approximate solutions in terms of the Hamming distance to the exact solutions as well as for different strengths of the bias field. In Sect. <xref rid=\"Sec7\" ref-type=\"sec\">4</xref>, we solve the MAX-CUT problem by combining WS-QAOA with QAOA and compare its efficacy to QAOA. Finally, in Sect. <xref rid=\"Sec8\" ref-type=\"sec\">5</xref>, we summarize our results.</p>" ]

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[ "<title>Conclusion</title>", "<p id=\"Par33\">In this work, we systematically studied how the performance of WS-QAOA depends on the quality of approximate solutions by numerical simulations on the MAX-CUT problem on w3R graphs. We found that WS-QAOA yields higher fidelities and approximation ratios than QAOA when one uses approximate solutions that are close enough to the exact solutions in terms of the Hamming distance. More specifically, WS-QAOA with () produces higher fidelities on average than QAOA if the relative Hamming distance of approximate solutions to the exact ones, , is below 0.2–0.3 (0.1–0.25). We also obtained theoretical curves that explain those properties. Furthermore, we showed that QAOA could serve as a capable way to find approximate solutions for WS-QAOA. We found out that WS-QAOA combined with QAOA shows higher fidelity and approximation ratio than QAOA specifically when the depth is limited to a small number.</p>", "<p id=\"Par34\">We believe that our findings could allow one to make a clear understanding of the efficacy of WS-QAOA. They might also be helpful to determining the criteria of approximate solutions for WS-QAOA. Lastly, we mention several future studies of interest. In Ref.^{##UREF##26##31##}, the authors predicted the circuit depth of standard QAOA to reach a certain approximation ratio for various graph symmetries by machine learning technique. It would be interesting to extend their results to WS-QAOA and investigate the necessary conditions for the Hamming distance of the approximation solution as well as the circuit depth. In the context of industrial applications, it would be also intriguing to see how our results would look like for more practical optimization problems.</p>" ]

[ "<p id=\"Par1\">Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA achieves higher fidelity (probability that exact solutions are observed) and approximation ratio than QAOA as the Hamming distance of approximate solutions to the exact ones becomes smaller. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having higher fidelity and approximation ratio than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions.</p>", "<title>Subject terms</title>" ]

[ "<title>Formulation</title>", "<title>MAX-CUT problem</title>", "<p id=\"Par7\">As a prototypical combinatorial optimization problem, we consider the MAX-CUT problem, which is known as NP-hard. It is defined on a graph , where <italic>V</italic> represents a set of vertices, and <italic>E</italic> represents a set of edges between the vertices. We denote the number of vertices in <italic>G</italic> as <italic>n</italic>. The MAX-CUT problem is to find a partition of <italic>V</italic> into two subsets that maximizes the total number of edges between one subset and the other. In a general case that each edge is associated with a real-valued weight , one evaluates the weighted sum of those edges. The problem is formulated as maximization of the following objective functionwhere denotes a binary variable associated with vertex <italic>i</italic>\n. We note that bit strings and () give the same value of <italic>C</italic>. In the following, we denote and as the single pair of solutions.</p>", "<p id=\"Par8\">In the language of physics, the MAX-CUT problem is encoded in finding the ground state of the corresponding Ising Hamiltonian, which is obtained by replacing for (<italic>Z</italic>: the Pauli <italic>Z</italic> matrix) in the objective function <italic>C</italic> and changing the whole sign. The Hamiltonian readswhere the constant termis left off.</p>", "<title>QAOA</title>", "<p id=\"Par9\">QAOA searches for the ground state of the Hamiltonian using a QA-inspired ansatz with 2<italic>p</italic> variational parameters for depth <italic>p</italic>^{##UREF##6##8##}. The ansatz is constructed by alternating applications of the driver operation and mixer operation to the equal-weight superposition state . It is written down with variational parameters and \n asHere the driver and mixer are defined as and , respectively, where (<italic>X</italic>: the Pauli <italic>X</italic> matrix) represents a transverse-field term. One can deduce the ansatz via the Trotter decomposition of the QA procedure and parametrization of each time step. In QA, the wave function evolves under the Hamiltonianwith a schedule function <italic>u</italic>(<italic>t</italic>) ( and ).</p>", "<title>WS-QAOA</title>", "<p id=\"Par10\">QA has had considerable success in solving combinatorial optimization problems^{##UREF##7##9##–##REF##32235066##11##}. However, when gap closing occurs during the annealing, it often gets stuck at suboptimal solutions. Reverse QA is an effective variant to circumvent this challenge, which incorporates in the annealing process an approximate solution obtained in advance^{##UREF##20##25##}. In this procedure, the state adiabatically evolves from the approximate solution at the beginning to the exact solution at the end, driven by quantum fluctuations of a transverse field with a mountain-like time profile. The dynamics is described by the Hamiltonian \n, where yields the approximate solution as the ground state, and <italic>h</italic>(<italic>t</italic>) is a concave function with . It was shown that the performance of reverse QA is largely dominated by the Hamming distance of the approximate solution from the exact one^{##UREF##20##25##}.</p>", "<p id=\"Par11\">Recently Graß^{##REF##31633984##23##} proposed a similar but simpler QA procedure to make use of an approximate solution, which introduces a longitudinal bias field that favors the approximate solution. The procedure, which we call biased quantum annealing (BQA) hereafter, is governed by the Hamiltonianwhere represents a site-dependent longitudinal field defined asHere represents the <italic>i</italic>-th bit in the bit string of an approximate solution , and denotes strength of the bias field. The author numerically showed that BQA achieves higher fidelity than QA in small instances of the exact-cover problem when one prepares approximate solutions that are close enough to the exact solutions in terms of the Hamming distance^{##REF##31633984##23##}.</p>", "<p id=\"Par12\">Here we formulate a QAOA version of BQA, which actually corresponds to WS-QAOA^{##UREF##17##21##,##UREF##18##22##}. One can derive the ansatz via the Trotter decomposition of BQA under the Hamiltonian and parametrization of each time step in the same manner as one deduces from . Then the WS-QAOA ansatz is represented aswhere is defined as . The initial state is written down as (<italic>Y</italic>: the Pauli <italic>Y</italic> matrix) represents a -rotation around the <italic>y</italic>-axis. For , corresponds to the QAOA ansatz . The WS-QAOA ansatz is almost identical to that in Ref.^{##UREF##17##21##} except a small difference in representation of the mixer; the latter implements with three layers of rotation gates, whereas the former uses a decomposed form with two layers.</p>", "<title>Numerical simulations</title>", "<p id=\"Par13\">In this section, we examine how the WS-QAOA performance varies with choice of approximate solutions . For that purpose, we numerically study the MAX-CUT problem on weighted 3-regular (w3R) graphs^{##UREF##10##13##,##UREF##21##26##}. In w3R graphs, each vertex is connected to three others chosen at random, and each edge has weight randomly set from [0, 1). We employ a fast quantum circuit simulator Qulacs^{##UREF##22##27##}.</p>", "<p id=\"Par14\">For optimization of the parameters, we use two methods, random initialization (RI) and an interpolation-based heuristic termed INTERP^{##UREF##10##13##}. In RI, we take the best sample out of 50 randomizations of the initial values. Given the translational symmetry of the ansatz , initial values of are set from for , for , and otherwise, whereas those of are set from . On the other hand, in INTERP, the parameters are optimized incrementally from depth 1 to depth <italic>p</italic>. Here initial values of the parameters at depth <italic>p</italic>, and \n, are uniquely determined via an interpolation of the optimized values at depth as (). It has been revealed that INTERP works more efficiently than RI for QAOA on w3R graphs^{##UREF##10##13##}. In this work, based on our benchmark calculations, we choose a better method, depending on , <italic>p</italic>. For QAOA (), we use INTERP. For WS-QAOA, with , we use INTERP, whereas, with , we use RI at and INTERP at . We note that, regardless of , we use RI when corresponds to the exact solution. In large instances of practical interest where exact solutions are unknown, one would choose either of the methods only according to and <italic>p</italic>. In both methods, parameters are updated via a gradient descent until the gradient becomes lower than a certain threshold value.</p>", "<p id=\"Par15\">In WS-QAOA, we set approximate solutions by flipping <italic>d</italic> bits randomly selected from <italic>n</italic> bits in the solution . In other words, <italic>d</italic> represents the Hamming distance of to . Figure ##FIG##0##1## show the optimized parameters of QAOA , and WS-QAOA with for on 50 graph instances of . Fig. ##FIG##0##1##a,d show that in QAOA, () decreases (increases) with <italic>s</italic>, which resembles the process of QA^{##UREF##10##13##}. We observe a similar trend in WS-QAOA with in Fig. ##FIG##0##1##b, e. Meanwhile, when , the parameters are not monotonic against <italic>s</italic>, which may reflect that the property of QA declines as becomes larger. Moreover, the optimized parameters do not seem transferable between instances for (Fig. ##FIG##0##1##c,f) in comparison to those for QAOA (Fig. ##FIG##0##1##a,d) and (Fig. ##FIG##0##1##b,e). We think that further studies would be needed on parameter transferability^{##UREF##23##28##,##UREF##24##29##} for WS-QAOA.</p>", "<p id=\"Par16\">We compare the performance of WS-QAOA to that of QAOA. As a performance indicator, we use the fidelity of the optimized ansatz . We define the fidelity of a wave function asLater, we also discuss our results in terms of approximation ratio, defined as . In Fig. ##FIG##1##2##a, <italic>F</italic> of WS-QAOA with at is plotted against that of QAOA on 50 graph instances of . In the following, we focus on . We refer to Sect. I of SM for a closer look at dependence. Figure ##FIG##1##2##a indicates that the relative performance of WS-QAOA against QAOA is dominated by the Hamming distance <italic>d</italic>. Importantly, becomes higher as <italic>d</italic> decreases. We find that WS-QAOA outperforms QAOA in all cases for and in most cases for (Fig. ##FIG##1##2##a). We note that is always almost unity for . The enhanced fidelity with the decrease in <italic>d</italic> has also been observed in BQA^{##REF##31633984##23##}.</p>", "<p id=\"Par17\">Success of WS-QAOA with small <italic>d</italic> is also manifested in the bit string with highest probability, , in the optimized ansatz. Figure ##FIG##1##2##b shows the histogram over <italic>d</italic> and the Hamming distance of to , , on 50 instances of . One can see that the closer the approximate solution is to the exact solution, the more likely is to correspond with the exact solution () (Fig. ##FIG##1##2##b). It is notable that for , the optimized ansatz still yields the solution as the highest-probability string in about a half of the instances.</p>", "<p id=\"Par18\">We proceed to study the graph size dependence. In Fig. ##FIG##2##3##a,c, the averaged fidelity of WS-QAOA at is shown against the number of vertices <italic>n</italic>, together with that of QAOA (). Figure ##FIG##2##3##a,c correspond to and , respectively. We present the entire data for in Sect. II of SM. In both WS-QAOA and QAOA, <italic>F</italic> shows a nearly exponential decay with <italic>n</italic>, but importantly it decreases less steeply in WS-QAOA than in QAOA. As a result, with larger <italic>n</italic>, WS-QAOA outperforms QAOA with even larger <italic>d</italic>. We also compare and . Figure ##FIG##2##3##a,c indicate that as <italic>d</italic> increases incrementally, fidelity decreases roughly by a constant multiplicative factor (aside from ) and that the factor is smaller for than for . These features seem to stem from the initial state at least in part. In Fig. ##FIG##2##3##b,d, we present the fidelity of for and , which is derived from Eqs. (##FORMU##118##10##) and (##FORMU##46##9##) with asIn Fig. ##FIG##2##3##b,d, one can observe similar behaviors to Fig. ##FIG##2##3##a,c, although the magnitude of the fidelity is significantly improved by the optimized circuit.</p>", "<p id=\"Par19\">We also present the <italic>n</italic> dependence of approximation ratio <italic>r</italic> with in Fig. ##FIG##3##4##. Figure ##FIG##3##4##a–d correspond to , and Fig. ##FIG##3##4##e–h to . As in the case of fidelity <italic>F</italic> (Fig. ##FIG##2##3##), WS-QAOA has higher <italic>r</italic> than QAOA when the Hamming distance <italic>d</italic> is sufficiently small. <italic>r</italic> of WS-QAOA also decreases as <italic>d</italic> increases. Notably, <italic>r</italic> of WS-QAOA tends to increase with <italic>n</italic> as opposed to <italic>F</italic>.</p>", "<p id=\"Par20\">The calculations above indicate how close approximate solutions should be to the exact solutions for WS-QAOA to outperform QAOA. From the graph size dependence of the fidelity (Fig. ##FIG##2##3##a,c, and S2) as well as the approximation ratio (Fig. ##FIG##3##4##), we estimate the critical Hamming distance of , , which determines whether WS-QAOA outperforms QAOA or not. For example, we estimate for from the fidelity data in Fig. ##FIG##2##3##a. Figures ##FIG##4##5##a and ##FIG##4##5##b show scaled by the graph size <italic>n</italic> for and , respectively. The blue (red) points represent for fidelity (approximation ratio). For fidelity, ranges within [0.2, 0.3) for , whereas it hovers from 0.1 to 0.25 for . For approximation ratio, is smaller, mostly within [0.1, 0.25) for and [0.05, 0.2] for . The important implication with respect to scalability is that the Hamming distance <italic>d</italic> could be allowed to scale linearly with <italic>n</italic> when <italic>d</italic>/<italic>n</italic> is below those threshold values.</p>", "<p id=\"Par21\">We also theoretically derive for the fidelity of the initial state starting from (see Sect. III of SM), which readsWe draw the curve of Eq. (##FORMU##194##12##) in Figs. ##FIG##4##5##. One can see that in both , estimated from the actual fidelity is smaller than the theoretical curve for the initial state. This indicates that QAOA gains more fidelity by the optimized unitary circuit than WS-QAOA.</p>", "<p id=\"Par22\">We also study how much or whether WS-QAOA improves approximation ratio as compared to approximate solutions employed in WS-QAOA. Figure ##FIG##5##6## display the graph size dependence of approximation ratio <italic>r</italic> for WS-QAOA as well as approximate solutions employed with . Fig. ##FIG##5##6##a–f correspond to and Fig. ##FIG##5##6##g–l to . In most cases, WS-QAOA yields higher approximation ratio on average than approximate solutions for with (Figs. ##FIG##5##6##c–f, ##FIG##5##6##i–l) and with (Fig. ##FIG##5##6##b, ##FIG##5##6##h). This makes it clear that WS-QAOA helps to improve upon the approximate solutions obtained in advance.</p>", "<p id=\"Par23\">Finally, to see the scalability of the methods, we examine the minimal depth <italic>p</italic> that reaches a target approximation ratio, . Here we set the target approximation ratio as , the value guaranteed by the classical Goemans-Williamson algorithm for MAX-CUT problems^{##UREF##25##30##}. In Figs. ##FIG##6##7##a and ##FIG##6##7##b, we plot as a function of <italic>n</italic> for WS-QAOA with and , respectively, along with that for QAOA. Figure ##FIG##6##7## show that <italic>p</italic> can be smaller for WS-QAOA with than for QAOA to reach the target approximation ratio. Meanwhile, since our data are limited to and due to finite computational resources, it seems difficult to discuss the size dependence for the vanilla and warm-start approaches from Figs. ##FIG##6##7##. We expect that one could reveal the scalability by increasing <italic>n</italic> and <italic>p</italic> significantly.</p>", "<title>WS-QAOA combined with QAOA</title>", "<p id=\"Par24\">\n\n</p>", "<p id=\"Par25\">In the previous section, we studied the dependence of the WS-QAOA performance on approximate solutions and revealed that their Hamming distance to the exact solutions plays a crucial role. In this section, we solve the MAX-CUT problem with WS-QAOA while finding approximate solutions by QAOA. This resembles the approach in the previous study of BQA, where approximate solutions are obtained by QA beforehand^{##REF##31633984##23##}.</p>", "<p id=\"Par26\">In Fig. ##FIG##7##8##, we depict a flow diagram of our procedure. We call this procedure QAOA+WS hereafter. First, we solve the problem using QAOA and pick up <italic>M</italic> bit strings with highest probabilities, (), based on the distribution from . Then we conduct WS-QAOA with as an approximate solution and obtain the distribution from . At the end, we obtain the final distribution by averaging out <italic>M</italic> distributions .</p>", "<p id=\"Par27\">We compare the fidelity of QAOA+WS to that of QAOA. The fidelity of QAOA+WS is calculated as the average over the fidelities of <italic>M</italic> runs of WS-QAOA. Figures ##FIG##8##9## present fidelities of QAOA+WS with against those of QAOA over 50 graph instances of . In Fig. ##FIG##8##9##a,b, we set and for QAOA+WS, respectively. We note that if the exact solutions are included in <italic>M</italic> approximate solutions, we drop them off, considering that almost always yields the perfect fidelity (Figs. ##FIG##1##2##a, ##FIG##2##3##a). For , QAOA+WS shows a sizable variance of the fidelity especially as <italic>p</italic> increases. It shows a better performance for most instances than QAOA at , but not necessarily at . Meanwhile, for , QAOA+WS shows a smaller variance and outperforms QAOA at for most instances. Smaller variance with larger <italic>M</italic> seems to be natural, because the approximate solutions are more likely to have a wide range of the Hamming distance to the exact solutions as <italic>M</italic> increases.</p>", "<p id=\"Par28\">We also study the graph size dependence. Figure ##FIG##9##10## present the fidelity of QAOA+WS with along with that of QAOA plotted against the number of vertices. In Fig. ##FIG##9##10##a–d, we set , respectively. The fidelity is averaged over 50 graph instances for , 20 for , and 15 for . Importantly, the fidelity decays more slowly with <italic>n</italic> in QAOA+WS than in QAOA for (Fig. ##FIG##9##10##). As a result, QAOA+WS on average outperforms QAOA for all <italic>M</italic> as <italic>n</italic> increases; for at , at , at , and at . It should be also mentioned that QAOA+WS becomes more beneficial for smaller <italic>p</italic>, because the difference in the decay with <italic>n</italic> seems to decrease as <italic>p</italic> increases.</p>", "<p id=\"Par29\">We also evaluate the performance of QAOA+WS by approximation ratio. As in the fidelity, the approximation ratio <italic>r</italic> for QAOA+WS is estimated by averaging out <italic>r</italic> for <italic>M</italic> runs of WS-QAOA. Figure ##FIG##10##11##a–d show the graph size dependence of <italic>r</italic> for , respectively. QAOA+WS achieves higher <italic>r</italic> than QAOA except for . As in the fidelity (Fig. ##FIG##9##10##), the difference in <italic>r</italic> increases with <italic>n</italic> and decreases as <italic>p</italic> increases. It should be noted that <italic>r</italic> of QAOA+WS has a tendency to increase with <italic>n</italic> as opposed to <italic>F</italic> (Fig. ##FIG##9##10##).</p>", "<p id=\"Par30\">We present the minimal depth for the target approximation quality for QAOA+WS. Figure ##FIG##11##12## shows for QAOA+WS with as well as QAOA as a function of <italic>n</italic> (see Sect. <xref rid=\"Sec6\" ref-type=\"sec\">3</xref> for the definition of ). One can see that the minimal <italic>p</italic> is smaller for QAOA+WS than for QAOA (Fig. ##FIG##11##12##). We note that, as in Fig. ##FIG##6##7##, it is hard to discuss the scalability of the results due to the limited range of <italic>n</italic> and <italic>p</italic>.</p>", "<p id=\"Par31\">As indicated in Fig. ##FIG##11##12##, QAOA+WS needs lower circuit depth to reach certain solution qualities than QAOA. Meanwhile, we should remember that QAOA+WS needs more variational circuits than QAOA, where QAOA+WS involves circuits ( variational parameters) in comparison to a single circuit (2<italic>p</italic> variational parameters) for QAOA (Fig. ##FIG##7##8##). In small instances, one may rather use QAOA than QAOA+WS because might be small enough for QAOA to be reliably executed on current NISQ devices. However, would be much larger for large problems of practical interest. Then one can expect that it would be more important to reduce the circuit depth than the number of variational circuits, considering that circuit fidelity exponentially decreases with depth on NISQ devices due to hardware noise. In such cases, QAOA+WS could be more advantageous than QAOA.</p>", "<p id=\"Par32\">It should be mentioned that approximate solutions fed to WS-QAOA can be obtained by classical solvers instead of QAOA as in Refs.^{##UREF##17##21##,##UREF##18##22##}. When classical methods give better solution qualities than QAOA, there is not much reason for employing QAOA to obtain approximate solutions. Even when classical methods give solution qualities comparable to QAOA, using classical methods for approximate solutions might be still preferable because it saves quantum resources. In light of these considerations, QAOA+WS would be beneficial in cases that one intends to improve upon QAOA when QAOA already provides better solution qualities than classical methods in the future.</p>", "<title>Supplementary Information</title>", "<p>\n</p>" ]

[ "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1038/s41598-023-50406-8.</p>", "<title>Acknowledgements</title>", "<p>This work was supported by MEXT via the “Program for Promoting Researches on the Supercomputer Fugaku” (JP-MXP1020200205) and JSPS KAKENHI via the “Grant-in-Aid for Scientific Research(A)” Grant Number 21H04553. This work was also supported in part by MEXT Quantum Leap Flagship Program (MEXTQLEAP) Grant No. JPMXS0120319794. Part of numerical calculation was carried out at the Supercomputer Center, Institute for Solid State Physics, University of Tokyo.</p>", "<title>Author contributions</title>", "<p>The project was conceived by K.N.O., H.N., and Y.M. K.N.O. wrote the code with help from H.N. and performed numerical simulations. K.N.O. conducted mathematical analyses. All authors actively discussed the results and contributed to preparation of the manuscript.</p>", "<title>Data availibility</title>", "<p>The data generated in this study are available from the corresponding author upon reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par35\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Optimized and of (<bold>a</bold>,<bold>d</bold>) QAOA and WS-QAOA with (<bold>b</bold>,<bold>e</bold>) and (<bold>c</bold>,<bold>f</bold>) for on 50 instances of w3R graph (). The ansatz depth is . The parameters are optimized by INTERP in (<bold>a</bold>,<bold>b</bold>,<bold>d</bold>,<bold>e</bold>) and RI in (<bold>c</bold>,<bold>f</bold>).</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Performance of WS-QAOA with at on 50 instances of w3R graph (). <italic>d</italic> represents the Hamming distance between the approximate solution and exact one . (<bold>a</bold>) Fidelity of WS-QAOA () versus that of QAOA (). The dotted line corresponds to . (<bold>b</bold>) Histogram over <italic>d</italic> and . is the Hamming distance of to . The dotted line corresponds to .</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>(<bold>a</bold>,<bold>c</bold>) Graph size dependence of the average fidelity obtained by WS-QAOA with different <italic>d</italic> compared to QAOA () for . (<bold>a</bold>) corresponds to and (<bold>c</bold>) to . The fidelity is averaged over 50 instances for , 20 for , 15 for , and 10 for . The error bar represents standard error of the mean. (<bold>b</bold>,<bold>d</bold>) Calculated fidelity for the initial state of the ansatz, Eq. (##FORMU##163##11##). (<bold>b</bold>) corresponds to , (<bold>d</bold>) to and black lines to QAOA ().</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Graph size dependence of the approximation ratios of WS-QAOA along with QAOA (<bold>a</bold>–<bold>d</bold>) and (<bold>e</bold>-<bold>h</bold>) . (<bold>a</bold>) and (<bold>e</bold>) correspond to , (<bold>b</bold>) and (<bold>f</bold>) to , (<bold>c</bold>) and (<bold>g</bold>) to , and (<bold>d</bold>) and (<bold>h</bold>) to . The approximation ratio is averaged over 50 graph instances for , 20 for , 15 for , and 10 for . The error bar stands for standard error of the mean.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Critical relative Hamming distance plotted against <italic>n</italic> for (<bold>a</bold>) and (<bold>b</bold>) . The blue points are derived from the fidelity in Fig. ##FIG##2##3##a,c, and S2, and red ones are from the approximation ratio in Fig. ##FIG##3##4##. When approximate solutions are less-than- away from exact solutions, WS-QAOA outperforms QAOA on average. The black line denotes the theoretical value of estimated for the fidelity of the initial state (see Eq. (##FORMU##194##12##) in the text).</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Graph size dependence of the approximation ratios of WS-QAOA as well as approximate solutions employed for (<bold>a</bold>–<bold>f</bold>) and (<bold>g</bold>–<bold>l</bold>) . (<bold>a</bold>) and (<bold>g</bold>) correspond to , (<bold>b</bold>) and (<bold>h</bold>) to , (<bold>c</bold>) and (<bold>i</bold>) to , (<bold>d</bold>) and (<bold>j</bold>) to , (<bold>e</bold>) and (<bold>k</bold>) to , (<bold>f</bold>) and (<bold>l</bold>) to . The approximation ratio is averaged over 50 graph instances for , 20 for , 15 for , and 10 for . The error bar stands for standard error of the mean.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Minimal <italic>p</italic> that reaches the target approximation ratio plotted as a function of <italic>n</italic> for WS-QAOA with (<bold>a</bold>) and (<bold>b</bold>) .</p></caption></fig>", "<fig id=\"Fig8\"><label>Figure 8</label><caption><p>Flow diagram of QAOA+WS.</p></caption></fig>", "<fig id=\"Fig9\"><label>Figure 9</label><caption><p>Fidelity of QAOA+WS versus that of QAOA for 50 instances of with (<bold>a</bold>) and (<bold>b</bold>) . For WS-QAOA in QAOA+WS, we set .</p></caption></fig>", "<fig id=\"Fig10\"><label>Figure 10</label><caption><p>Graph size dependence of the fidelities of QAOA+WS along with QAOA at (<bold>a</bold>–<bold>d</bold>) . The fidelity is averaged over 50 graph instances for , 20 for , and 15 for . For WS-QAOA in QAOA+WS, we set . The error bar represents standard error of the mean.</p></caption></fig>", "<fig id=\"Fig11\"><label>Figure 11</label><caption><p>Graph size dependence of the approximation ratios of QAOA+WS along with QAOA at (<bold>a</bold>–<bold>d</bold>) . The approximation ratio <italic>r</italic> is averaged over 50 graph instances for , 20 for , and 15 for . For WS-QAOA in QAOA+WS, we set . The error bar represents standard error of the mean.</p></caption></fig>", "<fig id=\"Fig12\"><label>Figure 12</label><caption><p>Minimal depth <italic>p</italic> to reach the target approximation ratio plotted as a function of <italic>n</italic> for QAOA+WS with and QAOA.</p></caption></fig>" ]

[]

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\n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i\\}$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq6\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{{\\overline{x}}_i\\}$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:mrow><mml:mo 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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{{\\overline{x}}^{\\rm sol}_i\\}$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x_i$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(1-Z_i)/2$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} H_{\\rm C}=\\sum _{(i,j)\\in E}\\frac{w_{ij}}{2}Z_iZ_j, \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M26\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>∈</mml:mo><mml:mi>E</mml:mi></mml:mrow></mml:munder><mml:mfrac><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi 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columnalign=\"right\"><mml:mrow><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>∈</mml:mo><mml:mi>E</mml:mi></mml:mrow></mml:munder><mml:mfrac><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ij</mml:mi></mml:mrow></mml:msub><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\rm C}$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{\\rm C}$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{\\rm T}$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| + \\right\\rangle ^{\\otimes n}$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:msup><mml:mfenced close=\"〉\" open=\"|\"><mml:mo>+</mml:mo></mml:mfenced><mml:mrow><mml:mo>⊗</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _s$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma _s$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq18\"><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(1\\le s\\le p)$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>s</mml:mi><mml:mo>≤</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\left| \\Psi _{\\rm QAOA} \\right\\rangle =\\prod _{s=1}^pU_{\\rm T}(\\beta _s)U_{\\rm C}(\\gamma _s)\\left| + \\right\\rangle ^{\\otimes n}. \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M44\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:munderover><mml:mo>∏</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>p</mml:mi></mml:munderover><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msup><mml:mfenced close=\"〉\" open=\"|\"><mml:mo>+</mml:mo></mml:mfenced><mml:mrow><mml:mo>⊗</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq19\"><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{\\rm C}(\\gamma _s)=e^{-i\\gamma _s H_{\\rm C}}$$\\end{document}</tex-math><mml:math id=\"M46\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq20\"><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{\\rm T}(\\beta _s)=e^{-i\\beta _s H_{\\rm T}}$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq21\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\rm T}=-\\sum _iX_i$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq22\"><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _{\\rm QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M52\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} H_{\\rm QA}(t)=(1-u(t))H_{\\rm T}+u(t)H_{\\rm C} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M54\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">QA</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq23\"><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$u(0)=0$$\\end{document}</tex-math><mml:math id=\"M56\"><mml:mrow><mml:mi>u</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq24\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$u(T)=1$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:mrow><mml:mi>u</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq25\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\rm RQA}(t)=(1-t/T)H_{\\rm I}+h(t)H_{\\rm T}+(t/T)H_{\\rm C}$$\\end{document}</tex-math><mml:math id=\"M60\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">RQA</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">I</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq26\"><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(0\\le t\\le T)$$\\end{document}</tex-math><mml:math id=\"M62\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>t</mml:mi><mml:mo>≤</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq27\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\rm I}$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">I</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq28\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$h(0)=h(T)=0$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:mrow><mml:mi>h</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} H_{\\rm BQA}(t)=(1-u(t))(H_{\\rm T}+H_{\\rm L})+u(t)H_{\\rm C}, \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M68\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">BQA</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq30\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\rm L}$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} H_{\\rm L}=-\\alpha \\sum _i\\left( 1-2x_i^0\\right) Z_i. \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M72\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi>α</mml:mi><mml:munder><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:mfenced close=\")\" open=\"(\"><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:mfenced><mml:msub><mml:mi>Z</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq31\"><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x_i^0$$\\end{document}</tex-math><mml:math id=\"M74\"><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq32\"><alternatives><tex-math id=\"M75\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^0\\}$$\\end{document}</tex-math><mml:math id=\"M76\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq33\"><alternatives><tex-math id=\"M77\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M78\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq34\"><alternatives><tex-math id=\"M79\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\rm BQA}(t)$$\\end{document}</tex-math><mml:math id=\"M80\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">BQA</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq35\"><alternatives><tex-math id=\"M81\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _{\\rm QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M82\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq36\"><alternatives><tex-math id=\"M83\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$H_{\\rm QA}(t)$$\\end{document}</tex-math><mml:math id=\"M84\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">QA</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\left| \\Psi _\\mathrm{WS-QAOA} \\right\\rangle =\\prod _{s=1}^pU_{\\rm T}(\\beta _s)U_{\\rm L}(\\beta _s)U_{\\rm C}(\\gamma _s)\\left| \\Psi _0 \\right\\rangle , \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M86\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:munderover><mml:mo>∏</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>p</mml:mi></mml:munderover><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq37\"><alternatives><tex-math id=\"M87\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{\\rm L}$$\\end{document}</tex-math><mml:math id=\"M88\"><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq38\"><alternatives><tex-math id=\"M89\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$U_{\\rm L}(\\beta _s)=e^{-i\\beta _s H_{\\rm L}}$$\\end{document}</tex-math><mml:math id=\"M90\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq39\"><alternatives><tex-math id=\"M91\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _0 \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M92\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M93\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\left| \\Psi _0 \\right\\rangle =\\prod _{i=1}^n\\otimes R_Y\\left( -\\frac{\\pi }{2}+\\left( 1-2x_i^0\\right) \\tan ^{-1}\\alpha \\right) \\left| 0 \\right\\rangle . \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M94\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:munderover><mml:mo>∏</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mo>⊗</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>Y</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mo>-</mml:mo><mml:mfrac><mml:mi>π</mml:mi><mml:mn>2</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:mfenced><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mfenced><mml:mfenced close=\"〉\" open=\"|\"><mml:mn>0</mml:mn></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M95\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R_Y(\\theta )=e^{i(\\theta /2)Y}$$\\end{document}</tex-math><mml:math id=\"M96\"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>Y</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>θ</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>θ</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mi>Y</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M97\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\theta$$\\end{document}</tex-math><mml:math id=\"M98\"><mml:mi>θ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq42\"><alternatives><tex-math id=\"M99\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0$$\\end{document}</tex-math><mml:math id=\"M100\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq43\"><alternatives><tex-math id=\"M101\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _\\mathrm{WS-QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M102\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq44\"><alternatives><tex-math id=\"M103\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _{\\rm QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M104\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq45\"><alternatives><tex-math id=\"M105\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _\\mathrm{WS-QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M106\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq46\"><alternatives><tex-math id=\"M107\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$e^{-i\\beta _s (H_{\\rm T}+H_{\\rm L})}$$\\end{document}</tex-math><mml:math id=\"M108\"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq47\"><alternatives><tex-math id=\"M109\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$e^{-i\\beta _s H_{\\rm T}}e^{-i\\beta _s H_{\\rm L}}$$\\end{document}</tex-math><mml:math id=\"M110\"><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">T</mml:mi></mml:msub></mml:mrow></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">L</mml:mi></mml:msub></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq48\"><alternatives><tex-math id=\"M111\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^0\\}$$\\end{document}</tex-math><mml:math id=\"M112\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq49\"><alternatives><tex-math id=\"M113\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w_{ij}$$\\end{document}</tex-math><mml:math id=\"M114\"><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">ij</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq50\"><alternatives><tex-math id=\"M115\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _\\mathrm{WS-QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M116\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq51\"><alternatives><tex-math id=\"M117\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _s$$\\end{document}</tex-math><mml:math id=\"M118\"><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq52\"><alternatives><tex-math id=\"M119\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$[-\\frac{\\pi }{4}, \\frac{\\pi }{4})$$\\end{document}</tex-math><mml:math id=\"M120\"><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mo>-</mml:mo><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq53\"><alternatives><tex-math id=\"M121\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0$$\\end{document}</tex-math><mml:math id=\"M122\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq54\"><alternatives><tex-math id=\"M123\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$[-\\frac{\\pi }{2}, \\frac{\\pi }{2})$$\\end{document}</tex-math><mml:math id=\"M124\"><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mo>-</mml:mo><mml:mfrac><mml:mi>π</mml:mi><mml:mn>2</mml:mn></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mi>π</mml:mi><mml:mn>2</mml:mn></mml:mfrac><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq55\"><alternatives><tex-math id=\"M125\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M126\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq56\"><alternatives><tex-math id=\"M127\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$[-\\pi , \\pi )$$\\end{document}</tex-math><mml:math id=\"M128\"><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mo>-</mml:mo><mml:mi>π</mml:mi><mml:mo>,</mml:mo><mml:mi>π</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq57\"><alternatives><tex-math id=\"M129\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma _s$$\\end{document}</tex-math><mml:math id=\"M130\"><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq58\"><alternatives><tex-math id=\"M131\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$[-2\\pi , 2\\pi )$$\\end{document}</tex-math><mml:math id=\"M132\"><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq59\"><alternatives><tex-math id=\"M133\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _s[p]$$\\end{document}</tex-math><mml:math id=\"M134\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq60\"><alternatives><tex-math id=\"M135\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma _s[p]$$\\end{document}</tex-math><mml:math id=\"M136\"><mml:mrow><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq61\"><alternatives><tex-math id=\"M137\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(1\\le s\\le p)$$\\end{document}</tex-math><mml:math id=\"M138\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>s</mml:mi><mml:mo>≤</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq62\"><alternatives><tex-math id=\"M139\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p-1$$\\end{document}</tex-math><mml:math id=\"M140\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq63\"><alternatives><tex-math id=\"M141\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _s[p]=\\frac{s-1}{p-1}\\beta _{s-1}[p-1]+\\left( 1-\\frac{s-1}{p-1}\\right) \\beta _s[p-1]$$\\end{document}</tex-math><mml:math id=\"M142\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>s</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac><mml:msub><mml:mi>β</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mi>s</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac></mml:mfenced><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq64\"><alternatives><tex-math id=\"M143\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _0[p-1]=\\beta _p[p-1]=0$$\\end{document}</tex-math><mml:math id=\"M144\"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq65\"><alternatives><tex-math id=\"M145\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M146\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq66\"><alternatives><tex-math id=\"M147\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0$$\\end{document}</tex-math><mml:math id=\"M148\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq67\"><alternatives><tex-math id=\"M149\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M150\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq68\"><alternatives><tex-math id=\"M151\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M152\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq69\"><alternatives><tex-math id=\"M153\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p\\le 3$$\\end{document}</tex-math><mml:math id=\"M154\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≤</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq70\"><alternatives><tex-math id=\"M155\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=4$$\\end{document}</tex-math><mml:math id=\"M156\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq71\"><alternatives><tex-math id=\"M157\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha (\\ne 0)$$\\end{document}</tex-math><mml:math id=\"M158\"><mml:mrow><mml:mi>α</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mo>≠</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq72\"><alternatives><tex-math id=\"M159\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^0\\}$$\\end{document}</tex-math><mml:math id=\"M160\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq73\"><alternatives><tex-math id=\"M161\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M162\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq74\"><alternatives><tex-math id=\"M163\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _s$$\\end{document}</tex-math><mml:math id=\"M164\"><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq75\"><alternatives><tex-math id=\"M165\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma _s$$\\end{document}</tex-math><mml:math id=\"M166\"><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq76\"><alternatives><tex-math id=\"M167\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M168\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq77\"><alternatives><tex-math id=\"M169\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M170\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq78\"><alternatives><tex-math id=\"M171\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=1$$\\end{document}</tex-math><mml:math id=\"M172\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq79\"><alternatives><tex-math id=\"M173\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=10$$\\end{document}</tex-math><mml:math id=\"M174\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq80\"><alternatives><tex-math id=\"M175\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=3$$\\end{document}</tex-math><mml:math id=\"M176\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq81\"><alternatives><tex-math id=\"M177\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^0\\}$$\\end{document}</tex-math><mml:math id=\"M178\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq82\"><alternatives><tex-math id=\"M179\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^{\\rm sol}\\}$$\\end{document}</tex-math><mml:math id=\"M180\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq83\"><alternatives><tex-math id=\"M181\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^0\\}$$\\end{document}</tex-math><mml:math id=\"M182\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq84\"><alternatives><tex-math id=\"M183\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm sol}_i\\}$$\\end{document}</tex-math><mml:math id=\"M184\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq85\"><alternatives><tex-math id=\"M185\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\alpha =0)$$\\end{document}</tex-math><mml:math id=\"M186\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq86\"><alternatives><tex-math id=\"M187\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4, 1$$\\end{document}</tex-math><mml:math id=\"M188\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq87\"><alternatives><tex-math id=\"M189\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=1$$\\end{document}</tex-math><mml:math id=\"M190\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq88\"><alternatives><tex-math id=\"M191\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=10$$\\end{document}</tex-math><mml:math id=\"M192\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq89\"><alternatives><tex-math id=\"M193\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _s$$\\end{document}</tex-math><mml:math id=\"M194\"><mml:msub><mml:mi>β</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq90\"><alternatives><tex-math id=\"M195\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma _s$$\\end{document}</tex-math><mml:math id=\"M196\"><mml:msub><mml:mi>γ</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq91\"><alternatives><tex-math id=\"M197\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M198\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq92\"><alternatives><tex-math id=\"M199\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M200\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq93\"><alternatives><tex-math id=\"M201\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M202\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq94\"><alternatives><tex-math id=\"M203\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M204\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq95\"><alternatives><tex-math id=\"M205\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M206\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq96\"><alternatives><tex-math id=\"M207\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M208\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq97\"><alternatives><tex-math id=\"M209\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=3$$\\end{document}</tex-math><mml:math id=\"M210\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq98\"><alternatives><tex-math id=\"M211\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=14$$\\end{document}</tex-math><mml:math id=\"M212\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq99\"><alternatives><tex-math id=\"M213\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^0_i\\}$$\\end{document}</tex-math><mml:math id=\"M214\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq100\"><alternatives><tex-math id=\"M215\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm sol}_i\\}$$\\end{document}</tex-math><mml:math id=\"M216\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq101\"><alternatives><tex-math id=\"M217\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_\\mathrm{WS-QAOA}$$\\end{document}</tex-math><mml:math id=\"M218\"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq102\"><alternatives><tex-math id=\"M219\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_{\\rm QAOA}$$\\end{document}</tex-math><mml:math id=\"M220\"><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq103\"><alternatives><tex-math id=\"M221\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_\\mathrm{WS-QAOA}=F_{\\rm QAOA}$$\\end{document}</tex-math><mml:math id=\"M222\"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq104\"><alternatives><tex-math id=\"M223\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm hp}$$\\end{document}</tex-math><mml:math id=\"M224\"><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq105\"><alternatives><tex-math id=\"M225\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm hp}$$\\end{document}</tex-math><mml:math id=\"M226\"><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq106\"><alternatives><tex-math id=\"M227\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm hp}_i\\}$$\\end{document}</tex-math><mml:math id=\"M228\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq107\"><alternatives><tex-math id=\"M229\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm sol}_i\\}$$\\end{document}</tex-math><mml:math id=\"M230\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq108\"><alternatives><tex-math id=\"M231\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm hp}=d$$\\end{document}</tex-math><mml:math id=\"M232\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq109\"><alternatives><tex-math id=\"M233\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _\\mathrm{WS-QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M234\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq110\"><alternatives><tex-math id=\"M235\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Phi \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M236\"><mml:mfenced close=\"〉\" open=\"|\"><mml:mi mathvariant=\"normal\">Φ</mml:mi></mml:mfenced></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ10\"><label>10</label><alternatives><tex-math id=\"M237\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} F=|\\left\\langle \\{x^{\\rm sol}_i\\}|\\Phi \\right\\rangle |^2+|\\left\\langle \\{{\\overline{x}}^{\\rm sol}_i\\}|\\Phi \\right\\rangle |^2. \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M238\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mfenced close=\"〉\" open=\"〈\"><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mi mathvariant=\"normal\">Φ</mml:mi></mml:mfenced><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mfenced close=\"〉\" open=\"〈\"><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mrow><mml:mover><mml:mi>x</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mi mathvariant=\"normal\">Φ</mml:mi></mml:mfenced><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq111\"><alternatives><tex-math id=\"M239\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r=-(\\left\\langle \\Phi |H_{\\rm C}|\\Phi \\right\\rangle +D)/C(\\{x^{\\rm sol}_i\\})$$\\end{document}</tex-math><mml:math id=\"M240\"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mfenced close=\"〉\" open=\"〈\"><mml:mrow><mml:mi mathvariant=\"normal\">Φ</mml:mi><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant=\"normal\">C</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mi mathvariant=\"normal\">Φ</mml:mi></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>C</mml:mi><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq112\"><alternatives><tex-math id=\"M241\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M242\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq113\"><alternatives><tex-math id=\"M243\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=3$$\\end{document}</tex-math><mml:math id=\"M244\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq114\"><alternatives><tex-math id=\"M245\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=14$$\\end{document}</tex-math><mml:math id=\"M246\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq115\"><alternatives><tex-math id=\"M247\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4, 1$$\\end{document}</tex-math><mml:math id=\"M248\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq116\"><alternatives><tex-math id=\"M249\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M250\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq117\"><alternatives><tex-math id=\"M251\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_\\mathrm{WS-QAOA}$$\\end{document}</tex-math><mml:math id=\"M252\"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq118\"><alternatives><tex-math id=\"M253\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d\\le 2$$\\end{document}</tex-math><mml:math id=\"M254\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>≤</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq119\"><alternatives><tex-math id=\"M255\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=3$$\\end{document}</tex-math><mml:math id=\"M256\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq120\"><alternatives><tex-math id=\"M257\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_\\mathrm{WS-QAOA}$$\\end{document}</tex-math><mml:math id=\"M258\"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq121\"><alternatives><tex-math id=\"M259\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=0$$\\end{document}</tex-math><mml:math id=\"M260\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq122\"><alternatives><tex-math id=\"M261\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm hp}_i\\}$$\\end{document}</tex-math><mml:math id=\"M262\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq123\"><alternatives><tex-math id=\"M263\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm hp}_i\\}$$\\end{document}</tex-math><mml:math id=\"M264\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq124\"><alternatives><tex-math id=\"M265\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm sol}_i\\}$$\\end{document}</tex-math><mml:math id=\"M266\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">sol</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq125\"><alternatives><tex-math id=\"M267\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm hp}$$\\end{document}</tex-math><mml:math id=\"M268\"><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq126\"><alternatives><tex-math id=\"M269\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=14$$\\end{document}</tex-math><mml:math id=\"M270\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq127\"><alternatives><tex-math id=\"M271\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^{\\rm hp}_i\\}$$\\end{document}</tex-math><mml:math id=\"M272\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq128\"><alternatives><tex-math id=\"M273\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm hp}=0$$\\end{document}</tex-math><mml:math id=\"M274\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">hp</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq129\"><alternatives><tex-math id=\"M275\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=4$$\\end{document}</tex-math><mml:math id=\"M276\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq130\"><alternatives><tex-math id=\"M277\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0$$\\end{document}</tex-math><mml:math id=\"M278\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq131\"><alternatives><tex-math id=\"M279\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=3$$\\end{document}</tex-math><mml:math id=\"M280\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq132\"><alternatives><tex-math id=\"M281\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M282\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq133\"><alternatives><tex-math id=\"M283\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M284\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq134\"><alternatives><tex-math id=\"M285\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n\\le 14$$\\end{document}</tex-math><mml:math id=\"M286\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≤</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq135\"><alternatives><tex-math id=\"M287\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=16$$\\end{document}</tex-math><mml:math id=\"M288\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq136\"><alternatives><tex-math id=\"M289\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=18$$\\end{document}</tex-math><mml:math id=\"M290\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq137\"><alternatives><tex-math id=\"M291\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=20$$\\end{document}</tex-math><mml:math id=\"M292\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq138\"><alternatives><tex-math id=\"M293\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M294\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq139\"><alternatives><tex-math id=\"M295\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M296\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq140\"><alternatives><tex-math id=\"M297\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0$$\\end{document}</tex-math><mml:math id=\"M298\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq141\"><alternatives><tex-math id=\"M299\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=3$$\\end{document}</tex-math><mml:math id=\"M300\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq142\"><alternatives><tex-math id=\"M301\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0$$\\end{document}</tex-math><mml:math id=\"M302\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq143\"><alternatives><tex-math id=\"M303\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M304\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq144\"><alternatives><tex-math id=\"M305\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M306\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq145\"><alternatives><tex-math id=\"M307\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1-4$$\\end{document}</tex-math><mml:math id=\"M308\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq146\"><alternatives><tex-math id=\"M309\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M310\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq147\"><alternatives><tex-math id=\"M311\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M312\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq148\"><alternatives><tex-math id=\"M313\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=0\\rightarrow 1$$\\end{document}</tex-math><mml:math id=\"M314\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq149\"><alternatives><tex-math id=\"M315\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M316\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq150\"><alternatives><tex-math id=\"M317\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M318\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq151\"><alternatives><tex-math id=\"M319\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _0 \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M320\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq152\"><alternatives><tex-math id=\"M321\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M322\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq153\"><alternatives><tex-math id=\"M323\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M324\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq154\"><alternatives><tex-math id=\"M325\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Phi \\right\\rangle =\\left| \\Psi _0 \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M326\"><mml:mrow><mml:mfenced close=\"〉\" open=\"|\"><mml:mi mathvariant=\"normal\">Φ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ11\"><label>11</label><alternatives><tex-math id=\"M327\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\begin{aligned} F_0&amp;=\\cos ^{2d}\\left( \\frac{\\pi }{4}+\\frac{\\tan ^{-1}\\alpha }{2}\\right) \\cos ^{2(n-d)}\\left( \\frac{\\pi }{4}-\\frac{\\tan ^{-1}\\alpha }{2}\\right) \\\\&amp;+\\cos ^{2d}\\left( \\frac{\\pi }{4}-\\frac{\\tan ^{-1}\\alpha }{2}\\right) \\cos ^{2(n-d)}\\left( \\frac{\\pi }{4}+\\frac{\\tan ^{-1}\\alpha }{2}\\right) . \\end{aligned} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M328\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:msub><mml:mi>F</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mo>cos</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mfenced><mml:msup><mml:mo>cos</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>d</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mo>cos</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mfenced><mml:msup><mml:mo>cos</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>d</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq155\"><alternatives><tex-math id=\"M329\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M330\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq156\"><alternatives><tex-math id=\"M331\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M332\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq157\"><alternatives><tex-math id=\"M333\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1$$\\end{document}</tex-math><mml:math id=\"M334\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq158\"><alternatives><tex-math id=\"M335\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=2$$\\end{document}</tex-math><mml:math id=\"M336\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq159\"><alternatives><tex-math id=\"M337\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=3$$\\end{document}</tex-math><mml:math id=\"M338\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq160\"><alternatives><tex-math id=\"M339\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=4$$\\end{document}</tex-math><mml:math id=\"M340\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq161\"><alternatives><tex-math id=\"M341\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n\\le 14$$\\end{document}</tex-math><mml:math id=\"M342\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≤</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq162\"><alternatives><tex-math id=\"M343\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=16$$\\end{document}</tex-math><mml:math id=\"M344\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq163\"><alternatives><tex-math id=\"M345\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=18$$\\end{document}</tex-math><mml:math id=\"M346\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq164\"><alternatives><tex-math id=\"M347\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=20$$\\end{document}</tex-math><mml:math id=\"M348\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq165\"><alternatives><tex-math id=\"M349\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1-4$$\\end{document}</tex-math><mml:math id=\"M350\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq166\"><alternatives><tex-math id=\"M351\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M352\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq167\"><alternatives><tex-math id=\"M353\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M354\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq168\"><alternatives><tex-math id=\"M355\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^0_i\\}$$\\end{document}</tex-math><mml:math id=\"M356\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq169\"><alternatives><tex-math id=\"M357\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}$$\\end{document}</tex-math><mml:math id=\"M358\"><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq170\"><alternatives><tex-math id=\"M359\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}=3$$\\end{document}</tex-math><mml:math id=\"M360\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq171\"><alternatives><tex-math id=\"M361\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=12, \\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M362\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>12</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq172\"><alternatives><tex-math id=\"M363\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}$$\\end{document}</tex-math><mml:math id=\"M364\"><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq173\"><alternatives><tex-math id=\"M365\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M366\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq174\"><alternatives><tex-math id=\"M367\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M368\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq175\"><alternatives><tex-math id=\"M369\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M370\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq176\"><alternatives><tex-math id=\"M371\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M372\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq177\"><alternatives><tex-math id=\"M373\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M374\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq178\"><alternatives><tex-math id=\"M375\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M376\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq179\"><alternatives><tex-math id=\"M377\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M378\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq180\"><alternatives><tex-math id=\"M379\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M380\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq181\"><alternatives><tex-math id=\"M381\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M382\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq182\"><alternatives><tex-math id=\"M383\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M384\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq183\"><alternatives><tex-math id=\"M385\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _0 \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M386\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq184\"><alternatives><tex-math id=\"M387\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$F_0(\\alpha )=F_0(\\alpha =0)$$\\end{document}</tex-math><mml:math id=\"M388\"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>α</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ12\"><label>12</label><alternatives><tex-math id=\"M389\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} \\begin{aligned} \\frac{d_{\\rm c}}{n}&amp;=\\frac{\\log \\left( \\cos \\frac{\\pi }{4}/\\cos \\left( \\frac{\\pi }{4}-\\frac{\\tan ^{-1}\\alpha }{2}\\right) \\right) }{\\log \\tan \\left( \\frac{\\pi }{4}-\\frac{\\tan ^{-1}\\alpha }{2}\\right) }\\\\&amp;+\\frac{1}{2n}\\frac{\\log \\left( 1+\\sqrt{1-\\sin ^{2n}\\left( \\frac{\\pi }{2}-\\tan ^{-1}\\alpha \\right) }\\right) }{\\log \\tan \\left( \\frac{\\pi }{4}-\\frac{\\tan ^{-1}\\alpha }{2}\\right) }. \\end{aligned} \\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M390\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:mfrac><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mi>n</mml:mi></mml:mfrac></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>log</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mo>cos</mml:mo><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo stretchy=\"false\">/</mml:mo><mml:mo>cos</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mfenced></mml:mfenced></mml:mrow><mml:mrow><mml:mo>log</mml:mo><mml:mo>tan</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mfenced></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:mfrac><mml:mfrac><mml:mrow><mml:mo>log</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msqrt><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mo>sin</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>2</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mfenced></mml:mrow></mml:msqrt></mml:mfenced></mml:mrow><mml:mrow><mml:mo>log</mml:mo><mml:mo>tan</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mi>π</mml:mi><mml:mn>4</mml:mn></mml:mfrac><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mo>tan</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>α</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mfenced></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq185\"><alternatives><tex-math id=\"M391\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M392\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq186\"><alternatives><tex-math id=\"M393\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M394\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq187\"><alternatives><tex-math id=\"M395\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M396\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq188\"><alternatives><tex-math id=\"M397\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M398\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq189\"><alternatives><tex-math id=\"M399\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M400\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq190\"><alternatives><tex-math id=\"M401\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}$$\\end{document}</tex-math><mml:math id=\"M402\"><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq191\"><alternatives><tex-math id=\"M403\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M404\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq192\"><alternatives><tex-math id=\"M405\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _0 \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M406\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq193\"><alternatives><tex-math id=\"M407\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^0\\}$$\\end{document}</tex-math><mml:math id=\"M408\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq194\"><alternatives><tex-math id=\"M409\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=0-5$$\\end{document}</tex-math><mml:math id=\"M410\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>-</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq195\"><alternatives><tex-math id=\"M411\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M412\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq196\"><alternatives><tex-math id=\"M413\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M414\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq197\"><alternatives><tex-math id=\"M415\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d\\ge 2$$\\end{document}</tex-math><mml:math id=\"M416\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq198\"><alternatives><tex-math id=\"M417\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p\\ge 1$$\\end{document}</tex-math><mml:math id=\"M418\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq199\"><alternatives><tex-math id=\"M419\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=1$$\\end{document}</tex-math><mml:math id=\"M420\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq200\"><alternatives><tex-math id=\"M421\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p\\ge 2$$\\end{document}</tex-math><mml:math id=\"M422\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq201\"><alternatives><tex-math id=\"M423\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x_i^0\\}$$\\end{document}</tex-math><mml:math id=\"M424\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq202\"><alternatives><tex-math id=\"M425\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M426\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq203\"><alternatives><tex-math id=\"M427\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M428\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq204\"><alternatives><tex-math id=\"M429\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=0$$\\end{document}</tex-math><mml:math id=\"M430\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq205\"><alternatives><tex-math id=\"M431\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=1$$\\end{document}</tex-math><mml:math id=\"M432\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq206\"><alternatives><tex-math id=\"M433\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=2$$\\end{document}</tex-math><mml:math id=\"M434\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq207\"><alternatives><tex-math id=\"M435\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=3$$\\end{document}</tex-math><mml:math id=\"M436\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq208\"><alternatives><tex-math id=\"M437\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=4$$\\end{document}</tex-math><mml:math id=\"M438\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq209\"><alternatives><tex-math id=\"M439\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=5$$\\end{document}</tex-math><mml:math id=\"M440\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq210\"><alternatives><tex-math id=\"M441\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n\\le 14$$\\end{document}</tex-math><mml:math id=\"M442\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≤</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq211\"><alternatives><tex-math id=\"M443\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=16$$\\end{document}</tex-math><mml:math id=\"M444\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq212\"><alternatives><tex-math id=\"M445\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=18$$\\end{document}</tex-math><mml:math id=\"M446\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq213\"><alternatives><tex-math id=\"M447\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=20$$\\end{document}</tex-math><mml:math id=\"M448\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq214\"><alternatives><tex-math id=\"M449\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{\\min }$$\\end{document}</tex-math><mml:math id=\"M450\"><mml:msub><mml:mi>p</mml:mi><mml:mo movablelimits=\"true\">min</mml:mo></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq215\"><alternatives><tex-math id=\"M451\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r_{\\rm t} = 0.878$$\\end{document}</tex-math><mml:math id=\"M452\"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant=\"normal\">t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.878</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq216\"><alternatives><tex-math id=\"M453\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{\\min }$$\\end{document}</tex-math><mml:math id=\"M454\"><mml:msub><mml:mi>p</mml:mi><mml:mo movablelimits=\"true\">min</mml:mo></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq217\"><alternatives><tex-math id=\"M455\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M456\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq218\"><alternatives><tex-math id=\"M457\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M458\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq219\"><alternatives><tex-math id=\"M459\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d\\le 1$$\\end{document}</tex-math><mml:math id=\"M460\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq220\"><alternatives><tex-math id=\"M461\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n\\le 20$$\\end{document}</tex-math><mml:math id=\"M462\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≤</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq221\"><alternatives><tex-math id=\"M463\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p\\le 4$$\\end{document}</tex-math><mml:math id=\"M464\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≤</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq222\"><alternatives><tex-math id=\"M465\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r_{\\rm t}=0.878$$\\end{document}</tex-math><mml:math id=\"M466\"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant=\"normal\">t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.878</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq223\"><alternatives><tex-math id=\"M467\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M468\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq224\"><alternatives><tex-math id=\"M469\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M470\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq225\"><alternatives><tex-math id=\"M471\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^m_i\\}$$\\end{document}</tex-math><mml:math id=\"M472\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq226\"><alternatives><tex-math id=\"M473\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m=0,...,M-1$$\\end{document}</tex-math><mml:math id=\"M474\"><mml:mrow><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq227\"><alternatives><tex-math id=\"M475\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P_{\\rm QAOA}$$\\end{document}</tex-math><mml:math id=\"M476\"><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq228\"><alternatives><tex-math id=\"M477\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _{\\rm QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M478\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq229\"><alternatives><tex-math id=\"M479\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\{x^m_i\\}$$\\end{document}</tex-math><mml:math id=\"M480\"><mml:mrow><mml:mo stretchy=\"false\">{</mml:mo><mml:msubsup><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi></mml:msubsup><mml:mo stretchy=\"false\">}</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq230\"><alternatives><tex-math id=\"M481\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P^m_\\mathrm{WS-QAOA}$$\\end{document}</tex-math><mml:math id=\"M482\"><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow><mml:mi>m</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq231\"><alternatives><tex-math id=\"M483\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left| \\Psi _\\mathrm{WS-QAOA} \\right\\rangle$$\\end{document}</tex-math><mml:math id=\"M484\"><mml:mfenced close=\"〉\" open=\"|\"><mml:msub><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow></mml:msub></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq232\"><alternatives><tex-math id=\"M485\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P_\\mathrm{QAOA+WS}$$\\end{document}</tex-math><mml:math id=\"M486\"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">QAOA</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"normal\">WS</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq233\"><alternatives><tex-math id=\"M487\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$P^m_\\mathrm{WS-QAOA}$$\\end{document}</tex-math><mml:math id=\"M488\"><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi mathvariant=\"normal\">WS</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">QAOA</mml:mi></mml:mrow><mml:mi>m</mml:mi></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq234\"><alternatives><tex-math id=\"M489\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=20$$\\end{document}</tex-math><mml:math id=\"M490\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq235\"><alternatives><tex-math id=\"M491\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=3$$\\end{document}</tex-math><mml:math id=\"M492\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq236\"><alternatives><tex-math id=\"M493\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=8$$\\end{document}</tex-math><mml:math id=\"M494\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq237\"><alternatives><tex-math id=\"M495\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M496\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq238\"><alternatives><tex-math id=\"M497\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M498\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq239\"><alternatives><tex-math id=\"M499\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=20$$\\end{document}</tex-math><mml:math id=\"M500\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq240\"><alternatives><tex-math id=\"M501\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=3$$\\end{document}</tex-math><mml:math id=\"M502\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq241\"><alternatives><tex-math id=\"M503\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=8$$\\end{document}</tex-math><mml:math id=\"M504\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq242\"><alternatives><tex-math id=\"M505\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d=0$$\\end{document}</tex-math><mml:math id=\"M506\"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq243\"><alternatives><tex-math id=\"M507\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=3$$\\end{document}</tex-math><mml:math id=\"M508\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq244\"><alternatives><tex-math id=\"M509\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1$$\\end{document}</tex-math><mml:math id=\"M510\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq245\"><alternatives><tex-math id=\"M511\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p\\ge 2$$\\end{document}</tex-math><mml:math id=\"M512\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq246\"><alternatives><tex-math id=\"M513\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=8$$\\end{document}</tex-math><mml:math id=\"M514\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq247\"><alternatives><tex-math id=\"M515\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p\\le 3$$\\end{document}</tex-math><mml:math id=\"M516\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≤</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq248\"><alternatives><tex-math id=\"M517\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1-4$$\\end{document}</tex-math><mml:math id=\"M518\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq249\"><alternatives><tex-math id=\"M519\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=10, 12, 14, 20$$\\end{document}</tex-math><mml:math id=\"M520\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mn>12</mml:mn><mml:mo>,</mml:mo><mml:mn>14</mml:mn><mml:mo>,</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq250\"><alternatives><tex-math id=\"M521\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=16$$\\end{document}</tex-math><mml:math id=\"M522\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq251\"><alternatives><tex-math id=\"M523\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=18$$\\end{document}</tex-math><mml:math id=\"M524\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq252\"><alternatives><tex-math id=\"M525\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M526\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq253\"><alternatives><tex-math id=\"M527\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M528\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq254\"><alternatives><tex-math id=\"M529\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1-4$$\\end{document}</tex-math><mml:math id=\"M530\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq255\"><alternatives><tex-math id=\"M531\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=10, 12, 14, 20$$\\end{document}</tex-math><mml:math id=\"M532\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mn>12</mml:mn><mml:mo>,</mml:mo><mml:mn>14</mml:mn><mml:mo>,</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq256\"><alternatives><tex-math id=\"M533\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=16$$\\end{document}</tex-math><mml:math id=\"M534\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq257\"><alternatives><tex-math id=\"M535\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=18$$\\end{document}</tex-math><mml:math id=\"M536\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq258\"><alternatives><tex-math id=\"M537\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1-4$$\\end{document}</tex-math><mml:math id=\"M538\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq259\"><alternatives><tex-math id=\"M539\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n\\ge 10$$\\end{document}</tex-math><mml:math id=\"M540\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq260\"><alternatives><tex-math id=\"M541\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1$$\\end{document}</tex-math><mml:math id=\"M542\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq261\"><alternatives><tex-math id=\"M543\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n\\ge 14$$\\end{document}</tex-math><mml:math id=\"M544\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq262\"><alternatives><tex-math id=\"M545\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=2$$\\end{document}</tex-math><mml:math id=\"M546\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq263\"><alternatives><tex-math id=\"M547\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n\\ge 16$$\\end{document}</tex-math><mml:math id=\"M548\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq264\"><alternatives><tex-math id=\"M549\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=3$$\\end{document}</tex-math><mml:math id=\"M550\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq265\"><alternatives><tex-math id=\"M551\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=20$$\\end{document}</tex-math><mml:math id=\"M552\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq266\"><alternatives><tex-math id=\"M553\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=4$$\\end{document}</tex-math><mml:math id=\"M554\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq267\"><alternatives><tex-math id=\"M555\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1-4$$\\end{document}</tex-math><mml:math id=\"M556\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq268\"><alternatives><tex-math id=\"M557\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=10, 12, 14, 20$$\\end{document}</tex-math><mml:math id=\"M558\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mn>12</mml:mn><mml:mo>,</mml:mo><mml:mn>14</mml:mn><mml:mo>,</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq269\"><alternatives><tex-math id=\"M559\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=16$$\\end{document}</tex-math><mml:math id=\"M560\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq270\"><alternatives><tex-math id=\"M561\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=18$$\\end{document}</tex-math><mml:math id=\"M562\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq271\"><alternatives><tex-math id=\"M563\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M564\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq272\"><alternatives><tex-math id=\"M565\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p=1-4$$\\end{document}</tex-math><mml:math id=\"M566\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq273\"><alternatives><tex-math id=\"M567\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$n=10, p=4$$\\end{document}</tex-math><mml:math id=\"M568\"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq274\"><alternatives><tex-math id=\"M569\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{\\rm min}$$\\end{document}</tex-math><mml:math id=\"M570\"><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant=\"normal\">min</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq275\"><alternatives><tex-math id=\"M571\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=1$$\\end{document}</tex-math><mml:math id=\"M572\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq276\"><alternatives><tex-math id=\"M573\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{\\rm min}$$\\end{document}</tex-math><mml:math id=\"M574\"><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant=\"normal\">min</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq277\"><alternatives><tex-math id=\"M575\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r_{\\rm t}=0.878$$\\end{document}</tex-math><mml:math id=\"M576\"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant=\"normal\">t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.878</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq278\"><alternatives><tex-math id=\"M577\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M=1$$\\end{document}</tex-math><mml:math id=\"M578\"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq279\"><alternatives><tex-math id=\"M579\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(M+1)$$\\end{document}</tex-math><mml:math id=\"M580\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>M</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq280\"><alternatives><tex-math id=\"M581\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2p(M+1)$$\\end{document}</tex-math><mml:math id=\"M582\"><mml:mrow><mml:mn>2</mml:mn><mml:mi>p</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>M</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq281\"><alternatives><tex-math id=\"M583\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{\\rm min}$$\\end{document}</tex-math><mml:math id=\"M584\"><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant=\"normal\">min</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq282\"><alternatives><tex-math id=\"M585\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p_{\\rm min}$$\\end{document}</tex-math><mml:math id=\"M586\"><mml:msub><mml:mi>p</mml:mi><mml:mi mathvariant=\"normal\">min</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq283\"><alternatives><tex-math id=\"M587\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0.4$$\\end{document}</tex-math><mml:math id=\"M588\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq284\"><alternatives><tex-math id=\"M589\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =1$$\\end{document}</tex-math><mml:math id=\"M590\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq285\"><alternatives><tex-math id=\"M591\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$d_{\\rm c}/n$$\\end{document}</tex-math><mml:math id=\"M592\"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

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[ "<media xlink:href=\"41598_2023_50406_MOESM1_ESM.pdf\"><caption><p>Supplementary Information.</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">With the gradual improvement of Chinese economic level, substantial progress has been achieved in mitigating the regional disparity between economic development patterns and the allocation of water resources. The water conveyance tunnel, a central component of long-distance cross-basin water transfer projects, assumes a pivotal role in addressing this regional incongruity. Nevertheless, the intricate geological composition and the dense prevalence of active faults in the high seismic-intensity area of southwest China pose significant challenges. This is particularly evident in the context of the Central Yunnan Water Diversion Project, which seeks to fundamentally solve water scarcity issues in central Yunnan, and consequently necessitates traversing multiple active fault zones. These active fault zones pose a serious threat to the safe operation of the tunnel project, thereby underscoring the urgent and imperative need for a comprehensive investigation into the anti-dislocation design of tunnels crossing such active fault zones. The most famous tunnel impairment due to active fault creep is exemplified by the Claremont Water Tunnel, wherein movement along the Hayward fault led to a 13-inch dislocation over a period exceeding 80 years of service. Consequently, the bypass of the tunnel segment passing through active faults was reconstructed in 2006. This extensive endeavor, involving a 500 m bypass reconstruction, extended over a duration of three years and incurred a total cost of $34 million.</p>", "<p id=\"Par3\">Active fault zones are potential seismogenic zones that are susceptible to dislocations due to geotectonic force, thereby giving rise to seismic events^{##UREF##0##1##}. Meanwhile, stick–slip active faults exhibit sudden and rapid energy release, resulting in instantaneous dislocation, which can lead to severe damage to engineering structures. Recognizing the potential movement of bedrock faults as a significant threat to existing tunnels located in seismically active areas, Cai^{##UREF##1##2##} conducted centrifugal model tests to investigate the deformation mechanism of existing tunnels experiencing normal fault dislocation. The study also addressed the effects of different tunnel boundary conditions and lengths on the response of lining structures under the action of normal fault dislocation. Burridge et al.^{##UREF##2##3##} conducted a series of centrifuge shaking table tests on a limited-length tunnel model, allowing for a quantitative analysis of the bending and stress response induced by fault dislocation during passage through a fault zone. Liu et al.^{##UREF##3##4##–##UREF##5##6##} simulated the stress-deformation response characteristics of tunnels orthogonal to a normal fault with dip angle of 45°, 60°, and 75° respectively, under the action of stick–slip dislocation, employing an indoor flask test with a similitude ratio of 1:50. As for the case of Sabzkouh Tunnel crossing the Sulaghan Fault in Iran, Ghadimi et al.^{##UREF##6##7##} used numerical methods to study the influence of tunnel location, lining thickness, intersection angle between the fault and the tunnel, mechanical properties of the surrounding soil and the fault dip angle on tunnel stability under the action of reverse fault dislocation. Jiao^{##UREF##7##8##} used finite difference software to establish a corresponding numerical model for an actual tunnel project, shedding light on the effects of earthquake-induced inverse fault dislocation on tunnels crossing the active faults orthogonally and revealing its underlying influence mechanism. Jeon et al.^{##UREF##8##9##} discussed the influence of weak contact surface between the tunnel lining and the surrounding fault rock on the lining structure through numerical analysis. This comprehensive analysis attests to the substantial progress achieved in elucidating the damage mechanisms and evolution law of tunnels passing through active fault zones.</p>", "<p id=\"Par4\">However, studies on adaptive anti-dislocation design of tunnels crossing active fault zones are relatively scarce, mainly focusing on engineering experience and conceptual design, such as articulated design^{##UREF##9##10##}, over-excavation design^{##UREF##10##11##,##UREF##11##12##}, isolation efficiency design^{##UREF##12##13##} etc., Among them, the most widely applied “articulated design” is aimed to design the structure into one with the same characteristics of a chain hinge, thus forcing the structure to move in a hinged way under the action of fault dislocation, Then the structure can absorb and dissipate the deformation through the sliding hinged segment that can slide and twist along the tunnel axis, so that the damage will be concentrated in the connection part, thus avoiding overall damage to the structure^{##UREF##13##14##,##UREF##14##15##}. The Claremont Tunnel in San Francisco crossing the Hayward Fault once faced the threat of fault dislocation^{##UREF##15##16##}. Its lining is hinged, with a 0.3 m-wide shear joint reserved for every 1.5 m long lining segment, in assuming that the lining can absorb the deformation caused by the fault shear under the action of fault dislocation, thus avoiding the overall damage to the tunnel. The Koohrang-III water conveyance tunnel in central Iran crosses at least four fault zones, the largest of which is the Zarab Fault. To reduce the strength and stiffness of connecting materials, absorb the deformation caused by fault dislocation and protect the lining structure, measures are taken to set steel lining in the inner layer and set plastic concrete connecting sections between lining segments^{##UREF##16##17##}. From a theoretical perspective, it is possible to select appropriate design parameters in a hinge design based on the potential fault movement, and achieve targeted active fortification; from the perspective of construction, in tunnel construction, only the construction steps of articulated segments are added, which is convenient for implementation; in addition, from the perspective of effectiveness, in the case of large range of fault dislocation, the damage to the tunnel can be localized as the strength and stiffness of the flexible connection materials at the articulated segments are low, thus avoiding overall damage to the tunnel and reducing the cost of maintenance and repair^{##UREF##17##18##}.</p>", "<p id=\"Par5\">To date, a lack of standardized specifications and norms governing the design of anti-dislocation measures for tunnels passing through active fault zones has necessitated a rigorous evaluation process in anti-dislocation design. This study focuses on examining the influence of fault dislocation on the tunnel adaptive structure, employing the case of the Xianglushan Tunnel, which crossing active fault zones within the Central Yunnan Water Diversion Project. Taking the Longpan-Qiaohou Fault F10-1 as a typical case, this paper evaluated the influence of the active fault on the anti-dislocation adaptive structure of the Xianglushan Tunnel from the aspects of displacement, relative deformation, maximum principal stress, longitudinal equivalent internal force and other factors of the key tunnel parts. The research results can be directly applied to the engineering design and construction of water conveyance tunnels crossing active faults, and furnish a substantive foundation for the development of related tunnels.</p>" ]

[ "<title>Shahidi &amp; Vafaeian’s estimation method</title>", "<p id=\"Par12\">Shahidi &amp; Vafaeian proposed an estimation method for the articulated design in the anti-dislocation study of the Koohrang-III Tunnel in 2005^{##UREF##16##17##}. The fundamental concept is as follows: Following a fault dislocation event, the tunnel’s lining structure undergoes an “S” shaped bending in the vertical plane, with axial deformation illustrated in the Fig. ##FIG##3##4##. Here, denotes the vertical displacement resulting from fault dislocation, signifies the segment length, , represents the width of the flexible connection, and denotes the ultimate bending curvature of lining under the action of surrounding rock conditions during fault dislocation.</p>", "<p id=\"Par13\">Then, the relationship between the fault dislocation range and the lining segment length and the flexible connection width can be expressed as the following formula.where, is the vertical fault dislocation range; is the lining segment length; is the flexible connection width; is the ultimate bending curvature of the lining segment.</p>", "<p id=\"Par14\">This present estimation formula neglects the requirement for establishing multiple articulated segments within a broad fault zone, a deficiency that will be rectified in this investigation. When the consideration of multiple hinged segments is warranted, it remains imperative to ensure the fulfillment of the following equation:</p>", "<p id=\"Par15\">Here, is the tolerable dislocation of each articulated segment; is the total dislocation of the fault zone; is the width of the fault zone.</p>", "<p id=\"Par16\">As for , Shahidi &amp; Vafaeian did not give an estimation method, but Jalali^{##UREF##14##15##} proposed a simplified estimation method as follows.</p>", "<p id=\"Par17\">According to the above formula, and given a tunnel fault width of 200 m, a fortified dislocation range of 40 cm, and a tunnel diameter of 10 m, it can be deduced that for a fortified segment length of 6 m, the requisite minimum width for the articulated segment is approximately 10 cm.</p>" ]

[]

[ "<title>Discussion</title>", "<p id=\"Par31\">Summarizing the above analysis results, the mechanism of the anti-dislocation measures can be obtained as follows:</p>", "<p id=\"Par32\">The anti-dislocation measures effectively reduce the tensile force on the entire lining inside the fault zone, and has a certain degree of improvement on the compressive state at the junction with the fault zone. Under the condition of anti-dislocation measures, the bending moment caused by the misalignment of the lining also has a significant reduction trend. The anti-dislocation measures has a limited effect on reducing the shear force of the tunnel lining, and only in some sections, the shear force of the lining has a certain degree of reduction.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par33\">In this paper, the anti-dislocation design of the Xianglushan Tunnel of the Central Yunnan Water Diversion Project is checked. Taking the Longpan-Qiaohou Fault F10-1 as a typical case.<list list-type=\"order\"><list-item><p id=\"Par34\">The influence of the active fault of F10-1 on the anti-dislocation adaptive structure of the Xianglushan Tunnel is evaluated, and its effect on reducing the internal force and deformation of the lining is verified based on numerical calculation. The research results can be directly applied to the engineering design and construction of water conveyance tunnels crossing active faults, and provide favorable support for the construction of related tunnels.</p></list-item><list-item><p id=\"Par35\">The F10-1 Longpan-Qiaohou Fault is used as a typical representative to carry out the studies on surrounding rock, structural stability and anti-dislocation adaptability. The anti-dislocation measures considered are as follows: the segment length is 6 m; the hinged joint width is 5 cm, the fortified length is 1.5D, i.e., for a fault zone with a width of 200 m, it extends to the hanging wall and foot wall by 50 cm each, and the hinged joint is filled with plastic concrete materials with an elastic modulus of 500 MPa.</p></list-item><list-item><p id=\"Par36\">The results show that one side wall of the tunnel is under tension due to the fault movements mainly being strike-slip, and the tensile stress value is small, about 5 MPa. Results show that the maximum normal deformation of the hinged joints is about 3.5 cm, which is located between the central segments of the fault zone; and the maximum tangential deformation is about 1.5 cm, which also occurs between the central segments of the fault zone. The relative deformation of the hinged joints is less than the reserved width, i.e., 5 cm. The hinged design of adaptive structure can effectively improve the stress state of the lining under dislocation.</p></list-item></list></p>" ]

[ "<p id=\"Par1\">In the context of long-distance cross-basin water transfer projects, the water conveyance tunnel serves as a pivotal component in mitigating regional disparities between economic development and water resources allocation. However, in high seismic-intensity areas of southwest China, geological complexities and densely distributed active faults present formidable challenges. Consequently, the construction of water conveyance tunnels necessitates traversing one or more active fault zones. This study examines the impact of an adaptive tunnel structure in the presence of fault dislocation, focusing on the Xianglushan Tunnel, a constituent of the Central Yunnan Water Diversion Project. Taking the Longpan-Qiaohou Fault F10-1 as a case study, we assess the influence of active faults on the anti-dislocation adaptive structure of the Xianglushan Tunnel, considering factors such as displacement, relative deformation, maximum principal stresses, and longitudinal equivalent internal force in critical tunnel sections. Numerical calculations validate the efficacy of this adaptive structure in reducing induced internal forces and deformations of the tunnel lining. The results show that, under the influence of strike-slip dominated fault movement, one side of the tunnel exhibits tensile stress, with a magnitude of approximately 5 MPa. The maximum normal and tangential deformation of the hinge joint is concentrated in the central section of the fault zone. The incorporation of an articulated adaptive design significantly enhances the stress state of lining under dislocation condition. These research results directly inform the engineering design and construction of water conveyance tunnels traversing active fault regions, providing valuable guidance for related tunnel construction endeavors.</p>", "<title>Subject terms</title>" ]

[ "<title>Background project</title>", "<p id=\"Par6\">The Central Yunnan Water Diversion Project constitutes a pivotal strategic infrastructure initiative executed in China, with the primary objective of optimizing the water distribution in Yunnan province and alleviating water scarcity in the Central region. Upon completion, this project is anticipated to provide a sustained mitigation of water scarcity in Central Yunnan, improve the ecological and hydrological conditions of rivers and plateau lakes in the recipient area, and play an important role in promoting the coordinated and sustainable economic and social development of Yunnan Province. It is estimated that by the design level year of 2040, the annual average water diversion volume of this project in Central Yunnan is expected to reach 3.403 billion cubic meters (as measured at the head works), including 2.231 billion cubic meters for urban domestic and industrial usage, 500 million cubic meters for agricultural irrigation and 672 million cubic meters for lake water replenishment.</p>", "<p id=\"Par7\">Xianglushan Tunnel constitutes the linchpin of this extensive cross-basin water diversion (transfer) project, and stands as a representative project of long-distance water conveyance tunnel in China. Spanning a length of 63.426 km, with a maximum burial depth of 1450 m. The total length of the tunnel segments with a buried depth greater than 1000 m is 21.427 km, accounting for 34.23% of the total length of the tunnel. Additionally, the total length of the tunnel segments with a buried depth greater than 600 m is 42.175 km, accounting for 67.38% of the total length of the tunnel. The geological terrain in the vicinity of the Xianglushan Tunnel is notably intricate, with several Holocene regional active faults tracing the route, including the Longpan-Qiaohou Fault (F10) (as shown in Fig. ##FIG##0##1##), Lijiang-Jianchuan Fault (F11) and Heqing-Ergyuan Fault (F12). For the 100 year displacement fortification due to Holocene active faults, the horizontal vector value is 1.50–2.20 m and the vertical vector value is 0.26–0.34 m. The safety construction and operation of the tunnel are gravely imperiled by these active faults. Therefore, undertaking studies elucidating the mechanisms of dislocation-induced damage and anti-dislocation measures in water conveyance tunnels passing through active fault zones holds profound scientific and engineering import.</p>", "<title>Modeling and parameters</title>", "<p id=\"Par8\">The Longpan-Qiaohou Fault F10-1 was used as a typical representative fault to analyze the anti-dislocation design of tunnels. The local 3D analysis model containing the tunnel crossing the Longpan-Qiaohou Fault F10-1 was built in FLAC3D, as shown in Fig. ##FIG##1##2##. The numerical model, addressing a solitary main fault zone, was established with the tunnel’s axial direction (340°) as the Y axis and the vertical direction as the Z axis. The numerical model featured a spatial extension of 100 m in both positive and negative x-directions, centered on the tunnel’s midpoint, 300 m along the y-axis (aligned with the tunnel’s axial direction), centered on the main fault zone, and 100 m in the z-direction, centered on the tunnel’s midpoint. In the context of the tunnel segment crossing F10-1, a burial depth of 400 m was considered, and the corresponding vertical stress was imposed at the top according to the weight of the upper rock mass in the numerical model. The radius of net tunnel flow section is 4.6 m, and the initial support shotcrete and secondary lining of the tunnel are collectively considered as a 1.05 m-thick concrete lining. This paper mainly focused on the creep-slip fault, addressing issues from a static force perspective, so rendering the load associated with movable displacement as a static load acting on the boundary of the moving wall in the model.</p>", "<p id=\"Par9\">According to previous researches on the inversion of ground stress field in engineering area^{##UREF##18##19##}, the inverted ground stress field detailed in Table ##TAB##0##1## will be employed as a foundational framework in the structural adaptability assessment study for the Longpan-Qiaohou fault area. The relationship between the direction of the ground stress field and the tunnel is shown in Table ##TAB##1##2## and Fig. ##FIG##2##3##. It can be seen that, the intersection angle between the maximum principal stress of the ground stress field and the longitudinal axis of the tunnel is substantial, exerting a profound impact on the tunnel stability.</p>", "<p id=\"Par10\">For the mechanical parameters of the rock mass in the Longpan-Qiaohou Fault (F10-1) area, the mechanical parameters in Table ##TAB##2##3##, which estimated by geologists based on engineering experience and laboratory tests, were used in the analysis.</p>", "<title>Consideration of the adaptive measures</title>", "<p id=\"Par11\">The articulated design of the lining involves critical design parameters include lining segment length, connecting section length, fortification length, and connecting section’s filling materials. Of these, the most important design parameters are the lining segment length and the connecting section length. For these two design parameters, there is no mature and common design method, but scholars have proposed estimation methods based on research pertaining to as-built tunnel traversing active faults. In this section, two such estimation methods will be used to estimate the lining segment length, connecting section length and other pertinent design parameters relevant to the Xianglushan Tunnel.</p>", "<title>Jalali’s estimation method</title>", "<p id=\"Par18\">Jalali^{##UREF##14##15##} proposed another estimation method for the articulated design considering displacement mode in 2018 for the Karaj Tunnel. The fundamental concept is as follows:</p>", "<p id=\"Par19\">The tunnel structure traversing the fault zone was conceptualized as a clamped beam fixed at both ends with uneven settlement of support, as shown in Fig. ##FIG##4##5##. This beam had infinite stiffness or large finite stiffness, with no or limited bending capacity, and all or most of the corners were located at the “articulated position” arranged at specific spacing along the beam.</p>", "<p id=\"Par20\">For the clamped beam fixed at both ends, when there is a vertical displacement at one end, the deflection curve equation of the beam is:where, is the vertical displacement, is the length of the beam, and is the position of a point on the beam in the coordinate system.</p>", "<p id=\"Par21\">The deflection curve of the forced beam is similar to the theoretical deflection curve of a clamped beam fixed at both ends with uneven settlement of the supports, and the corner at the “articulated position” on the beam is the corner that needs to be satisfied at the articulated segment with respect to the current hinge spacing. The estimated width of the dislocation joint at this articulated position can then be derived from Fig. ##FIG##5##6##.</p>", "<p id=\"Par22\">By employing the aforementioned method, given a tunnel fault width of 200 m, a fortified dislocation range of 40 cm and a tunnel diameter of 10 m, it can be determined that for a fortified segment length of 6 m, the requisite minimum width of the articulated segment is approximately 4.2 cm. Conversely, for a fortified segment length of 10 m, the minimum required width for the articulated segment is approximately 7.7 cm.</p>", "<p id=\"Par23\">In light of these two estimation formulas, under the same conditions of a 200 m tunnel fault width, a 40 cm fortified dislocation range, and a 10 m tunnel diameter, when the length of the fortified segment is fixed at 6 m, the minimum width of the articulated segment is projected to fall within the range of 4.2 to 10 cm.</p>", "<title>Anti-dislocation design check of tunnels passing through active faults</title>", "<p id=\"Par24\">The anti-dislocation measures considered are as follows: a segment length of 6 m; a hinged joint width of 5 cm; a fortified length extending 1.5 times the fault width, signifying that for a fault zone measuring 200 m in width, it extends 50 m into both the hanging wall and foot wall directions. The hinged joint is filled with plastic concrete materials with an elastic modulus of 500 MPa. In the calculation, the “S” displacement mode with the applied active fault displacement proposed in this study was used^{##UREF##19##20##}, in which the maximum fortification value is considered to be 60 cm horizontally and 12 cm vertically. The reason why the value of 60 cm was used is to more conservatively check whether the design parameters can meet the requirements.</p>", "<title>Overall deformation and damage trend of tunnel</title>", "<p id=\"Par25\">Figure ##FIG##6##7## shows the deformation pattern of the tunnel with a fortified dislocation value of 60 cm. Upon amplification by a factor of 50, it can be clearly seen that the articulated design of the tunnel has played a significant role—all hinged joints exhibit rotational and stretched state, indicative of their effective functioning.</p>", "<p id=\"Par26\">Figure ##FIG##7##8## is the longitudinal stress cloud chart of the tunnel, while Figs. ##FIG##8##9## and ##FIG##9##10## is the maximum principal stress cloud chart and the minimum principal stress cloud chart of the tunnel lining, respectively. Notably, one side wall of the tunnel experiences tension primarily due to the predominant strike-slip fault movements, with a tensile stress value of approximately 5 MPa.</p>", "<p id=\"Par27\">Figures ##FIG##10##11## and ##FIG##11##12## show the relative normal and tangential deformations of the hinged joints. Results show that the maximum normal deformation of the hinged joints is about 3.5 cm, which is located within the central segments of the fault zone. Similarly, the maximum tangential deformation is about 1.5 cm, which also occurs within the central segments of the fault zone. Importantly, the relative deformation of the hinged joint is less than the 5 cm reserved width.</p>", "<title>Tunnel displacement under different dislocation values</title>", "<p id=\"Par28\">Figures ##FIG##12##13## and ##FIG##13##14## shows the relative deformation between the left and right walls and between the vault and arch bottom of the tunnel under different dislocation values. These results show that relative deformation values basically escalate with an increase in fault dislocation, with the convergence of the left and right walls playing a dominant role, complemented by settlement of the vault towards the arch bottom. The maximum relative deformation of the tunnel is about 3.5 cm with the 60 cm dislocation value, which occurs within the central segment of the dislocation zone.</p>", "<title>Stress and internal force of tunnel under different dislocation values</title>", "<p id=\"Par29\">Figure ##FIG##14##15## shows the longitudinal stress in different parts of the tunnel under different dislocation values. While Fig. ##FIG##15##16## shows the distribution of internal force values along the axial direction of tunnel, including axial force, horizontal bending moment and horizontal shear force, when the tunnel lining is treated as a flexible beam. Significant longitudinal stress and internal force values can be noted in the tunnel lining within the fault. As for the longitudinal stress, the longitudinal stress at the vault and arch bottom are larger that of the left and right side walls. the maximum longitudinal stress is about 5 ~ 6 MPa in those portions.</p>", "<p id=\"Par30\">Both in Figs. ##FIG##14##15## and ##FIG##15##16##, a similar phenomenon can be found that the stresses and internal forces does not tend to increase significantly with the dislocation after the dislocation reaches 30 cm. The possible reason for this is because the main deformation occurs in the hinged joint rather than the lining segment, after the 30 cm dislocation. This phenomenon is good for the stability of the tunnel, that the hinge joints are functioning, effectively improving the bearing state of the lining under fault dislocation.</p>" ]

[ "<title>Acknowledgements</title>", "<p>This work is supported by Yunnan Major Science and Technology Special Program (202102AF080001), National Key R&amp;D Programs for Young Scientists (no. 2023YFB2390400), National Natural Science Foundation of China (nos. U21A20159, 52079133, 52379112, 41902288), the project of Key Laboratory of Water Grid Project and Regulation of Ministry of Water Resources (QTKS0034W23291), Visiting Researcher Fund Program of State Key Laboratory of Water Resources Engineering and Management (Grant No. 2023SGG07), Key Research Program of the Ministry of Water Resources (SKS-2022103), and the Youth Innovation Promotion Association CAS (2019323)</p>", "<title>Author contributions</title>", "<p>F.B., X.H. and Y.Z. wrote the main manuscript text; Z.C., X.M. and J.L. prepared the figures.</p>", "<title>Data availability</title>", "<p>The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.</p>", "<title>Competing interests</title>", "<p id=\"Par37\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Distribution of Longpan-Qiaohou fault and profile of water diversion line axis.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Three-dimensional analysis model of Longpan-Qiaohou Fault F10-1.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Relationship between the regional ground stress field direction and the tunnel axis.</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>Schematic diagram of the axis deformation of articulated lining^{##UREF##16##17##}.</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>Calculation method proposed by Jalali for the ultimate bending curvature of the articulated segment.</p></caption></fig>", "<fig id=\"Fig6\"><label>Figure 6</label><caption><p>Calculation model proposed by Jalali^{##UREF##14##15##}.</p></caption></fig>", "<fig id=\"Fig7\"><label>Figure 7</label><caption><p>Deformation pattern of the tunnel under 60 cm fortified dislocation.</p></caption></fig>", "<fig id=\"Fig8\"><label>Figure 8</label><caption><p>Longitudinal stress of the tunnel under 60 cm fortified dislocation.</p></caption></fig>", "<fig id=\"Fig9\"><label>Figure 9</label><caption><p>Maximum principal stress of the tunnel under 60 cm fortified dislocation (tension + compression−).</p></caption></fig>", "<fig id=\"Fig10\"><label>Figure 10</label><caption><p>Minimum principal stresses of the tunnel under 60 cm fortified dislocation. (tension + compression−).</p></caption></fig>", "<fig id=\"Fig11\"><label>Figure 11</label><caption><p>Normal relative deformation of hinged joints under 60 cm fortified dislocation.</p></caption></fig>", "<fig id=\"Fig12\"><label>Figure 12</label><caption><p>Tangential relative deformation of hinged joints under 60 cm fortified dislocation.</p></caption></fig>", "<fig id=\"Fig13\"><label>Figure 13</label><caption><p>Curve of relative deformation of the left and right side walls of the tunnel under different dislocation values.</p></caption></fig>", "<fig id=\"Fig14\"><label>Figure 14</label><caption><p>Curve of relative deformation of arched roof-arch bottom of the tunnel under different dislocation values.</p></caption></fig>", "<fig id=\"Fig15\"><label>Figure 15</label><caption><p>Change curve of the longitudinal stresses of articulated tunnel lining along the axial direction.</p></caption></fig>", "<fig id=\"Fig16\"><label>Figure 16</label><caption><p>Change curve of internal forces of articulated tunnel lining along the axial direction.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>In situ stress fields used in current study.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Burial depth/m</th><th align=\"left\">Maximum principal stress/MPa</th><th align=\"left\">Maximum principal stress azimuth/°</th><th align=\"left\">Medium principal stress/MPa</th><th align=\"left\">Minimum principal stress/MPa</th></tr></thead><tbody><tr><td align=\"left\">400</td><td align=\"left\">16</td><td align=\"left\">40</td><td align=\"left\">13</td><td align=\"left\">11</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>The relationship between the direction of ground stress field and the direction of tunnel axis.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Azimuth of tunnel axis/°</th><th align=\"left\" rowspan=\"2\">Maximum principal stress azimuth/°</th><th align=\"left\" rowspan=\"2\">Angle between the maximum principal stress and the tunnel axis /°</th><th align=\"left\" colspan=\"7\">Component of ground stress in the tunnel cross section/MPa*</th></tr><tr><th align=\"left\">Burial depth/m</th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th></tr></thead><tbody><tr><td align=\"left\">340</td><td align=\"left\">40</td><td align=\"left\">60</td><td align=\"left\">400</td><td char=\".\" align=\"char\">14.75</td><td char=\".\" align=\"char\">12.25</td><td char=\".\" align=\"char\">13.00</td><td char=\".\" align=\"char\">2.17</td><td char=\".\" align=\"char\">0.00</td><td char=\".\" align=\"char\">0.00</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Mechanical parameters of rock masses used in current study.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Position</th><th align=\"left\" rowspan=\"2\">Rock type</th><th align=\"left\" colspan=\"5\">Mechanical parameters</th></tr><tr><th align=\"left\">Elasticity modulus/GPa</th><th align=\"left\">Poisson’s ratio</th><th align=\"left\">Friction coefficient</th><th align=\"left\">Cohesion/MPa</th><th align=\"left\">Tensile strength/MPa</th></tr></thead><tbody><tr><td align=\"left\">Hanging wall</td><td align=\"left\">IV</td><td char=\".\" align=\"char\">3.00</td><td char=\".\" align=\"char\">0.30</td><td char=\".\" align=\"char\">0.65</td><td char=\".\" align=\"char\">0.55</td><td char=\".\" align=\"char\">0.25</td></tr><tr><td align=\"left\">Fault zone</td><td align=\"left\">V</td><td char=\".\" align=\"char\">0.80</td><td char=\".\" align=\"char\">0.34</td><td char=\".\" align=\"char\">0.50</td><td char=\".\" align=\"char\">0.40</td><td char=\".\" align=\"char\">0.15</td></tr><tr><td align=\"left\">Foot wall</td><td align=\"left\">IV ~ V</td><td char=\".\" align=\"char\">1.50</td><td char=\".\" align=\"char\">0.33</td><td char=\".\" align=\"char\">0.55</td><td char=\".\" align=\"char\">0.50</td><td char=\".\" align=\"char\">0.20</td></tr></tbody></table></table-wrap>" ]

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id=\"M24\"><mml:msub><mml:mi>L</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq4\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\varphi }_{u}$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:msub><mml:mi>φ</mml:mi><mml:mi>u</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} 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id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${L}_{j}$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:msub><mml:mi>L</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq8\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\varphi }_{u}$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:msub><mml:mi>φ</mml:mi><mml:mi>u</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{\\Delta {u}_{{\\text{F}}}}{\\Delta u}\\le \\frac{{L}_{F}}{{L}_{j}+{L}_{p}}$$\\end{document}</tex-math><mml:math id=\"M38\" display=\"block\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mtext>F</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mi 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[ "<table-wrap-foot><p>The coordinate convention on the cross-section of the tunnel is: to the right, into the plane, and to the vertical.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par3\">Liver fibrosis is culpable for the evolution of chronic liver diseases to liver cirrhosis and even liver cancer, one of the most common causes of morbidity and mortality worldwide [##REF##29427496##1##, ##REF##30266282##2##]. Upon chronic insult, liver parenchyma is collapse and gradual replacement by excessive amounts of extracellular matrix (ECM), resulting formation of liver fibrosis [##REF##26013123##3##–##REF##18480812##5##]. However, the mechanism underlining fibrogenesis is an ongoing debate. The increasing number of patients with liver fibrosis implies imperative need to develop mechanistic-based therapies.</p>", "<p id=\"Par4\">Hepatic stellate cells (HSCs) are one of the major cell types to contribute liver fibrosis [##REF##15690074##6##, ##REF##18195085##7##]. Following stimulation by fibrotic insult, quiescent HSCs (qHSCs) undergo droplet depletion and transform into activated HSCs (aHSCs), which are capable of producing collagen and ECM [##REF##28487545##8##]. During this process, the proliferation of HSCs significantly contributes to the pool of myofibroblasts [##UREF##0##9##].</p>", "<p id=\"Par5\">Liver fibrosis involves dynamic cellular communication between parenchymal hepatocytes and non-parenchymal cells, such as HSCs, endothelial cells (ECs), and immune cells. As the primary cell type in the liver, hepatocytes exhibit aberrant crosstalk between ECs and macrophages in response to liver injury [##REF##34280515##10##, ##REF##35868156##11##]. Within the disrupted internal environment, hepatocytes gradually lose their epithelial features and simultaneously acquire mesenchymal features, a process known as epithelial-mesenchymal transition (EMT), which contributes to the liver fibrogenesis [##UREF##1##12##]. Therefore, elucidating the molecular regulators of hepatocyte EMT and the associated cell crosstalk help uncover the mechanism of liver fibrosis.</p>", "<p id=\"Par6\">Periostin, a secreted matricellular protein, is expressed in collagen-rich fibrous connective tissues and was originally identified as a crucial regulator of bone formation [##REF##8363580##13##, ##UREF##2##14##]. Recent publications have reported the fibrogenic role of Periostin, demonstrating the significant effect of Periostin-expressing subset of cardiac fibroblasts on myocardial fibrosis [##REF##27447449##15##, ##REF##27140435##16##]. Considering the role of Periostin in the tissue microenvironment due to its secretory properties [##UREF##3##17##], it is intriguing to explore the cellular communication associated with Periostin in the context of liver fibrosis.</p>", "<p id=\"Par7\">In this study, we unveil a significant increase in proliferative aHSCs characterized by Periostin during liver fibrosis, highlighting their prominent role in the liver fibrogenesis. Mechanistically, bone morphogenetic protein-1 (Bmp-1) is essential involved in the pro-fibrotic communication between Periostin-expressing aHSCs and hepatocytes, consequently promoting the progression of liver fibrosis.</p>" ]

[ "<title>Materials and methods</title>", "<title>Human sample</title>", "<p id=\"Par8\">Normal liver tissue samples were obtained from the parahemangioma sites of patients with hepatic hemangioma, and paired liver fibrosis samples were collected from patients with hepatitis B virus (HBV)-related liver fibrosis before any therapeutic intervention. Human serum samples were collected from healthy volunteers and patients with liver fibrosis. Informed consent was obtained from all patients prior to their inclusion in the study. The Clinical Research Ethics Committee of the Third Affiliated Hospital of Sun Yat-Sen University approved this procedure. The basic information of the patients examined in this study is summarized in Table ##SUPPL##0##S1## and ##SUPPL##0##2##.</p>", "<title>Animal studies</title>", "<p id=\"Par9\"><italic>αSMA</italic>-thymidine kinase (<italic>αSMA</italic>-TK) and <italic>Periostin</italic> knockout (<italic>Periostin</italic> KO) mice in the C57BL/6 background were procured from the Jackson Laboratory (Bar Harbor, USA), while C57BL/6 mice were sourced from the Nanjing University Model Animals Institute. The mice were bred to obtain the necessary genotypes for the experiment, and littermates with the wild type phenotype served as the control. All animal protocols were approved by the Institutional Animal Ethics Committee of Sun Yat-Sen University.</p>", "<title>Statistical analysis</title>", "<p id=\"Par10\">Statistical analyses were performed using SPSS (Version 25.0) and R software (Version 4.3.0). A one-way analysis of variance (one-way ANOVA), Student’s <italic>t</italic>-test, the Mann-Whitney rank sum test, and the Mann-Whitney test (unpaired; two-tailed) were used to compare the changes between groups. <italic>p</italic> &lt; 0.05 was considered significant.</p>", "<p id=\"Par11\">The rest of materials and methods are available in the Supplemental Information.</p>" ]

[ "<title>Results</title>", "<title>Proliferation of activated HSCs occurs in the livers of both humans and mice with liver fibrosis</title>", "<p id=\"Par12\">To depict the fate-mapping of HSCs, we performed an analysis on a published single-cell RNA sequencing (scRNA-seq) dataset of the mouse liver (GSE171904) [##UREF##4##18##] (Fig. ##FIG##0##1A## and Fig. ##SUPPL##0##S1A–C##). Uniform manifold approximation and projection visualization of HSCs identified two distinct cell subpopulations: quiescent HSCs (qHSCs) and activated HSCs (aHSCs). Notably, the aHSCs demonstrated elevated levels of the activation markers <italic>αSMA</italic> and <italic>Col1a1</italic> [##REF##28487545##8##] (Fig. ##FIG##0##1B–C##). In accordance with the established dogma [##UREF##5##19##], aHSCs predominantly localized in the livers of fibrotic mice (Fig. ##SUPPL##0##S1D##). HSC proliferation is implicated in the expansion of the aHSC population and the development of liver fibrosis [##REF##33128017##20##]. Gene Ontology (GO) enrichment analysis of scRNA-seq data further identified pathways associated with aHSC proliferation (Fig. ##SUPPL##0##S1E, F##). The CCK-8 assays demonstrated significant proliferation in both primary mouse HSCs and the rat HSC cell line HSC-T6 upon exposure to fibrotic insult (Fig. ##FIG##0##1D##). After treatment with TGF-β, the expression of the activation marker α-SMA, as well as proliferation markers CCNE1, Ki-67, and PCNA, increased in HSCs, indicating the occurrence of HSC proliferation during their activation (Fig. ##FIG##0##1E, F##). The analysis of scRNA-seq data revealed that proliferative HSCs (pHSCs), based on known markers of proliferation, were predominantly located in the region of aHSCs instead of qHSCs, constituting more than half of the aHSC population (Fig. ##FIG##0##1G–H## and Fig. ##SUPPL##0##S1G##). Immunofluorescence analysis revealed broad co-staining areas of Ki-67, Collagen-I (Col-I), and α-SMA in the fibrotic liver of mice, consistent with the omics results (Fig. ##FIG##0##1I##). Furthermore, the expression of α-SMA, CCNE1, and PCNA was significantly increased in primary HSCs isolated from CCl₄-treated mice, confirming the involvement of HSC proliferation in their activation under chronic injury conditions (Fig. ##FIG##0##1J##). Akin to the results in mouse liver, analysis of the scRNA-seq dataset of normal and fibrotic livers from humans (GSE136103) revealed that pHSCs were primarily localized within the aHSC region (Fig. ##FIG##0##1K–M## and Fig. ##SUPPL##0##S1H–J##). In vitro experiments were conducted to confirm the substantial proliferation of LX-2 cells, a human HSC cell line, in response to injury stimuli (Fig. ##FIG##0##1N##). Treatment with TGF-β significantly upregulated both mRNA and protein levels of α-SMA, CCNE1, and PCNA in LX-2 cells (Fig. ##FIG##0##1O, P##). Finally, a pronounced colocalization of α-SMA and Ki-67 was detected in fibrotic liver sections obtained from patients (Fig. ##FIG##0##1Q##). The data indicate a substantial proportion of proliferative aHSCs within the aHSC pool, underscoring their critical role in the expansion of the aHSC population during liver fibrogenesis.</p>", "<title>Depletion of proliferative aHSCs attenuates liver fibrosis</title>", "<p id=\"Par13\">We utilized <italic>αSMA</italic>-TK transgenic mice to investigate the contribution of proliferative aHSCs to liver fibrosis. These mice allowed for the ganciclovir (GCV)-inducible ablation of proliferating myofibroblasts [##REF##23817022##21##]. In the carbon tetrachloride (CCl₄)-induced liver fibrosis model, GCV treatment significantly decreased the population of α-SMA-expressing HSCs in the liver of <italic>αSMA</italic>-TK mice (Fig. ##FIG##1##2A, B##). Primary HSCs isolated from <italic>αSMA</italic>-TK mice treated with GCV showed downregulated expression of α-SMA, CCNE1, and PCNA, confirming the depletion of proliferative HSCs (Fig. ##FIG##1##2C##). The <italic>αSMA</italic>-TK mice from the GCV group showed improved serum liver function, including alanine aminotransferase (ALT) and aspartate aminotransferase (AST), compared to the control group (Fig. ##FIG##1##2D##). Moreover, the deficiency of proliferating α-SMA⁺ cells in the liver was associated with a decrease in the fibrotic area, as evidenced by histological staining, and a decline in the expression of fibrotic markers in the liver tissue (Fig. ##FIG##1##2E–G##). Similarly, in the 3,5-diethoxycarbonyl-1,4-dihydrocollidine (DDC)-administrated <italic>αSMA</italic>-TK mice, the progression of liver fibrosis was hindered due to the decrease in hepatic α-SMA⁺ cells (Fig. ##SUPPL##0##S2A–D##). These results indicate that deletion of proliferative HSCs hampers liver fibrogenesis induced by various chronic liver injury.</p>", "<title>Periostin is identified as the hallmark of proliferative aHSCs</title>", "<p id=\"Par14\">To gain in-depth insight into the mechanisms by which proliferative aHSCs participate in fibrogenesis, we integrated liver scRNA-seq dataset obtained from control or CCl₄-treated WT (wild type) mice (GSE171904) and liver bulk RNA sequencing (RNA-seq) profile obtained from CCl₄-induced <italic>αSMA</italic>-TK mice treated with or without GCV (Fig. ##FIG##2##3A##). Following a step-by-step filtration of the scRNA-seq data, we selected <italic>Ckap4</italic>, <italic>Periostin</italic>, and <italic>Ybx</italic> as markers that represent HSCs with both proliferative and activated phenotypes for further analysis (Fig. ##FIG##2##3B## and Fig. ##SUPPL##0##S3A, B##). However, upon integrating the gene expression profiling data of <italic>αSMA</italic>-TK mice, we observed a downregulation of <italic>Periostin</italic> expression in both the the proliferative aHSC gene set and bulk liver of fibrotic <italic>αSMA</italic>-TK mice treated with GCV (Fig. ##FIG##2##3C##), indicating <italic>Periostin</italic> as a potential marker for this aHSC subpopulation. The transcriptomic alterations were validated through quantitative real-time polymerase chain reaction (qPCR) and western blotting. The results showed that among these 3 genes, only Periostin was increased in the fibrotic liver of WT mice, while decreased in fibrotic <italic>αSMA</italic>-TK mice treated with GCV (Fig. ##FIG##2##3D, E## and Fig. ##SUPPL##0##S3C, D##). At the single-cell level, Periostin was mainly distributed within HSCs, rather than parenchyma and other non-parenchyma cells, according to human and mouse scRNA-seq data (Fig. ##SUPPL##0##S3F##). Furthermore, compared with controls, the area of Periostin staining was expanded in liver section from CCl₄-induced mice, and largely co-localised with α-SMA and Ki-67, but not albumin (hepatocyte marker) and F4/80 (monocyte marker), suggesting that Periostin was mainly increased in proliferative and activated HSCs (Fig. ##FIG##2##3F##). The reduced co-localization of Periostin and α-SMA in the <italic>αSMA</italic>-TK mice confirmed that the Periostin expression was accordingly weakened, as the depletion of proliferative aHSCs (Fig. ##FIG##2##3G##). In vitro experiments, Periostin expression was higher in LX-2 cells (HSCs) than LO-2 cells (hepatocytes) and THP-1 cells (monocytes), and increased Periostin levels were detected in LX-2 under pro-fibrotic stimuli (Fig. ##FIG##2##3H## and Fig. ##SUPPL##0##S3E##). Consistent with the mouse liver tissues, similar change of Periostin expression was observed in primary HSCs isolated from WT and <italic>αSMA</italic>-TK mice (Fig. ##FIG##2##3H##). Subsequently, we observed activation-like morphology and increased levels of Ki-67, PCNA, Vimentin (Vim), and α-SMA (aHSC markers) in primary HSCs (derived from un-injured WT mice) and LX-2 cells, while PPAR-γ and GFAP (qHSC markers) were decreased after <italic>Periostin</italic> overexpression (Fig. ##FIG##2##3I–K## and Fig. ##SUPPL##0##S3G##). This finding demonstrates that Periostin induces the conversion of HSCs from a resting phenotype to a proliferative and activated phenotype, which are distinguishing characteristics of proliferative aHSCs (as depicted in Fig. ##FIG##0##1##). Overall, these findings suggest that Periostin may serve as a dependable marker for proliferative aHSCs during liver fibrosis.</p>", "<title>Periostin is elevated in liver fibrosis patients</title>", "<p id=\"Par15\">We subsequently conducted validation of Periostin expression in human liver. The analysis of bulk RNA-seq datasets from diverse cohorts showed an elevated expression of <italic>Periostin</italic> in the fibrotic liver of patients with non-alcoholic fatty liver disease (NAFLD) (GSE48452), and higher levels of hepatic <italic>Periostin</italic> were associated with a poor prognosis in liver fibrosis patients infected with HBV (GSE14520) (Fig. ##FIG##3##4A, B##). In the hepatitis C virus (HCV)-related cohort, elevated levels of <italic>Periostin</italic> in the liver indicate an increased likelihood of adverse outcomes, such as hepatocellular carcinoma (HCC), in patients with liver fibrosis (GSE15654) (Fig. ##FIG##3##4C## and Fig. ##SUPPL##0##S4A##). At the single-cell level, <italic>Periostin</italic> expression was predominantly restricted to aHSCs, while minimal expression was observed in qHSCs, as indicated by the human scRNA-seq dataset (GSE136103) (Fig. ##SUPPL##0##S4B##). Furthermore, human samples were collected to further validate the upregulated mRNA and protein levels of Periostin in fibrotic liver tissues (Fig. ##FIG##3##4D–F##). The elevated levels of Periostin in fibrotic livers, compared to those in normal controls, were found to be widely distributed in regions positive for α-SMA and Ki-67 (Fig. ##FIG##3##4G## and Fig. ##SUPPL##0##S4C##). Importantly, elevated levels of Periostin were detected in the serum of patients with liver fibrosis (Fig. ##FIG##3##4H##), indicating a strong correlation between Periostin and the progression of liver fibrosis.</p>", "<title>Periostin deficiency attenuates liver fibrosis by inhibiting the proliferation of HSCs</title>", "<p id=\"Par16\">We then investigated the role of Periostin in liver fibrosis using WT and <italic>Periostin</italic> KO mice. After chronic CCl₄ injury, the serum levels of ALT and AST were found to be improved in <italic>Periostin</italic> KO mice (Fig. ##FIG##4##5A, B##). Compared to WT mice, <italic>Periostin</italic> KO mice exhibited reduced collagen deposition and downregulated expression of Col-I and α-SMA in liver tissue (Fig. ##FIG##4##5C, D##). Furthermore, absence of Periostin impeded the proliferation of HSCs in liver fibrotic mice (Fig. ##FIG##4##5E##). Similarly, in the DDC-induced fibrosis model, <italic>Periostin</italic> KO mice exhibited reduced liver fibrosis (Fig. ##SUPPL##0##S5A–C##). Interestingly, the attenuated fibrosis in Periostin-deficient mice was reversed after obtaining exogenous Periostin (Fig. ##SUPPL##0##S6##). These results provide evidence that the deficiency of Periostin mitigates liver fibrosis through the inhibition of HSC proliferation and activation.</p>", "<title>Periostin reverses attenuation of liver fibrosis in mice with deficient proliferative aHSCs</title>", "<p id=\"Par17\">A recombinant Periostin-His tagged protein (rPeriostin) was administered to CCl₄-induced <italic>αSMA</italic>-TK mice via tail vein injection, concomitant with GCV treatment (Fig. ##FIG##4##5F##). Immunofluorescence staining showed that treatment with rPeriostin led to an increase in an augmentation of aHSCs (α-SMA) in the livers of <italic>αSMA</italic>-TK mice. Concurrently, a substantial co-localization of rPeriostin His-tag and α-SMA was observed, indicating the internalization of Periostin by aHSCs (Fig. ##FIG##4##5G##). <italic>αSMA</italic>-TK mice in the rPeriostin group exhibited elevated serum levels of ALT and AST (Fig. ##FIG##4##5H##). We observed that administration of rPeriostin abrogated the improvement of liver fibrosis in GCV-treated <italic>αSMA</italic>-TK mice (Fig. ##FIG##4##5I, J## and Fig. ##SUPPL##0##S7A##). Nothc-1 is a potential downstream receptor for Periostin [##UREF##6##22##]. Treatment with rPeriostin led to an elevation in Notch-1 levels, accompanied by substantial co-localization with the rPeriostin in the liver tissue of <italic>αSMA</italic>-TK mice (Fig. ##FIG##4##5J## and Fig. ##SUPPL##0##S7A, B##). However, suppression of Notch-1 abolished the conversion of qHSCs to aHSCs induced by Periostin (Fig. ##FIG##4##5K## and Fig. ##SUPPL##0##S7C##). Additionally, consistent results were detected in the DDC mouse models (Fig. ##SUPPL##0##S5D–F##), highlighting a significant association between Periostin and proliferative aHSCs in liver fibrogenesis.</p>", "<title>Periostin-expressing HSC-derived Bmp-1 induces epithelial-mesenchymal transition in hepatocytes</title>", "<p id=\"Par18\">The hepatocyte EMT plays a crucial role in the progression of liver fibrosis [##UREF##7##23##, ##UREF##8##24##], as demonstrated by GO enrichment analysis of RNA sequencing data obtained from a publicly available dataset of human fibrotic liver tissue (GSE171294) (Fig. ##FIG##5##6A##). Consistent with the functional enrichment result, we observed that EMT, characterized by decreased expression of the epithelial marker E-cadherin (E-cad) and increased expression of the mesenchymal markers N-cadherin (N-cad) and Vim, occurred in the livers of CCl₄-induced mice. However, in the absence of Periostin, the reversal of this EMT and suggests that Periostin plays a significant role in this process (Fig. ##FIG##5##6B, C## and Fig. ##SUPPL##0##S8A##). The dysregulation of cellular communication between HSCs and hepatocytes during liver fibrosis has been previously confirmed in our research [##UREF##9##25##]. In addition, Cellchat analysis from scRNA-seq data (GSE171904) uncovered potential crosstalk between proliferative HSCs and hepatocytes in the fibrotic liver (Fig. ##SUPPL##0##S8B##). Therefore, we performed a co-culture experiment where we observed the downregulation of E-cad and the upregulation of N-cad and Vim in hepatocytes co-cultured with <italic>Periostin</italic>-overexpressing HSCs (representing the phenotypes of proliferative aHSCs) as the culture time increased (Fig. ##FIG##5##6D–F## and Fig. ##SUPPL##0##S8C##). Proteomics of culture medium from rPeriostin-treated HSCs and protein-protein interaction analysis indicated a significant association between Periostin and Bmp-1, a member of the Bmp family (Fig. ##FIG##5##6G–H## and Fig. ##SUPPL##0##S8D, E##). Bmp family plays a crucial role in cell crosstalk, causing the phenotypic transition of hepatocytes [##UREF##1##12##, ##REF##28336518##26##]. Blocking Bmp-1, which was found to be elevated in HSCs following an increase in Periostin, resulted in co-cultured hepatocytes surprisingly regaining their epithelial properties (Fig. ##FIG##5##6I–J## and Fig. ##SUPPL##0##S8F–I##). Treatment with recombinant Bmp-1-His tagged protein (rBmp-1) induced the expression of Vim and α-SMA in hepatocytes, which subsequently enhanced the activation of HSCs (Fig. ##FIG##5##6K and N## and Fig. ##SUPPL##0##S8J, K##). Furthermore, primary hepatocytes (isolated from un-injured control mice) co-cultured with primary HSCs isolated from CCl₄-induced mice exhibited EMT, while co-culturing them with primary HSCs derived from fibrotic <italic>Periostin</italic> KO mice suppressed hepatocyte EMT. The addition of exogenous Bmp-1 reversed this suppression (Fig. ##FIG##5##6L–M## and Fig. ##SUPPL##0##S8L##). We further revealed that the EGFR, which serves as a critical epidermal growth factor receptor in the EMT of hepatocytes [##REF##23091115##27##, ##REF##21168239##28##], demonstrated increased expression in hepatocytes treated with rBmp-1 (Fig. ##SUPPL##0##S8M##). The mesenchymal properties of hepatocytes induced by Bmp-1 were abolished by AZD9291, an EGFR inhibitor (Fig. ##FIG##5##6N##). Interesting, AZD9291 treatment attenuated liver fibrosis in mice induced by chronic CCl₄ injury (Fig. ##FIG##5##6O##). Our findings suggest that Periostin-expressing proliferative aHSCs release Bmp-1, which activates the EGFR signalling, inducing hepatocyte EMT and contributing to liver fibrogenesis (Fig. ##FIG##5##6P##).</p>", "<title>Bmp-1 exacerbates liver fibrosis in <italic>Periostin</italic>-deficient mice through hepatocyte epithelial-mesenchymal transition</title>", "<p id=\"Par19\">To investigate the role of Bmp-1 in Periostin-regulated liver fibrogenesis, we administered rBmp-1 to <italic>Periostin</italic> KO mice via tail vein injection, along with intraperitoneal injection of CCl₄ (Fig. ##FIG##6##7A##). The administration of rBmp-1 led to an increase in serum ALT and AST levels in fibrotic <italic>Periostin</italic> KO mice (Fig. ##FIG##6##7B##). In rBmp-1-treated <italic>Periostin</italic> KO mice with fibrosis, there was an increase in histological injury, inflammatory infiltration, collagen deposition, and expression of fibrotic markers (Fig. ##FIG##6##7C–E##). In line with the exacerbated liver fibrosis and elevated Bmp-1 levels, the expression of hepatocyte EMT markers, including N-cad, Vim, and EGFR was increased, while E-cad expression decreased in the livers of <italic>Periostin</italic>-deficient mice (Fig. ##FIG##6##7F–G##). Furthermore, liver fibrosis was alleviated in DDC-induced <italic>Periostin</italic> KO mice after administering rBmp-1 (Fig. ##SUPPL##0##S9A–D##). The findings provide evidence of the essential role of Bmp-1 in Periostin-provoked liver fibrosis through hepatocyte EMT.</p>", "<title>Bmp-1 aggravates liver fibrosis in <italic>αSMA</italic>-TK mice</title>", "<p id=\"Par20\">To further investigate the involvement of Bmp-1 in liver fibrosis mediated by Periostin-expressing aHSC subpopulation, rBmp-1 was administered to <italic>αSMA</italic>-TK mice induced with CCl4 through tail vein injection, concomitant with GCV treatment (Fig. ##FIG##6##7H##). Following rBmp-1treatment, the serum liver function indicators, collagen deposition, and fibrotic marker levels were deteriorated in <italic>αSMA</italic>-TK mice. Intriguingly, treatment with rBmp-1 reverses the mitigation of serum liver function and liver fibrosis in <italic>αSMA</italic>-TK mice (Fig. ##FIG##6##7I–L##). Similarly, an exacerbation of liver fibrosis was observed in DDC-induced <italic>αSMA</italic>-TK mice treated with rBmp-1 (Fig. ##SUPPL##0##S9E–H##).</p>", "<title>Dabrafenib alleviates liver fibrosis in murine models by targeting Periostin</title>", "<p id=\"Par21\">We subsequently sought to identify Periostin-targeting antifibrotic treatments that could perturb pro-fibrotic HSC subset. After utilizing the differentially expressed genes of HSCs, derived from <italic>Periostin</italic> perturbation, as a query, we computationally scrutinized the chemogenomic data of transcriptomics in the Cmap database. As a result, dabrafenib was identified as the most suitable candidate compound (Fig. ##FIG##7##8A##). To more precisely delineate its therapeutic effects, we administered dabrafenib treatment to mice with liver fibrosis (Fig. ##FIG##7##8B##). Surprisingly, dabrafenib significantly improved liver function and reduced liver fibrosis in mice (Fig. ##FIG##7##8C–F##). In comparison to those in mice in the control group, fibrotic mice treated with dabrafenib exhibited decreased Periostin, Bmp-1, and α-SMA in the liver, along with attenuated EMT (Fig. ##FIG##7##8E–H##). Similar results were observed in vitro (Fig. ##FIG##7##8I–K## and Fig. ##SUPPL##0##S10##). The livers of DDC-induced mice treated with dabrafenib also showed a comparable reduction in fibrosis (Fig. ##SUPPL##0##S11##). The data suggest that dabrafenib has the potential to reverse liver fibrosis by inhibiting Periostin.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par22\">This study investigated the role and underlying mechanism of Periostin-expressing proliferative aHSCs the progression of liver fibrosis. Through the analysis of scRNA-seq transcriptomics and utilization of transgenic mice models, we have obtained insights that shed light on the pivotal role of proliferative aHSCs in liver fibrogenesis. Periostin was subsequently identified as the hallmark of proliferative aHSCs. It plays a crucial role in mediating the pro-fibrotic communication between HSCs and hepatocytes through the involvement of Bmp-1, thereby influencing the development of liver fibrosis.</p>", "<p id=\"Par23\">HSCs undergo a distinct phenotypic shift during the process of liver fibrogenesis [##REF##33128017##20##]. Through analysis of scRNA-seq data obtained from human and mouse livers, we discovered that approximately half of the aHSCs displayed a proliferative phenotype during liver fibrosis, while almost all pHSCs exhibited activation. This finding indicates that pHSCs are a pivotal subset within the population of aHSCs, supported by results obtained from fibrotic livers of both humans and mice. Furthermore, to further elucidate the role of the aHSC subset, we utilized <italic>αSMA</italic>-TK transgenic mice and demonstrated their crucial involvement in driving the progression of liver fibrosis.</p>", "<p id=\"Par24\">Due to the current lack of a specific marker for proliferative aHSCs, we identified Periostin as the hallmark of this particular subpopulation through the integration of multi-omics data. Abnormal expression of Periostin has been reported in various fibrotic tissues, including the heart, skin, and kidney, attributed to its involvement in tissue injury repair [##REF##27140435##16##, ##REF##24146092##29##–##UREF##11##32##]. However, studies focusing on the role of Periostin in liver fibrosis remain limited. In line with this finding, we also observed elevated expression of Periostin in the fibrotic livers of both humans and mice, predominantly localized in aHSCs expressing α-SMA, particularly those in a proliferative state. The overexpression of Periostin in HSCs led to the acquisition of a proliferative and activated phenotype that closely resembled the characteristics of proliferative aHSCs. Interestingly, upon the deletion of proliferative HSCs, the expression of Periostin was found to be reduced in the livers of <italic>αSMA</italic>-TK liver fibrosis mice, further supporting the significant association between Periostin and proliferative aHSCs. By utilizing <italic>Periostin</italic> KO mice, we demonstrated that the absence of Periostin markedly reduced liver fibrosis. Moreover, dabrafenib exhibited antifibrotic effects by targeting Periostin.</p>", "<p id=\"Par25\">A meaningful discovery arisen from our study is that Bmp-1 serves as a pivotal mediator of pro-fibrotic communication between Periostin-expressing aHSCs and hepatocytes. Liver cells, including parenchymal hepatocytes, non-parenchymal HSCs, and ECs, demonstrate aberrant cellular communication within the disrupted microenvironment of liver fibrosis [##REF##34280515##10##, ##REF##34648896##33##]. In previous research, we uncovered dysregulation in the crosstalk between HSCs and hepatocytes in the context of liver fibrosis [##UREF##9##25##]. Here, we have further confirmed the crosstalk between proliferative subpopulation of aHSCs and hepatocytes.Notably, there was a significant correlation between hepatocyte EMT and the expression of Periostin in fibrotic livers. The co-culture experiments revealed that Periostin-overexpressing HSCs were capable of inducing EMT in hepatocytes. Bmp-1 assumes a crucial function in this process by activating EGFR signalling in hepatocytes.Additionally, in fibrotic mice with a deficiency in Periostin, the reduction in liver fibrosis was counteracted by the introduction of exogenous Bmp-1, which coincided with the progression of EMT. These results demonstrate that Periostin-expressing aHSCs release Bmp-1 to induce EMT in hepatocytes, consequently facilitating the progression of liver fibrosis. The specific role and potential mechanism of hepatocytes in liver fibrogenesis after acquiring mesenchymal features, especially their ability to enhance the activation of HSCs, need to be explored. Further investigation in future studies is necessary to elucidate the mechanism of Bmp-1 release by Periostin-expressing aHSCs.</p>", "<p id=\"Par26\">In conclusion, our study provides the proof of concept that proliferative aHSCs, characterized by Periostin, significantly contribute to liver fibrogenesis. Periostin in aHSCs drives their acquisition of a proliferative phenotype and the release of Bmp-1. Proliferative aHSC-derived Bmp-1 inducing hepatocyte EMT through EGFR signalling, thereby promoting liver fibrogenesis. These findings provide insights into a unique perspective on the potential mechanism of liver fibrosis, and targeting of Bmp-1 and Periostin to normalize pro-fibrotic cellular crosstalk presents a promising therapeutic strategy for patients with liver fibrosis.</p>" ]

[]

[ "<p id=\"Par1\">Liver fibrosis is a reparative response to injury that arises from various etiologies, characterized by activation of hepatic stellate cells (HSCs). Periostin, a secreted matricellular protein, has been reported to participate in tissue development and regeneration. However, its involvement in liver fibrosis remains unknown. This study investigated the roles and mechanisms of Periostin in phenotypic transition of HSCs and relevant abnormal cellular crosstalk during liver fibrosis. The fate of hepatic stellate cells (HSCs) during liver fibrogenesis was investigated using single-cell and bulk RNA sequencing profiles, which revealed a significant proliferation of activated HSCs (aHSCs) in fibrotic livers of both humans and mice. <italic>αSMA</italic>-TK mice were used to demonstrate that depletion of proliferative aHSCs attenuates liver fibrosis induced by carbon tetrachloride and 3,5-diethoxycarbonyl-1,4-dihydrocollidine. Through integrating data from single-cell and bulk sequencing, <italic>Periostin</italic> was identified as a distinctive hallmark of proliferative aHSC subpopulation. Elevated levels of Periostin were detected in fibrotic livers of both humans and mice, primarily within aHSCs. However, hepatic Periostin levels were decreased along with depletion of proliferative aHSCs. Deficiency of Periostin led to reduced liver fibrosis and suppressed hepatocyte epithelial-mesenchymal transition (EMT). Periostin-overexpressing HSCs, exhibiting a proliferative aHSC phenotype, release bone morphogenetic protein-1 (Bmp-1), which activates EGFR signaling, inducing hepatocyte EMT and contributing to liver fibrosis. In conclusion, Periostin in aHSCs drives their acquisition of a proliferative phenotype and the release of Bmp-1. Proliferative aHSC subpopulation-derived Bmp-1 induces hepatocyte EMT via EGFR signaling, promoting liver fibrogenesis. Bmp-1 and Periostin should be potential therapeutic targets for liver fibrosis.</p>", "<p id=\"Par2\">\n\n</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41419-024-06437-8.</p>", "<title>Acknowledgements</title>", "<p>We thank all members of the Bin Wu’s lab for their excellent technical assistance.</p>", "<title>Author contributions</title>", "<p>SW and XL contributed equally to this study. SW designed and performed the experiments. XL performed the experiments and analyzed the data. RS collected clinical samples and analyzed the data. HL and JJ contributed the essential reagents and conducted the animal study. BW designed the whole project and supervised the research. SW and BW wrote the paper.</p>", "<title>Funding</title>", "<p>This work was supported by the National Natural Science Foundation of China [82070574], and the Natural Science Foundation Team Project of Guangdong Province [2018B030312009].</p>", "<title>Data availability</title>", "<p>All data generated or analyzed during this study are included in this published article and its supplementary information files. The raw sequencing data will be deposited in Gene Expression Omnibus.</p>", "<title>Competing interests</title>", "<p id=\"Par27\">The authors declare no competing interests.</p>", "<title>Ethical approval</title>", "<p id=\"Par28\">This study was approved by the Clinical Research Ethics Committee of the Third Affiliated Hospital of Sun Yat-Sen University and the Institutional Animal Ethics Committee of the Third Affiliated Hospital of Sun Yat-Sen University.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Proliferation of activated HSCs occurs in the livers of both humans and mice with liver fibrosis.</title><p><bold>A</bold>, <bold>B</bold> Analysis of mouse liver single-cell RNA sequencing (scRNA-seq) dataset (GSE171904) showed that pool of HSCs obtained from control or CCl₄-treated mice was classified into two distinct subpopulations: quiescent HSCs (qHSCs) and activated HSCs (aHSCs). <bold>C</bold> Expression and distribution of aHSC markers <italic>αSMA</italic> and <italic>Col1a1</italic> in pooled HSCs obtained from control or CCl₄-treated mice (GSE171904). <bold>D</bold> CCK-8 assay showed significant proliferation in mouse primary HSCs and HSC-T6 cells after treatment with TGF-β (5 ng/ml). <bold>E</bold> Immunofluorescence staining of α-SMA (green) and Ki-67 (red) in HSC-T6 cells treated with or without TGF-β (5 ng/ml) for 48 h (Scale bar: 25 μm). <bold>F</bold> mRNA levels of <italic>αSMA</italic> and <italic>CCNE1</italic>, <italic>Ki-67</italic>, and <italic>PCNA</italic> (proliferation markers) in mouse primary HSCs and HSC-T6 cells under different treatment conditions. <bold>G</bold> UMAP visualization showed the spatial distribution of proliferative HSCs (pHSCs) within the pool of HSCs obtained from control or CCl₄-treated mice (GSE171904). <bold>H</bold> Analysis of normalized percentages of non-pHSCs and pHSCs in the qHSCs and aHSCs regions showed that pHSCs constitute more than half of the total aHSC pool in mouse livers (GSE171904). <bold>I</bold> Immunofluorescence staining of Ki-67 (red) and Col-I or α-SMA (green) in liver sections from control or CCl₄-treated mice. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>J</bold> Protein expression levels of CCNE1, PCNA, and α-SMA in primary HSCs isolated from control or CCl₄-treated mice. The data were quantified (<italic>n</italic> = 3 per group). <bold>K</bold>, <bold>L</bold> Analysis of human liver scRNA-seq dataset (GSE136103) showed the classification of HSC pool obtained from normal controls and liver fibrosis patients into qHSCs and aHSCs, as well as non-pHSCs and pHSCs. <bold>M</bold> Normalized percentages of non-pHSCs and pHSCs were calculated in the qHSCs and aHSCs regions, respectively, of human liver (GSE136103). <bold>N</bold> CCK-8 assay was performed on LX-2 cells treated with or without TGF-β (5 ng/ml). <bold>O</bold>, <bold>P</bold> mRNA and protein levels of α-SMA, CCNE1, Ki-67, and PCNA were downregulated in TGF-β-treated LX-2 cells. <bold>Q</bold> Immunofluorescence staining of Ki-67 (red) and α-SMA (green) in human fibrotic liver samples (Scale bar: 50 μm). All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. scRNA-seq single-cell RNA sequencing, UMAP uniform manifold approximation and projection, CCl₄ carbon tetrachloride, qHSCs quiescent HSCs, aHSCs activated HSCs, pHSCs proliferative HSCs, Col-I Collagen-I, CCNE1 Cyclin E1.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Depletion of proliferative HSCs attenuates liver fibrosis in mice.</title><p><bold>A</bold> Ganciclovir (GCV)-administration strategy in <italic>αSMA</italic>-TK mice treated with CCl₄ to evaluate the impact of proliferative aHSCs on liver fibrogenesis (<italic>n</italic> = 6 per group). <bold>B</bold> Immunofluorescence staining showed a decrease in α-SMA levels in CCl₄-induced α<italic>SMA</italic>-TK mice treated with GCV. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>C</bold> Protein expression levels of CCNE1, PCNA, and α-SMA in primary HSCs isolated from <italic>αSMA</italic>-TK mice treated with or without GCV. The data were quantified (<italic>n</italic> = 3 per group). <bold>D</bold> Serum ALT and AST levels in <italic>αSMA</italic>-TK mice from indicated groups. <bold>E</bold> H&amp;E and Sirius red staining in liver sections of <italic>αSMA</italic>-TK mice from indicated groups. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 100 μm). <bold>F</bold>, <bold>G</bold> After treatment with GCV, mRNA and protein levels of Collagen-I (Col-I), Collagen-IV (Col-IV), and α-SMA were reduced in αSMA-TK mice. All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. TK thymidine kinase, CCl₄ carbon tetrachloride, GCV ganciclovir, CCNE1 cyclin E1, ALT alanine aminotransferase, AST aspartate aminotransferase, Col-I Collagen-I, Col-IV Collagen-IV.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Periostin is identified as the hallmark of proliferative aHSCs.</title><p><bold>A</bold> Schematic diagram illustrating the process of marker identification for proliferative aHSCs. This involves integrating liver scRNA-seq data from control or CCl₄-treated WT mice (GSE171904), as well as liver bulk RNA sequencing data from CCl₄-induced <italic>αSMA</italic>-TK mice with or without GCV treatment. <bold>B</bold>, <bold>C</bold> Venn plot and heatmap showing that <italic>Ckap4</italic>, <italic>Periostin</italic>, and <italic>Ybx</italic> are genes that overlap in the gene sets of aHSCs and pHSCs. However, only <italic>Periostin</italic> exhibited decreased levels in the bulk liver transcriptomic profile of <italic>αSMA</italic>-TK mice treated with GCV. <bold>D</bold>, <bold>E</bold> mRNA and protein levels of Periostin and α-SMA in liver tissues of WT and <italic>αSMA</italic>-TK mice from indicated groups. <bold>F</bold> Immunofluorescence staining of albumin (hepatocyte marker), F4/80 (monocyte marker), α-SMA (aHSC marker), Ki-67 (proliferation marker), and Periostin in liver sections from WT mice (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>G</bold> Immunofluorescence staining of Periostin and α-SMA in liver sections from <italic>αSMA</italic>-TK mice (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>H</bold> Protein expression levels of Periostin and α-SMA were measured in primary HSCs isolated from WT or <italic>αSMA</italic>-TK mice, as well as in LX-2 cells, from indicated groups. The data were quantified (<italic>n</italic> = 3 per group). <bold>I</bold>–<bold>J</bold> mRNA and protein levels of Periostin, PPAR-γ, GFAP, Vimentin (Vim), α-SMA, PCNA in primary HSCs (derived from un-injured mice) and LX-2 cells from the indicated groups. <bold>K</bold> Immunofluorescence staining showed increased expression of α-SMA (green) and Ki-67 (red) in LX-2 cells overexpressing <italic>Periostin</italic> (Scale bar: 25 μm). All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. WT wild type, TK thymidine kinase; scRNA-seq single-cell RNA sequencing; RNA-seq RNA sequencing; aHSCs activated HSCs; pHSCs proliferative HSCs; CCl₄ carbon tetrachloride; GCV ganciclovir; Vim, Vimentin.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Periostin is elevated in liver fibrosis patients.</title><p><bold>A</bold>\n<italic>Periostin</italic> upregulation in the livers of patients with liver fibrosis in a NAFLD-related cohort. <bold>B</bold> Kaplan–Meier survival curves demonstrated that high <italic>Periostin</italic> levels in the liver were associated with a poorer overall prognosis compared to low Periostin levels in liver fibrosis patients infected with HBV (left). Predictive performance of liver <italic>Periostin</italic> levels in predicting the survival time of these patients with liver fibrosis (right). <bold>C</bold> HCV-infected liver fibrosis patients with high levels of Periostin in the liver exhibited an increased probability of developing HCC. <bold>D</bold> Sirius red staining was used to assess the extent of fibrosis in human samples from indicated groups. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 100 μm). <bold>E</bold>, <bold>F</bold> Western blot and qPCR analyses revealed increased levels of Periostin, Col-I, and α-SMA in human liver samples with fibrosis. <bold>G</bold> Immunofluorescence staining showed that elevated Periostin is predominantly localized in α-SMA-positive regions of human fibrotic liver sections (Scale bar: 50 μm). <bold>H</bold> ELISA revealed the serum Periostin levels in normal control individuals and patients with liver fibrosis (<italic>n</italic> = 10 per group). All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. NAFLD non-alcoholic fatty liver disease, HBV hepatitis B virus; HCV hepatitis C virus; HCC hepatocellular carcinoma; Col-I Collagen-I.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Periostin is implicated in the development of liver fibrosis in mice.</title><p><bold>A</bold> Schematic overview illustrating the construction process of the CCl₄-induced liver fibrosis model in WT and <italic>Periostin</italic> knockout (<italic>Periostin</italic> KO) mice (<italic>n</italic> = 6 per group). <bold>B</bold>, <bold>C</bold> Serum levels of ALT and AST, as well as the protein levels of Periostin, Col-I, and α-SMA in liver tissues, were measured in the indicated groups. <bold>D</bold> H&amp;E, Sirius red, and α-SMA staining demonstrated that the absence of Periostin mitigated liver fibrosis in murine models induced by CCl₄. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>E</bold> Western blot analyses indicated decreased levels of CCNE1, PCNA, and α-SMA in primary HSCs isolated from <italic>Periostin</italic> KO mice treated with CCl₄. <bold>F</bold> Schematic overview illustrating the experimental strategy of administering recombinant Periostin-His tagged protein (rPeriostin) in CCl₄-induced <italic>αSMA</italic>-TK mice treated with GCV (<italic>n</italic> = 6 per group). <bold>G</bold> Immunofluorescence staining demonstrated the rPeriostin (red) were internalized by the elevated population of aHSCs (green) in the liver of α<italic>SMA</italic>-TK mice treated with rPeriostin (Scale bar: 50 μm). <bold>H</bold> Serum ALT and AST levels were measured in indicated groups. <bold>I</bold> H&amp;E and Sirius red staining in liver sections of <italic>αSMA</italic>-TK mice from indicated groups. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>J</bold> Protein expression levels of Periostin, Notch-1, Col-I, and α-SMA in liver tissues from <italic>αSMA</italic>-TK mice from the indicated groups. <bold>K</bold> Protein expression levels of Notch-1, PPAR-γ, GFPA, Vim, and α-SMA in rPeriostin treated-primary HSCs (isolated from un-injured WT mice) with or without administration of Notch-1 inhibitor (10 μM). All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. WT wild type, KO knockout, CCl₄ carbon tetrachloride, ALT alanine aminotransferase, AST aspartate aminotransferase, Col-I Collagen-I, CCNE1 cyclin E1, TK thymidine kinase, GCV ganciclovir, Vim Vimentin.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Periostin-expressing HSC-derived Bmp-1 induces epithelial-mesenchymal transition in hepatocytes.</title><p><bold>A</bold> GO enrichment analysis of RNA-sequencing dataset from normal control and human fibrotic liver tissues. <bold>B</bold>, <bold>C</bold> Immunofluorescence staining and qPCR were performed to examine the expression of epithelial marker E-cadherin (E-cad), and mesenchymal markers N-cadherin (N-cad) and Vimentin (Vim) in livers of WT and <italic>Periostin</italic> KO mice treated with or without CCl₄.The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>D</bold> Schematic diagram illustrating the co-culture of hepatocytes with HSCs transfected with vector or <italic>Periostin</italic>-overexpressing lentivirus. <bold>E</bold>, <bold>F</bold> The levels of E-cad were downregulated, while N-cad and Vim were upregulated in LO-2 cells co-cultured with <italic>Periostin</italic>-overexpressing LX-2 cells at 72 h. <bold>G</bold> Secreted protein profile analysis of culture medium from LX-2 cells treated with or without rPeriostin. <bold>H</bold> Protein-protein interaction network of Periostin was constructed by utilizing STRING database. <bold>I</bold> ELISA showed the Bmp-1 content in the culture medium of LX-2 transfected with vector or <italic>Periostin</italic>-overexpressing lentivirus, and meanwhile these cells were treated with or without Bmp-1 inhibitor (10 μM). <bold>J</bold> Protein expression levels of E-cad, N-cad, and Vim in LO-2 cells co-cultured with <italic>Periostin</italic>-overexpressing LX-2 in indicated groups. <bold>K</bold> Immunofluorescence staining of Vim in LO-2 treated with or without recombinant Bmp-1-His tagged protein (rBmp-1) (10 μM) (Scale bar: 25 μm). <bold>L</bold>, <bold>M</bold> Primary hepatocytes (isolated from un-injured WT mice) co-cultured with primary HSCs isolated from CCl₄-induced <italic>Periostin</italic> KO mice exhibited upregulated levels of E-cad and downregulated levels of N-cad and Vim when compared to CCl₄-WT mice, and these effects were blunted by treatment with rBmp-1 (<italic>n</italic> = 3 independent experiments). <bold>N</bold> Western blot analysis for EGFR, p-EGFR, N-cad, and α-SMA in primary hepatocytes (isolated from un-injured WT mice) with or without treatment of rBmp-1 and EGFR inhibitor (AZD9291, 10 μM) (<italic>n</italic> = 3 independent experiments). <bold>O</bold> H&amp;E and Sirius red staining demonstrated that treatment with AZD9291 attenuated liver fibrosis in mice after chronic CCl₄ injury. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>P</bold> Periostin-expressing proliferative aHSCs release Bmp-1, which activates the EGFR signalling, inducing hepatocyte EMT and contributing to liver fibrogenesis. All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. GO Gene Ontology, CCl₄ carbon tetrachloride, KO knockout, E-cad E-cadherin, N-cad N-cadherin, Vim Vimentin, rBmp-1 recombinant Bmp-1-His tagged protein, EMT epithelial-mesenchymal transition, aHSCs activated HSCs.</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><title>Bmp-1 plays a crucial role in the progression of liver fibrosis in mice.</title><p><bold>A</bold> Schematic overview depicting the administration strategy of rBmp-1 in <italic>Periostin</italic> KO mice treated with CCl₄ (<italic>n</italic> = 6 per group). <bold>B</bold> Serum ALT and AST levels in <italic>Periostin</italic> KO mice treated with or without rBmp-1. <bold>C</bold> H&amp;E, Sirius red, and α-SMA staining demonstrated the reversal of liver fibrosis attenuation in <italic>Periostin</italic> KO mice following treatment with rBmp-1. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>D</bold>, <bold>E</bold> qPCR and western blot analysis demonstrated that treatment with rBmp-1 significantly upregulated the levels of Bmp-1, Col-I, and α-SMA in liver tissues of CCl₄-induced <italic>Periostin</italic> KO mice. <bold>F</bold> Immunofluorescence staining of E-cad and N-cad in liver sections of <italic>Periostin</italic> KO mice from different groups. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>G</bold> Protein expression levels of EGFR, p-EGFR, E-cad, and Vim in liver tissues of <italic>Periostin</italic> KO mice from different groups. The data were quantified (<italic>n</italic> = 3 per group). <bold>H</bold> Schematic overview illustrating the experimental strategy of administering rBmp-1 in CCl₄-induced <italic>αSMA</italic>-TK mice treated with GCV (<italic>n</italic> = 6 per group). <bold>I</bold> Serum ALT and AST levels in <italic>αSMA</italic>-TK mice treated with or without rBmp-1. <bold>J</bold> H&amp;E and Sirius red staining in liver sections of <italic>αSMA</italic>-TK mice from indicated groups. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 50 μm). <bold>K</bold>, <bold>L</bold> The levels of Bmp-1, Col-I, and α-SMA were upregulated in liver tissues of <italic>αSMA</italic>-TK mice, following rBmp-1 treatment. All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. KO knockout, CCl₄ carbon tetrachloride, rBmp-1 recombinant Bmp-1-His tagged protein, ALT alanine aminotransferase, AST aspartate aminotransferase, Col-I Collagen-I, E-cad E-cadherin, N-cad N-cadherin, Vim Vimentin, TK thymidine kinase, GCV ganciclovir.</p></caption></fig>", "<fig id=\"Fig8\"><label>Fig. 8</label><caption><title>Dabrafenib alleviates liver fibrosis by targeting Periostin.</title><p><bold>A</bold> Dabrafenib was identified as potential target compound using the differentially expressed genes in HSCs following <italic>Periostin</italic> perturbation. <bold>B</bold> Schematic overview of the experimental setup for assessing the efficacy of dabrafenib in a CCl₄-induced liver fibrosis mouse model (<italic>n</italic> = 6 per group). <bold>C</bold> Dabrafenib treatment significantly improved the serum levels of ALT and AST in mice with CCl₄-induced liver fibrosis. <bold>D</bold> Dabrafenib treatment in CCl₄-induced mice resulted in reduced liver fibrosis, as indicated by H&amp;E and Sirius red staining. The data were quantified (<italic>n</italic> = 6 per group) (Scale bar: 100 μm). <bold>E</bold>, <bold>F</bold> mRNA and protein levels of Bmp-1, Col-I, Col-IV, and α-SMA in liver tissues of mice from different groups. <bold>G</bold> Immunofluorescence staining of Periostin and α-SMA in liver sections of mice from different groups (Scale bar: 50 μm). <bold>H</bold> Protein expression levels of Periostin, Bmp-1, and N-cad decreased, while levels of E-cad increased in the liver tissues of CCl₄-induced mice treated with dabrafenib. The data were quantified (<italic>n</italic> = 3 per group). <bold>I</bold> Protein expression levels of Periostin, Bmp-1, PCNA, and α-SMA in <italic>Periostin</italic>-overexpressing primary HSCs (isolated from un-injured mice) treated with or without dabrafenib. <bold>J</bold> ELISA showed the Bmp-1 content in the culture medium of LX-2 cells under different treatment conditions. <bold>K</bold> Protein expression levels of E-cad, N-cad, and Vim in rBmp-1-treated primary hepatocytes (isolated from un-injured mice) in the indicated groups. All results are shown as mean ± SEM. *<italic>p</italic> &lt; 0.05; ***<italic>p</italic> &lt; 0.001. DEGs differentially expressed genes, WT wild type, CCl₄ carbon tetrachloride, ALT alanine aminotransferase, AST aspartate aminotransferase, Col-I Collagen-I, Col-IV Collagen-IV, E-cad E-cadherin, N-cad N-cadherin, OE overexpression, rBmp-1 recombinant Bmp-1-His tagged protein.</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM3\"></supplementary-material>" ]

[ "<fn-group><fn><p>Edited by Professor Yufang Shi</p></fn><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Sizhe Wan, Xianzhi Liu.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41419_2024_6437_MOESM1_ESM.docx\"><caption><p>Supplemental Material</p></caption></media>", "<media xlink:href=\"41419_2024_6437_MOESM2_ESM.pdf\"><caption><p>Original western blots</p></caption></media>", "<media xlink:href=\"41419_2024_6437_MOESM3_ESM.pdf\"><caption><p>Aj-checjlist</p></caption></media>" ]

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[ "<title>Introduction</title>", "<p id=\"Par3\">Animal populations often inhabit hazardous environments characterized by pronounced mortality due to a high presence of natural enemies, parasites and predators. A common goal in agricultural and ecosystem management is to enhance the population density of certain target species, which can be challenging in hazardous environments^{##UREF##0##1##}. Among other factors, the availability of local safe zones such as refuges or shelters, with lower mortality and/or higher reproduction rates, seems to be beneficial for population proliferation^{##UREF##1##2##}. For example, the creation of artificial shelters in aquatic farms, or, generally, promotion of heterogeneity in natural aquatic systems is believed to be an efficient practical tool to reduce the stress of fish and protect them from parasites and predators^{##UREF##2##3##,##UREF##3##4##}. Overall, one can consider safe zones as a sort of generalized resource; therefore providing an extra vital resource to a population is expected to produce a positive impact as compared to the scenario without this resource (all other conditions being equal). Here we question this conventional ecological wisdom, and we argue that the presence of safe zones, being largely beneficial at the scale of an individual, can be harmful at the scale of the entire population. Using a theoretical model with realistic parameters, describing salmonids-parasites interactions, we uncover a counter-intuitive scenario, where the behavioral structuring in a heterogeneous environment has a negative impact on the overall survival and proliferation of the population.</p>", "<p id=\"Par4\">Animal populations are often behaviorally structured, in terms of the strategies individuals use to compete with each other and evade their natural enemies^{##UREF##4##5##}. Such structuring can be dynamic, when individuals can use different strategies under different circumstances. For example, boldness in the pumpkinseed sunfish (<italic>Lepomis gibbosus</italic>) disappears when fish are in social and ecological isolation^{##UREF##5##6##}. Within a single population, individuals can split into groups that implement distinct behavioral strategies. For example, for many fish species, a part of the individuals can use shoaling (grouping)^{##UREF##6##7##}, whereas the other part of the population can show strong territoriality (sheltering)^{##UREF##7##8##}. On the other hand, structured behavior can also be permanent over the lifetime of an organism: individuals can highly vary in their rates of exploration of the environment, risk-taking willingness, reactivity, aggressiveness, or overall activity^{##REF##16701288##9##–##REF##17437562##12##}. Although behavioral structuring (dynamic or/and permanent) is now well-recognized in the ecological literature^{##UREF##9##13##,##UREF##10##14##}, it is still unclear how this could mediate intraspecific competition for vital resources when competition comes at a high cost and how this could affect the population density. It is also unknown how dynamic behavioral structuring triggered by external stimuli, such as natural enemies and/or environmental heterogeneity (e.g. the presence of safe zones), interacts with permanent behavioral structuring to shape the size of the entire population.</p>", "<p id=\"Par5\">To assess the role of behavioral structuring in population proliferation, we build a generic mathematical model involving several time scales: behavioral, demographic and evolutionary. We are interested in whether adding safe zones (shelters) for individuals in a hostile environment formed by natural enemies (parasites and/or predators) is always beneficial. Using the theoretical model with realistic parameters related to fish farming, we show that the dynamical behavioral structuring caused by spatial heterogeneity mostly lowers the population density, in the case where the available safe zones are insufficient. The permanent structuring of the population in terms of boldness, aggressiveness, or reactivity has the opposite effect. The mentioned positive effect seems to be generic, observed both in clonal and non-clonal scenarios of the inheritance of behavioral traits. The model predicts that permanent behavioral structuring can arise from an initially uniform (monomorphic) population as a result of disruptive evolution via evolutionary branching.</p>", "<p id=\"Par6\">As a practical application of our theory, we consider the interaction between salmonid fish and trematode parasites in the presence of artificial shelters in fish farms. The dynamical behavioral structuring in salmonids includes shoaling (grouping) and sheltering (territoriality)^{##UREF##6##7##,##UREF##7##8##}: both tactics, besides the direct effect of antipredator defense, reduce stress and the ventilation rate in fish^{##UREF##11##15##–##UREF##13##17##}. Salmonids prefer shelters to shoals making shelters very contestable^{##UREF##7##8##,##REF##20051120##18##}. Fighting for shelter is costly due to the threat of predation and acquisition of extra parasites resulting in higher mortality^{##UREF##7##8##,##UREF##14##19##,##REF##28127051##20##}. We apply our theoretical model to the system comprising rainbow trout <italic>Oncorhynchus mykiss</italic>, widely grown in fish farms, and the common trematode parasite, eye-fluke <italic>Diplostomum pseudospathaceum</italic>. For this system, we also experimentally explore the missed so far connection between permanent behavioral structuring of rainbow individuals (reactivity) with vulnerability to infection by <italic>D. pseudospathaceum</italic> as well as the consequences of using various antipredator strategies for parasite acquisition.</p>", "<p id=\"Par7\">We conclude that installing an insufficient number of shelters in aquaculture and restoration programs would be counter-productive in terms of having a higher parasite acquisition, and a decrease in the overall population size. The proposed theoretical framework can be also applied to better understand the role of behavioral structuring on the population dynamics of some coral fish^{##UREF##15##21##} as well as freshwater fish^{##UREF##16##22##}.</p>" ]

[ "<title>Methods</title>", "<title>Theoretical modeling framework</title>", "<p id=\"Par39\">We developed a generic theoretical model to explore the role of intraspecific competition over a limited number of safe zones (shelters) in a behaviorally structured population in a hostile environment. The model is primarily focused on fish-parasite interactions. We consider that individuals within a population can adopt two anti-predator and anti-parasite tactics: (i) territoriality when they often reside within a shelter and guard it, or (ii) shoaling when they stay in a group. We stress that the shoaling compartment can be understood as an ensemble of a large number (e.g. hundreds) of independent shoals, which are homogeneously spread over space. The transition between the two behavioral states occurs via a short-term solitary phase, not modeled explicitly. We assume that the territorial strategy is more beneficial as it results in less mortality, as is the case study of the trout-parasite system.</p>", "<p id=\"Par40\">Along with dynamic behavioral structuring (shoaling/sheltering), we consider a permanent behavioral structuring according to the level of boldness of each individual, assuming that boldness is positively correlated with reactivity, exploration, aggressiveness and risk-taking ability^{##REF##16701288##9##,##UREF##37##55##–##REF##31913322##57##}. For example, in the empirical trout study, the fast fish would correspond to bold strains, whereas the slow ones would be less bold, i.e. shy strains. For each of the <italic>n</italic> different behavioral strains, we quantify the level of the boldness of strain <italic>i</italic> by the parameter <italic>B</italic>_{<italic>i</italic>}, where 0≤<italic>B</italic>_{<italic>i</italic>}≤1, with 1 being the highest possible boldness: this approach is used in the literature^{##REF##28450699##30##}. The existence of the highest possible boldness is due to physiological constraints for the life history traits of the given species. Each strain <italic>i</italic> can adopt two tactics, territoriality and shoaling, in numbers denoted by <italic>T</italic>_{<italic>i</italic>} and <italic>S</italic>_{<italic>i</italic>}, respectively. These two components make up the population density of the strain <italic>i</italic>, i.e. <italic>F</italic>_{<italic>i</italic>} = <italic>T</italic>_{<italic>i</italic>} + <italic>S</italic>_{<italic>i</italic>}. The total number of shelters, <italic>N</italic>, is fixed, and we assume that they are always fully occupied by some individuals, so the total number of individuals adopting territorial tactics is .</p>", "<p id=\"Par41\">An important feature of our model is the consideration of two distinct time scales corresponding to different types of processes: changes in the dynamical behavioral state of individuals (shoal/shelter) take place on a fast time scale, whereas demographic processes such as reproduction and mortality take place on a slow time scale. This approach of time scale separation is well-known in ecological modeling^{##UREF##34##51##–##UREF##36##53##}. Note that evolutionary modeling adds an extra (third) time scale (see the end of this section).</p>", "<p id=\"Par42\">First, let us consider the fast time scale on which the population density of each strain <italic>F</italic>_{<italic>i</italic>} remains constant. The exchange rate of individuals between <italic>T</italic>_{<italic>i</italic>} and <italic>S</italic>_{<italic>i</italic>} is described by the following function <italic>M</italic>_{<italic>i</italic>}The first term in the above expression describes individuals who enter a shelter from the shoal by successfully invading an occupied shelter. After the invasion of a shelter, the defeated shelter dweller loses its shelter and returns to the shoal, described by the second term of the equation. The function <italic>I</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}, <italic>T</italic>_{<italic>j</italic>}) is the rate at which an individual from the shoal with boldness <italic>B</italic>_{<italic>i</italic>} displaces an individual with boldness <italic>B</italic>_{<italic>j</italic>} occupying a shelter after a contest given that <italic>T</italic>_{<italic>j</italic>} individuals with boldness <italic>B</italic>_{<italic>j</italic>} are currently occupying shelters, the formulation of which is given further in Eq. (##FORMU##15##5##). The fast exchange of individuals between shoals and shelters can be modeled by</p>", "<p id=\"Par43\">We assume that this process occurs instantaneously in comparison to the slow demographic processes. As such, we can fix the population sizes <italic>F</italic>_{<italic>i</italic>}, so the values of <italic>T</italic>_{<italic>i</italic>} and <italic>S</italic>_{<italic>i</italic>} are given by the stationary state of (##FORMU##9##2##) and are functions of <italic>F</italic>_{<italic>i</italic>}, i.e. (<italic>T</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}), <italic>S</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>})), with the condition <italic>T</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}) + <italic>S</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}) = <italic>F</italic>_{<italic>i</italic>}. The stationary states of (##FORMU##9##2##) are determined by <italic>M</italic>_{<italic>i</italic>} = 0. Our numerical simulation shows that all stationary states are stable, see Supplementary Note ##SUPPL##0##7##, Fig. ##SUPPL##0##S5##. They can be found by solving the following <italic>n-</italic>dimensional systemfor <italic>i</italic> = 1: <italic>n</italic>, this follows directly from (##FORMU##8##1##) and with <italic>S</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}) = <italic>F</italic>_{<italic>i</italic>} − <italic>T</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}). This can be simplified by setting , which follows directly from , to following <italic>n</italic> − 1 dimensional systemfor <italic>i</italic> = 1: <italic>n</italic> − 1. Once the system is solved for <italic>T</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}), <italic>i</italic> = 1: <italic>n</italic> − 1, we can determine and, finally, <italic>S</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}) = <italic>F</italic>_{<italic>i</italic>} − <italic>T</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}).</p>", "<p id=\"Par44\">We parameterize the function <italic>I</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}, <italic>T</italic>_{<italic>j</italic>}) as followswhere <italic>I</italic>₀ describe the maximal rate at which a shoal individual encounters a single shelter, the term <italic>ν</italic>(<italic>B</italic>_{<italic>i</italic>}) the role of boldness in the search for shelters (this function is discussed below). It is well-known that contests between a shy invader and a bold shelter occupant are usually rare in nature^{##UREF##39##58##–##UREF##42##62##}. Therefore, we introduce a conditional probability <italic>ω</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}) for shoal individuals with boldness <italic>B</italic>_{<italic>i</italic>} to invade a shelter occupied by an individual with boldness <italic>B</italic>_{<italic>j</italic>}, provided the invader has already approached the shelter and visually assessed the boldness of the shelter’s occupier. Within this study, a sigmoid function is considered, defined asIn the case where <italic>B</italic>_{<italic>i</italic>} and <italic>B</italic>_{<italic>j</italic>} substantially differ from each other and <italic>B</italic>_{<italic>i</italic>} &lt; <italic>B</italic>_{<italic>j</italic>} (a shy invader and a bold occupier), <italic>B</italic>_{<italic>i</italic>} will almost never attempt an invasion, so <italic>ω</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}) ≈ 0. For <italic>B</italic>_{<italic>i</italic>} &gt; <italic>B</italic>_{<italic>j</italic>} (a bold invader and a shy occupier), <italic>B</italic>_{<italic>i</italic>} will almost always attempt an invasion, so <italic>ω</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}) ≈ 1. For <italic>B</italic>_{<italic>i</italic>} ≈ <italic>B</italic>_{<italic>j</italic>} we have <italic>ω</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>i</italic>}) ≈ 0.5. 1/<italic>δ</italic>_{<italic>ω</italic>} gives the width of the transition layer, which is assumed to be narrow. Therefore, the considered sigmoid form with a sharp transition (a smooth version of a step-wise function) is a natural way to describe the absence of contests between a shy invader and a bold occupier.</p>", "<p id=\"Par45\">On the slow demographic time scale, individuals reproduce and suffer mortality (either natural background mortality or due to parasitism or predation). The demographic model for the population density of the strain <italic>i</italic> is given bywhere the bold symbols denote vectors with components corresponding to all strains (i.e. <bold>F</bold> = [<italic>F</italic>₁, . . . <italic>F</italic>_{<italic>n</italic>}], <bold>T</bold>(<bold>F</bold>) = [<italic>T</italic>₁(<italic>F</italic>₁), . . . , <italic>T</italic>_{<italic>n</italic>}(<italic>F</italic>_{<italic>n</italic>})] and <bold>S</bold>(<bold>F</bold>) = <bold>F</bold> − <bold>T</bold>(<bold>F</bold>)).</p>", "<p id=\"Par46\">The first term in (##FORMU##17##7##) accounts for reproduction, where the kernel <italic>R</italic>(<italic>B</italic>_{<italic>i</italic>}, <bold>F</bold>) governs the redistribution of offspring, as it is explained in detail below; is described by the logistic function (of the form ). We do not consider age structuring so that the equations remain tractable. The next three terms account for mortality. <italic>m</italic>₀<italic>F</italic>_{<italic>i</italic>} is the background mortality; the other rates stand for the additional mortality due to residing within the shoal and shelter (Δ<italic>m</italic>_{<italic>S</italic>}(<italic>B</italic>_{<italic>i</italic>})<italic>S</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>}) and Δ<italic>m</italic>_{<italic>T</italic>}(<italic>B</italic>_{<italic>i</italic>})<italic>T</italic>_{<italic>i</italic>}(<italic>F</italic>_{<italic>i</italic>})). The last term <italic>G</italic>(<italic>B</italic>_{<italic>i</italic>}, <bold>S</bold>(<bold>F</bold>), <bold>T</bold>(<bold>F</bold>)) represents extra mortality caused by competition for shelters. Individuals from the shoal constantly attempt to invade an occupied shelter, engaging in fights with shelter residents. For strain <italic>i</italic>, the number of contests for shelters per unit of time by individuals currently staying in a shoal is proportional to the sum of <italic>S</italic>_{<italic>i</italic>}<italic>I</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}, <italic>T</italic>_{<italic>j</italic>}) over all possible types of residents <italic>B</italic>_{<italic>j</italic>} of the shelters. The mortality term due to contesting shelters is given byThe term <italic>m</italic>_{<italic>p</italic>}(<italic>B</italic>_{<italic>i</italic>}) = <italic>ν</italic>_{<italic>μ</italic>}(1 − <italic>ϵ</italic><italic>B</italic>_{<italic>i</italic>}) describes the extra mortality rate due to fighting (counted per a single individual); <italic>ν</italic>_{<italic>μ</italic>} is the coefficient, combining effects of the cost of fighting and the search rate for shelters; the multiplier (1 − <italic>ϵ</italic><italic>B</italic>_{<italic>i</italic>}) takes into account the dependence on the boldness in parasite acquisition (using a linear functional form is done for simplicity purposes); <italic>ν</italic>(<italic>B</italic>_{<italic>i</italic>}) takes into account the role of boldness in the search of shelters (similar to the term <italic>I</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}, <italic>T</italic>_{<italic>j</italic>})).</p>", "<p id=\"Par47\">The parameter <italic>D</italic> &lt; 1 describes the reduction in the cost of fighting when defending a shelter: the invader usually suffers a high parasitic cost, whereas the defending resident suffers a reduced cost. The requirement that <italic>D</italic> &lt; 1 for the owners of shelters has empirical justification. For fish-parasite interactions, when fighting more aggressive dominants usually receive fewer parasites than the subordinates, which is related to differences in ventilation rate: elevated ventilation results in an increased infection rate^{##REF##24411014##31##}. Social status often affects ventilation rate via different mechanisms^{##UREF##12##16##,##REF##7878128##63##,##UREF##43##64##}. For example, the low social status of subordinate fish often experiences more stress which increases their metabolic rate^{##REF##11731977##65##}, while the dominants, as owners of the shelter, have lower maintenance metabolism^{##UREF##44##66##}.</p>", "<p id=\"Par48\">To describe relation between boldness <italic>B</italic> and extra mortality rates Δ<italic>m</italic>_{<italic>S</italic>}(<italic>B</italic>_{<italic>i</italic>}) and Δ<italic>m</italic>_{<italic>T</italic>}(<italic>B</italic>_{<italic>i</italic>}) we use the following linear parameterizationswhere Δ_{<italic>S</italic>} and Δ_{<italic>T</italic>} are coefficients that depend on the level of natural enemies (predator or parasite) in the environment. The dimensionless parameter <italic>ϵ</italic> describes the variation of mortality rates with an increase in boldness. Positive values of 0 &lt; <italic>ϵ</italic> &lt; 1 signify a decrease of mortality with boldness; this scenario occurs in the here-considered case study of trout-parasite interactions (rough estimation based on our empirical study gives <italic>ϵ</italic> ∈ (0.075, 0.6), see the next subsection below). Some other biological systems also show a similar correlation^{##REF##25635765##67##}. On the other hand, it was reported that few other biological systems may show a positive correlation between mortality and boldness^{##UREF##10##14##,##REF##28450699##30##}. We also considered the cases, where <italic>ϵ</italic> = 0. Finally, we must stress that using a linear functional form was done for simplicity purposes only to be able to connect the model with our empirical data on trout-parasite interactions.</p>", "<p id=\"Par49\">Following some previous studies^{##REF##32437709##68##}, the reproduction kernel <italic>R</italic>(<italic>B</italic>_{<italic>i</italic>}, <bold>F</bold>) that describes the redistribution of offspring <italic>B</italic>_{<italic>i</italic>} around the boldness trait of the parent <italic>B</italic>_{<italic>j</italic>} is modeled using the Gaussian law. This way is used in mathematical modeling in quantitative genetics^{##REF##25360145##69##}where <italic>A</italic>_{<italic>j</italic>} is the normalizing constant, and <italic>D</italic>_{<italic>w</italic>} is the width of the kernel which determines the heritability of boldness. In particular, in the extreme cases where <italic>D</italic>_{<italic>w</italic>} ≫ 1, we have uniform mixing, whereas for <italic>D</italic>_{<italic>w</italic>} ≪ 1 we have clonal reproduction.</p>", "<p id=\"Par50\">We assume that the dimensionless function <italic>ν</italic>(<italic>B</italic>), accounting for boldness in the search for shelters, is described via the sigmoid functionHere <italic>μ</italic> &gt; 2 and 0.1 &lt; <italic>B</italic>_{<italic>ν</italic>} &lt; 0.7 are model parameters. Very shy individuals do not attempt to invade occupied shelters, with <italic>ν</italic>(0) = 0, while <italic>ν</italic>(<italic>B</italic>) is an increasing function of <italic>B</italic> with an inflection point at an intermediate value of <italic>B</italic>, so that individuals with maximal boldness <italic>B</italic> = 1 attempt to invade at a rate close to 1. Along with the above sigmoid function, we briefly explored the model predictions for two more scenarios, in particular for <italic>ν</italic>(<italic>B</italic>) = <italic>B</italic>, <italic>ν</italic>(<italic>B</italic>) = <italic>B</italic>(1 + <italic>B</italic>_{<italic>ν</italic>})/(<italic>B</italic>_{<italic>ν</italic>} + <italic>B</italic>), which are a linear and a hyperbolic functions, respectively.</p>", "<p id=\"Par51\">For our system comprising trout and its parasites, we estimated model parameters using available empirical data (see the next subsection below). We summarize the meanings of all model variables, functions, and parameters, as their values and units in Table ##TAB##0##1##.</p>", "<p id=\"Par52\">In the case where a single strain of a certain boldness is present (i.e. the population is monomorphic), the model equation for the total population density <italic>F</italic> substantially simplifies to becomeIn Supplementary Note ##SUPPL##0##4##, it is shown how the above equation can be obtained directly using similar steps of reasoning as for the polymorphic population.</p>", "<p id=\"Par53\">We also study the evolution of boldness using the adaptive dynamics framework^{##UREF##18##25##,##UREF##19##26##,##UREF##45##70##}, which considers the long-term evolutionary outcome of the invasion of a rare mutant with boldness into the environment formed by a resident. The outcome is characterized by invasion fitness (defined as the long-term average growth rate of a rare invading mutant), where positive fitness indicates a successful invasion, with the mutant displacing the resident. This process occurs iteratively, with successive mutant invasions which, when successful, exclude the resident^{##UREF##20##27##–##UREF##22##29##,##UREF##45##70##}. Pairwise Invasibility Plots^{##UREF##46##71##} (PIPs) are graphical illustrations of the invasion success of potential mutants, displaying all the mutant traits for which the invasion fitness is positive, i.e. a successful invasion, for each resident. These PIPs suggest the subsequent evolutionary behavior of an evolutionary singularity^{##UREF##20##27##,##UREF##22##29##}. The singularities can either be stable (an evolutionary attractor), unstable (an evolutionary repellor), or a branching point. We stress that evolution modeling involves adding an extra timescale, the evolutionary time scale, which is much slower than the demographic one. More information on the adaptive dynamics framework is provided in Supplementary Note ##SUPPL##0##5##.</p>", "<p id=\"Par54\">The corresponding computer codes for numerical simulations are available in ref. ^{##UREF##47##72##}.</p>", "<title>Biological system and experimental design</title>", "<p id=\"Par55\">Rainbow trout, <italic>Oncorhynchus mykiss</italic>, a commonly farmed fish across the globe, is known to serve as a suitable intermediate host for a trematode <italic>Diplostomum pseudospathaceum</italic>^{##REF##4415952##73##,##REF##21061592##74##}. The entire life cycle of the parasite is presented in Supplementary Note ##SUPPL##0##1##, Fig. ##SUPPL##0##S1##. Cercariae of <italic>D. pseudospathaceum</italic> mainly infects fish by entering through the gills^{##REF##24411014##31##}. This parasite is not horizontally transmitted between individual fish. After infection, metacercariae grow and develop in the lenses of the fish’s eyes. Mature, infective metacercariae produce alterations in host behavior, making fish more vulnerable to predation by piscivorous birds, the final hosts of <italic>D. pseudospathaceum</italic>^{##REF##20051120##18##,##UREF##23##32##,##UREF##48##75##}. The rate of infection can be quantifiable by the number of metacercariae in the eye lenses, which will be positively correlated to an increase in mortality from predation^{##REF##20051120##18##,##UREF##23##32##,##UREF##48##75##}.</p>", "<p id=\"Par56\">The fish specimens of rainbow trout used in our experiments were obtained from a commercial fish farm in Finland, where they were reared in indoor tanks supplied with groundwater and were free of <italic>D. pseudospathaceum</italic> infection. The mean ± s.d. fish fork length (FL) of Young-Of-the-Year (YOY) fish was 86.4 ± 9.2 mm. FL is the length of the fish measured from the tip of the snout to the end of the middle caudal fin rays. Prior to the experiments, about 400 fish were kept in a flow-through tank of 2.5 m³ on 15:9 L : D cycle at 15–16 °C; fed with commercial pelleted food (1.5 mm size, Nutra Parr LB, Norway).</p>", "<p id=\"Par57\">Cercariae of <italic>D. pseudospathaceum</italic> were obtained from 14 naturally infected <italic>Lymnaea stagnalis</italic> snails (the first intermediate host of the parasite) collected from Lake Konnevesi. <italic>D. pseudospathaceum</italic> is the only diplostomid species found in this snail in Lake Konnevesi^{##REF##20804859##76##,##REF##21554995##77##}. Snails were kept in a refrigerator at 7 °C and transferred to the laboratory conditions (at 18 °C, daylight) to induce cercariae production. We pooled all cercariae produced within 6 h and estimated their density from ten 1-ml subsamples of the suspension. The infectivity of <italic>D. pseudospathaceum</italic> cercariae did not decrease even 10 h after shedding at 20 °C^{##REF##12964824##78##}.</p>", "<p id=\"Par58\">Before exposure to parasites, 120 fish were sorted according to their behavioral trait which we define as ‘reactivity’. Fish were placed individually into a novel compartmentalized tank, and the time before fish moved from one compartment to another was recorded. If the fish stayed longer than 30 min in the initial compartment, they were unused in further experiments. Fish were considered ‘fast’ (more reactive) if it took them 5 or fewer minutes to move to a different compartment, and ‘slow’ (less reactive) if they stayed longer. Overall, 55 fish were considered as ‘fast’, and 57 as ‘slow’. The frequency distribution of the reaction time, i.e. the time before a fish moved to the other compartment, across the experimental fish population, is presented in Supplementary Note ##SUPPL##0##2##, Table ##SUPPL##0##S1##.</p>", "<p id=\"Par59\">Experiments were conducted at the Konnevesi Research Station, University of Jyväskylä, in July-August 2012 (Exp. 1) and August 2013 (Exp. 2) to answer the questions below. Descriptions of the experimental settings are provided below. For the raw data in each experiment see Supplementary Note ##SUPPL##0##3##, Tables ##SUPPL##0##S2##–##SUPPL##0##S5##.</p>", "<p id=\"Par60\">(Exp.1) Infection rates in fast and slow fish. Fish from both groups were infected individually in 2-liter tanks and then kept in separate 10-L flow-through tanks. 40 fast and 40 slow fish were exposed to parasites at the concentration of 200 cercariae per liter for 15 min. To check whether individual vulnerability to parasites was consistent, we exposed fish to the same concentration of cercariae 12 days after the 1^st infection. 20 fast and 20 slow fish (different individuals from the previous experiment) were used. Parasites acquired during the 1^st and 2^nd infection were recognized by their size, morphology and motility. We used a structured habitat and fish in groups to better understand the differences in behavior, i.e. individual variation in their ability to avoid parasitized areas (Supplementary Note ##SUPPL##0##3##). We used a homogeneous environment to explore innate physiological (non-behavioral) differences of individual fish in terms of their vulnerability to infection.</p>", "<p id=\"Par61\">(Exp.2) Variation of infection burden of fish under different anticipated threats. In all experiments, fish were threatened by the novelty of the environment, which is known as an efficient stressing factor^{##REF##21676791##79##–##REF##24198397##81##}. To assess the vulnerability of fish to <italic>D. pseudospathaceum</italic>, we compared infection rates in fish demonstrating either territorial or grouping behavior with that of a solitary fish deprived of shelters and conspecifics. Solitary fish were tested over either a dark or light bottom. The white background is assumed to be more stressful than the dark one over which fish are cryptic^{##REF##20051120##18##}. We tested individual fish or a group of 5 fish in the open field arena and individual fish in a tank with a covered shelter on the bottom. The tests on solitary fish were carried out in 10 l light or dark plastic tanks and light tanks with cover shelter on the bottom. Groups of fish were tested in 50 l light plastic tanks. Fish were exposed to 100 ind l⁻¹<italic>D. pseudospathaceum</italic> cercariae for 20 minutes after 30 minutes of acclimation. Twenty replicates of each of the trials were completed. In each experiment, we used random (unsorted) mixed groups of fish, in terms of their reaction time. (for details see Supplementary Note ##SUPPL##0##3##, Table ##SUPPL##0##S5##)</p>", "<p id=\"Par62\">The choice of the group size (4 to 5 fish) in the above experiments was related to the number of individuals necessary to initiate social relations^{##UREF##49##82##} in the tank of 0.51 m² bottom and volume of 180 <italic>l</italic>. Such fish densities of YOY salmonids are typical of nursery grounds^{##UREF##50##83##} and experimental studies^{##UREF##51##84##}. Too high or too low density could provoke abnormal behavior^{##UREF##49##82##}. The chosen concentration of parasites is commonly used in experimental infections of salmonid fish^{##UREF##23##32##}. This concentration is within the range reported in a natural environment^{##UREF##52##85##,##REF##4825437##86##}.</p>", "<title>Estimation of model parameters</title>", "<p id=\"Par63\">Here we estimate model parameters for the considered biological system of rainbow trout and its parasites. Note that in the case where we could not find the accurate values of parameters for the above-mentioned system, we consider broader data ranges available for salmonids, or other fish families.</p>", "<p id=\"Par64\">We consider a habitat with the area of 10⁴ m² = 1 ha. For simplicity, we assume that the habitat has a square shape. This corresponds to the estimate for the carrying capacity to be <italic>K</italic> = 10⁴\n<italic>i</italic><italic>n</italic><italic>d</italic><italic>i</italic><italic>v</italic><italic>i</italic><italic>d</italic><italic>u</italic><italic>a</italic><italic>l</italic><italic>s</italic> of fish (of all age categories) in absolute numbers within the considered area^{##UREF##53##87##,##UREF##54##88##}. We allow <italic>K</italic> to vary within the range of 10³ &lt; <italic>K</italic> &lt; 2.5 ⋅ 10⁴\n<italic>i</italic><italic>n</italic><italic>d</italic><italic>i</italic><italic>v</italic><italic>i</italic><italic>d</italic><italic>u</italic><italic>a</italic><italic>l</italic><italic>s</italic>.</p>", "<p id=\"Par65\">The reproduction rate for salmonids can be estimated from the data on the recruitment/stock ratio^{##REF##22505845##89##–##UREF##56##91##}. Empirical observation provides the following range for the ratio between the number of age 1 rainbow trout individuals and the number of fish in the stock: 5–150 (measured at low stock density). Assuming that reproduction occurs annually, this signifies for the annual growth rate <italic>b</italic>₀ to vary within 1.6 &lt; <italic>b</italic>₀ &lt; 5 year⁻¹.</p>", "<p id=\"Par66\">The natural mortality <italic>m</italic>₀ of the rainbow trout can be estimated to vary from 0.6% to 2% per month^{##REF##34449889##92##}. This gives the estimated mortality rates to be approximately 0.07 &lt; <italic>m</italic>₀ &lt; 0.25 year⁻¹. Note that similar mortality values are reported for the Atlantic salmon^{##REF##34449889##92##}.</p>", "<p id=\"Par67\">The mortality due to parasites and predators is more variable, and its value largely depends on the abundance of natural enemies. For salmonids, recapture data estimate the ratio between the parasite/predator-induced mortality and the natural mortality to vary between 1.5 and 50^{##UREF##57##93##–##REF##36695034##95##}. This ratio is highly variable throughout the year, therefore a more correct estimation should include averaging over the period of observation, which reduces the upper bound to approximately 10. For the non-sheltering (shoaling) fish, this gives an approximate range of 0.1 &lt; Δ_{<italic>S</italic>} &lt; 2.5 ye<italic>a</italic><italic>r</italic>⁻¹. The mortality due to parasites and predators for the sheltering fish can be roughly estimated using the empirical results of the current study, showing that the parasite load for the sheltering fish is 1.5–2 times smaller as compared to the shoaling individuals. Also, we should keep in mind that sheltering individuals will have a smaller predation risk. This gives the following range 0.05 &lt; Δ_{<italic>T</italic>} &lt; 1.6 year⁻¹.</p>", "<p id=\"Par68\">The reduction in the cost of fighting, when defending a shelter, described by the dimensionless parameter <italic>D</italic> can be estimated as follows. It is known that residents (shelter owners) are less stressed and more familiar with surroundings than invaders, i.e. 0 &lt; <italic>D</italic> &lt; 1^{##UREF##44##66##}. Residents are known to be more efficient combatants, which spend less energy and have lower ventilation rates. The latter allows them to decrease infection rate, compared to intruders by a factor ranging from 0.4 to 0.9^{##UREF##3##4##}. By assuming mortality rates to be proportional to the infection load in the fish, we have <italic>D</italic> = 0.4. However, we allow the parameter <italic>D</italic> to vary in a broader range: 0.2 &lt; <italic>D</italic> &lt; 1.</p>", "<p id=\"Par69\">The parameter <italic>ϵ</italic>, which accounts for the difference in mortality/parasite acquisition, is hard to estimate. Our empirical data, presented in this study (Fig. ##FIG##5##6##A, B), show that this parameter is positive for the considered experimental settings, signifying that parasite acquisition decreases with boldness. Unfortunately, the obtained data do not allow us to reveal the functional dependence between <italic>ϵ</italic> and the mortality rates, therefore, here we suggest the simplest linear relationship between the mortality and the boldness. The ratio of acquired parasites between the bold and the shy groups may largely vary from 0.075 to 0.6. We assume that within the considered ranges of parasite concentration, the mortality rate is proportional to the number of parasites in the fish, in this case, <italic>ϵ</italic> ∈ (0.075, 0.6). However, we also briefly consider negative values (see Supplementary Note ##SUPPL##0##4##), as it was reported that few systems (non-rainbow-parasite systems) show a positive correlation between mortality and boldness^{##UREF##10##14##}. We also consider the case of <italic>ϵ</italic> = 0 to see how important is the dependence of the boldness on mortality for the generality of our modeling results (see Supplementary Note ##SUPPL##0##4##).</p>", "<p id=\"Par70\">The dimensionless function <italic>ν</italic>(<italic>B</italic>), relating the boldness <italic>B</italic> and the rate of search of shelters, is not well documented not only for salmonids but for other fish families. Various measurements of fish boldness exist in the literature, for example, boldness is often measured based on the time needed to emerge from a cover in experiments^{##REF##28450699##30##,##UREF##58##96##}. It was reported that bolder fish individuals are more active and persistent in their search^{##UREF##59##97##,##REF##23874804##98##} and this is related to the so-called behavioral syndrome^{##REF##21284626##99##}. Our measurements of the time of rainbow trout individuals staying undercover show a wide range of values, in particular, we can see examples of staying in the cover for a long time (see Supplementary Note ##SUPPL##0##2##, Fig. ##SUPPL##0##S2##). This is also observed in other fish species^{##REF##28450699##30##}. Therefore, we can assume that for search rate by a very shy individual (<italic>B</italic> ≈ 0), we have <italic>ν</italic>(0) ≈ 0. On the other hand, common sense reasoning tells us that at very high values of boldness, the exploration efficiency should decelerate. This can occur for several reasons. For example, bold individuals may be extra persistent in staying for a longer time in a particular location and exploring nearby objects^{##REF##29935279##100##}, whereas a more efficient search strategy would be to continue moving across the entire habitat by following other (shyer) individuals. Finally, some studies show that the exploration propensity in fish shows acceleration within the intermediate range of boldness^{##REF##28450699##30##,##UREF##59##97##}. Using the above reasoning, we considered the following sigmoid function: , where <italic>B</italic>₀ and <italic>μ</italic> &gt; 1 are positive dimensionless parameters. For <italic>B</italic>₀ we require to be close to the mid-point of the entire boldness range (<italic>B</italic>₀ = 0.5); however, we also include other values: 0.2 &lt; <italic>B</italic>₀ &lt; 0.8. In this case, we have <italic>ν</italic>(1) close to one. For <italic>μ</italic>, we are required to stay within the range 2 &lt; <italic>μ</italic> &lt; 8 to avoid a too sharp switch between the accelerating and the decelerating parts of the curve. Due to the mentioned uncertainty in the shape of the function <italic>ν</italic>(<italic>B</italic>), we also tested two other functional forms of <italic>ν</italic>(<italic>B</italic>), in particular, the linear dependence <italic>ν</italic>(<italic>B</italic>) = <italic>B</italic>, and the Monod-type hyperbolic function (we have <italic>ν</italic>(1) = 1). Using those non-sigmoid parameterizations allows us to explore the generality of our results to other biological systems.</p>", "<p id=\"Par71\">We proceed to estimating the key parameter <italic>ν</italic>_{<italic>μ</italic>}, which quantifies the extra mortality due to fish fighting for a shelter. This parameter incorporates the search rate for a shelter as well as the amount of parasites acquired by individuals due to contesting shelters. We must say that it is hard to obtain an accurate value for <italic>ν</italic>_{<italic>μ</italic>}, therefore, we are only able to provide some rough estimates. We assume that the mortality of infected fish is proportional to the amount of parasites acquired. For simplicity, we assume that each individual fish within the shoaling fraction has the same parasite load for the same value of boldness <italic>B</italic>. The same concerns the sheltering fraction of fish (note that the shoaling and the sheltering fractions may differ in terms of parasite loads). We assume (based some empirical facts, see below) that the parasite load in the shoaling or sheltering fish, measured as the number of metacercariae per individual, can be estimated using a simple differential equationwhere <italic>P</italic> is the number of metacercariae per individual, <italic>r</italic> is the maximal rate of acquisition of parasites by an individual in the absence of contests for shelters; <italic>r</italic>₁ is the maximal rate of acquisition of parasites by an individual due to contesting shelters. The term <italic>α</italic><italic>P</italic> describes the effects of saturation: it is known that an increase in the numbers of metacercariae inside a host reduces the rate of acquisition of new parasites^{##UREF##60##101##,##UREF##61##102##}, <italic>α</italic> is a positive parameter. Note that for the shoaling and the sheltering fish, the parameters <italic>r</italic>, <italic>r</italic>₁, <italic>α</italic> can differ. It is easy to show that at equilibrium (<italic>d</italic><italic>P</italic>/<italic>d</italic><italic>t</italic> = 0), the number of metacercariae per fish <italic>P</italic>^* is given byEmpirical estimates provide the following values of <italic>r</italic> in an infected environment^{##UREF##3##4##}: <italic>r</italic> = 5 <italic>metacercariae/day</italic> or <italic>r</italic> = 5 ⋅ 365 <italic>metacercariae/year</italic>. It is also known that the cost of a single fight is estimated to be about 10 or 15 metacercariae per fish^{##UREF##3##4##}. To find <italic>r</italic>₁, one needs to estimate the frequency of fighting for a single shelter by a single fish. We are unaware of direct empirical observation of the frequency of fighting of rainbow trout within the considered spatial area. Therefore, we use a combination of modeling and the existing data.</p>", "<p id=\"Par72\">We first assume that the search can be described by a simple uncorrelated random walk, often used in ecological modeling^{##REF##18426776##103##}. More sophisticated patterns of spatial motion can be considered as well as an extension of our simple approach. The corresponding equations of spatial motion of fish are given by:where <italic>X</italic>(<italic>t</italic>_{<italic>i</italic>}) and <italic>Y</italic>(<italic>t</italic>_{<italic>i</italic>}) are the spatial coordinates of the considered individual at time <italic>t</italic>_{<italic>i</italic>}; Δ_{<italic>x</italic>}(<italic>t</italic>_{<italic>i</italic>}) and Δ_{<italic>y</italic>}(<italic>t</italic>_{<italic>i</italic>}) are the spatial increments of individual’s position, when moving from time <italic>t</italic>_{<italic>i</italic>} to <italic>t</italic>_{<italic>i</italic>+1}. For the uncorrelated random walk, we have , , with <italic>L</italic>(<italic>t</italic>_{<italic>i</italic>}) being a Gaussian random variable (the length of the spatial displacement) and <italic>ϕ</italic>(<italic>t</italic>_{<italic>i</italic>}) being the angle of the direction of movement, which is uniformly distributed in the range of [0, 2<italic>π</italic>]. <italic>L</italic>(<italic>t</italic>_{<italic>i</italic>}) is described by a normal law with a zero mean and the standard deviation <italic>σ</italic>.</p>", "<p id=\"Par73\">We should stress that the above simple movement model accounts for the fact that a fish individual spends a large proportion of time in some shoal (or multiple shoals): fish can switch between shoals by leaving it during the daytime or joining a new shoal at dawn (since every evening, shoals disappear to re-emerge the next day with possibly different new members).</p>", "<p id=\"Par74\">The value of <italic>σ</italic> can be estimated based on the experiments with the release of trout with a further recapture^{##UREF##62##104##}: in 1-2 month time after a release of fish, the mean squared displacement can be estimated to very from 50 to 200 <italic>m</italic>. This gives an estimate for <italic>σ</italic> in the random walk simulations to be approximately 0.5<italic>m</italic> &lt; <italic>σ</italic> &lt; 3<italic>m</italic> (provided the time step between change of directions is approximately 20-30 min).</p>", "<p id=\"Par75\">We further estimate the frequency of finding a (single) shelter by a fish when moving randomly within the considered spatial area with impenetrable boundaries. In our modeling, we set the maximal distance for the fish to see the shelter to be 1.5 − 2m, which has empirical evidence^{##UREF##53##87##,##UREF##60##101##}. We put a single shelter at the center of the habitat, however, this is not crucial for our estimates. In our simulation, a fish starts its search from some randomly chosen starting point. We simulated our system for a long time (corresponding to several years) from 1000 different starting points. We found that the frequency of finding a single shelter varies from 4 to 28 times per year for the habitat of size of 10⁴<italic>m</italic>². This also gives an estimate for the parameter <italic>I</italic>₀ (the rate of encountering a single shelter by a single fish): 4 &lt; <italic>I</italic>₀ &lt; 28 year⁻¹.</p>", "<p id=\"Par76\">We can now estimate the value of <italic>r</italic>₁ (defined above). This value is given by the product between the number of metacercariae received by a fish in a single contest (Δ_{<italic>c</italic>} = 10 − 15 metacercariae) and the average number of the contests per year (estimated in the above paragraph), i.e. <italic>r</italic>₁ = Δ_{<italic>c</italic>}<italic>I</italic>₀. We can evaluate <italic>ν</italic>_{<italic>μ</italic>} using the estimates for Δ_{<italic>S</italic>}, based on the same assumption that the mortality is proportional to the parasite load <italic>P</italic>^*. Since, in the absence of shelters, we have <italic>P</italic>^* = <italic>r</italic>/<italic>α</italic>, and this corresponds to empirically reported values 0.1 &lt; Δ_{<italic>S</italic>} &lt; 2.5 year⁻¹ (see above estimates), adding an extra influx of parasites into the fish, modeled by <italic>r</italic>₁, should be proportional to the increase of the corresponding mortality term. This reasoning gives an estimateTherefore, we have the range of 0.02 &lt; <italic>ν</italic>_{<italic>μ</italic>}/Δ_{<italic>S</italic>} &lt; 0.2, and 0.002 &lt; <italic>ν</italic>_{<italic>μ</italic>} &lt; 0.5 year⁻¹. We also allow for some smaller values for the lower bound for <italic>ν</italic>_{<italic>μ</italic>} to take into account the fact that a fish, which can potentially see a shelter (i.e. when passing within 1.5-2 <italic>m</italic> nearby), may miss that shelter or ignore it. Therefore, we consider a wider range 0.0005 &lt; <italic>ν</italic>_{<italic>μ</italic>} &lt; 0.5 year⁻¹.</p>", "<title>Ethical note</title>", "<p id=\"Par77\">We used 0+ Oncorhynchus mykiss, with equal number males and females. The level of experimental <italic>D. pseudospathaceum</italic> infection was maintained at a much lower level than the maximum values reported for naturally occurring infections (up to 200-500 individuals per fish), see^{##UREF##52##85##,##REF##4825437##86##}. The mortality of infected fish in the experiments was less than 1% and did not exceed that of the control fish. No visible damage was observed in any fish. We minimized the required number of animals that were killed and dissected. Experimental fish were killed at the end of the tests with an overdose of MS222 and dissected. In total, 240 experimentally infected fish were killed. The experiments were conducted with the permission of the National Animal Experiment Board, Center for Economic Development, Transport and Environment of South Finland (license number ESAVI/6759/04.10.03/2011). We have complied with all relevant ethical regulations for animal use.</p>", "<title>Statistics and reproducibility</title>", "<p id=\"Par78\">The empirical data were analyzed using the Mann–Whitney U test (Exp. 1) and one-way ANOVA (Exp. 2). Prior to the analysis, the experimental data were checked for normality with Shapiro–Wilk’s W test. Tukey HSD test was applied for post-hoc pairwise comparisons (see details in Supplementary Notes ##SUPPL##0##2## and ##SUPPL##0##3##). The sample sizes represent independent biological replicates. In experiments with individual fish, replicates were defined as the infection load of each individual (measured in the number of metacercariae); in experiments with a group of fish, replicates were defined as the mean infection load of a group. The number of replicates was 20 or 40 (when comparing the infection load of individually infected fast and slow fish). The sample size in the experiment comparing infection rate in fast and slow fish (Exp. 1) was 120 fish, in the experiment on the effect of anticipated threat (Exp. 2), the sample size was 160 fish. Other relevant information is provided in Fig. ##FIG##5##6## legend as well as in Supplementary Notes ##SUPPL##0##2## and ##SUPPL##0##3##.</p>", "<title>Reporting summary</title>", "<p id=\"Par79\">Further information on research design is available in the ##SUPPL##1##Nature Portfolio Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<p id=\"Par8\">We developed a theoretical model (see Methods) exploring the role of intraspecific competition within a behaviorally structured population that resides in a hostile environment, containing parasites. The model uses parameters describing interaction between salmonids and their trematode parasites (see Methods). The meaning of the variables and model parameters is summarized in Table ##TAB##0##1##. Using the model, we assess the population density under different scenarios.</p>", "<title>Monomorphic population</title>", "<p id=\"Par9\">First, we explore the scenario, where all individuals are identical in terms of their permanent behavioral structuring, however, the population is heterogeneous dynamically in terms of defence behavior. We are interested in the dependence of the equilibrium population density <italic>F</italic>^* on the number of available safe zones (shelters) <italic>N</italic> for different levels of threat from natural enemies (parasites and predators) in the system. Fig. ##FIG##0##1##A displays the dependence of the population density <italic>F</italic>^* on shelter numbers <italic>N</italic> for various levels of abundance of natural enemies. Since the abundance of the natural enemies affects three related parameters Δ_{<italic>T</italic>}, Δ_{<italic>S</italic>} and <italic>ν</italic>_{<italic>m</italic>} (mortality rates), we consider that variation of one parameter (e.g. Δ_{<italic>T</italic>}) results in a proportional change of the other two. The figure shows that for larger levels of top-down regulation leading to higher mortality (Δ_{<italic>T</italic>} = 1.1 year⁻¹) individuals cannot survive in shoals and the population size approximately equals the number of shelters, <italic>F</italic>^* ≈ <italic>N</italic>. In this case, installing artificial shelters in the environment would therefore be highly beneficial. For lower levels of natural enemies, we observe an initial decrease in <italic>F</italic>^* when installing few shelters. For a further increase in <italic>N</italic>, after passing the minimal density, the population density starts increasing and, eventually, for large <italic>N</italic> it becomes larger than its value in the absence of shelters.</p>", "<p id=\"Par10\">In Fig. ##FIG##0##1##B, the amount of natural enemies in the system is fixed, with the cost of contesting shelters <italic>ν</italic>_{<italic>μ</italic>} being varied. Note that the parameter <italic>ν</italic>_{<italic>μ</italic>} combines the effects of the cost of fighting and the frequency of finding a shelter (see Methods). At low <italic>ν</italic>_{<italic>μ</italic>}, adding shelters in the environment only results in a small drop in <italic>F</italic>^*. Higher values of <italic>ν</italic>_{<italic>μ</italic>} (high costs of a contest or/and fast rates of finding a shelter) result in a pronounced drop in the population density after adding shelters. Our simulations of the model for other values of parameters do not qualitatively change the patterns shown in Fig. ##FIG##0##1## (see Supplementary Note ##SUPPL##0##8##, Figs. ##SUPPL##0##S6##–##SUPPL##0##S12)##. Overall, the model suggests that only the creation of a sufficiently high number of shelters in the environment would increase the population density compared to the homogeneous habitat (<italic>N</italic> = 0). The detrimental impact of introducing an insufficient number of shelters is related to the conflict between individuals contesting shelters: fighting for shelters results in higher mortality imposed by parasites and predators. However, increasing the number of shelters at some point can compensate the negative effect of contests: the losses due to fighting for shelters become smaller than the benefits of staying in shelters.</p>", "<title>Polymorphic population</title>", "<p id=\"Par11\">Now we consider a population that combines a permanent behavior structuring, which we denote by the term ‘boldness’, with dynamical structuring in terms of defence strategy. The total population density at equilibrium is plotted as a function of the number of shelters <italic>N</italic> (see Fig. ##FIG##1##2##). In the example, we consider <italic>n</italic> = 20 different strains of boldness for varying values of <italic>D</italic>_{<italic>w</italic>}, describing the strength of heredity of the boldness trait. For comparison, we also show the curve corresponding to the monomorphic population with boldness <italic>B</italic> = 0.5. One can see that in a behaviorally polymorphic population, adding shelters does not cause as drastic a drop in the population density compared to the monomorphic scenario. For a clonal reproduction scenario, the introduction of shelters did not affect the total population density. With uniform genetic mixing, the effect of adding shelters becomes beneficial for some large numbers of shelters (&gt;25% of the carrying capacity) since the population density is larger than in a fully homogeneous environment.</p>", "<p id=\"Par12\">The fact that a large drop in <italic>F</italic>^* is not observed in a polymorphic population—contrary to the monomorphic scenario—can be elucidated by plotting the normalized distributions of boldness for varying values of <italic>N</italic> and <italic>D</italic>_{<italic>w</italic>}. The results are shown in Fig. ##FIG##2##3##. For clonal reproduction (Fig. ##FIG##2##3##A), the introduction of shelters in an initially homogeneous habitat triggers the emergence of two peaks in the distribution: one corresponding to intermediate values of boldness and the other one having the maximal boldness 1. Simulations show that individuals from the less-bold cohort mostly stay in the shoal, whereas shelters are occupied by the cohort with maximal boldness. The boldness of this shoal-based strain is the maximal boldness such that individuals can coexist in the shoal without competing with the bolder cohort for their shelter. This lack of competition between the shoal-based and the shelter-based individuals drastically drops the mortality as compared to the scenario with a monomorphic population, where all shoal-based individuals are constantly in competition for shelter. This is because shy individuals avoid contests with bold ones. Analytical computation using a simplified model confirms that for cohorts with distinctly different boldness, the total population density <italic>F</italic>^* is independent of <italic>N</italic> (Supplementary Note ##SUPPL##0##6##).</p>", "<p id=\"Par13\">For a non-clonal inheritance of boldness, distributions of boldness become more even (see Fig. ##FIG##2##3##B). This is especially true for uniform genetic mixing (Fig. ##FIG##2##3##C). For a small number of shelters (<italic>N</italic> ≪ <italic>F</italic>^*(0)), individuals with a high degree of boldness are rare. Adding more shelters generally results in the emergence of a gap between bold and shy cohorts, with a larger proportion of bold individuals. We also find that shelters are mostly occupied by bold individuals (see Fig. ##FIG##2##3##D, E). This reduces the negative effects of competition for shelters. An important feature of the distributions in Fig. ##FIG##2##3##B, C is the absence of a single dominant cohort for values of <italic>N</italic>, which corresponded to the drop in <italic>F</italic>^* in a monomorphic population. This largely reduces the mortality caused by contests for shelters in a polymorphic population. The eventual dominance by high-boldness cohorts for very large <italic>N</italic> (e.g. &gt;25% of the carrying capacity) does not have pronounced negative impacts on the population density since in this case most of the population would use territorial tactics and stay in shelters. The lower peaks are dampened due to reproductive mutations, governed by the value of <italic>D</italic>_{<italic>w</italic>}, if mutations occur often (e.g. for <italic>D</italic>_{<italic>w</italic>} = 0.02) then selection cannot maintain the two distinct strains of boldness.</p>", "<p id=\"Par14\">When shelters become abundant in the environment, the total population density increases when genetic mixing is pronounced, especially for uniform mixing (Fig. ##FIG##1##2##). The reason for this is that for large <italic>N</italic>, the proportion of the population with bold behavior becomes dominant; those individuals -mostly occupying shelters- largely contribute to the reproduction of the shy cohorts, which in turn, mostly use the shoaling tactics. As a result, the per capita growth rate of shy cohorts increases, whereas their contribution to the production of bolder individuals decreases. This leads to an increase in the total population density. The above reasoning is confirmed by analytical computation in a simplified model with uniform mixing of two strains (Supplementary Note ##SUPPL##0##6##). The effect of increasing <italic>F</italic>^* for large <italic>N</italic>, however, is not observed in a structured population with clonal reproduction (Supplementary Note ##SUPPL##0##6##, Fig. ##SUPPL##0##S4##). Extensive simulation of the model shows that variation of key model parameters does not qualitatively change the patterns obtained for the polymorphic population (see Supplementary Note ##SUPPL##0##8##, Figs. ##SUPPL##0##S13##–##SUPPL##0##S17##).</p>", "<title>Impact of behavioral structuring on the success of natural enemies</title>", "<p id=\"Par15\">We briefly explore the effects of behavioral structuring in the population on the success of its natural enemies. Here we focus on the proliferation of parasites in the environment. We do not model the dynamics of parasites explicitly but quantify the success of parasites using parasite-induced mortality as a proxy for parasite fitness. Figure ##FIG##3##4## shows the dependence of the total parasite-induced mortality on the number of shelters for both monomorphic and polymorphic populations. For convenience, we separately plot the parasite-induced mortality due to fighting for shelters and the mortality, induced by parasites, when staying in the shoal or shelters.</p>", "<p id=\"Par16\">Although the parasite-induced mortality due to contesting shelters is higher for a monomorphic population (Fig. ##FIG##3##4##B, D), the total parasite-induced mortality is larger for a polymorphic population (Fig. ##FIG##3##4##A). This occurs since the total number of potential hosts exploited by parasites is smaller for a monomorphic population due to a dramatic drop in the overall host population density. The proportionality between the fighting parasite-induced mortality and population density (or potential hosts) can explain the intermediate drop in the mortality for the monomorphic population (dashed blue curve in Fig. ##FIG##3##4##D). This signifies that having bold and shy individuals within a population should increase the transmission of parasites in the system, thus increasing their reproduction success. For a monomorphic population, a reduction in the number of shelters may reduce the total amount of parasites in the environment.</p>", "<title>Evolutionary branching as a possible scenario of behavioral structuring</title>", "<p id=\"Par17\">Next, using mathematical modeling, we address the fundamental question about a possible scenario of emergence of bold/shy strains as a result of evolution. In fact, evolution of boldness is largely related to expression of particular receptors in the brain of the fish, which is considered to be fast and energetically cheap process^{##REF##17182101##23##,##UREF##17##24##}. Boldness is related to other traits, such as exploration, defence, foraging, and other behaviors. Therefore, by considering evolution of boldness, we take into account evolution of the above mentioned traits, which substantially influence fitness and mortality. For the sake of simplicity, we assume clonal reproduction and implement the adaptive dynamics framework^{##UREF##18##25##,##UREF##19##26##} outlined in Supplementary Note ##SUPPL##0##5## (see also Methods). We start with an initially monomorphic population characterized by a single boldness strain <italic>B</italic>. The expression for invasion fitness, measuring the success of mutations, is derived in Supplementary Note ##SUPPL##0##5##. Using the invasion fitness, we construct a Pairwise Invasibility Plot (PIP) to reveal any evolutionarily singular points. A typical PIP is shown in Fig. ##FIG##4##5##A. The figure shows two possible evolutionarily singularities at which the gradient of invasion fitness vanishes, the larger of which is an evolutionary repeller, the smaller of which is convergence stable but not evolutionarily stable, suggesting evidence of branching behavior whereby the initially monomorphic population becomes dimorphic and separates into shy and bold cohorts^{##UREF##20##27##–##UREF##22##29##}.</p>", "<p id=\"Par18\">We simulated the evolution of boldness, starting with a single strain of intermediate boldness <italic>B</italic> = 0.5. The evolutionary outcome is shown in Fig. ##FIG##4##5##B, where the vertical axis denotes evolutionary time, as represented by the succession of mutation events in the system. The boldness initially evolves as a monomorphic population towards the smaller evolutionary singularity (<italic>B</italic> = 0.2). However, having reached the neighborhood of this point, the monomorphic strain exhibits branching behavior, and two distinct branches of coexisting boldness strains emerge. Further evolution results in the bolder strain achieving its maximum boldness of 1, whereas the shyer branch evolves to the boldness of approximately <italic>B</italic> = 0.6. Note that this behavior is observed only when the initial boldness is less than the evolutionary repellor in Fig. ##FIG##4##5##A, otherwise, we observe a monomorphic population evolving to the maximal boldness. The mechanism seen here is possible for a small and intermediate, as compared to <italic>F</italic>^*(0), numbers <italic>N</italic>. This suggests evolutionary branching as a possible explanation for the emergence of several strains in the population when the competition for shelters is strong. We checked the influence of the relation between mortality and boldness (measured by <italic>ϵ</italic>) on evolutionary branching. We found (see Supplementary Note ##SUPPL##0##8##, Figs. ##SUPPL##0##S22##–##SUPPL##0##S25##) that branching behavior is possible for both negative and positive <italic>ϵ</italic>, as well as in the absence of such a relation (<italic>ϵ</italic> = 0).</p>", "<p id=\"Par19\">In our simulations, the evolutionary branch with the highest boldness approaches its maximal possible level of <italic>B</italic> = 1. A more accurate (but more sophisticated) model should include negative effects of being ‘too bold’. For example, bold animals often have increased risk of predation due to underestimation of risk, also their reproduction rate may be reduced due to very frequent contests with conspecies^{##REF##28450699##30##}. This can be incorporated in the model by multiplying the corresponding term by a function, which would abruptly reduce the fitness close to the boundary <italic>B</italic> = 1. Our preliminary simulation shows that the evolutionary trajectory will never reach the critical boundary in this case. However, to avoid unjustified complexity, we prefer to use the original simplified model predicting the trajectory approaching the highest values of boldness.</p>", "<p id=\"Par20\">For abundant sheltering (<italic>N</italic> is of the same order of magnitude as <italic>F</italic>^*(0)), branching behavior does not occur. Instead, a single strain evolves towards the trait with maximal boldness; in this case, we observe a severe reduction in the equilibrium population <italic>F</italic>^* as in the monomorphic population. Even in the absence of a branching point, however, starting from a configuration of multiple initial strains can lead to the coexistence of bold and shy strains (e.g. Fig. ##FIG##2##3##). Thus, for large <italic>N</italic>, the system is evolutionary bi-stable, as the outcome will depend on the initial presence of strains.</p>", "<title>Empirical case study: interactions between rainbow trout <italic>Oncorhynchus mykiss</italic> and trematodes</title>", "<p id=\"Par21\">A straightforward application of the above theory can be commercial fish farming, which is often affected by parasite contamination in the environment. We explore a particular case study of the interaction between rainbow trout and trematode parasites as well as the role of artificial shelters installed in fish farms. The biological system of rainbow trout <italic>Oncorhynchus mykiss</italic> and its trematode parasite, eye-fluke <italic>Diplostomum pseudospathaceum</italic>, is briefly discussed in the Methods section along with experimental design. Previous studies indicate a high cost of fish fighting for shelters^{##UREF##3##4##}. Here we experimentally explore a few key aspects of this system which have remained unaddressed so far, namely: (i) whether parasite acquisition consistently varies between individual fish with permanent behavioral structuring (measured in terms of reactivity of individuals) infected individually and in groups, and (ii) difference in infection rates between fish possessing a shelter and groups in open water (this is related to dynamic behavioral structuring). Measuring the reactivity of individual fish is discussed in Supplementary Note ##SUPPL##0##2##. In short, fish were divided into two groups, ‘fast’ and ‘slow’; more reactive fish faster resumed their activity in a novel environment. Our novel experimental findings are the following:<list list-type=\"simple\"><list-item><label>(i)</label><p id=\"Par22\">For both individual and group scenarios of infection, fast (more reactive) individuals received a lower, on average, parasite load compared to slow (less reactive) specimens. The results are, graphically, presented in Fig. ##FIG##5##6##A, B, where we show the total amount of parasites (measured in terms of the number of metacercariae in the eyes) received by each category of fish. We also present separately the outcome (intensity of parasitism) of the first and the second rounds of infection of each particular individual fish used in the experiments (see Supplementary Note ##SUPPL##0##3##, Fig. ##SUPPL##0##S3##). This demonstrates an overall consistency of the vulnerability of individuals to parasite infection: there is a positive correlation between the number of parasites received in the first and second infection of the experiment.</p></list-item><list-item><label>(ii)</label><p id=\"Par23\">We consider four types of habitats with increasing levels of anticipated threat by fish (a description of the habitats can be found in Supplementary Note ##SUPPL##0##3##). Figure ##FIG##5##6##C shows that infection load with <italic>D. pseudospathaceum</italic> metacercariae gradually increases as fish anticipate more threats from a hostile environment, with the best defence behavior being to stay in a covered shelter. The smallest infection load is observed when individuals stay in a covered dark shelter, while parasite load increases for fish staying in a group in the open water and adopting shoal tactics. The largest parasite load is observed for solitary fish when the bottom is light. Our observations indicate that the gradual increase in parasite load is due to an increased stress response in the fish with higher anticipation of threat, resulting in a higher ventilation rate^{##REF##24411014##31##}.</p></list-item></list></p>", "<p id=\"Par24\">From our empirical study, we conclude that (a) slow (shy) fish, on average, receive more parasites than fast (bold) fish. In other words, there is a negative correlation between reactivity and the parasite load. A possible explanation is that slow fish are more often and easily stressed by various biotic and abiotic factors, e.g., exposure to a new environment. The main mechanism is that when stressed, fish increase their ventilation rate and more cercariae can be transported through the gills^{##REF##24411014##31##} (more detail are provided in the Discussion section). We found that (b) sheltering defensive strategy provides better protection against parasites as compared to shoaling. We show, as well, that (c) for an individual fish, vulnerability to parasite infection remains relatively constant over time.</p>", "<p id=\"Par25\">The above experimental results, as well as some previous empirical research (see refs. ^{##UREF##3##4##,##REF##24411014##31##}), provide support for the implementation of our theoretical model to mimic rainbow trout-trematode interactions in fish farms. The parameters of the model are discussed in Methods. We should stress, however, that linking the experiments and the model requires the suggestion that an increased parasite load signifies increased mortality via predation. This suggestion is confirmed by the previously published evidence that parasites enhance the susceptibility of fish to predation (e.g. by piscivorous birds) through host manipulation (e.g.^{##UREF##23##32##}). Therefore, we can conclude that the mortality in a shelter should be lower than that in the shoal (Δ_{<italic>S</italic>} &gt; Δ_{<italic>T</italic>}), and there is a negative correlation between parasite-induced mortality and the reactivity of individuals, interpreted as boldness (<italic>ϵ</italic> &gt; 0). This information was used in parameterization of the theoretical model.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par26\">Our theoretical model shows that in a hazardous environment, the dynamical structuring of a population in terms of using different behavioral tactics, where one tactic requires access to some limited resource, may have negative consequences on the population’s survival. Even if the resource itself is highly beneficial to each user, insufficient level of this resource may have a negative impact at the population level due to strong intraspecific competition. Therefore, the provision of extra vital resources in insufficient amounts could act as poison for the proliferation and success of the population. Only in a very hostile environment, where population persistence would not be possible without adding a particular resource (e.g. safe zones) would the use of such a resource be justified. For fish-parasite interactions, the vital resource includes shelters which provide an individual with a physical defence against predators but also substantially reduce the stress of the organism^{##UREF##12##16##,##REF##24411014##31##}, which in turn, results in a lower infection load (see Fig. ##FIG##5##6##C). Therefore, the model predicts that installing an insufficient amount of shelters in fish farms will be counter-productive since it will increase the exposure of the population to natural enemies (parasites and predators).</p>", "<p id=\"Par27\">We apply our theoretical model to explore the interaction between salmonids and their parasites. However, we also expect that similar mechanisms should be generic for other fish-parasite interactions. The main mechanism driving the intense infection of fish in a heterogeneous environment is the dynamical structuring of the population in terms of their antipredator behavior: using either shoaling or sheltering. The negative effect of dynamical structuring in fish is amplified by a ‘ghost’ of predation: individuals prefer shelters to the shoal even in the physical absence of predators, and when shelters provide a higher risk of infection than the surrounding environment^{##UREF##3##4##}. Therefore, only in the case where a large proportion of the entire fish population in a farm is sheltered can one expect a positive response to the use of shelters. Alternatively, when the level of parasites in a fish farm is very low, adding shelters becomes always beneficial.</p>", "<p id=\"Par28\">Another ecological application is the restoration of endangered natural fish populations in shallow water habitats, which serve as nursery grounds for various young fish species with flexible behavior, including salmonids in the freshwater phase. When an insufficient number of contestable resources (shelters, food patches) are introduced, fish start fighting for them, making themselves more vulnerable to natural enemies. Habitat enrichment is an important part of the restoration of nursery grounds for juvenile salmonids and marine fish^{##UREF##2##3##,##UREF##24##33##–##UREF##26##35##}, thus our study suggests a hypothesis (to be tested empirically) that only an optimal pattern of habitat enrichment can facilitate the availability of vital resources to fish without increasing vulnerability to predators and parasites. The proposed theoretical framework can be used to explain the observed population density of some species of coral fish^{##UREF##15##21##}, which contest refuges in corals. The model predicts that a gradual decrease in shelters due to the degradation of a coral reef would result in a severe drop in population density.</p>", "<p id=\"Par29\">Finally, one may arguably apply the theoretical approach to modeling the social dynamics of humans, competing amongst each other for scarce jobs in certain prestigious companies and/or organizations (in place of shelters) in a hostile financial climate and under societal pressure. In this case, the shoal should be understood as a less desirable job or profession (e.g. a scholar can move from science to industry) due to disappointment and high competition with colleagues. Mortality should be understood as a person giving up their profession entirely (i.e. retirement or moving to a completely new career field).</p>", "<p id=\"Par30\">Allowing for individual behavioral variability gives different outcomes to a single strain scenario. The detrimental effects on the population density due to an insufficient number of shelters are largely compensated for permanent behavioral structuring in boldness, or more generally, a behavioral syndrome around such structuring can efficiently mediate the negative effects of dynamical structuring in defense tactics. The key factor in the interplay between permanent and dynamical structuring is the boldness-based hierarchy of competitive dominance: shy individuals do not contest shelters occupied by bold ones, largely decreasing the number of contests for shelters and lowering the mortality of individuals staying in the shoal. This mechanism of mortality reduction seems to be generic, holding even when bold and shy individuals are only different in terms of their competitive dominance but are identical regarding their mortality rates. Our results lead us to conclude, however, that even for a population with distinct boldness cohorts, a sufficiently large number of shelters needs to be installed, or provided by the environment, before the population density will be effectively increased. For a polymorphic population, however, this critical number of shelters should be smaller than for a monomorphic one. The existence of a shy/bold axis of behavioral variation has been reported in a large number of species in their responses to different external stimuli, such as exploration for resources, mating, or avoidance of natural enemies^{##UREF##27##36##–##UREF##29##38##}. In some fish species, boldness is amplified by the presence of predators and parasites but disappears when fish are in social and ecological isolation^{##UREF##5##6##,##REF##9790704##39##}. Our model predicts that increased boldness in the presence of natural enemies should act as a mechanism for reducing population mortality.</p>", "<p id=\"Par31\">Previously, it was shown that the structuring of a population, in terms of boldness, can have a wide range of ecological consequences, including stationary population dynamics, such as stability or stationary densities^{##REF##22239107##40##,##REF##22727728##41##}. Bolder behavior might stabilize the system through an increase in competition^{##REF##22239107##40##}, but it has also been suggested that bolder strains may destabilize an equilibrium due to their fast-changing dynamics^{##UREF##30##42##}. Behavioral structuring may also have potential impacts on equilibrium density: interaction rates, such as fighting, may increase as bolder individuals are more active^{##REF##22239107##40##,##REF##19341130##43##}, but intraspecific competition may also decrease if the distinct strains use different resources and habitats^{##REF##22727728##41##}. Kendall and collaborators^{##UREF##10##14##} considered a theoretical model describing the dynamics of a behaviorally heterogeneous population comprising two strains with different boldness. Their main conclusion was that in low-predation environments, the equilibrium abundance of the population will be smaller than in environments with higher predation. The main mechanism of the increase of the population density in a highly hostile environment seen in^{##UREF##10##14##} is a reduction in aggression by bold cohort individuals in the presence of large numbers of predators. Our simulation shows the opposite outcomes for variation of density with a gradual increase of parasite/predator levels in the environment. The mismatch between the model predictions can be potentially explained by the difference in model structures. We consider the same reproduction rate for all individuals, the reproduction kernel in our model is assumed to be frequency independent, and we assume a hierarchy of competitive dominance when modeling contests between individuals of different cohorts.</p>", "<p id=\"Par32\">Previous studies revealed possible mechanisms for the emergence of diversity in animal personality traits, such as boldness, aggressiveness, or risk-taking behavior. Trade-offs between current and future reproduction potential have been shown to lead to behavioral structuring in the long term^{##REF##17538618##44##}. Another possible mechanism is the variability of metabolic rates for different individuals^{##REF##24107368##45##}. Behavioral structuring can be a consequence of a variable or noisy environment: differing behavioral traits can be a response to external stimuli, with some individuals being far more responsive to these changes than others^{##UREF##31##46##,##REF##18838685##47##}. A combination of both metabolic rates and responses to external stimuli has also been proposed to drive the emergence of behavioral traits, termed the Pace-Of-Life Syndrome (POLS) hypothesis: individuals with a fast POLS will grow faster and die earlier than those with a slower POLS due to a more intense metabolism and a higher mortality risk^{##REF##29311619##48##}. Finally, it has been suggested that individual differences in trust and trustworthiness can be explained by the feedback in cooperation among individuals driven by communication and ‘social awareness’^{##UREF##32##49##,##UREF##33##50##}.</p>", "<p id=\"Par33\">To the best of our knowledge, our system reveals a novel mechanism for the emergence and maintenance of behavioral structuring. The proposed scenario is the result of the interplay of three factors: (i) the spatial heterogeneity, generating two different types of anti-predator defence: shoaling and territorial behavior; (ii) strong intraspecific competition for a better spatial resource: shelters; (iii) the boldness hierarchy determines the outcome of competition for a shelter. The first two factors are amplified by a high level of natural enemies such as parasites and predators. Intensive intraspecific competition has, so far, rarely been considered a major factor in the coexistence of bold and shy strains in the literature. Importantly, the branching behavior, which results in the emergence of two or more types of coexisting strains, seems to be generic since it is observed for both <italic>ϵ</italic> &gt; 0 and <italic>ϵ</italic> &lt; 0, and in the case with <italic>ϵ</italic> = 0 (Supplementary Note ##SUPPL##0##8##, Figs. ##SUPPL##0##S22##–##SUPPL##0##S25##).</p>", "<p id=\"Par34\">Assume, for simplicity, that inheritance in the population is clonal. The main evolutionary force pushing the initially monomorphic population to the branching point (see Fig. ##FIG##4##5##) is strong intraspecific competition over shelters resulting in high overall mortality. The eventual switch to the dimorphic state results in a larger total population density as a consequence of the drop in the mean mortality rate within the population: competition for shelters becomes largely reduced. The mechanism assuring stable long-term coexistence of the distinct shy and bold cohorts is of particular interest since, regardless of the defence strategy used, shy cohorts have lower fitness than bolder ones. The main reason why shy individuals can still successfully persist and even reach high proportions in the total population is the emergence of density-dependent mortality in bold cohorts. Such density-dependent mortality occurs due to the heterogeneity of the environment: bold individuals in the shoal constantly challenge their bold conspecifics residing in shelters. This results in an extra mortality for bold cohorts, which is not suffered by shy individuals. Although possessing a higher fitness in a homogeneous habitat, bold individuals become victims of their superiority in the heterogeneous environment.</p>", "<p id=\"Par35\">A key question is about sensitivity of our theoretical results to the variation of parameters and model functions. Extensive computer simulations showed that moderate deviation from the realistic default values of parameters listed in Table ##TAB##0##1## does not alter our key findings (Supplementary Note ##SUPPL##0##4##). Therefore, the patterns presented in Figs. ##FIG##0##1##–##FIG##4##5## are robust in the sense that they can be observed within a wide range of parameters. We should stress that here by the robustness we understand the occurrence of a pronounced (&gt;10−20%) decrease in the population size <italic>F</italic>^* after adding shelters in the system (for a monomorphic population) and only small (&lt;5%) variation in the fish numbers in the case of a polymorphic population. To explore the generality of our results, we also use analytical tools, which, for a monomorphic and a dimorphic populations, predict a drop in the population size after adding shelters (Supplementary Notes ##SUPPL##0##6## and ##SUPPL##0##8##). Including the dependence of the per capita reproduction rate on boldness (as in^{##UREF##10##14##}) does not affect the case of clonal reproduction, and one can prove this fact analytically in a similar way as in Supplementary Note ##SUPPL##0##6##. We found that for non-clonal reproduction, assuming a higher reproduction rate in bold individuals results in a reduction in the number of shelters required to have a beneficial effect for large <italic>N</italic>. However, at small and intermediate <italic>N</italic>, the generic pattern of the dependence <italic>F</italic>^*(<italic>N</italic>) remains. Finally, we stress that our central assumption is that the boldness hierarchy determines the outcome of competition for a shelter, so by omitting this assumption the model would predict a distinct result, which is beyond the scope of this paper.</p>", "<p id=\"Par36\">We also briefly checked the robustness of our model to the variation of the most uncertain model function, <italic>ν</italic>(<italic>B</italic>), which describes the dependence of the search rate on boldness. We considered the two following non-sigmoid forms: (i) <italic>ν</italic> = <italic>B</italic> (a linear function) and (ii) <italic>ν</italic> = <italic>B</italic>(1 + <italic>B</italic>_{<italic>μ</italic>})/(<italic>B</italic> + <italic>B</italic>_{<italic>μ</italic>}) (a hyperbolic function). The results are partly provided in Supplementary Note ##SUPPL##0##8##, Figs. ##SUPPL##0##S18##–##SUPPL##0##21##. We found that using these two non-sigmoid functional forms do not affect the previous results regarding the behavior of the total population size <italic>F</italic>^* for the polymorphic population. Also, simulations predict coexistence of bold and shy groups within a population. However, using non-sigmoid functional forms <italic>ν</italic>(<italic>B</italic>) predict different shapes of PIPs, in particular, we do not observe an evolutionary branching point for the hyperbolic function (see Supplementary Note ##SUPPL##0##8##, Figs. ##SUPPL##0##S26##–##SUPPL##0##S28##). Therefore, the mutual coexistence of shy and bold strains for the scenario involving a decelerating function <italic>ν</italic>(<italic>B</italic>) should be explained via some other mechanisms, for example, via non-small genetic mutations, or others.</p>", "<p id=\"Par37\">Our model of population dynamics operates on two different time scales, assuming an instantaneous exchange between the shoal and shelter compartment, and slow demographic processes (for modeling evolution we introduce a third, evolutionary time scale). Using a standard approach^{##UREF##34##51##–##UREF##36##53##}, one can combine these two systems into a single model for variables <italic>T</italic>_{<italic>i</italic>} and <italic>S</italic>_{<italic>i</italic>} by multiplying the terms corresponding to demographic processes by some small parameter <italic>ϵ</italic>₀ ≪ 1. When testing such a model, we found that provided <italic>ϵ</italic>₀ &lt; 0.1, the combined and reduced model predict similar results, which justifies the separation of time scales.</p>", "<p id=\"Par38\">Among possible perspectives, we can cite the following. A notable extension would be modeling parasites as a dynamical variable rather than a static background variable, which would allow us to explore their role in regulating the population dynamics as well as the maintenance of behavioral structuring of the host population. The current model shows a polymorphic host population assures a higher parasitic transmission than a population with a single boldness strain. However, in a real-life ecosystem, the total amount of parasites should depend dynamically on the transmission rate making the resultant outcome uncertain. Another insightful perspective would be the inclusion of sexual dimorphism in behavioral traits such as boldness. An important feature of sexual dimorphism is that, even though individuals of a particular sex may not exhibit strong boldness, and thus not fight for shelter, they may have an essential influence on the distribution of behavioral traits and population dynamics through their offspring of the opposite sex. For example, in zebrafish <italic>Danio rerio</italic> males have significantly higher tendencies than females to adopt antipredator tactics in the presence of predators^{##REF##29410809##54##}. Finally, we should admit that for implementing the theoretical prediction to optimize fish farming one needs accurate values of parameters, in particular, this concerns mortality terms. This would require extensive experimental observation work, which we plan to conduct in the future.</p>" ]

[]

[ "<p id=\"Par1\">Increasing the population density of target species is a major goal of ecosystem and agricultural management. This task is especially challenging in hazardous environments with a high abundance of natural enemies such as parasites and predators. Safe locations with lower mortality have been long considered a beneficial factor in enhancing population survival, being a promising tool in commercial fish farming and restoration of threatened species. Here we challenge this opinion and revisit the role of behavior structuring in a hostile environment in shaping the population density. We build a mathematical model, where individuals are structured according to their defensive tactics against natural enemies. The model predicts that although each safe zone enhances the survival of an individual, for an insufficient number of such zones, the entire population experiences a greater overall mortality. This is a result of the interplay of emergent dynamical behavioral structuring and strong intraspecific competition for safe zones. Non-plastic structuring in individuals’ boldness reduces the mentioned negative effects. We demonstrate emergence of non-plastic behavioral structuring: the evolutionary branching of a monomorphic population into a dimorphic one with bold/shy strains. We apply our modelling approach to explore fish farming of salmonids in an environment infected by trematode parasites.</p>", "<p id=\"Par2\">A theoretical model, based on empirical data, predicts that population structuring according to defensive tactics used against natural enemies enhances the population mortality, whereas nonplastic (permanent) structuring reduces this negative effect.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s42003-023-05731-z.</p>", "<title>Acknowledgements</title>", "<p>The authors thank the two anonymous reviewers’ comments which largely helped us to improve the manuscript. The study was supported by the EPSRC grant EP/W522326/1, United Kingdom. We are grateful to the technical staff of the Konnevesi research station (University of Jyväskylä, Finland) for their assistance. The study was carried out within the state assignment of the Ministry of Science and Higher Education of the Russian Federation. FMWE-2024-0021 (AP), FFER-2021-0004 (VM).</p>", "<title>Author contributions</title>", "<p>S.S.: Formal Analysis, Investigation, Methodology, Software, Writing. V.N.M., A.F.P., and J.T.: Data Curation, Formal Analysis, Investigation. A.M.: Conceptualization, Formal Analysis, Methodology, Project Administration, Supervision, Validation, Visualization, Writing.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par80\"><italic>Communications Biology</italic> thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editors: Quan-Xing Liu and David Favero.</p>", "<title>Data availability</title>", "<p>Experimental data can be found in the file ‘Supplementary Information’, Supplementary Notes ##SUPPL##0##2##, ##SUPPL##0##3##.</p>", "<title>Code availability</title>", "<p>The custom computer code can be found via 10.5281/zenodo.10376104.</p>", "<title>Competing interests</title>", "<p id=\"Par81\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Dependence of the equilibrium population density <italic>F</italic>^* (measured in individuals) on the number of shelters <italic>N</italic> in a behaviorally monomorphic population.</title><p>Panel (<bold>A</bold>) shows the graphs <italic>F</italic>^*(<italic>N</italic>) obtained for different mortality pressures due to variation of the abundance of natural enemies, described by the parameter Δ_{<italic>T</italic>} (measured in year⁻¹). Here we assume that the parameters Δ_{<italic>T</italic>} and <italic>ν</italic>_{<italic>m</italic>}, accounting for the mortality due to natural enemies, vary proportionally with Δ_{<italic>T</italic>}, since they incorporate the abundance of the natural enemies. The coefficients of proportionality are computed using the default values of parameters (see Table ##TAB##0##1##). Panel (<bold>B</bold>) shows the graphs <italic>F</italic>^*(<italic>N</italic>) constructed for different values of the parasite acquisition rate <italic>ν</italic>_{<italic>μ</italic>} (measured in year⁻¹) due to fighting for shelters. The considered spatial area is 1 ha. The other parameters are the same as in Table ##TAB##0##1##.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Dependence of the total population density (measured in individuals) on the number of shelters <italic>N</italic> in a population of 20 strains of different, uniformly spaced, boldness of equal initial density (with <italic>B</italic> = 0.5 for the monomorphic population).</title><p>The curves are obtained for varying values of <italic>D</italic>_{<italic>w</italic>}. Clonal reproduction is assumed when <italic>D</italic>_{<italic>w</italic>} ≤ 10⁻⁶ and uniform reproduction is assumed when <italic>D</italic>_{<italic>w</italic>} ≥ 10⁶. Equilibrium densities are modeled using Eq. (##FORMU##17##7##) (the demographic model) along with the solutions to the fast system given by (##FORMU##13##4##); the model parameters are as given in Table ##TAB##0##1##. The initial distribution of individuals across boldness cohorts is assumed to be uniform. The considered spatial area is 1<italic>h</italic><italic>a</italic>.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Distributions of boldness within the fish population for different mutation scenarios.</title><p>Normalized distributions of boldness for various numbers of shelters <italic>N</italic> in the system in the cases where the redistribution of offspring is clonal (<bold>A</bold>), using a Gaussian mutation kernel with width <italic>D</italic>_{<italic>w</italic>} = 0.02 (<bold>B</bold>), and the uniform genetic mixing (<bold>C</bold>). <bold>D</bold> The proportion of the bold individuals (defined as <italic>B</italic> &gt; 0.7) using territorial tactics (staying in shelters) calculated for the distributions in the upper panel. <bold>E</bold> Proportions of all sheltered individuals who are bold. All model parameters and settings are as described in Fig. ##FIG##1##2##.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Dependence of parasite-induced mortality rates on the number of shelters <italic>N</italic>, with multiple boldness strains, for varying values of <italic>D</italic>_{<italic>w</italic>}.</title><p>The dashed curve shows the parasite-induced mortality in a single-strain population. <bold>A</bold> Total parasite-induced mortality (measured as individuals lost per year). <bold>B</bold> Relative contribution of fighting for shelters to the overall mortality; (<bold>C</bold>) and (<bold>D</bold>) present, respectively, the non-fighting and the fighting-related parasite-induced mortality rates (measured as individuals lost per year). All model parameters and settings are as described in Fig. ##FIG##1##2##.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>Evolution of boldness via the adaptive dynamics framework.</title><p><bold>A</bold>, <bold>C</bold> Pairwise Invasibility Plots (PIP) describing the invasion fitness of a rare mutant (<italic>B</italic>_{<italic>m</italic>}) into the population of a resident strain (<italic>B</italic>_{<italic>r</italic>}). The white regions represent a positive invasion fitness (<italic>λ</italic> &gt; 0) and therefore a successful invasion, whereas the black regions represent a negative invasion fitness (<italic>λ</italic> &lt; 0) and an unsuccessful invasion. White circles represent branching points, a gray-filled circle represents a repeller. <bold>B</bold>, <bold>D</bold> Direct numerical simulations demonstrate evolutionary branching in the system. The population densities of various strains were modeled using Eq. (##FORMU##17##7##) along with the solutions to the system given by (##FORMU##13##4##). We start with a single strain of boldness with <italic>B</italic> = 0.5. Panels (<bold>A</bold>, <bold>B</bold>) are constructed for <italic>ϵ</italic> = 0.1, panels (<bold>C</bold>, <bold>D</bold>) are constructed for <italic>ϵ</italic> = 0.5. All other parameters are as given in Table ##TAB##0##1##.</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><title>Experimental results (presented as box and whiskers plots) on interactions between rainbow trout <italic>Oncorhynchus</italic> and its parasite eye-fluke <italic>D. pseudospathaceum</italic>.</title><p><bold>A</bold> Isolated slow fish received more infection of <italic>D. pseudospathaceum</italic> than isolated fast fish (Mann-Whitney U-test, <italic>p</italic> = 0.013). <bold>B</bold> When kept in groups in a structured habitat (two interconnected compartments: one containing parasites, another free of them), slow fish received more infection (Mann–Whitney <italic>U</italic> test, <italic>p</italic> = 0.036). In both cases, fish were exposed to the same average concentration of parasites. <bold>C</bold> Infection load by <italic>D. pseudospathaceum</italic> metacercariae increases with an increase of threat anticipation by the fish. Sheltering (Sh)—solitary fish possessing a cover shelter. Grouping (Gr)—a group of 5 fish in a tank with a light bottom. Cryptic habitat (Cr)—solitary fish in a tank with a dark bottom. Dangerous habitat (Da) - solitary fish in a tank with a light bottom without shelter. ANOVA showed a pronounced effect of the anticipated threat on parasite acquisition (<italic>p</italic> &lt; 0.0001). Pairwise comparisons (Tukey HSD test) showed that all pairs except Gr - Cr were significantly different (Da - Sh: <italic>p</italic> = 0.0001; Da - Gr: <italic>p</italic> = 0.015; Da - Cr: <italic>p</italic> = 0.050; Cr - Gr: <italic>p</italic> = 0.969; Cr - Sh: <italic>p</italic> = 0.001; Gr - Sh: <italic>p</italic> = 0.005). In total, 160 fish were used: 100 fish in the group test, 60 in the test with solitary fish: 20 with shelters, 20 without shelters and a dark-bottomed tank, 20 without shelters and a light-bottomed tank. For details on statistical analysis see Methods.</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Definitions of model variables, functions, parameters, units as well as their ranges and default values for the rainbow trout—parasites system.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Component</th><th>Meaning</th><th>Formulation, parameter range, unit, and default value (DEF)</th></tr></thead><tbody><tr><td><italic>B</italic>_{<italic>i</italic>}</td><td>Boldness of individuals of strain <italic>i</italic></td><td>0≤<italic>B</italic>_{<italic>i</italic>}≤1, dimensionless</td></tr><tr><td><italic>T</italic>_{<italic>i</italic>}</td><td>Individuals of strain <italic>i</italic> currently showing behavior T (sheltering)</td><td><italic>i</italic><italic>n</italic><italic>d</italic><italic>i</italic><italic>v</italic><italic>i</italic><italic>d</italic><italic>u</italic><italic>a</italic><italic>l</italic><italic>s</italic></td></tr><tr><td><italic>S</italic>_{<italic>i</italic>}</td><td>Individuals of strain <italic>i</italic> currently showing behavior S (shoaling)</td><td><italic>i</italic><italic>n</italic><italic>d</italic><italic>i</italic><italic>v</italic><italic>i</italic><italic>d</italic><italic>u</italic><italic>a</italic><italic>l</italic><italic>s</italic></td></tr><tr><td><italic>F</italic>_{<italic>i</italic>}</td><td>Total number of individuals of strain <italic>i</italic></td><td><italic>i</italic><italic>n</italic><italic>d</italic><italic>i</italic><italic>v</italic><italic>i</italic><italic>d</italic><italic>u</italic><italic>a</italic><italic>l</italic><italic>s</italic></td></tr><tr><td><italic>K</italic></td><td>Carrying capacity of the population</td><td>10³ &lt; <italic>K</italic> &lt; 2.5 ⋅ 10⁴\n<italic>i</italic><italic>n</italic><italic>d</italic><italic>i</italic><italic>v</italic><italic>i</italic><italic>d</italic><italic>u</italic><italic>a</italic><italic>l</italic><italic>s</italic>, DEF: <italic>K</italic> = 10⁴\n<italic>i</italic><italic>n</italic><italic>d</italic><italic>i</italic><italic>v</italic><italic>i</italic><italic>d</italic><italic>u</italic><italic>a</italic><italic>l</italic><italic>s</italic></td></tr><tr><td><italic>N</italic></td><td>Total number of shelters</td><td>0≤<italic>N</italic>≤<italic>K</italic>, <italic>s</italic><italic>h</italic><italic>e</italic><italic>l</italic><italic>t</italic><italic>e</italic><italic>r</italic><italic>s</italic></td></tr><tr><td><italic>ω</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>})</td><td>Probability that an individual in the shoal of strain <italic>i</italic> attempts to invade a shelter occupied by an individual of strain <italic>j</italic></td><td></td></tr><tr><td><italic>δ</italic>_{<italic>ω</italic>}</td><td>Characteristic coefficient in the probability function <italic>ω</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>})</td><td><italic>δ</italic>_{<italic>ω</italic>} &gt; 20, DEF: <italic>δ</italic>_{<italic>ω</italic>} = 30, dimensionless</td></tr><tr><td><italic>I</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>}, <italic>T</italic>_{<italic>j</italic>})</td><td>Rate at which shoal individuals of strain <italic>i</italic> attempt to invade shelters of territorial individuals of strain <italic>j</italic></td><td><italic>I</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>T</italic>_{<italic>j</italic>}) = <italic>I</italic>₀<italic>ν</italic>(<italic>B</italic>_{<italic>i</italic>})<italic>ω</italic>(<italic>B</italic>_{<italic>i</italic>}, <italic>B</italic>_{<italic>j</italic>})<italic>T</italic>_{<italic>j</italic>}</td></tr><tr><td><italic>I</italic>₀</td><td>Maximal search rate for shelters</td><td><italic>I</italic>₀ ∈ [4, 28]<italic>y</italic><italic>e</italic><italic>a</italic><italic>r</italic>⁻¹, DEF:<italic>I</italic>₀ = 15 year⁻¹</td></tr><tr><td><italic>ν</italic>(<italic>B</italic>_{<italic>i</italic>})</td><td>Dependence of the search rate for shelters on boldness <italic>i</italic></td><td></td></tr><tr><td><italic>B</italic>_{<italic>ν</italic>}, <italic>μ</italic></td><td>Parameters characterizing <italic>ν</italic>(<italic>B</italic>_{<italic>i</italic>})</td><td>2 &lt; <italic>μ</italic> &lt; 8 DEF <italic>μ</italic> = 5; 0.2 &lt; <italic>B</italic>_{<italic>ν</italic>} &lt; 0.7 DEF: <italic>B</italic>_{<italic>ν</italic>} = 0.5, dimensionless</td></tr><tr><td><italic>R</italic>(<italic>B</italic>_{<italic>i</italic>}, <bold>F</bold>^a)</td><td>Redistribution of offspring of strain <italic>i</italic></td><td>, where <italic>A</italic>_{<italic>j</italic>} are normalizing constants</td></tr><tr><td><italic>D</italic>_{<italic>w</italic>}</td><td>Width of the kernel <italic>R</italic>(<italic>B</italic>_{<italic>i</italic>}, <bold>F</bold>)</td><td>1 ⋅ 10⁻⁶≤<italic>D</italic>_{<italic>w</italic>}≤1 ⋅ 10⁶, dimensionless</td></tr><tr><td></td><td>Per capita growth rate of all strains</td><td></td></tr><tr><td><italic>b</italic>₀</td><td>Maximal per capita birth rate</td><td>1.6 &lt; <italic>b</italic>₀ &lt; 5<italic>y</italic><italic>e</italic><italic>a</italic><italic>r</italic>⁻¹, DEF: <italic>b</italic>₀ = 2 year⁻¹</td></tr><tr><td><italic>D</italic></td><td>Reduction in the cost of fighting when defending a shelter</td><td>0.2 &lt; <italic>D</italic> &lt; 1 DEF: <italic>D</italic> = 0.4, dimensionless</td></tr><tr><td><italic>m</italic></td><td>Natural background mortality rate</td><td>0.07 &lt; <italic>m</italic>₀ &lt; 0.25 year⁻¹ DEF: <italic>m</italic>₀ = 0.13 yea<italic>r</italic>⁻¹</td></tr><tr><td>Δ<italic>m</italic>_{<italic>S</italic>}(<italic>B</italic>_{<italic>i</italic>})</td><td>Parasite/predator mortality for shoaling individuals of strain <italic>i</italic></td><td>Δ<italic>m</italic>_{<italic>S</italic>}(<italic>B</italic>_{<italic>i</italic>}) = Δ_{<italic>S</italic>}(1 − <italic>ϵ</italic><italic>B</italic>_{<italic>i</italic>}), 0.1 &lt; Δ_{<italic>S</italic>} &lt; 2.5 year⁻¹, DEF: Δ_{<italic>S</italic>} = 0.9 year⁻¹</td></tr><tr><td>Δ<italic>m</italic>_{<italic>T</italic>}(<italic>B</italic>_{<italic>i</italic>})</td><td>Parasite/predator mortality for sheltering individuals of strain <italic>i</italic></td><td>Δ<italic>m</italic>_{<italic>T</italic>}(<italic>B</italic>_{<italic>i</italic>}) = Δ_{<italic>T</italic>}(1 − <italic>ϵ</italic><italic>B</italic>_{<italic>i</italic>}), 0.05 &lt; Δ_{<italic>T</italic>} &lt; 1.6 year⁻¹, DEF: Δ_{<italic>T</italic>} = 0.45 year⁻¹</td></tr><tr><td><italic>m</italic>_{<italic>p</italic>}(<italic>B</italic>_{<italic>i</italic>})</td><td>Extra mortality due to competitions for shelters between resident and invading shoal individuals</td><td><italic>m</italic>_{<italic>p</italic>}(<italic>B</italic>_{<italic>i</italic>}) = <italic>ν</italic>_{<italic>m</italic>}(1 − <italic>ϵ</italic><italic>B</italic>_{<italic>i</italic>})</td></tr><tr><td><italic>ν</italic>_{<italic>m</italic>}</td><td>Maximal mortality rate due to contests for shelters (per shelter)</td><td>0.0005 &lt; <italic>ν</italic>_{<italic>m</italic>} &lt; 0.5year⁻¹, DEF: <italic>ν</italic>_{<italic>m</italic>} = 0.02 year⁻¹</td></tr><tr><td><italic>ϵ</italic></td><td>Parameter, incorporating dependence on mortality rate on boldness</td><td>0.075 &lt; <italic>ϵ</italic> &lt; 1, DEF: <italic>ϵ</italic> = 0.1, dimensionless</td></tr></tbody></table></table-wrap>" ]

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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$b(\\mathop{\\sum }\\nolimits_{j = 1}^{n}{F}_{j})={b}_{0}\\left(1-\\frac{\\mathop{\\sum }\\nolimits_{j = 1}^{n}{F}_{j}}{K}\\right)$$\\end{document}</tex-math><mml:math id=\"M10\"><mml:mi>b</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq6\"><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${F}^{* }=\\sum {F}_{i}^{* }$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mo>∑</mml:mo><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq7\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${F}^{* }=\\sum {F}_{i}^{* }$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mo>∑</mml:mo><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq8\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$T\\equiv \\mathop{\\sum }\\nolimits_{j = 1}^{n}{T}_{j}=N$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:mi>T</mml:mi><mml:mo>≡</mml:mo><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>N</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${M}_{i}=\\mathop{\\sum }\\limits_{j=1}^{n}\\left({S}_{i}I({B}_{i},{B}_{j},{T}_{j})-{S}_{j}I({B}_{j},{B}_{i},{T}_{i})\\right).$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{array}{l}\\frac{{{{{{\\rm{d}}}}}}{T}_{i}}{{{{{{\\rm{d}}}}}}t}={M}_{i};\\quad \\frac{{{{{{\\rm{d}}}}}}{S}_{i}}{{{{{{\\rm{d}}}}}}t}=-{M}_{i}.\\end{array}$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mtable><mml:mtr><mml:mtd columnalign=\"left\"><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>;</mml:mo><mml:mspace width=\"1.0em\"/><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${M}_{i}=0=({F}_{i}-{T}_{i}({F}_{i}))\\mathop{\\sum }\\limits_{j=1}^{n}I({B}_{i},{B}_{j},{T}_{j}({F}_{j})) \\\\ -\\mathop{\\sum }\\limits_{j=1}^{n}({F}_{j}-{T}_{j}({F}_{j}))I({B}_{j},{B}_{i},{T}_{i}({F}_{i}))$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq9\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${T}_{n}({F}_{n})=N-\\mathop{\\sum }\\nolimits_{j = 1}^{n-1}{T}_{j}({F}_{j})$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$T\\equiv \\mathop{\\sum }\\nolimits_{j = 1}^{n}{T}_{j}=N$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:mi>T</mml:mi><mml:mo>≡</mml:mo><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>N</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${M}_{i}= 0=\t({F}_{i}-{T}_{i}({F}_{i}))\\left(\\mathop{\\sum }\\limits_{j=1}^{n-1}I({B}_{i},{B}_{j},{T}_{j}({F}_{j}))+I({B}_{i},{B}_{n},N-\\mathop{\\sum }\\limits_{j=1}^{n-1}{T}_{j}({F}_{j}))\\right)\\\\ \t-\\mathop{\\sum }\\limits_{j=1}^{n-1}({F}_{j}-{T}_{j}({F}_{j}))I({B}_{j},{B}_{i},{T}_{i}({F}_{i}))-({F}_{n} \\\\ \t-(N-\\mathop{\\sum }\\limits_{j=1}^{n-1}{T}_{j}({F}_{j})))I({B}_{n},{B}_{i},{T}_{i}({F}_{i}))$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfenced><mml:mo>−</mml:mo><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${T}_{n}({F}_{n})=N-\\mathop{\\sum }\\nolimits_{j = 1}^{n-1}{T}_{j}({F}_{j})$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$I({B}_{i},{B}_{j},{T}_{j})={I}_{0}\\nu ({B}_{i})\\omega ({B}_{i},{B}_{j}){T}_{j},$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mi>ν</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>ω</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\omega ({B}_{i},{B}_{j})=\\frac{{e}^{-{\\delta }_{\\omega }({B}_{j}-{B}_{i})}}{1+{e}^{-{\\delta }_{\\omega }({B}_{j}-{B}_{i})}}.$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:mi>ω</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mi>ω</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mi>ω</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{{{{{\\rm{d}}}}}}{F}_{i}}{{{{{{\\rm{d}}}}}}t}= \tb\\left(\\mathop{\\sum }\\limits_{j=1}^{n}{F}_{j}\\right)R({B}_{i},{{{{{{{\\bf{F}}}}}}}})-{m}_{0}{F}_{i}-\\Delta {m}_{S}({B}_{i}){S}_{i}({F}_{i}) \\\\ \t-\\Delta {m}_{T}({B}_{i}){T}_{i}({F}_{i})\\\\ \t-G({B}_{i},{{{{{{{\\bf{S}}}}}}}}({{{{{{{\\bf{F}}}}}}}}),{{{{{{{\\bf{T}}}}}}}}({{{{{{{\\bf{F}}}}}}}})),$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant=\"bold\">F</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>G</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant=\"bold\">S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">F</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi mathvariant=\"bold\">T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant=\"bold\">F</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$b(\\mathop{\\sum }\\nolimits_{j = 1}^{n}{F}_{j})$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:mi>b</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${b}_{0}\\left(1-\\frac{\\mathop{\\sum }\\nolimits_{j = 1}^{n}{F}_{j}}{K}\\right)$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$G({B}_{i},{{{{{{{\\bf{S}}}}}}}},{{{{{{{\\bf{T}}}}}}}})={m}_{p}({B}_{i})\\left(\\nu ({B}_{i}){S}_{i}\\mathop{\\sum }\\limits_{j=1}^{n}\\omega ({B}_{i},{B}_{j}){T}_{j}+D{T}_{i}\\mathop{\\sum }\\limits_{j=1}^{n}{S}_{j}\\nu ({B}_{j})\\omega ({B}_{j},{B}_{i})\\right).$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mi>G</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant=\"bold\">S</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=\"bold\">T</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>ν</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:mi>ω</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>D</mml:mi><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:munderover accent=\"false\" accentunder=\"false\"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mi>ν</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>ω</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equa\"><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\Delta {m}_{S}({B}_{i})={\\Delta }_{S}(1-\\epsilon {B}_{i});\\Delta {m}_{T}({B}_{i})={\\Delta }_{T}(1-\\epsilon {B}_{i}),$$\\end{document}</tex-math><mml:math id=\"M44\"><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>ϵ</mml:mi><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>ϵ</mml:mi><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$R({B}_{i},{{{{{{{\\bf{F}}}}}}}})=\\mathop{\\sum}\\limits_{j}{A}_{j}{F}_{j}\\exp \\left(-\\frac{{({B}_{j}-{B}_{i})}^{2}}{{D}_{w}}\\right),$$\\end{document}</tex-math><mml:math id=\"M46\"><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant=\"bold\">F</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mi>exp</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equb\"><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\nu (B)=\\frac{{B}^{\\mu }}{{B}^{\\mu }+{B}_{\\nu }^{\\mu }}.$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:mi>ν</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equc\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{{{{{\\rm{d}}}}}}F}{{{{{{\\rm{d}}}}}}t}= \tb(F)F-\\left(mF+\\Delta {m}_{S}(F-N)+\\Delta {m}_{T}N\\right)\\\\ \t-{m}_{p}(F-N)N(1+D)\\nu /2.$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>F</mml:mi><mml:mo>−</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>m</mml:mi><mml:mi>F</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>F</mml:mi><mml:mo>−</mml:mo><mml:mi>N</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mi>N</mml:mi></mml:mrow></mml:mfenced><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>F</mml:mi><mml:mo>−</mml:mo><mml:mi>N</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>D</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>ν</mml:mi><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>.</mml:mo></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\nu (B)=\\frac{{B}^{\\mu }}{{B}^{\\mu }+{B}_{0}^{\\mu }}$$\\end{document}</tex-math><mml:math id=\"M52\"><mml:mi>ν</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\nu (B)=\\frac{B(1+{B}_{0})}{B+{B}_{0}}$$\\end{document}</tex-math><mml:math id=\"M54\"><mml:mi>ν</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ10\"><label>10</label><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{{{{{\\rm{d}}}}}}P}{{{{{{\\rm{d}}}}}}t}=r+{r}_{1}-\\alpha P,$$\\end{document}</tex-math><mml:math id=\"M56\"><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>r</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>α</mml:mi><mml:mi>P</mml:mi><mml:mo>,</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equd\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${P}^{* }=\\frac{r+{r}_{1}}{\\alpha }.$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:msup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>r</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Eque\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$X({t}_{i+1})=X({t}_{i})+{\\Delta }_{x}({t}_{i}),$$\\end{document}</tex-math><mml:math id=\"M60\"><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>X</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equf\"><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Y({t}_{i+1})=Y({t}_{i})+{\\Delta }_{y}({t}_{i}),$$\\end{document}</tex-math><mml:math id=\"M62\"><mml:mi>Y</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>Y</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\Delta }_{x}({t}_{i})=L({t}_{i})\\cos (\\phi ({t}_{i}))$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>cos</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\Delta }_{y}({t}_{i})=L({t}_{i})\\sin (\\phi ({t}_{i}))$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>sin</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>ϕ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equg\"><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\nu }_{\\mu }\\approx {\\Delta }_{S}\\frac{{r}_{1}}{r}={\\Delta }_{S}\\frac{{\\Delta }_{c}\\cdot {I}_{0}}{r}.$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub><mml:mo>≈</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:math></alternatives></disp-formula>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>" ]

[ "<table-wrap-foot><p>The considered spatial area is 1<italic>h</italic><italic>a</italic>. The estimates of model parameters are discussed in the subsection ‘Estimation of model parameters’ of the ‘Methods’ section. Italic and bold highlighting styles correspond to scalar and vector (multi-variable) quantities, respectively.</p><p>^aBold variable <bold>F</bold> is a vector with components <italic>F</italic>_{<italic>i</italic>}.</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"42003_2023_5731_MOESM1_ESM.pdf\"><caption><p>Supplementary information</p></caption></media>", "<media xlink:href=\"42003_2023_5731_MOESM2_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par3\">Cancer is a heterogeneous disease, and the evolution of cell states and cell types in the tumor microenvironment can influence response to treatment^{##REF##29115304##1##–##REF##959840##5##}. Peripheral nervous system Schwann cells develop from the neural crest^{##UREF##0##6##}, a multipotent embryonic cell population characterized by remarkable molecular and functional diversity^{##REF##25564621##7##}. Schwannoma tumors have a low burden of somatic mutations that do not change after treatment with ionizing radiation^{##REF##27723760##8##,##REF##28409725##9##}, but schwannomas that are treated with radiotherapy periodically swell and shrink for many years^{##REF##29518221##10##,##REF##27885955##11##}. In clinical practice, symptomatic schwannoma oscillations are treated with empiric immunosuppressive corticosteroids or surgical decompression, and preoperative schwannoma growth is associated with immune cell infiltration^{##UREF##1##12##,##REF##32642684##13##}.</p>", "<p id=\"Par4\">Here we test the hypothesis that epigenetic mechanisms shape schwannoma cell states and the immune microenvironment during schwannoma responses to radiotherapy. To do so, we interrogate human schwannomas, primary patient-derived schwannoma cells, and Schwann and schwannoma cell lines using bulk and single-cell bioinformatics, functional genomic, proteomic, metabolomic, and mechanistic approaches. We find schwannomas are comprised of 2 molecular groups that are distinguished by tumor and immune cell types and can arise de novo (Fig. ##FIG##0##1##) but undergo epigenetic interconversion in response to radiotherapy (Fig. ##FIG##1##2##). Genome-wide CRISPR interference (CRISPRi) screening^{##REF##25307932##14##,##UREF##2##15##} identifies epigenetic regulators driving schwannoma cell reprogramming and immune cell infiltration in response to ionizing radiation (Fig. ##FIG##2##3##), and a technique integrating single-nuclei ATAC, RNA, and CRISPRi perturbation sequencing elucidates concordant chromatin accessibility, transcription factor activity, and gene expression programs underlying schwannoma cell state evolution that are conserved in human tumors (Fig. ##FIG##3##4##). In sum, these data shed light on the molecular landscape of schwannomas and reveal epigenetic mechanisms underlying tumor heterogeneity and response to radiotherapy (Fig. ##FIG##4##5##).</p>" ]

[ "<title>Methods</title>", "<title>Vestibular schwannomas</title>", "<p id=\"Par20\">This study was approved by the UCSF Institutional Review Board (#10-01318, #18-24633) and complied with all relevant ethical regulations. Patients presenting for resection of sporadic vestibular schwannoma who gave written consent for tumor sampling for research were included in the retrospective discovery cohort or in single-cell RNA sequencing and CyTOF experiments (Supplementary Data ##SUPPL##3##1##). Exclusion criteria included a history of neurofibromatosis type 2 and, with the exception of prospectively obtained schwannomas for single-cell RNA sequencing and CyTOF experiments, less than 18 months of magnetic resonance imaging (MRI) follow-up. Vestibular schwannomas used for DNA methylation profiling, bulk RNA sequencing, and single-nucleus RNA sequencing were identified from the UCSF Brain Tumor Center Biorepository &amp; Histology Core. All samples from patients meeting inclusion and exclusion criteria were included, resulting in 75 clinically heterogeneous retrospective and prospective schwannomas from 67 patients who were treated from 2003 to 2020. In an attempt to optimize outcomes, many patients in this cohort were initially treated with hybrid strategies employing primary tumor debulking followed by adjuvant radiotherapy^{##REF##25181431##63##,##REF##26645964##64##}. As a result, 6 of these patients had tissue from recurrent as well as primary tumors. However, such strategies are now known to be associated with higher recurrence rates and are not recommended. All cases with available material were reviewed by a board-certified neuropathologist for diagnostic confirmation (MP). Additional clinical variables were analyzed by chart review (SJL, JDB, DRR).</p>", "<title>Annotation of radiologic features</title>", "<p id=\"Par21\">A comprehensive radiologic review of preoperative magnetic resonance imaging studies for the patients comprising the retrospective discovery cohort (Supplementary Data ##SUPPL##3##1##) was performed by a board-certified neuroradiologist who was blinded to all clinical and molecular data (JEVM). Anatomic magnetic resonance images including T2, T2 fluid attenuated inversion recovery (FLAIR), and post-contrast T1 weighted images were reviewed. Diffusion weighted imaging (DWI) including derived apparent diffusion coefficient (ADC) maps were also evaluated. Radiologic features of enhancement pattern (homogeneous or heterogeneous), cystic change, mass effect, peritumoral edema, indistinct brain-tumor interface, lobulated margins, and hydrocephalus were scored in categoric binary fashion and were not found to be significantly different between molecular groups of schwannomas unless stated otherwise. Hydrocephalus was further characterized as non-communicating or communicating. Diffusion characteristics were assessed qualitatively (reduced or facilitated) in vestibular schwannomas for which diffusion weighted imaging was acquired.</p>", "<title>DNA methylation profiling and analysis</title>", "<p id=\"Par22\">Genomic DNA was isolated from schwannomas by mechanical homogenization (Qiagen TissueLyser) followed by the All-Prep Universal Kit for DNA and RNA isolation (Qiagen, #80224). DNA quality was tested by spectrophotometry and clean-up was performed using DNA precipitation as needed. Genome-wide methylation profiles were obtained with the Illumina MethylationEPIC 850K array for each schwannoma. Data preprocessing and normalization was performed using <italic>minfi</italic> version 1.30 in R version 3.6.0^{##REF##28035024##65##,##REF##24478339##66##}. Methylation probes with detection significance p &gt; 0.05 were excluded from analysis. Normalization was performed using functional normalization^{##REF##25599564##67##}. Probes were filtered according to the following criteria: (i) exclusion of probes mapping to sex chromosomes (n = 11,551), (ii) exclusion of probes containing a common single nucleotide polymorphism (SNP) within the targeted CpG site or on an adjacent base pair (n = 24,536), and (iii) exclusion of probes not mapping uniquely to the human reference genome hg19 (n = 9,993). A total of 815,630 probes were retained for further analysis. Methylation β values were calculated as the ratio of methylated probe intensity to the sum of methylated and unmethylated probe intensities and visualized on heatmaps in an absolute scale^{##REF##16449502##68##}. Variable probes were identified by ranking all methylation probes by β value variance across all schwannomas. The top 2000 probes by variance were then subjected to consensus clustering using complete linkage hierarchical clustering with 1-Pearson correlation as distance matrix, sampling between 2–6 possible clusters with 20 resampling iterations. Schwannomas belonging to each of the 2 molecular groups by hierarchical clustering were used for differential methylation analysis against methylation β values using the dmpFinder function in <italic>minfi</italic>. The resulting differentially methylated probes with False Discovery Rate (FDR) &lt; 0.05 were ranked by log odds values between the 2 molecular groups, and the top and bottom 1000 differentially methylated probes (total 2000) were used for hierarchical clustering of schwannomas. Gene ontology analysis of probes was performed by extracting the associated gene body annotation from each probe using the Bioconductor package IlluminaHumanMethylationEPICanno.ilm10b2.hg19 and inputting the gene lists grouped based on the results of hierarchical clustering into Enrichr^{##REF##20709693##19##,##REF##27141961##69##}.</p>", "<p id=\"Par23\">To compare DNA methylation with RNA sequencing expression data, we used all methylation probes corresponding to each gene as annotated in the Illumina MethylationEPIC manifest, which includes transcription start site (TSS), gene body, and 3’/5’ UTR probes, in order to interrogate beyond promoter methylation. We ranked the differentially methylated probes from most to least significant according to the FDR and compared the most significant probe for each gene to the expression fold change for each differentially expressed gene in RNA sequencing analysis.</p>", "<p id=\"Par24\">Random forest classification of global methylation profiles was performed to compare each methylation profile with a broader set of CNS malignancies as previously described^{##REF##29539639##16##}, revealing that immune enriched schwannomas classified as either inflammatory tumor microenvironment or reactive tumor microenvironment (Fig. ##FIG##0##1a##), consistent with the significant immune cell infiltration in these tumors. External validation methylation data was obtained from GSE79009^{##REF##27723760##8##} and preprocessed and normalized as above. The overlapping set of DNA methylation probes between the external validation cohort (Illumina Methylation 450K array) and the 2000 differentially methylated probes from the discovery cohort (Illumina MethylationEPIC 850K array) was used for complete linkage hierarchical clustering of external validation cohort schwannomas with 1-Pearson correlation. Differential methylation analysis of clinical variables was performed by separating schwannoma methylation profiles based on binary variables (sex, prior surgery, prior radiotherapy) or bisecting the cohort at the median of continuous variables (size, growth rate, age) and performing differential methylation analysis as described above. DNA methylation probes at neural crest enhancers were identified by overlapping the coordinates of each methylation site with those of neural crest enhancers active in development^{##UREF##9##70##}.</p>", "<p id=\"Par25\">To classify prospective vestibular schwannomas analyzed using single-cell RNA sequencing and CyTOF into molecular groups, a methylation-based classifier using differentially methylated probes from our discovery cohort of 66 tumors was used to construct a support vector machine (SVM) using <italic>caret</italic> version 6.0 in R version 3.6.0. A linear kernel SVM was constructed using training data comprising 75% of randomly selected samples from the discovery cohort with 10-fold cross validation. The top 2000 differentially methylated probes were used as variables. The model was applied to a test set comprising 25% of randomly selected samples from the discovery cohort, and receiver operating characteristics were acquired for 1000x resampling of test data. The SVM distinguished neural crest from immune-enriched schwannomas with 100% accuracy when used to classify randomly selected test sets of samples from our initial cohort (95% CI 78.2-100%, p = 8.04x10⁻⁵).</p>", "<p id=\"Par26\">Copy number variant (CNV) calling was performed from schwannoma DNA methylation profiles, and revealed that loss of chromosome 22q, which contains the tumor suppressor <italic>NF2</italic>, was the most common CNV and occurred in 32% of tumors (Supplementary Data ##SUPPL##3##1##). To evaluate whether we could identify single nuclei CNVs from prospective schwannomas that demonstrated loss of chromosome 22q based on DNA methylation profiling, we applied CONICS^{##REF##29897414##71##}, but were unable to identify a distinct tumor population harboring 22q loss, likely due, in part, to technical factors related to single-nuclei sequencing data from frozen specimens and minimal chromosomal instability of schwannomas^{##REF##27723760##8##,##REF##28409725##9##}. Methylation arrays were deconvolved to identify tumor cell purity and constituent cell types (Supplementary Data ##SUPPL##3##1##) based on published approaches enabling comparison to a reference atlas of pure methylation profiles^{##REF##30498206##72##} or with a random forest classifier trained on the ABSOLUTE method developed by the TCGA for whole exome sequencing^{##UREF##10##73##}. Using DNA methylation-based deconvolution, we compared immune-enriched tumors with a prior history of SRS to immune-enriched tumors without SRS, and identified no significant differences in the degree of immune (0.037 versus 0.025, p = 0.37), stroma (0.030 versus 0.010, p = 0.14) or microenvironment scores (0.067 vs. 0.036, p = 0.13).</p>", "<title>Fluorescence microscopy</title>", "<p id=\"Par27\">Fluorescence microscopy was performed on a Zeiss LSM 800 confocal laser scanning microscope with Airyscan. Images were processed and quantified from at least 2 regions per condition using ImageJ^{##REF##22930834##74##}. Cilia prevalence was quantified as the ratio of cilia to nuclei, and ciliary fluorescence intensity was quantified from regions of interest normalization to background fluorescence.</p>", "<title>Histology and light microscopy</title>", "<p id=\"Par28\">Formalin-fixed and paraffin-embedded whole slide sections were reviewed for histologic features including presence of capsule, cystic degeneration, Verocay bodies, biphasic morphology (Antoni A and Antoni B zones), degenerative atypia, hypercellular zones (bone-to-back or overlapping nuclei), hyalinized/thick-walled intratumor vessels, necrosis, hemosiderin deposition, calcification, hyalinization, and mitoses by a board-certified neuropathologist who was blinded to all clinical and molecular data (MP). Mitotic activity was noted in regions of maximal activity as the number of mitotic figures per 10 consecutive high-power fields measuring 0.24 mm^{##REF##27157931##75##}. Inflammatory infiltrate including lymphocytes and macrophages were scored on H&amp;E-stained sections as no immune cells, scattered immune cells, or abundant immune cells. All vestibular schwannomas with sufficient tissue were included in tissue microarrays (TMAs) containing 4 μm thick paraffin sections from 2 mm cores in duplicate for each case. In cases with biphasic histology, the cores predominantly targeted the cellular Antoni A zones and avoided areas with near-complete macrophage infiltrate or necrosis. All histologic features and stains were scored for each TMA core separately and were averaged for each case.</p>", "<title>Immunofluorescence and immunohistochemistry</title>", "<p id=\"Par29\">Immunofluorescence for schwannoma SOX10 and cilia expression was performed using whole slide sections and TMAs. Sections were deparaffinized in xylene, rehydrated through graded ethanol dilutions and subjected to antigen retrieval using CC1 TRIS buffer (Ventana Medical Systems, #950-124); labeled with primary antibodies including SOX10 to mark schwannoma cells (API 3099, Biocare; labeling validated in schwannoma and melanoma), Pericentrin (PA5-54109, Thermo Fisher Scientific; labeling validated by Pericentrin knockdown) and γTubulin (T5192, Sigma; labeling validated in human and chicken cells) to mark centrosomes, and Acetylated Tubulin to mark cilia (T6793, Sigma; labeling validated in vertebrate and invertebrate organisms); labeled with Alexa Fluor secondary antibodies and DAPI to mark DNA (62248, Thermo Fisher Scientific); and mounted in ProLong Diamond Antifade Mountant (Thermo Fisher Scientific, #P36970).</p>", "<p id=\"Par30\">Immunofluorescence for Human Schwann Cells (HSC) and Mouse Schwann Cells (MSC) cilia was performed on glass coverslips. Cells were fixed in 4% paraformaldehyde, blocked in 2.5% FBS, 200 mM glycine and 0.1% Triton X-100 in PBS for 30 min at room temperature (Thermo Fisher Scientific), and labeled with Smoothened (ab72130, Abcam; labeling validated by competition with immunizing peptide) and Centriolin (sc-365521, Santa Cruz Biotechnology; labeling validated using THP-1, SK-BR-3, and U-937 cell lysates) primary antibodies at 4 °C overnight. Cells were labeled with Alexa Fluor secondary antibodies, Hoescht to mark DNA (H3570, Life Technologies), and Acetylated Tubulin Alexa Fluor 647 Conjugate to mark cilia (sc-23950, Santa Cruz Biotechnology; labeling validated using A2058, 3T3-L1, and Jurkat cell lysates), for 1 hour at room temperature. Cells were mounted in ProLong Diamond Antifade Mountant (Thermo Fisher Scientific, #P36970).</p>", "<p id=\"Par31\">Immunohistochemical stains for T cells and macrophages were performed using TMAs using standard techniques. In brief, slides were subjected to antigen retrieval and labeled with CD3 (A0452, Agilent Technologies, Santa Clara, CA; labeling validated by over-expression) or CD68 (M0814, Agilent Technologies; labeling validated using human B-cell lymphoma) primary antibodies. Detection was performed using the UltraView Universal DAB Detection Kit on the Ventana Benchmark Platform (Ventana Medical Systems, #760-500). CD3 was scored as the number of positive cells in each core as negative (≤10), low (11–50), moderate (51–100), and abundant (&gt;100). CD68 was scored as negative (no positive cells recognizable at high power), weak staining in &lt;10% of cells), moderate (staining in 10–20% of cells), or abundant (staining in &gt;20% of cells, easily visible at low power). Immunohistochemistry for BCL1 (RM9104R7, Thermo Fisher Scientific labeling validated using MAD109 cell lysate) was performed as described for T cells and macrophages but on whole slide sections and with scoring as was done for CD68.</p>", "<title>Cell culture and treatments</title>", "<p id=\"Par32\">Human Schwann cells (HSC, ScienCell Research Laboratories #1700) and Mouse Schwann Cells (MSC, ScienCell Research Laboratories #M1700-57) were cultured in complete Schwann Cell Medium on Poly-L-Lysine coated substrates (ScienCell Research Laboratories, #1701). HEI-193 schwannoma cells were a gift from Marco Giovannini and cultured in Dulbecco’s Modified Eagle Medium (Gibco, #11960069) supplemented with 10% fetal bovine serum (FBS) (Life Technologies, #16141), glutamine (Thermo Fisher Scientific, #10378016)^{##REF##10024671##38##}. HEK-293T cells were a gift from Luke Gilbert and cultured in Dulbecco’s Modified Eagle Medium (Gibco, #11960069) supplemented with 10% fetal bovine serum (FBS) (Life Technologies, #16141). Cell cultures were authenticated by STR analysis at the UC Berkeley DNA Sequencing Facility, as well as routinely tested for mycoplasma using the MycoAlert Detection Kit (Lonza, #75866-212). Subconfluent HSC and HEI-193 schwannoma cells were irradiated with an X-Rad 320 (Precision X-Ray) irradiator using a 320 KV output at a rate of 3 Gy/min, with rotating a platform supporting cell culture plates. Cells were quantified by manual hemocytometer during routine cell culture passaging. Crystal violet staining of HEI-193 cells was quantified with background subtraction using ImageJ^{##REF##22930834##74##}. For ciliation and Hedgehog signaling assays, cultures were transitioned to OptiMEM (Thermo Fisher Scientific, #31985062) and treated with recombinant Sonic Hedgehog 1 μg/ml (1845, R&amp;D Systems, Minneapolis, MN) or vehicle control for 24 h. Subconfluent HSC cultures in 96 well plates were treated with vismodegib (Genentech) for 72 h, and cell proliferation was assayed on a GloMax Discovery plate reader (Promega, #PAGM3000) using the CellTiter 96 Non-Radioactive Cell Proliferation kit (Promega, #G4100). For proteomic mass spectrometry, cells were grown in serum-free N5 media consisting of Neurobasal A (Life Technologies, #10888022) supplemented with N2 (Gemini Bio-Products, #400-163) and B27 supplements without vitamin A (Gibco, #12587010), <sc>l</sc>-glutamine 2 mM, antibiotic-antimycotic (Thermo Fisher Scientific, #15240112), bFGF 20 ng/mL (VWR, #119–126), and human EGF 20 ng/mL (PeproTech, #AF-100-15). Cells were irradiated, and cell-free conditioned media was isolated by centrifugation for 10 min at 4000<italic>g</italic> and filtering through a 0.45 μm syringe for mass spectrometry. TUNEL assays for apoptosis were performed using the APO-BrdU TUNEL Assay Kit with Alexa Fluor 488 Anti-BrdU (Thermo Fisher Scientific, #A23210).</p>", "<title>CRISPR interference</title>", "<p id=\"Par33\">HEI-193 schwannoma cells stably expressing the CRISPRi components dCas9-KRAB were generated as previously described^{##REF##25307932##14##,##REF##23849981##40##}. HEI-193 schwannoma cells were transduced with lentivirus harboring SFFV-dCas9-BFP-KRAB, and the top ~25% of cells expressing BFP were FACS sorted and expanded. For single gene targeted knockdowns, sgRNA protospacer sequences (Supplementary Data ##SUPPL##3##11##) were cloned into a lentiviral expression vector (U6-sgRNA EF1Alpha-puro-T2A-BFP) by annealing and ligation. HEI-193 schwannoma CRISPRi cells were then transduced with sgRNA lentivirus and selected with puromycin 1 μg/mL for at least 4 days before experimentation.</p>", "<title>Lymphocyte isolation and migration</title>", "<p id=\"Par34\">Peripheral blood lymphocytes were isolated from the human blood of healthy volunteers^{##UREF##11##76##}. A Polymorph density gradient (Accurate Chemical &amp; Scientific Corporation, #AN221725) was used to isolate peripheral blood mononuclear cells that were subsequently selected and differentiated into T cell lymphocytes in Roswell Park Memorial Institute 1640 media (Life Technologies, #11875093) supplemented with 10% FBS, 1% penicillin/streptomycin, phytohemagglutinin 1 μg/ml (10576015, Thermo Fisher Scientific) and recombinant human IL-2 20 ng/ml (202-IL, R&amp;D Systems). The QCM Leukocyte Migration Assay (MilliporeSigma, # ECM557) and a GloMax Discovery plate reader (Promega, #PAGM3000) were used to quantify transwell T cell lymphocyte migration from the apical chamber over 4 h at 37 °C. Unconditioned HEI-193 media served as a negative control, unconditioned HEI-193 media supplemented with recombinant human CCL21 600 ng/ml (366-6C, R&amp;D Systems) served as a positive control, HEI-193 media 5 days after 12.5 Gy in 1 fraction, or HEI-193 media without radiation were placed in the basolateral chamber. All conditions were free from serum or other supplements unless specifically indicated.</p>", "<title>Mass cytometry by time-of-flight cell preparation and analysis</title>", "<p id=\"Par35\">All mass cytometry by time-of-flight (CyTOF) antibodies and concentrations used for analysis can be found in Supplementary Data ##SUPPL##3##5##. Primary conjugates of antibodies were prepared using the MaxPAR antibody conjugation kit (Fluidigm, #201153A). Following labeling, antibodies were diluted in Candor PBS Antibody Stabilization solution (Candor Bioscience, #131050) supplemented with 0.02% NaN3 to between 0.1 and 0.3 mg/mL final concentration and stored long-term at 4 °C. Each antibody clone and lot were titrated to optimal staining concentrations using primary human samples.</p>", "<p id=\"Par36\">All tissue preparations were performed simultaneously from each sample, as previously described^{##REF##26160952##29##}. Tumors were finely minced and digested in L-15 medium with 800 units/ml collagenase IV (Worthington, #LS004186) and 0.1 mg/ml DNase I (Sigma). After digestion, re-suspended cells were quenched with PBS/EDTA at 4 °C. To determine viability, all tissues were washed with PBS/EDTA and re-suspended 1:1 with PBS/EDTA and 100 mM Cisplatin (Enzo Life Sciences, #ALX-400-040-M050) for 60 s before quenching 1:1 with PBS/EDTA/BSA^{##REF##26160952##29##}. Cells were centrifuged at 500<italic>g</italic> for 5 min at 4 °C and re-suspended in PBS/EDTA/BSA at a density between 1 and 10 × 10⁶ cells/ml. Suspensions were fixed for 10 min at room temperature using 1.6% paraformaldehyde and frozen at −80 °C.</p>", "<p id=\"Par37\">Mass-tag cell barcoding was performed as previously described^{##REF##25612231##77##}. Briefly, 10⁶ cells from each sample were barcoded with distinct combinations of stable Pd isotopes in 0.02% saponin in PBS. Samples were then barcoded together. Cells were washed once with cell staining media (PBS with 0.5% BSA and 0.02% NaN₃), once with 1× PBS, and pooled into a single FACS tube (BD Biosciences). After data collection, each condition was deconvoluted using a single-cell debarcoding algorithm^{##REF##25612231##77##}.</p>", "<p id=\"Par38\">Cells were resuspended in cell staining media comprised of PBS with 0.5% BSA and 0.02% NaN₃, and antibodies against CD16/32 were added at 20 mg/mL for 5 min at room temperature on a shaker to block Fc receptors. Surface marker antibodies were then added, yielding 500 µL final reaction volumes, and stained for 30 min at room temperature on a shaker. Following staining, cells were washed 2 times with cell staining media, permeabilized with permeabilization buffer (eBioscience, #00-8333-56), and stained with intracellular antibodies in 500 µL for 60 min at 4 °C on a shaker. Cells were washed twice in cell staining media and stained with 1 mL of 1:4000 191/193Ir DNA intercalator (Fluidigm, #201192A) and diluted in PBS with 1.6% paraformaldehyde overnight. Cells were washed once with cell staining media and 2 times with double-deionized water. Care was taken to assure buffers preceding analysis were not contaminated with metals in the mass range above 100 Da. Mass cytometry samples were diluted in Cell Acquisition Solution (Fluidigm, #201237) containing bead standards (see below) to approximately 10⁶ cells per mL and then analyzed on a CyTOF-2 mass cytometer (Fluidigm) equilibrated with Cell Acquisition Solution.</p>", "<p id=\"Par39\">Data normalization was performed as previously described^{##REF##25612231##77##}. All mass cytometry files were normalized together using the mass cytometry data normalization algorithm^{##REF##25612231##77##}, which uses the intensity values of a sliding window of bead standards to correct for instrument fluctuations over time and between samples. After normalization and debarcoding of files, singlets were gated by event length and DNA. Live cells were identified by cisplatin-negative cells. All positive populations, negative populations, and antibody staining concentrations were determined by titration on positive and negative control cell populations.</p>", "<p id=\"Par40\">Scaffold maps were generated as previously described^{##REF##26160952##29##} using the open-source Statistical Scaffold R package available at github.com/SpitzerLab/statisticalScaffold. Landmark reference nodes were gated from peripheral blood mononuclear cells, while unsupervised clusters were generated via Clustering Large Applications (CLARA) clustering from samples pooled together, with each sample contributing an equal number of cells. Uniform manifold approximation and projection (UMAP) was performed on ArcSinh (cofactor = 5) transformed protein expression values on equal numbers of cells from each sample by randomly subsampling cells with parameters min.dist = 1.0. Clusters were identified by CLARA clustering using cells from all samples concatenated together.</p>", "<title>Proteomic mass spectrometry</title>", "<p id=\"Par41\">HSC and HEI-193 media samples were prepared for mass spectrometry as described above, and 50 μL of media was mixed with 50 μL of lysis buffer containing 75 mM ammonium bicarbonate, 1% sodium deoxycholate, 5 mM TCEP and 40 mM chloroacetamide and incubated at 37 °C for 30 min to reduce and alkylate proteins. Proteins were digested with endoproteinase LysC (Wako Chemicals) and trypsin (Promega) overnight at 37 °C, followed by sodium deoxycholate and 2% TFA precipitation and centrifugation for 15 minutes at maximum speed. Peptides were desalted using MicroSpin Columns (The Nest Group) and resuspended in 4% formic acid and 3% acetonitrile. Approximately 1 μg of digested peptides per sample was loaded onto a 75 μm ID column packed with 25 cm of Reprosil C18 1.9 μm, 120 Å particles (Dr. Maisch GmbH HPLC), and eluted into an Orbitrap Fusion Lumos Tribrid mass spectrometer (Thermo Fisher Scientific) over the course of a 120-min acquisition by gradient elution delivered by an Easy1200 nLC system (Thermo Fisher Scientific). The composition of mobile phases A and B were 0.1% formic acid in water and 0.1% formic acid in 80% acetonitrile, respectively. All MS spectra were collected with orbitrap detection, and the most abundant ions were fragmented by higher energy collision dissociation and detected in the ion trap, with a 1-s cycle time between MS1 spectra. All data were searched against the UniProt human proteome database. Peptide and protein identification searches were performed using the MaxQuant data analysis algorithm, and all peptide and protein identifications were filtered to a 1% false discovery rate^{##REF##19029910##78##,##UREF##12##79##}. Label-free quantification and statistical testing were performed using the MSstats statistical R-package^{##REF##24794931##80##}. The mass spectrometry data files (raw and search results) have been deposited to the ProteomeXchange Consortium via the PRIDE partner repository with dataset identifier PXD014798^{##REF##26527722##81##}. Parallel reaction monitoring (PRM) measurements were acquired by LC–MS/MS on a Q-Exactive Plus (Thermo Fisher Scientific, IQLAAEGAAPFALGMBDK) mass spectrometer equipped with an EASY-nLC 1200 system (Thermo Fisher Scientific, #LC140) using the same column configuration and HPLC settings as described above. All PRM data was analyzed by Skyline 4.2.0.19072^{##REF##20147306##82##}, quantified via MSstats, and have been deposited to Panorama Public^{##UREF##13##83##} with dataset identifier PXD014883.</p>", "<title>Targeted metabolite liquid chromatography–mass spectrometry</title>", "<p id=\"Par42\">HEI-193 cells were cultured and treated as described above, and 100 µL of cell-free supernatant (CFS) or cell pellets containing 10 million cells each were separately combined with cold H₂O:MeOH at a ratio of 1:1 containing internal standards of 2-amino-3-bromo-5-methylbenzoic acid and a labeled amino acid mixture (13C,15N) spiked-in at 1 µg/mL and 10 nM/mL, respectively. CFS and cell pellets were briefly vortexed or rotated overnight, respectively, and immediately chilled at 4 °C. All samples were centrifuged at 4 °C for 30 min at maximum speed, and the supernatant was aliquoted for quantification.</p>", "<p id=\"Par43\">Targeted liquid chromatography-high resolution mass spectrometry analysis was performed on a Sciex Exion UPLC equipped with a C18 Polar column (Phenomenex, 150 × 2.1 mm, 2.6 µm) and coupled to a Sciex QTRAP 7500 operated in negative mode with MRM acquisition of MS/MS data. A gradient of 0–90% acetonitrile over 16 min was used for compound separation. The XICs of all samples and QCs were visually inspected. All QCs displayed appropriate signals for analysis in addition to a significant peak capacity and retention time reproducibility. Raw data files were uploaded to SciExOS for processing, where filtering, feature detection, integration, and alignment of the chromatograms in each sample were performed. As a result, data matrices were generated with intensity values representing the area under the curve of significant chromatographic peaks above the lower limit of detection.</p>", "<title>Primary schwannoma cell culture, treatment, and metabolomic mass spectrometry</title>", "<p id=\"Par44\">Primary human vestibular schwannomas were cultured as previously described^{##UREF##14##84##}. Tumors were collected from the operating room and placed on ice for transfer to the lab. Under sterile conditions in a cell culture hood, the tissue was minced into 1 mm³ piece and then digested for 45 min at 37 °C in 0.25% trypsin/0.1% collagenase solution. Cells were resuspended in Dulbecco’s Modified Eagle Medium (Gibco, #11960069) supplemented with insulin (10 µg/mL, Sigma), 10% fetal bovine serum, and N2 supplement (Gemini Bio-Products, #400-163). The cell suspension was plated onto culture dishes pre-treated with poly-<sc>l</sc>-ornithine and laminin. Cultures were placed in a humidified incubator at 37 °C with 5.0% CO₂ and grown for 7–14 days without passage. Media was exchanged every 2–3 days. Cultures were treated with 0, 3, 10, or 20 Gy single fraction gamma-irradiation from a radioactive Cesium source. Six or 72 hours after radiotherapy, cultures were washed with ice-cold PBS and water and flash-frozen in liquid nitrogen. Derivatized metabolite extracts from these primary schwannoma cell cultures were analyzed by gas chromatography–mass spectrometry on a ThermoISQ Quadrupole. Raw data were analyzed with TraceFinder 4.1 (Thermo). Cell culture data were normalized to the total ion signal to control for extraction, derivatization, and/or loading effects.</p>", "<title>Quantitative polymerase chain reaction</title>", "<p id=\"Par45\">RNA was isolated using the RNEasy Mini Kit (Qiagen, #74106) and a QiaCube (Qiagen, #9001292), and cDNA was synthesized using the iScript cDNA Synthesis Kit (Bio-Rad, #1708891) and a ProFlex thermocycler (Thermo Fisher Scientific, #4484073). Target genes were amplified using PowerUp SYBR Green Master Mix (Thermo Fisher Scientific, #A25741) and a QuantStudio 6 thermocycler (Thermo Fisher Scientific, #4485691). Gene expression was calculated using the ΔΔCt method for candidate genes, with normalization to <italic>GAPDH</italic> (Supplementary Data ##SUPPL##3##11##).</p>", "<title>Bulk RNA sequencing and analysis</title>", "<p id=\"Par46\">RNA was isolated from frozen tumors or cell cultures using the All-Prep Universal Kit, and clean-up was performed using the RNEasy Kit as needed (Qiagen). RNA sequencing libraries were generated using the Illumina TruSeq Stranded mRNA Library Prep Kit and sequenced on an Illumina HiSeq-4000 using the paired-end 100 protocol for schwannomas and single-end 50 protocol for HEI-193 schwannoma cells. Reads were aligned to GRCh38 using the splice-aware aligner HISAT2 version 2.0.3 against an index containing SNP and transcript information (genome_snp_tran)^{##REF##25751142##85##}. Ensembl build 75 genes were quantified with featureCounts using uniquely mapped reads^{##REF##24227677##86##}. Differential expression analysis was performed using DESeq2 using the Wald test with an adjusted <italic>p</italic>-value threshold of 0.05 corrected for multiple hypotheses using the Benjamini-Hochberg method^{##REF##25516281##87##}. Complete linkage hierarchical clustering was performed using 1-Pearson correlation as the distance matrix with differentially expressed genes.</p>", "<title>Single-cell RNA sequencing and analysis</title>", "<p id=\"Par47\">HEI-193 schwannoma cells were dissociated in Trypsin–EDTA 0.25% (Thermo Fisher Scientific, #25200114), passed through a 40 μm strainer and washed/resuspended in phosphate-buffered saline. Fresh schwannomas were minced with sterile Bard-Parker #10 surgical scalpels (Aspen Surgical, #4–410) and incubated in 0.4% Collagenase Type 2 (Worthington, # LS004174) in pre-oxygenated Dulbecco’s Modified Eagle Medium (Thermo Fisher Scientific, #11960069) for 75 min at 37 °C while rotating at 800 rotations per minute on a thermomixer. The suspension was sequentially filtered through 70 μm (Corning, #352350) and 40 μm strainers (Corning, 352340), centrifuged at 300<italic>g</italic> for 5 min, and resuspended in cold phosphate-buffered saline. Single-cell suspensions were loaded onto a 10× Chromium controller using the Chromium Single Cell 3’ Library &amp; Gel Bead Kit v3 (10× Genomics). Libraries were sequenced on an Illumina NovaSeq (10× specific protocol) with &gt;50,000 reads per cell.</p>", "<p id=\"Par48\">Library demultiplexing, read alignment to human genome GRCh38, and unique molecular identifier (UMI) quantification was performed in Cell Ranger version 1.3.1 (10× Genomics). Schwannoma cells with greater than 200 unique genes were detected, and fewer than 15% of reads attributed to mitochondrial transcripts were retained. Data were normalized, and variance stabilized by SCTransform in Seurat version 3.0 using UMI count and percent of reads aligned to mitochondrial transcripts as covariates^{##REF##31178118##88##}. UMAP was performed on significant (<italic>p</italic> &lt; 0.05) principal components (determined by JackStraw analysis) and batch-corrected using Harmony with parameters min.dist = 0.3. Louvain clustering was performed with resolution = 0.3, and cluster markers were identified based on expression in at least 25% of cells and differential expression by more than 25% compared to all other clusters. For HEI-193 schwannoma cells, analysis was performed as above, except that cells with greater than 2000 UMIs and fewer than 20% of reads attributed to mitochondrial transcripts were retained, and UMAP was performed with min.dist = 0.2 without harmonization. Gene ontology analysis was performed using Enrichr without the inclusion of ribosomal subunits or mitochondrial genes^{##REF##27141961##69##}. Cell cluster identification was further analyzed using the AddModuleScore function within Seurat 3.0 to score expression signatures based on gene sets from the Molecular Signatures Database (MSigDB)^{##REF##26771021##89##}, intersected with differentially expressed cluster markers described above, and then normalized across all populations in UMAP space^{##REF##31178118##88##}.</p>", "<title>Single-nuclei RNA sequencing and analysis</title>", "<p id=\"Par49\">Flash-frozen archived schwannoma specimens were minced with sterile Bard-Parker #10 surgical scalpels (Aspen Surgical, #4–410) and mechanically dissociated with a Pestle Tissue Grinder (size A, Thomas Scientific, #3431E45) in ice-cold lysis buffer consisting of 0.32 M sucrose, 5 mM CaCl2, 3 mM MgAc2, 0.1 mM EDTA, 10 mM Tris-HCl, 1 mM DTT and 0.1% Triton X-100 in DEPC-treated water^{##REF##31097668##90##}. A sucrose solution consisting of 1.8 M sucrose, 3 mM MgAc2, 1 mM DTT, and 10 mM Tris-HCl in DEPC-treated water was added to the bottom of the lysis solution in ultracentrifuge tubes (Beckman Coulter) to form a gradient, which was ultracentrifuged at 107,000<italic>g</italic> for 2.5 h at 4 °C. Nuclei pellets were resuspended in phosphate-buffered saline and sequentially filtered twice in 30 μm strainers (Miltenyi Biotec, #130-098-458). Isolated nuclei were assessed with DAPI staining and loaded onto a 10× Chromium controller using the Chromium Single Cell 3’ Library &amp; Gel Bead Kit v2 (10× Genomics). Library sequencing and preprocessing for single nuclei were performed as described above for single-cell libraries, except that a pre-mRNA reference library (GRCh38), including intronic segments, was used for read alignment and quantification. Nuclei libraries with greater than 400 unique genes were detected, and fewer than 5% of reads attributed to mitochondrial transcripts were retained.</p>", "<p id=\"Par50\">To integrate single-nuclei and single-cell RNA sequencing data, all libraries passing respective QC filters described above were combined in silico and normalized with variance stabilization using SCTransform in Seurat version 3.0, with UMI count, percent of reads aligned to mitochondrial transcripts, and technique (single-cell versus single-nuclei) as covariates^{##REF##31178118##88##}. Principal component analysis was performed, and single nuclei and single-cell data were harmonized using Harmony in Seurat version 3.0 using technique and day-of tumor isolation as covariates. Clustering and marker identification was performed as described above for single cell-only analysis, with parameters min.dist = 0.3 and resolution = 0.3.</p>", "<title>CRISPR interference genome-wide screening</title>", "<p id=\"Par51\">CRISPRi screens were performed as described previously^{##REF##25307932##14##,##UREF##2##15##}. HEI-193 cells stably expressing CRISPRi components (dCas9-KRAB) were transduced with lentivirus supernatant containing the third-generation dual sgRNA CRISPRi library, which targets 20,528 genes and 1025 sgNTC^{##UREF##2##15##}. Screens were performed in triplicate cultures with coverage of at least 500× cells per construct. sgRNA-expressing cells were selected using puromycin (1 µm/mL) for 48 h and transferred to puromycin-free normal growth media for 48 h to allow recovery. Initial (T0) cell populations were then frozen in 10% DMSO and processed for genomic DNA alongside endpoint (T12) cell populations, which corresponded to 7.82 population doublings. Triplicate screens were also performed with radiotherapy (1.8 Gy × 5 fractions) delivered daily starting on T0, with the endpoints (T12) corresponding to 3.46 population doublings. Genomic DNA was harvested using the NucleoSpin Blood L Kit (Machery-Nagel, #740954.20) for each cell population, and sgRNA cassettes were amplified using 22 cycles of PCR using NEBNext Ultra II Q5 PCR MasterMix (New England Biolabs, #M0544L). Sequencing was performed on a NovaSeq 6000 (Illumina) using custom sequencing primers^{##UREF##2##15##}.</p>", "<p id=\"Par52\">sgRNA read counts were aligned using custom Python scripts derived from the ScreenProcessing package^{##UREF##2##15##}, without allowing mismatches. sgRNA counts with discordant target genes from the same vector, representative of vector recombination, or fewer than 100 reads detected in the T0 populations, were discarded from downstream analysis. Growth phenotype (gamma) was defined as log2(sgRNA count T12/sgRNA count T0) minus median sgNTC log2(sgRNA count T12/sgRNA count T0) as previously described^{##REF##25307932##14##}. Radiation phenotype (rho) was defined as log2(sgRNA count T12 (1.8 Gy × 5)/sgRNA count T12 (0 Gy)). Statistical significance was quantified using a two-sided Student’s <italic>t</italic>-test comparing replicate distributions of library-normalized counts for each sgRNA between conditions (rho) or time points (gamma). A discriminant threshold of 5, derived from the product of normalized gene-phenotype and −log10(<italic>p</italic>-value), corresponding to an empiric false discovery rate of ~1%, was selected for hit definitions^{##REF##25307932##14##}. To ascertain the fidelity of our screens, we overlapped all negative growth hits from our screen (without radiotherapy treatment) with common essential genes from DepMap^{##REF##29083409##91##} and found that 591 out of 918 total negative growth hits (64.4%) were also DepMap essential genes. The reproducibility of our screens was assessed by calculating the Pearson correlation coefficients of the screen hit phenotypes, which demonstrated a median R of 0.829 for no radiotherapy and 0.760 for radiotherapy conditions.</p>", "<title>Perturb-seq</title>", "<p id=\"Par53\">The single-cell Perturb-seq library was composed of sgRNAs targeting genes from RNA sequencing and DNA methylation profiling of human vestibular schwannomas (Supplementary Data ##SUPPL##3##11##). Using a single sgRNA vector strategy, protospacer sequences were selected from the optimized human CRISPRi v2.1 library^{##UREF##15##92##}. Library cloning was performed as previously described^{##REF##32231336##93##}. Insert lyophilized oligonucleotides (Twist Biosciences) containing the sgRNA sequences were resuspended at 100 nM in H₂O and amplified by PCR using HF Phusion polymerase (New England Biolabs, #M0531S). After verifying amplification on a 10% acrylamide gel, the PCR product was purified using MinElute Cleanup Kit (Qiagen, #28206). The pBA904 Perturb-seq sgRNA vector backbone (Addgene, #122238) was digested using FastDigest BstX1 (ThermoFisher Scientific, #FD1024) and Blp1 (ThermoFisher Scientific, #FD0094) and excised from a 0.8% agarose gel for purification using the NucleoSpin Gel Cleanup Kit (Macherey-Nagel, #740609.50). The insert pool and digested backbone were then ligated overnight at 16 °C using T4 DNA Ligase (New England Biolabs, #M0202T) with a vector-to-insert ratio of 1:1. The ligation reaction was purified by ethanol precipitation and transformed into Stellar Competent Cells (Takara, #636766) to assess library diversity by Sanger sequencing of 10 clones. For large-scale transformation, the library was transformed into MegaX Electrocompetent cells (ThermoFisher Scientific, #C640003) using electroporation on 15-cm LB carbenicillin plates. The library stock was prepared by scraping plates, followed by purification using the Midi Prep kit (Macherey-Nagel, #740410.50). Library sequencing was performed on an Illumina MiSeq run to ensure sgRNA uniformity. Using lentivirus, cells were transduced with the library at 1000× coverage at an MOI of 0.1, corresponding to approximately 95% of cells with a single integration. Seventy-two hours following transduction, sgRNA+ cells were FACS sorted (BFP+) and were recovered in DMEM 10% FBS. Sorted cultures were treated with either 0 Gy, 1.8 Gy × 5 daily fractions, or 12.5 Gy × 1 fraction of radiotherapy using the X-Rad 320 irradiator (Precision X-Ray). Twelve hours following the final fraction of radiotherapy, cells were trypsinized and harvested in single-cell suspension on the 10× Chromium Controller (10× Genomics, #1000204).</p>", "<p id=\"Par54\">Single-cell Perturb-seq libraries were processed using the Chromium Next GEM Single Cell 3’ GEM, Library &amp; Gel Bead Kit v3.1with Feature Barcoding (10× Genomics, #1000269), allowing direct capture of modified sgRNAs^{##REF##32231336##93##} and sequenced on an Illumina NovaSeq-6000. Cells from the 0 Gy condition were run across 2 GEM groups, while each of the radiation conditions was run on its own GEM group. Library demultiplexing, gene expression read alignment to human genome GRCh38, UMI quantification, and sgRNA assignment and quantification were performed in Cell Ranger version 6.1.2 with sgRNA barcoding (10× Genomics).</p>", "<p id=\"Par55\">Data analysis was performed using Seurat 4.3.0 in R version 4.2.2. Cells with greater than 200 detected features and UMIs mapping to only one sgRNA were retained. Target gene knockdown was quantified by library normalizing the transcriptome of each cell and obtaining the mean expression of each gene across all cells belonging to a given sgRNA within an individual GEM group (pseudobulk). RNA remaining for each gene target was calculated by dividing the pseudobulk expression into on-target cells with those of sgNTC cells, with a pseudo count of 0.01 added to each component. Only sgRNAs exerting greater than 75% knockdown in at least one of the two 0 Gy conditions, and also represented in at least 10 cells in each condition, were retained for analysis. To score expression changes of gene modules, marker genes were derived from Louvain clustering of human schwannoma cell types (Fig. ##FIG##0##1b##) and HEI-193 schwannoma cell states (Fig. ##FIG##1##2c##), as described above. The top 10 most specific cluster markers were used to interrogate each cell type or cell state, and the mean pseudobulk expression of these markers was obtained for each on-target sgRNA as well as for sgNTC cells, in each radiotherapy condition. sgRNA phenotypes were then normalized to pseudobulk cells containing sgNTC in the 0 Gy condition. These fold changes were log₂ transformed and grouped within radiotherapy conditions using hierarchical clustering with Pearson correlation and complete linkage.</p>", "<p id=\"Par56\">Differential expression analysis in Perturb-seq data was performed using the FindMarkers function in Seurat with MAST as the test type. Genes with <italic>p</italic> &lt; 0.05 and |log₂(fold change)| &gt; 1) were considered differentially expressed and used for gene ontology analyses in EnrichR with separate queries for all enriched or suppressed genes. To identify perturbations that preferentially generated phenotypes in radiotherapy conditions, the number of significantly differentially expressed genes was compared to identify perturbations with more than 40 excess differentially expressed genes in the radiotherapy (1.8 Gy × 5) conditions compared to control (0 Gy) conditions.</p>", "<title>Single-nuclei ATAC, RNA, and CRISPRi perturbation sequencing (snARC-seq)</title>", "<p id=\"Par57\">Genetic perturbations in snARC-seq rely on the CROP-seq vector (Addgene, pBA950)^{##REF##28099430##94##}, which allows for the capture of sgRNA identity from nuclear RNA transcripts. This design permits single sgRNA perturbations, and therefore we designed 2 independent sgRNA vectors per target gene, corresponding to each of the dual sgRNAs that targeted hit genes from the genome-wide CRISPRi V3 library^{##UREF##2##15##}. Oligonucleotides containing protospacer sequences (Supplementary Data ##SUPPL##3##11##) were ordered as a pool from Twist Bioscience and PCR amplified as described above. The oligonucleotide pool was ligated into the CROP-seq backbone using BstXI and BlpI digestion and T4 ligation. Library representation, including sgNTC overrepresentation, was performed on a MiSeq run to ensure sgRNA uniformity.</p>", "<p id=\"Par58\">The cloned library was packaged into lentivirus using HEK-293T cells. HEI-193 cultures were transduced to an MOI of 0.1, and FACS sorted for sgRNA+ cells after 48 h. Radiotherapy was then delivered to either 0 Gy or 1.8 Gy × 5 daily fractions using the X-Rad 320 irradiator (Precision X-Ray). Following completion of radiotherapy, cells were harvested with Trypsin and prepared following the Nuclei Isolation for Single Cell Multiome ATAC + Gene Expression Sequencing 10× Protocol (10× Genomics, CG000365 Rev C). Briefly, 1–2 × 10⁵ cells were incubated in chilled Lysis Buffer (Tris-HCl (pH 7.4) 10 mM, NaCl 10 mM, MgCl₂ 3 mM, Tween-20 0.1%, Nonidet P40 Substitute 0.1%, Digitonin 0.01%, BSA 1%, DTT 1mM, RNase inhibitor 1 U/µL) on ice for 4 min, washed with Wash Buffer (Tris-HCl (pH 7.4) 10 mM, NaCl 10 mM, MgCl₂ 3 mM, Tween-20 0.1%, BSA 1%, DTT 1 mM, RNase inhibitor 1 U/uL) 3 times, and resuspended in diluted nuclei buffer. Nuclei were counted, and membrane integrity was evaluated by Trypan staining on the Countess II FL Automated Cell Counter (Thermo, #TF-CACC2FL). Nuclei suspensions were diluted to approximately 3000 nuclei/µL and processed according to the 10× Chromium Next GEM Single Cell Multiome ATAC + Gene Expression protocol (CG000338 Rev A).</p>", "<p id=\"Par59\">To recover sgRNA identities from single-nuclei RNA fractions, CROP-seq guides were amplified into dual-indexed Illumina libraries from the cDNA product of the 10× multiome protocol as described above with a three-round hemi-nested PCR as previously described^{##REF##31422865##95##}. Totally, 15 ng of full-length cDNA product was amplified with primers binding to the sgRNA constant region and 10× Genomics Read 1 Adapter. Two subsequent PCR steps were performed to introduce i5 and i7 indices and Illumina P5 and P7 adapters. After the first round of PCR, each product was size-selected using SPRI beads at 1.0×. Subsequent PCRs were conducted with 1 ng product. The final PCR product was size selected with 0.5×, and then 1.0× SPRI beads, and library quality was assessed by TapeStation high-sensitivity D1000 analysis (Thermo, #5067-5584). CROP-seq libraries were pooled with gene expression libraries and sequenced on an Illumina NovaSeq 6000 using the paired-end 100 bp protocol.</p>", "<p id=\"Par60\">Library demultiplexing, read alignment to human genome GRCh38, and UMI quantification for the RNA and ATAC fractions were performed using Cell Ranger ARC version 2.0.1 (10× Genomics). Crop-seq sgRNAs were detected using kallisto bustools (v0.24.1)^{##REF##33795888##96##}. First, a sgRNA reference was built using kb ref with a k-mer size of 15 which was used as a reference for kb count. The sgRNA enrichment PCR sequences were then pseudo-aligned to this index using kallisto bustools, including the ARC multiome Gene Expression Whitelist version 1 (10× Genomics). For each cell barcode group, sgRNAs with less than 6 UMIs were filtered, and sgRNAs were assigned to cells using Geomux (v0.2.1)^{##REF##35981026##54##} (<ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/noamteyssier/geomux\">https://github.com/noamteyssier/geomux</ext-link>), which performs a hypergeometric test for each cell on its observed guide counts, then calculates a log₂-odds ratio between the two highest counts. Cells were assigned to their majority guide if their Benjamini–Hochberg corrected <italic>P</italic> value was below 0.05, the log-odds ratio was above 1, and the total number of UMIs was greater than 6. The resulting sgRNA assignments were used to determine cell barcode groups with a single detected sgRNA.</p>", "<p id=\"Par61\">Preprocessing of single-nuclei RNA and ATAC data was performed using Signac v1.8.0^{##REF##34725479##97##}. Cells containing the following quality measures were retained: ATAC UMI between 1000 and 100,000, RNA UMI between 50 and 25,000, nucleosome signal &lt;4, and TSS enrichment &gt;1. ATAC peak calling was performed using the MACS2 wrapper in Signac. Peaks were processed using term frequency-inverse document frequency (TF-IDF) normalization and singular value decomposition. RNA counts were normalized, and variance was stabilized by SCTransform using default parameters. ATAC UMAP projection was calculated using the latent semantic indexing reduction dimensions 2–30. RNA UMAP projection was calculated using principal component analysis dimensions 1:20, which was empirically determined using ElbowPlot. Louvain clustering for either ATAC or RNA data was performed using a resolution parameter of 0.5.</p>", "<p id=\"Par62\">Gene activity scores from the ATAC signal were generated by quantifying ATAC UMIs mapped to the promoter of each gene, defined as between the TSS and 2000 bp upstream of the TSS for each gene. To score gene activity changes of gene modules between radiotherapy and control conditions, gene activity scores were calculated for marker genes derived from Louvain clustering of human schwannoma cell types (Fig. ##FIG##0##1b##) and HEI-193 schwannoma cell states (Fig. ##FIG##1##2c##), as described above. Expression and gene activity were then pseudobulked according to the target gene and therefore included cells with either of the two targeting sgRNAs. The top ten most specific cluster markers were used for each cell type or cell state, and the mean pseudobulk gene activity of these markers was obtained for each on-target sgRNA as well as for sgNTC cells, in each radiotherapy condition. sgRNA phenotypes were then log₂ transformed, and the gene activity vector in radiotherapy (1.8 Gy × 5) conditions were subtracted by those in control conditions (0 Gy). These fold changes were clustered using hierarchical clustering with Pearson correlation and complete linkage.</p>", "<p id=\"Par63\">Transcription factor motif deviations in the setting of genetic or therapeutic perturbations were quantified using the ChromVAR^{##REF##28825706##59##} wrapper in Signac with default parameters against the peaks assay. Mean motif deviations for each sgRNA identity in each condition were quantified and subsetted to only motifs whose cognate transcription factors were expressed in HEI-193 cells using RNA sequencing data, as described above. To estimate the differential motif deviations for a given sgRNA perturbation in radiotherapy conditions versus control conditions, deviations were log₂ transformed, and deviations in radiotherapy conditions were subtracted by those in control conditions. To further quantify chromatin accessibility at motif regions as a consequence of epigenetic regulator snARC-seq perturbations, differentially accessible regions were determined using the FindMarkers function in Signac using logistic regression. Differentially accessible regions were further subsetted by those whose nearest neighbor gene was associated with ChIP-seq peaks derived from the ENCODE project (KLF13 accession ENCFF453MMH, SETDB1 accession ENCFF773RNU). Average ATAC profiles were obtained for each sgRNA condition at these restricted sets of differentially accessible regions with a window ±1000 bp and then normalized to the average read depth at 100 bps at each end flank of the distributions.</p>", "<title>Statistics</title>", "<p id=\"Par64\">All experiments were performed with independent biological replicates and repeated, and statistics were derived from biological replicates. Biological replicates are indicated in each figure panel or figure legend. No statistical methods were used to predetermine sample sizes, but sample sizes in this study are similar or larger to those reported in previous publications. Data distribution was assumed to be normal, but this was not formally tested. Investigators were blinded to conditions during clinical data collection and analysis of mechanistic or functional studies. Bioinformatic analyses were performed blind to clinical features, outcomes, or molecular characteristics. The clinical samples used in this study were retrospective and nonrandomized with no intervention, and all samples were interrogated equally. Thus, controlling for covariates among clinical samples is not relevant. Cells were randomized to experimental conditions. No clinical, molecular, or cellular data points were excluded from the analyses. Unless specified otherwise, lines represent means, and error bars represent the standard error of the means. In general, statistical significance is shown by asterisks (*<italic>p</italic> &lt; 0.05, **<italic>p</italic> ≤ 0.01, ***<italic>p</italic> ≤ 0.0001), but exact <italic>p-</italic>values are provided in the figure legends when possible. Lines show means ± standard error of the means. Boxplots show the 1st quartile, median, and 3rd quartile; whiskers represent a 1.5 inter-quartile range, and data outside this range are shown by points. Results were compared using Student’s <italic>t</italic>-tests, Fisher’s exact tests, and ANOVA, which are indicated in figure legends alongside approaches used to adjust for multiple comparisons. Multiple linear regression was performed in <italic>R</italic> (v 3.6.0). Recursive portioning analysis was performed using the <italic>rpart</italic> package in <italic>R</italic>, with a minimum split size of 10 and a complexity parameter of 0.02. Variables with a <italic>p</italic>-value of 0.1 or less on univariate analysis were included in RPA and multivariate analysis. Logistic regression models were constructed and evaluated using receiver operating characteristic analysis. A nomogram was created using the <italic>rms</italic> package in R, which generates a graphical nomogram based on a general linear model.</p>", "<title>Reporting summary</title>", "<p id=\"Par65\">Further information on research design is available in the ##SUPPL##4##Nature Portfolio Reporting Summary## linked to this article.</p>" ]

[ "<title>Results</title>", "<title>Schwannomas are comprised of neural crest and immune-enriched molecular groups</title>", "<p id=\"Par5\">DNA methylation profiling provides a robust classification of nervous system tumors and identifies biological drivers of tumorigenesis and treatment response^{##REF##29539639##16##,##REF##35534562##17##}. To define a molecular architecture for mechanistic interrogation of schwannomas, DNA methylation profiling was performed on 66 sporadic vestibular schwannomas from the University of California San Francisco (Fig. ##FIG##0##1a##, Supplementary Figs. ##SUPPL##0##1## and ##SUPPL##0##2##, and Supplementary Data ##SUPPL##3##1–3##). Unsupervised hierarchical clustering and K-means consensus clustering of differentially methylated DNA probes revealed 2 molecular groups (Fig. ##FIG##0##1a## and Supplementary Fig. ##SUPPL##0##1a##). Differentially methylated DNA probes across schwannoma molecular groups were enriched at genes involved in nervous system development or immunologic signaling (Fig. ##FIG##0##1a## and Supplementary Data ##SUPPL##3##2##). Unsupervised hierarchical clustering of 125 sporadic spinal or vestibular schwannomas from an independent institution also identified 2 molecular groups that were distinguished by differential DNA methylation of nervous system development or immune genes (Supplementary Fig. ##SUPPL##0##1b##)^{##REF##27723760##8##}. Schwannoma clustering using DNA methylation probes overlapping with active enhancers during neural crest development recapitulated 2 molecular groups of tumors (Supplementary Fig. ##SUPPL##0##2a, b##)^{##REF##22981823##18##}. RNA sequencing and differential expression analysis on 11 neural crest and 13 immune-enriched schwannomas integrated with DNA methylation profiling revealed enrichment and hypomethylation of either neural crest genes and Hedgehog target genes or immune genes and apolipoprotein genes across the 2 molecular groups of schwannomas (Supplementary Fig. ##SUPPL##0##2c, d## and Supplementary Data ##SUPPL##3##3##)^{##REF##20709693##19##}. Immunofluorescence on 49 schwannomas showed the Schwann cell differentiation marker SOX10 was expressed in both molecular groups but was enriched in neural crest compared to immune-enriched tumors (Supplementary Fig. ##SUPPL##0##2e##). Histologic assessment of 66 schwannomas showed immune-enriched tumors were distinguished by greater macrophage and lymphocyte infiltration, hyalinized vessels, and coagulative necrosis compared to neural crest schwannomas (Supplementary Fig. ##SUPPL##0##2f##).</p>", "<p id=\"Par6\">To define cell types comprising schwannoma molecular groups, single-nuclei or single-cell RNA sequencing was performed on 4 neural crest schwannomas and 5 immune-enriched schwannomas (Fig. ##FIG##0##1b–d## and Supplementary Figs. ##SUPPL##0##3## and ##SUPPL##0##4##). Integration of 10,628 single-nuclei or single-cell transcriptomes using Harmony^{##REF##31740819##20##} revealed 13 cell clusters in uniform manifold approximation and projection (UMAP) space (Fig. ##FIG##0##1b##). The expression of Schwann cell differentiation markers <italic>S100B</italic> and <italic>SOX10</italic> was used to identify 7 clusters of schwannoma cells and 6 clusters of microenvironment cells (Supplementary Fig. ##SUPPL##0##3a, b##). Schwannoma and microenvironment cell types were defined using differentially expressed marker genes (Supplementary Fig. ##SUPPL##0##3c## and Supplementary Data ##SUPPL##3##4##), unbiased gene expression signatures (Supplementary Fig. ##SUPPL##0##4##), and genes associated with active enhancers during demyelinating nerve injury^{##REF##25614629##21##} (Supplementary Fig. ##SUPPL##0##3d##). Schwannoma cell types reflected different stages of nerve injury and regeneration (Fig. ##FIG##0##1b##), which collectively involves axon injury, progenitor cell proliferation, myelin remodeling, vascular remodeling, complement activation, immune recruitment, and neural regeneration^{##REF##17341159##22##}. Comparison of tumor cell types in immune-enriched versus neural crest schwannomas showed enrichment of (1) immune-like schwannoma cells expressing <italic>BCL1</italic> and <italic>CD74</italic>, a regulator of macrophage migration, axon repair, and survival of neural progenitor cells;^{##REF##22454509##23##,##REF##31026565##24##} (2) suppression of vascular remodeling schwannoma cells expressing <italic>ADGRB3</italic>, a regulator of angiogenesis and cell proliferation^{##REF##21724586##25##–##UREF##3##27##}, and (3) suppression of axon injury schwannoma cells expressing <italic>NRXN3</italic>, a regulator of synapse function^{##REF##19369540##28##} (Fig. ##FIG##0##1c, d##). In support of these findings, immunohistochemistry and immunofluorescence revealed schwannoma cells expressing BCL1 were more common in immune-enriched compared to neural crest schwannomas (Supplementary Fig. ##SUPPL##0##3e, f##).</p>", "<p id=\"Par7\">To complement our transcriptomics and better define immune cell types in the schwannoma microenvironment, mass cytometry by time-of-flight (CyTOF) analysis was performed on 375,355 cells from 3 neural crest schwannomas and 3 immune-enriched schwannomas (Fig. ##FIG##0##1e–h##, Supplementary Figs. ##SUPPL##0##5##–##SUPPL##0##9##, and Supplementary Data ##SUPPL##3##5##). CD45+ immune cells were visualized <italic>in toto</italic> using Scaffold v0.1 maps^{##REF##26160952##29##} (Fig. ##FIG##0##1e## and Supplementary Fig. ##SUPPL##0##5a##). Proliferating immune cells adjacent to spike-in landmark myeloid or lymphoid clusters were greater in immune-enriched compared to neural crest schwannomas, including memory and effector CD4 and CD8 T cells, γδT cells, NK cells, macrophages, and conventional and plasmacytoid dendritic cells (Fig. ##FIG##0##1e##). UMAP and PhenoGraph clustering were used to define myeloid and lymphoid immune cell phenotypes^{##REF##26095251##30##} (Fig. ##FIG##0##1f–h##, Supplementary Fig. ##SUPPL##0##5b##, and Supplementary Figs. ##SUPPL##0##6##–##SUPPL##0##9##). In comparison to neural crest schwannomas, myeloid cells in immune-enriched schwannomas accumulated more macrophages lacking CD206 and with lower CD163 expression, a pattern associated with anti-tumor activity^{##REF##33504575##31##–##REF##34298638##33##}. PD1 + TEMRA CD8 T cells, which are associated with differentiated effector function and tumor control^{##REF##9348298##34##,##REF##28446615##35##}, were also enriched in immune-enriched compared to neural crest schwannomas. In support of these phenotypes, immunohistochemistry for CD68, CD3, and PD1 was greater in immune-enriched compared to neural crest schwannomas (Supplementary Fig. ##SUPPL##0##5c##).</p>", "<p id=\"Par8\">To determine if schwannoma molecular groups could be identified preoperatively, we analyzed magnetic resonance (MR) imaging and clinical features for 31 neural crest and 35 immune-enriched schwannomas (Fig. ##FIG##0##1i, j##, Supplementary Fig. ##SUPPL##0##10##, and Supplementary Data ##SUPPL##3##1##). Neural crest schwannomas presented as solid masses with restricted MR diffusion compared to immune-enriched tumors (48% versus 15%, <italic>p</italic> = 0.005, Fisher’s exact test) (Fig. ##FIG##0##1i##). Immune-enriched schwannomas presented with communicating hydrocephalus (38% versus 15%, <italic>p</italic> = 0.04) and cystic changes (53% versus 27%, <italic>p</italic> = 0.03) and had residual tumor adherent to the brainstem after resection (56% versus 21%, <italic>p</italic> = 0.02, Fisher’s exact tests) even after adjusting for tumor size (OR 5.3, 95% CI: 1.4–24.1, <italic>p</italic> = 0.02). Univariate and recursive partitioning analyses of MR imaging and clinical features showed that prior schwannoma radiotherapy, cystic changes, and the absence of reduced diffusion were specific to immune-enriched schwannomas (Supplementary Fig. ##SUPPL##0##10a##). Logistic regression using these features yielded a model with 79% sensitivity and 77% specificity in distinguishing neural crest and immune-enriched schwannomas (AUC 0.79) (Fig. ##FIG##0##1j## and Supplementary Fig. ##SUPPL##0##10b##). Analysis of clinical outcomes showed local freedom from recurrence was equivalent across schwannoma molecular groups (Supplementary Fig. ##SUPPL##0##10c##).</p>", "<title>Radiotherapy is sufficient for epigenetic reprogramming of neural crest to immune-enriched schwannoma</title>", "<p id=\"Par9\">Patients with prior schwannoma radiotherapy (42.9% versus 6.5%, <italic>p</italic> = 0.0007, Fisher’s exact test) were more likely to have immune-enriched schwannomas than neural crest schwannomas (Fig. ##FIG##0##1a##, Supplementary Figs. ##SUPPL##0##11## and ##SUPPL##0##12##, and Supplementary Data ##SUPPL##3##1##). Analysis of DNA methylation profiles across clinical features revealed a disproportionately higher number of differentially methylated DNA probes in schwannomas could be attributed to prior radiotherapy (Supplementary Fig. ##SUPPL##0##11a##). Hierarchical clustering of differentially methylated DNA probes distinguishing schwannomas with prior radiotherapy showed hypomethylation of immune genes and hypermethylation of neuronal progenitor maintenance genes^{##REF##32474139##36##} (Supplementary Fig. ##SUPPL##0##11b##). Comparison of DNA methylation profiles between paired primary and recurrent schwannomas from 6 patients (Supplementary Data ##SUPPL##3##1##) revealed epigenetic interconversion of recurrent tumors compared to cognate primary tumors in every instance where radiotherapy was delivered between serial surgeries (Fig. ##FIG##1##2a##). All recurrent schwannomas with prior radiotherapy from this matched set were immune-enriched and clustered together with pairwise Pearson correlation coefficients that were indistinguishable from randomly-selected unpaired schwannomas with prior radiotherapy (Supplementary Fig. ##SUPPL##0##11c##). Moreover, primary neural crest schwannomas with classic histology were infiltrated by greater numbers of lymphocytes and macrophages that persisted for at least 4 years after radiotherapy (Fig. ##FIG##1##2b## and Supplementary Fig. ##SUPPL##0##12##).</p>", "<p id=\"Par10\">RNA sequencing and differential expression analysis showed Hedgehog target genes were enriched in schwannomas without prior radiotherapy (Supplementary Fig. ##SUPPL##0##11d## and Supplementary Data ##SUPPL##3##6##). Thus, we hypothesized Hedgehog signaling may underlie neural crest schwannomas. Hedgehog signals are transduced through primary cilia^{##REF##30707108##37##}. Immunofluorescence revealed schwannoma cell cilia were longer in neural crest compared to immune-enriched schwannomas (Supplementary Fig. ##SUPPL##0##13a##), and single-cell and single-nuclei RNA sequencing validated Hedgehog target gene expression in schwannoma cells from human tumors (Supplementary Fig. ##SUPPL##0##13b##). Primary cilia were also identified on cultured human Schwann cells, which accumulated Smoothened in cilia and activated the Hedgehog transcriptional program in response to recombinant Sonic Hedgehog (SHH) (Supplementary Fig. ##SUPPL##0##13c–e##). Schwann cell proliferation was blocked by the Smoothened antagonist vismodegib or radiotherapy (Supplementary Fig. ##SUPPL##0##13f, g##), and radiotherapy also reduced ciliary length, attenuated Smoothened accumulation in primary cilia, and blocked Hedgehog target gene expression (Supplementary Fig. ##SUPPL##0##13h–j##). To study these mechanisms in human schwannoma cells, we used the HEI-193 cell line, which encodes heterozygous loss of <italic>NF2</italic> on chromosome 22q and a distal splice site mutation in the remaining <italic>NF2</italic> allele^{##REF##10024671##38##,##UREF##5##39##}. CRISPRi suppression of <italic>NF2</italic> in HEI-193 cells stably expressing dCas9-KRAB^{##REF##25307932##14##,##REF##23849981##40##} promoted cell proliferation compared to HEI-193 cells expressing non-targeted control sgRNAs (sgNTC) (Supplementary Fig. ##SUPPL##0##13k, l##), suggesting <italic>NF2</italic> retains tumor suppressor functionality in this cell line. Consistent with results from human Schwann cells (Supplementary Fig. ##SUPPL##0##13h–j##), radiotherapy blocked HEI-193 Hedgehog target gene expression (Supplementary Fig. ##SUPPL##0##13m##). In human tumors, the intraflagellar transport gene <italic>IFT88</italic>, which is necessary for assembly of primary cilia^{##REF##30707108##37##} and regulates the G1-S transition^{##REF##17264151##41##,##REF##21441926##42##}, was hypermethylated and suppressed in immune-enriched compared to neural crest schwannomas (Supplementary Fig. ##SUPPL##0##13n, o##).</p>", "<p id=\"Par11\">To more broadly define schwannoma cell responses to ionizing radiation, HEI-193 schwannoma cells were treated with fractionated (1.8 Gy x 5 fractions) or hypofractionated (12.5 Gy x 1 fraction) radiotherapy, both of which are used to treat human schwannomas^{##UREF##0##6##}. Radiotherapy blocked the growth of schwannoma cells (Supplementary Fig. ##SUPPL##0##14a, b##), and qPCR assessment of genes distinguishing molecular groups of human schwannomas (Fig. ##FIG##0##1##) showed radiotherapy induced schwannoma cell expression of inflammatory apolipoproteins^{##REF##23720750##43##,##REF##30082772##44##}, immediate early genes that drive cell fate decisions^{##REF##21252999##45##}, and <italic>SOX6</italic>, an inhibitor of oligodendrocyte cell differentiation^{##REF##17084361##46##} (Supplementary Fig. ##SUPPL##0##14c##). To determine if these genes promoted schwannoma cell survival, <italic>APOD</italic> or <italic>SOX6</italic> were suppressed in HEI-193 cells using CRISPRi, which each attenuated schwannoma cell proliferation compared to cells expressing sgNTC (Supplementary Fig. ##SUPPL##0##14d, e##). DNA methylation profiling and RNA sequencing revealed hypomethylation and enriched expression of immune and apolipoprotein genes in surviving HEI-193 cells after radiotherapy (Supplementary Fig. ##SUPPL##0##14f, g##). To determine if radiotherapy reprograms schwannoma cell states, single cell RNA-sequencing was performed on HEI-193 cells after control, fractionated radiotherapy, or hypofractionated radiotherapy treatments (Supplementary Fig. ##SUPPL##0##14h##). Clustering of 39,569 single-cell transcriptomes revealed 15 cell states in UMAP space (Fig. ##FIG##1##2c##). Schwannoma cell states were defined using differentially expressed marker genes (Supplementary Fig. ##SUPPL##0##14i## and Supplementary Data ##SUPPL##3##7##), revealing activation of endoplasmic reticulum (ER) stress, interferon signaling, membrane signaling, and p53 signaling in response to radiotherapy (Fig. ##FIG##1##2c–e##).</p>", "<p id=\"Par12\">To define how schwannoma cell states (Fig. ##FIG##1##2c##) or cell types (Fig. ##FIG##0##1b##) respond to radiotherapy, we used Perturb-seq, a functional genomic approach coupling CRISPRi screening with transcriptomic phenotypes in single cells^{##REF##35688146##47##–##REF##27984733##49##}. Perturb-seq suppression of 15 genes distinguishing molecular groups of human schwannomas or schwannoma cell states (Fig. ##FIG##0##1##) was performed in HEI-193 cells with control, fractionated radiotherapy, or hypofractionated radiotherapy treatments (Supplementary Data ##SUPPL##3##8##). Integration of single-cell transcriptomes revealed intercellular heterogeneity that was dependent on radiotherapy dose and the cell cycle (Supplementary Fig. ##SUPPL##0##15a–e##). We then asked whether Perturb-seq gene suppression affected gene modules distinguishing the 15 schwannoma cell states from single-cell RNA sequencing of schwannoma cells (Fig. ##FIG##1##2c##), or the 7 schwannoma cell types reflecting different stages of nerve injury and regeneration from integrated single-nuclei and single-cell RNA sequencing of human schwannomas (Fig. ##FIG##0##1b##). Radiotherapy dose was the primary determinant of cell stress, p53 pathway, RNA splicing, and glutathione pathway activation, but genetic perturbations caused heterogenous changes in gene module expression with and without ionizing radiation (Fig. ##FIG##1##2f##). To identify perturbations selectively disrupting gene expression programs in combination with radiotherapy, differential expression analysis was performed on single cells expressing targeted versus non-targeted sgRNAs with or without radiotherapy (Supplementary Data ##SUPPL##3##9##). Suppression of <italic>SHH</italic>, <italic>SOX6</italic>, or the receptor tyrosine phosphatase <italic>PTPRG</italic>, which regulates neural developmental signaling^{##REF##20133774##50##}, exhibited greater numbers of differentially expressed genes after radiotherapy compared to control treatment (Fig. ##FIG##1##2g, h## and Supplementary Fig. ##SUPPL##0##15f##). Integrated single-nuclei and single-cell RNA sequencing showed <italic>PTPRG</italic> was expressed in schwannoma cells from human tumors (Fig. ##FIG##1##2i##), Perturb-seq suppression of <italic>PTPRG</italic> in schwannoma cells inhibited genes underlying nervous system development only in combination with radiotherapy (Fig. ##FIG##1##2h##), and CRISPRi suppression of <italic>PTPRG</italic> enhanced schwannoma cell apoptosis with radiotherapy (Fig. ##FIG##1##2j## and Supplementary Fig. ##SUPPL##0##15g, h##). These data reveal polygenic mechanisms underlie reprograming of neural crest to immune-enriched schwannoma and suggest a role for <italic>PTPRG</italic> in schwannoma response to radiotherapy.</p>", "<title>Epigenetic regulators reprogram schwannoma cells and drive immune cell infiltration in response to radiotherapy</title>", "<p id=\"Par13\">To more broadly define genomic drivers specifying schwannoma cell states in response to ionizing radiation, triplicate genome-wide CRISPRi screens were performed using dual sgRNA libraries comprised of 20,528 targeted sgRNAs and 1025 sgNTCs^{##UREF##2##15##} (Fig. ##FIG##2##3a##, Supplementary Fig. ##SUPPL##0##16##, ##SUPPL##0##17##, and Supplementary Data ##SUPPL##3##10##). The effect of genetic perturbations on HEI-193 schwannoma cell growth ± radiotherapy was defined by quantifying the relative DNA abundance of all sgRNAs in each sample using sequencing of integrated barcodes (Supplementary Data ##SUPPL##3##10##). Gene set enrichment analysis of radiotherapy sensitivity screen hits showed expected enrichment of cell cycle and DNA repair, but also revealed significant enrichment of epigenetic genes (Supplementary Fig. ##SUPPL##0##16a##). Examination of screen hits identified 29 epigenetic regulators associated with radiotherapy resistance or sensitivity phenotypes in schwannoma cells (Fig. ##FIG##2##3b, c##). In support of these findings, CRISPRi suppression of the histone demethylases <italic>KDM1A</italic> or <italic>KDM5C</italic> validated radiotherapy resistance or sensitivity phenotypes, respectively (Fig. ##FIG##2##3d, e## and Supplementary Fig. ##SUPPL##0##16b##).</p>", "<p id=\"Par14\">Cancer cell death from ionizing radiation leads to acute, transient recruitment of immune cells to the tumor microenvironment^{##UREF##6##51##}, but we identified surviving schwannoma cells alongside infiltrating immune cells for many years after treatment of human tumors with radiotherapy (Fig. ##FIG##1##2b## and Supplementary Fig. ##SUPPL##0##2f##, ##SUPPL##0##5c##, ##SUPPL##0##12##). To determine if schwannoma cell reprogramming contributes to immune cell infiltration of the tumor microenvironment, proteomic mass spectrometry was performed on conditioned media from surviving HEI-193 schwannoma cells after radiotherapy (Supplementary Fig. ##SUPPL##0##17a–c##). Ontology analyses of 425 differentially expressed proteins from conditioned media revealed enrichment of apolipoproteins after ionizing radiation (Fig. ##FIG##2##3f##), and a parallel reaction monitoring targeted assay validated secretion of APOA1 and other chemokines from surviving schwannoma cells (Fig. ##FIG##2##3g##). Transwell migration assays showed conditioned media from schwannoma cells recruited primary human peripheral blood lymphocytes after radiotherapy (Supplementary Fig. ##SUPPL##0##16c##), and conditioned media from schwannoma cells with CRISPRi suppression of the radiotherapy resistance hit <italic>KDM1A</italic> enhanced lymphocyte migration (Fig. ##FIG##2##3h##). In contrast, conditioned media from schwannoma cells with CRISPRi suppression of <italic>APOA1</italic> or the radiotherapy sensitivity hit <italic>KDM5C</italic> inhibited lymphocyte migration (Fig. ##FIG##2##3h## and Supplementary Fig. ##SUPPL##0##16b##). Thus, epigenetic mechanisms in schwannoma cells contribute to immune cell infiltration in response to radiotherapy.</p>", "<p id=\"Par15\">To determine if altered expression of epigenetic regulators mediates schwannoma responses to radiotherapy, we analyzed the 29 epigenetic hits from our genome-wide CRISPRi screen (Fig. ##FIG##2##3b, c##) across schwannoma cell types (Fig. ##FIG##0##1b##) and schwannoma cell states (Fig. ##FIG##1##2c##). Surprisingly, no epigenetic regulators were differentially expressed across either context, either with or without radiotherapy (Supplementary Data ##SUPPL##3##4,7##). Epigenetic regulator activity is dependent on metabolite cofactors that covalently modify histone subunits^{##REF##26492570##52##}. Thus, we hypothesized schwannoma cell metabolites may be altered in response to radiotherapy. To test this, we performed targeted metabolite profiling of HEI-193 cells after control, fractionated radiotherapy, or hypofractionated radiotherapy treatments using liquid chromatography mass spectrometry. Radiotherapy suppressed the KDM5C cofactor α-ketoglutarate and succinic acid, a biproduct of α-ketoglutarate metabolism (Fig. ##FIG##2##3i##). α-ketoglutarate was also suppressed by radiotherapy in primary schwannoma cells from 7 patients (Supplementary Fig. ##SUPPL##0##17d##). Moreover, radiotherapy suppressed the KDM1A cofactor flavin adenine dinucleotide (FAD) and increased the KDM5C cofactor ascorbic acid (Fig. ##FIG##2##3i##). RNA sequencing showed <italic>IDH1/2</italic> and <italic>MDH1/2</italic>, which produce α-ketoglutarate or succinic acid, respectively, were suppressed following schwannoma cell radiotherapy (Fig. ##FIG##2##3j##). <italic>DHCR7</italic>, which metabolizes ascorbic acid precursors^{##REF##12543708##53##}, was also suppressed after radiotherapy, but the nudix hydrolases <italic>NUTD1/4/14</italic>, which degrade FAD, were increased (Fig. ##FIG##2##3j##). These data suggest altered expression of metabolic enzymes and metabolite cofactors may influence epigenetic regulator activity during schwannoma radiotherapy responses.</p>", "<title>Single-nuclei ATAC, RNA, and CRISPRi perturbation sequencing identifies integrated genomic mechanisms driving schwannoma cell state evolution</title>", "<p id=\"Par16\">To define how epigenetic regulators shape chromatin accessibility and gene expression in schwannoma cells during tumor evolution, we developed a technique for simultaneous interrogation of chromatin accessibility and gene expression coupled with genetic and therapeutic perturbations in single-nuclei (Fig. ##FIG##3##4a##). <underline>S</underline>ingle-<underline>n</underline>uclei <underline>A</underline>TAC, <underline>R</underline>NA, and <underline>C</underline>RISPRi perturbation sequencing (snARC-seq) of the 29 epigenetic regulator hits from our genome-wide CRISPRi screen (Fig. ##FIG##2##3b, c##) was performed in HEI-193 cells with control or radiotherapy treatments (Supplementary Fig. ##SUPPL##0##18a##). sgRNA identities were assigned to individual cells using a hypergeometric test^{##REF##35981026##54##} (Supplementary Fig. ##SUPPL##0##18b, c##). Genome-wide ATAC signals were enriched at transcription start sites and 5’ nucleosome free regions^{##REF##19204718##55##} (Supplementary Fig. ##SUPPL##0##18d##). ATAC and RNA sequencing data exhibited heterogenous distributions in UMAP space^{##REF##28504683##56##} (Fig. ##FIG##3##4b##). Together, these data support successful simultaneous profiling of 3 genomic modalities in single-nuclei with or without radiotherapy (Fig. ##FIG##3##4a##).</p>", "<p id=\"Par17\">To determine if snARC-seq suppression of chromatin regulators reprograms the epigenetic landscape of schwannoma cells, we quantified gene activity scores for open chromatin regions nearby marker genes distinguishing schwannoma cell states (Fig. ##FIG##1##2c##) or cell types (Fig. ##FIG##0##1b##). Differential gene activity scores clustered according to gene ontologies of perturbed epigenetic regulators (e.g., histone demethylases, histone acetyltransferases) and CRISPRi screen phenotypes (radiotherapy sensitivity, negative rho; radiotherapy resistance, positive rho) (Fig. ##FIG##3##4c##). For instance, snARC-seq suppression of the elongator acetyltransferase complex component <italic>ELP6</italic> attenuated interferon signaling and ER stress schwannoma cell states that were normally activated by radiotherapy (Fig. ##FIG##1##2c–e##), consistent with the role of the elongator acetyltransferase complex in gene activation and sensitivity to genotoxic stress^{##REF##19834596##57##,##REF##10445034##58##}.</p>", "<p id=\"Par18\">To elucidate transcription factors underlying changes in gene expression programs with snARC-seq suppression of chromatin regulators, we scored transcription factor motif deviation with or without radiotherapy^{##REF##28825706##59##} (Fig. ##FIG##3##4d##). Restricting analysis to transcription factors in HEI-193 cells revealed heterogenous disruptions in chromatin accessibility that clustered based on CRISPRi screen phenotypes (Fig. ##FIG##3##4d##). snARC-seq suppression of the radiotherapy sensitivity hit <italic>KDM5C</italic> caused enrichment of open chromatin regions at KLF13 motifs with radiotherapy (Fig. ##FIG##3##4e##), and KLF13 target genes such as <italic>DDI2</italic> and <italic>PTPA</italic> were simultaneously accessible at their genomic loci and had enriched RNA expression in single-nuclei following snARC-seq suppression of <italic>KDM5C</italic> with radiotherapy (Supplementary Fig. ##SUPPL##0##18e##). <italic>ITIH4</italic>, a secreted protein that was enriched in conditioned media from schwannoma cells surviving radiotherapy (Fig. ##FIG##2##3g##), displayed closed chromatin and RNA suppression following snARC-seq suppression of <italic>KDM5C</italic> with radiotherapy (Supplementary Fig. ##SUPPL##0##18e##). Concordant changes in KLF13 gene activity were not observed following snARC-seq suppression of the radiotherapy resistance hit <italic>KDM1A</italic> with radiotherapy (Fig. ##FIG##3##4e##), consistent with opposing phenotypes of <italic>KDM1A</italic> and <italic>KDM5C</italic> in mediating schwannoma radiotherapy responses (Fig. ##FIG##2##3c##). snARC-seq suppression of the histone methyltransferase <italic>SETDB1</italic> increased accessibility at TCF3 motifs and expression of TCF3 target genes (Fig. ##FIG##3##4e##) such as <italic>RNF217</italic>, <italic>FOXO1</italic>, and <italic>RAD23B</italic> with radiotherapy (Supplementary Fig. ##SUPPL##0##18e##). Integrated single-nuclei and single-cell RNA sequencing showed TCF3 target genes were expressed in schwannoma cells from human tumors (Fig. ##FIG##3##4f##), and schwannoma clustering restricted to RNA sequencing of TCF3 target genes recapitulated neural crest and immune-enriched molecular groups of schwannomas (Fig. ##FIG##3##4g##). Thus, our snARC-seq technique for simultaneous interrogation of chromatin accessibility and gene expression coupled with genetic and therapeutic perturbations in single-nuclei reveals epigenetic dependances underlying radiotherapy responses in schwannomas cells that are conserved across molecular groups of human tumors.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par19\">Mutational and non-mutational mechanisms are critical for cancer evolution^{##REF##959840##5##,##REF##35022204##60##}. Schwannomas are the most common tumors of the peripheral nervous system and have a remarkably low burden of somatic mutations that is not increased by radiotherapy^{##REF##27723760##8##,##REF##28409725##9##,##UREF##7##61##}. Thus, schwannomas represent prototypical tumors for understanding epigenetic mechanisms specifying tumor cell states, tumor heterogeneity, and response to therapy. Our results reveal schwannomas are comprised of neural crest and immune-enriched molecular groups that are distinguished by schwannoma and immune cell types, and that radiotherapy is sufficient for epigenetic reprogramming of neural crest schwannomas to immune-enriched schwannomas (Fig. ##FIG##4##5##). By integrating multiplatform profiling of human tumors with multiomic functional genomic approaches, we show interconversion of schwannoma molecular groups, cell types, and cell states in response to radiotherapy, a treatment that is used for half of cancer patients worldwide^{##UREF##8##62##}. Future studies will be needed to determine if the epigenetic mechanisms we report are relevant to other treatment modalities or tumorigenesis. Intriguingly, patients in our study with autoimmune diseases and severe allergies were more liked to have immune-enriched schwannomas than neural crest schwannomas (25.7% vs 0%, p = 0.0025, Fischer’s exact test) (Fig. ##FIG##0##1a## and Supplementary Data ##SUPPL##3##1##), suggesting systemic factors may also influence the epigenetic architecture of cancer. To that end, we establish a framework for investigating how tumor evolution and responses to treatment are modulated by epigenetic reprogramming. This paradigm is bolstered by an innovative method for simultaneous profiling of epigenetic and transcriptional cell states coupled with genetic and therapeutic perturbations in single-nuclei (snARC-seq), a technique that may enable new discoveries in health and disease.</p>" ]

[]

[ "<p id=\"Par1\">Mechanisms specifying cancer cell states and response to therapy are incompletely understood. Here we show epigenetic reprogramming shapes the cellular landscape of schwannomas, the most common tumors of the peripheral nervous system. We find schwannomas are comprised of 2 molecular groups that are distinguished by activation of neural crest or nerve injury pathways that specify tumor cell states and the architecture of the tumor immune microenvironment. Moreover, we find radiotherapy is sufficient for interconversion of neural crest schwannomas to immune-enriched schwannomas through epigenetic and metabolic reprogramming. To define mechanisms underlying schwannoma groups, we develop a technique for simultaneous interrogation of chromatin accessibility and gene expression coupled with genetic and therapeutic perturbations in single-nuclei. Our results elucidate a framework for understanding epigenetic drivers of tumor evolution and establish a paradigm of epigenetic and metabolic reprograming of cancer cells that shapes the immune microenvironment in response to radiotherapy.</p>", "<p id=\"Par2\">Schwannomas are regularly treated with radiotherapy, but the molecular effects on these tumours and their microenvironment remain unclear. Here, the authors show that radiotherapy can induce epigenetic reprogramming and immune infiltration in schwannomas, and develop the snARC-seq approach to analyse the epigenomic evolution at the single-cell level.</p>", "<title>Subject terms</title>" ]

[ "<title>Supplementary information</title>", "<p>\n\n\n\n\n\n</p>", "<title>Source data</title>", "<p>\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1038/s41467-023-40408-5.</p>", "<title>Acknowledgements</title>", "<p>The authors thank Jeremy Reiter, Monika Sigg, Aparna Bhaduri, Aaron Tward, and Zora Arum for providing comments and reagents; Eric Chow, Derek Bogdanoff, Tomasz Nowakowski, Chang Kim, and Galina Schmunk for technical sequencing assistance and analysis; and Ken Probst and Noel Sirivansanti for Illustrations. This study was supported by the ASCO Conquer Cancer Sontag Foundation Young Investigator Award to SJL; NIH grants R21 HD106238 and R01 CA251221, and DOD grant NFRP NF200021 to D.R.R.; NIH grant U54 CA209891 to N.J.K.; a Children’s Tumor Foundation Young Investigator Award to H.N.V.; and an American Otological Society Fellowship Grant to M.C.D. Sequencing was performed at the UCSF CAT, supported by UCSF PBBR, RRP IMIA, and NIH grant S10 OD028511.</p>", "<title>Author contributions</title>", "<p>All authors made substantial contributions to the conception or design of the study; the acquisition, analysis, or interpretation of data; or drafting or revising the paper. All authors approved the paper. All authors agree to be personally accountable for individual contributions and to ensure that questions related to the accuracy or integrity of any part of the work are appropriately investigated, resolved, and the resolution documented in the literature. S.J.L., N.W.C., M.P., M.C.D., J.E.V.M., D.L.S., H.N.V., U.E.L., C.D.E., N.J.K., M.H., M.H.S., L.G., P.V.T., and D.R.R. designed the study and analyses. Experiments were performed by S.J.L., T.C.C., N.W.C., J.S., M.P., M.C.D., K.F., W.C.C., D.L.S., H.N.V., A.C., J.P., J.D.B., U.E.L., K.J.H.G., E.S., K.H.C., B.V.L., D.W., and D.R.R. Data analysis was performed by S.J.L., T.C.C., N.W.C., J.S., M.P., M.C.D., W.C.C., J.E.V.M., D.L.S., H.N.V., U.E.L., and D.R.R. The study was supervised by S.J.L., H.N.V., S.E.B., P.K.S., S.T.M., D.L., M.W.M., M.S.B., A.P., N.J.K., M.H., M.H.S., L.G., P.V.T., and D.R.R. The paper was prepared by S.J.L. and D.R.R. with input from all authors.</p>", "<title>Peer review</title>", "<title>Peer review information</title>", "<p id=\"Par66\"><italic>Nature Communications</italic> thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.</p>", "<title>Data availability</title>", "<p>DNA methylation array data are deposited on GEO under accession <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE222042\">GSE222042</ext-link>. The Hg19 human reference genome was used to analyze DNA methylation arrays [<ext-link ext-link-type=\"uri\" xlink:href=\"https://bioconductor.org/packages/IlluminaHumanMethylationEPICanno.ilm10b2.hg19/\">https://bioconductor.org/packages/IlluminaHumanMethylationEPICanno.ilm10b2.hg19/</ext-link>]. All sequencing raw data, including bulk RNA-seq, scRNA-seq, snRNA-seq, Perturb-seq, and snARC-seq using the Illumina Hiseq 4000 and Novaseq 6000 sequencers, are deposited on SRA under accession <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ncbi.nlm.nih.gov/bioproject/PRJNA917076/\">PRJNA917076</ext-link>. Proteomic mass spectrometry data have been deposited on ProteomeXchange under accession <ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ebi.ac.uk/pride/archive/projects/PXD014798\">PXD014798</ext-link>. Metabolomic mass spectrometry data have been deposited on MassIVE under accession <ext-link ext-link-type=\"uri\" xlink:href=\"ftp://massive.ucsd.edu/MSV000091760/\">MSV000091760</ext-link>. CyTOF raw data are deposited on [10.17632/hjmvnf48gh.1]^{##UREF##16##98##}. <xref ref-type=\"sec\" rid=\"Sec32\">Source data</xref> are provided in this paper.</p>", "<title>Code availability</title>", "<p>Computational code for data analysis is deposited on <ext-link ext-link-type=\"uri\" xlink:href=\"https://github.com/liujohn/schwannoma\">https://github.com/liujohn/schwannoma</ext-link> [10.24433/CO.0193242.v1]^{##UREF##17##99##}.</p>", "<title>Competing interests</title>", "<p id=\"Par67\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><title>Schwannomas are comprised of neural crest and immune-enriched molecular groups.</title><p><bold>a</bold> Hierarchical clustering of the top 2000 most differentially methylated probes from 66 vestibular schwannomas. Significant gene ontology terms corresponding to hypomethylated probes in neural crest schwannomas (NCS) or immune-enriched schwannomas (IES), clinical metadata, and the molecular neuropathology (MNP) DNA methylation classification of central nervous system tumors^{##REF##29539639##16##} are shown. <bold>b</bold> Integrated UMAP of 10,628 transcriptomes from harmonized schwannoma single-nuclei (<italic>n</italic> = 6) or single-cell (<italic>n</italic> = 3) RNA sequencing showing schwannoma cell (SC) types and tumor microenvironment cell types. <bold>c</bold> UMAPs from <bold>b</bold> with individual transcriptomes split according to a molecular group of origin. <bold>d</bold> Relative composition of SC types according to a molecular group of origin, colored as in (<bold>b</bold>). <bold>e</bold> Scaffold plot comprised of 375,355 Ki67+ immune cells from NCS (<italic>n</italic> = 3) or IES (<italic>n</italic> = 3) analyzed using mass cytometry time-of-flight (CyTOF). Manually gated landmark immune cell populations (black) are annotated. Schwannoma immune cell cluster is colored when the proportion of cells is statistically different between IES (positive) and NCS (negative). <bold>f</bold> CyTOF UMAPs of CD45+ immune cells with overlaid density plots for manually gated myeloid cells (top, 40,000 cells) or CD8 T cells (bottom, 6632 cells) in NCS (left) or IES (right). <bold>g</bold> UMAP feature plots of marker genes used to define myeloid or CD8 T cells in (<bold>f</bold>). <bold>h</bold> CyTOF proportion of schwannoma myeloid cells (left) or CD8 T cells (right) corresponding to M1 macrophages or PD1 + TEMRA CD8 T cells, respectively, in NCS (<italic>n</italic> = 3 independent tumors) or IES (<italic>n</italic> = 3 independent tumors). Lines represent means, and error bars represent the standard error of means (two-sided Student’s <italic>t</italic>-tests, *<italic>p</italic> = 0.0174, **<italic>p</italic> = 0.0065). <bold>i</bold> Representative preoperative magnetic resonance imaging of 66 vestibular schwannomas using T1 post-contrast, T2 diffusion-weighted, or apparent diffusion coefficient (ADC) sequences reveals NCS present as solid masses with reduced diffusion (dotted line) and IES present with cystic changes (arrows) and hydrocephalus. <bold>j</bold> Nomogram for schwannoma immune enrichment and molecular grouping based on non-invasive clinical and magnetic resonance imaging features. Source data are provided as a Source Data file.</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><title>Radiotherapy is sufficient for epigenetic reprogramming of neural crest to immune-enriched schwannoma.</title><p><bold>a</bold> Pairwise Pearson correlation coefficients grouped by hierarchical clustering of DNA methylation profiles from the patient (Pt) matched primary and recurrent schwannomas (<italic>n</italic> = 13). Arrows represent the reprogramming of primary NCS to IES at recurrence. <bold>b</bold> H&amp;E-stained sections of a patient-matched primary NCS and recurrent IES, showing Verocay bodies (top arrows) and abundant lymphocytes (bottom arrows) with foamy and hemosiderin-filled macrophages (asterisks). Scale bar, 100 μm. Similar findings were observed in two additional matched pairs. <bold>c</bold> UMAP of 38,754 transcriptomes from single-cell RNA sequencing of HEI-193 cells after treatment with 0Gy, 1.8Gy × 5, or 12.5Gy × 1 (<italic>n</italic> = 3 independent replicates per condition) of radiotherapy revealing 15 distinct schwannoma cell states. <bold>d</bold> UMAPs from <bold>c</bold> with individual transcriptomes split according to triplicate treatment conditions. <bold>e</bold> Relative composition of cell states from <bold>c</bold> according to treatment conditions. <bold>f</bold> Perturb-seq gene-set expression heatmap of 3546 pseudobulked transcriptomes from HEI-193 cells following sgRNA perturbations (columns) across treatment conditions. Expression values are normalized to cells harboring non-targeting control sgRNAs (sgNTC) with 0 Gy. <bold>g</bold> Number of differentially expressed genes (DEG) from schwannoma cell Perturb-seq with radiotherapy (y-axis) versus 0Gy (<italic>x</italic>-axis). sgRNA perturbations with ≥40 DEG after radiotherapy compared to control are orange. sgRNA not meeting this threshold are dark gray. sgNTCs are light gray. <bold>h</bold> Differential gene expression analysis from <italic>PTPRG</italic> perturbation compared to sgNTC in 0 Gy (left) versus 1.8 Gy × 5 conditions (right). Significant positive (red) or negative (blue) gene expression changes are colored (<italic>p</italic> &lt; 0.05, |log₂(fold change)| &gt; 1), corresponding to gene ontology (two-sided Fisher’s exact test without adjustments for multiple comparisons). <bold>i</bold> Feature plot of integrated UMAP from harmonized schwannoma single transcriptomes (Fig. ##FIG##0##1b##) showing <italic>PTPRG</italic> expression in schwannoma cells. <bold>j</bold> TUNEL staining for apoptosis in HEI-193 cells following CRISPRi suppression of <italic>PTPRG</italic> versus sgNTC after treatment with 0 Gy (<italic>n</italic> = 3 independent cultures), 1.8 Gy × 5 (<italic>n</italic> = 3 independent cultures across 2 sgRNAs each), or 12.5 Gy × 1 (<italic>n</italic> = 3 independent cultures across 2 sgRNAs each) of radiotherapy. Fold changes are normalized to sgNTC in each treatment condition. Lines represent means, and error bars represent the standard error of means (two-sided Student’s t-tests, *<italic>p</italic> = 0.030, **<italic>p</italic> = 0.0044). Source data are provided as a Source Data file.</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><title>Epigenetic regulators reprogram schwannoma cells and drive immune cell infiltration in response to radiotherapy.</title><p><bold>a</bold> Experimental workflow for genome-wide CRISPRi screens using dual sgRNA libraries comprised of 20,528 targeted sgRNAs and 1025 non-targeted control sgRNAs (sgNTC). Libraries were transduced into HEI-193 cells that were subsequently treated with 0 Gy or 1.8 Gy × 5 radiotherapy (<italic>n</italic> = 3 per condition). sgRNA barcodes were sequenced and quantified as proxies for cell enrichment or depletion. <bold>b</bold> CRISPRi screen results showing the average rho log₂(sgRNA in radiotherapy conditions/sgRNA in control conditions) and two-sided Student’s <italic>t</italic>-test <italic>p</italic> values across three replicates. On-target hit genes (purple), epigenetic regulator hit genes (orange), and sgNTCs called hits (green) at a false discovery rate of 1% are shown. <bold>c</bold> Rho phenotypes of epigenetic regulator CRISPRi screen hits genes from (<bold>b</bold>). <italic>n</italic> = 3 replicate screens. <bold>d</bold> Crystal violet staining of HEI-193 following CRISPRi of <italic>KDM1A</italic> or <italic>KDM5C</italic> compared to sgNTC after treatment with 0 Gy, 1.8 Gy × 5, or 12.5 Gy × 1 of radiotherapy. Scale bar, 100 μm. <bold>e</bold> Quantification of cell density from (<bold>d</bold>) (<italic>n</italic> = 3 independent cultures, two-sided Student’s <italic>t</italic>-test). <bold>f</bold> Volcano plot of 425 peptides identified using proteomic mass spectrometry of conditioned media from triplicate HEI-193 cultures after radiotherapy or control treatment. Significant gene ontology terms of enriched peptides after radiotherapy conditions annotated (two-sided Fisher’s exact test). <bold>g</bold> Proteomic mass spectrometry parallel reaction monitoring targeted assay validating secreted peptide enrichment in conditioned media from HEI-193 after radiotherapy (<italic>n</italic> = 3 independent cultures, two-sided Student’s <italic>t</italic>-test) as in (<bold>f</bold>). <bold>h</bold> Transwell primary human peripheral blood lymphocyte migration assays using conditioned media from HEI-193 (<italic>n</italic> = 3 independent cultures, two-sided Student’s <italic>t</italic>-test) following CRISPRi suppression of <italic>APOA1</italic>, <italic>KDM1A</italic>, or <italic>KDM5C</italic> ± radiotherapy as a chemoattractant. <bold>i</bold> Targeted metabolite mass spectrometry of HEI-193 after treatment with 0 Gy, 1.8 Gy × 5, or 12.5 Gy × 1 of radiotherapy (<italic>n</italic> = 3 independent cultures per condition, two-sided Student’s <italic>t</italic>-test). Fold changes normalized to 0 Gy treatment for each metabolite. <bold>j</bold> Metabolic enzymes gene expression changes from bulk RNA sequencing of HEI-193 cells ± radiotherapy (<italic>n</italic> = 3 independent cultures) (Supplementary Data ##SUPPL##3##6##). Fold changes normalized to 0 Gy treatment for each gene. Lines represent means, and error bars represent standard error of means (two-sided Student’s <italic>t</italic>-tests, *<italic>p</italic> ≤ 0.05, **<italic>p</italic> ≤ 0.01, ***<italic>p</italic> ≤ 0.0001). Source data are provided as a Source Data file.</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><title>Single-nuclei ATAC, RNA, and CRISPRi perturbation sequencing identify integrated genomic mechanisms driving schwannoma cell state evolution.</title><p><bold>a</bold> Experimental workflow for <underline>s</underline>ingle-<underline>n</underline>uclei <underline>A</underline>TAC, <underline>R</underline>NA, and <underline>C</underline>RISPRi perturbation <underline>seq</underline>uencing (snARC-seq). Triplicate HEI-193 cultures were transduced with sgRNA libraries targeting 29 epigenetic regulators driving radiotherapy responses from genome-wide CRISPRi screens (Fig. ##FIG##2##3c##) and treated with 0 Gy or 1.8 Gy × 5 of radiotherapy prior to isolation of single-nuclei for sequencing. sgRNA identities were recovered from CROP-seq tags in single-nuclei RNA sequencing data. <bold>b</bold> UMAPs of ATAC (left) or RNA (right) sequencing of 855 single nuclei passing snARC-seq quality control from triplicate control or radiotherapy conditions (Supplementary Fig. ##SUPPL##0##18##). <bold>c</bold> Hierarchical clustering of differential gene activity scores between radiotherapy and control conditions for each snARC-seq perturbation (columns). Gene activity modules (rows) were derived from HEI-193 schwannoma cell states ± radiotherapy (Fig. ##FIG##1##2c##) or from human schwannoma cell types (Fig. ##FIG##0##1b##). Gene ontology of perturbed epigenetic regulators and CRISPRi screen growth (gamma) or radiation response (rho) phenotypes from genome-wide CRISPRi screens (Fig. ##FIG##2##3c##) are shown. <bold>d</bold> Hierarchical clustering of differential ChromVAR transcription factor motif deviations between radiotherapy and control conditions for each snARC-seq perturbation (columns). <bold>e</bold> Average profile plots of normalized ATAC signal at <italic>KLF13</italic> or <italic>TCF3</italic> motifs with ENCODE ChIP-seq peak annotations and differential accessibility following snARC-seq perturbation of <italic>KDM1A</italic>, <italic>KDM5C</italic>, or <italic>SETDB1</italic>. <bold>f</bold> Feature plot of integrated UMAP from harmonized schwannoma single-nuclei and single-cell RNA sequencing (Fig. ##FIG##0##1b##) showing genes near TCF3 motifs that are differentially accessible following <italic>SETDB1</italic> snARC-seq perturbation. <bold>g</bold> Hierarchical clustering of human schwannoma RNA sequencing profiles using 56 differentially expressed SETDB1 targets with TCF3 motifs showing separation of NCS and IES molecular groups of schwannomas. Source data are provided as a Source Data file.</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><title>An integrated model of schwannoma tumorigenesis and epigenetic reprogramming in response to treatment.</title><p>Two molecular groups of schwannoma, neural crest schwannoma and immune-enriched schwannoma, are driven by distinct mechanisms. Radiotherapy can induce immune-enriched schwannoma through metabolic and epigenetic reprogramming.</p></caption></fig>" ]

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[ "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>These authors contributed equally: Tim Casey-Clyde, Nam Woo Cho.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"41467_2023_40408_MOESM1_ESM.pdf\"><caption><p>Supplementary Information</p></caption></media>", "<media xlink:href=\"41467_2023_40408_MOESM2_ESM.pdf\"><caption><p>Peer review file</p></caption></media>", "<media xlink:href=\"41467_2023_40408_MOESM3_ESM.pdf\"><caption><p>Description of Additional Supplementary Files</p></caption></media>", "<media xlink:href=\"41467_2023_40408_MOESM4_ESM.xlsx\"><caption><p>Supplementary Data 1-11</p></caption></media>", "<media xlink:href=\"41467_2023_40408_MOESM5_ESM.pdf\"><caption><p>Reporting Summary</p></caption></media>", "<media xlink:href=\"41467_2023_40408_MOESM6_ESM.xlsx\"><caption><p>Source Data</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par39\">In a myriad of industrial applications, ranging from nuclear reactors and automobiles to electronics, the role of fluids is pivotal in enhancing heat transfer rates (HTR). Traditional fluid options like water, oils, and ethylene glycol, however, exhibit limited thermal conductivity. This limitation has spurred extensive research endeavors aimed at elevating HTR for improved efficiency and performance. First, Choi and Eastman^{##UREF##0##1##} coined the term \"nanofluid (NF)\" by mixing non-metallic or metallic nanoparticles (NPs) in host fluid which dramatically augments HTR. The characteristics of such fluids depend upon different factors like the shape and size of suspended nanoparticles in host fluid, thermal conduction, etc. Later, many investigators^{##UREF##1##2##–##UREF##3##4##} followed his idea and worked on the enhancement of HTR. Similarly, the mixing of two or more nano-sized particles in the host fluid is known as a hybrid nanofluid (HNF). Continuous and different strategies have been adopted to enhance HTR. Jena et al.^{##UREF##4##5##} explored the recent development in heat transfer (HT) characteristics of NF by considering the non-uniform heat source and inclined magnetization. Parida et al.^{##UREF##5##6##} computationally discussed the dust particles in water and kerosene-based nanoliquid for HTR. Pattnaik et al.^{##UREF##6##7##,##UREF##7##8##} used different NPs like copper, aluminum, gold, and single-wall carbon nanotubes to explain HTR by using water as host fluid over permeable surfaces.</p>", "<p id=\"Par40\">In industrial sectors like aerodynamics, plastic sheet extrusion, continuous metallic plate extrusion, artificial fiber synthesis, and plastic film magnification, the motion of an incompressible fluid over an expanding surface is a frequently observed occurrence. The HTR at the deformable surface plays a substantial role in determining the overall quality of the product in each of these applications. Sakiadis^{##UREF##8##9##} gave the thought of boundary layer (BL) enhancement during the movement of the surface and attracted researchers' attention. The Sakiadis' problem was expanded by Erickson et al.^{##UREF##9##10##} who also looked at the causes of puffing or sucking at the moving sheet on HMT in the BL flow. Baag et al.^{##UREF##10##11##} for exploration of MHD boundary layer flow over porous exponentially SS with a uniform heat source. Nayak et al.^{##UREF##11##12##} considered the radially stretched sheet for discussion by incorporating the variable magnetic field. Mishra et al.^{##UREF##12##13##} investigated the HT influence on the MHD movement of micropolar liquid passing from a permeable medium considering a similar heat source. Upreti et al.^{##UREF##13##14##} used the Casson NF over SS utilizing the Cattaneo-Christov model in stagnation point flow to examine the shape factor. Seini and Makinde^{##UREF##14##15##} explored the magnetohydrodynamic (MHD) BL flow above the exponentially stretched sheet by considering the chemical reaction (CR). Arshad et al.^{##REF##37188712##16##} considered radiative heat and mass transfer (HMT) for HNF incorporating the inclined magnetic field. Upreti et al.^{##UREF##15##17##} explored the influence of shape factor on Casson gold-blood nanofluid flow through SS incorporating magnetic effect. Also, considered the impact of Ohmic heating, convective heating, and suction/injection on heat transfer rate. Singh et al.^{##UREF##16##18##} investigated the influence of Melting and CR on the immobility point flow of a micropolar fluid over a Porous SS Medium. Pandey et al.^{##UREF##17##19##,##UREF##18##20##} presented the multiple slip mechanism and volumetric heat generation over porous SS and cone respectively. Sreedevi and Reddy^{##UREF##19##21##} considered 3D NF flow above SS with radiation and CR for the exploration of thermo-diffusion and Brownian movement. They concluded that enhancing the Deborah number increases the temperature profile.</p>", "<p id=\"Par41\">In recent years, significant research attention has been directed toward Heat and Mass Transfer flows due to their essential nature, prevalent in various engineering and industrial sectors. An example is the extrudate from the die in a melt spinning process. Researchers have investigated multiple flow scenarios, including those involving a stretching surface (SS), chemical reaction (CR), mixed convection, and thermal radiation, to address HMT-related issues. Rao et al.^{##UREF##20##22##} delved into HMT aspects in the context of a thermally oscillating fluid. Arshad et al.^{##UREF##21##23##,##UREF##22##24##} explored HMT by considering thermal radiation and chemical reactions for different types of Newtonian fluids (NFs) and Hybrid Nanofluids (HNFs). Mathur et al.^{##UREF##23##25##} examined the Darcy–Forchheimer skin coefficients and explored the velocity slip properties of a micropolar NF. Upreti et al.^{##UREF##24##26##} explored thermodynamics and HT using the Riga plate for the magnetized Casson HNF. They also discussed the entropy generation. Jayavel et al.^{##UREF##25##27##} provided a discussion on heat transfer analysis and irreversibility in MHD Darcy-Forchheimer movement of Casson HNF flow over wedge and cone. They used nanofluid and hybrid nanofluid for their discussion. Hassan et al.^{##UREF##26##28##} used the molybdenum di-sulfide NPs to explore the HMT incorporating the non-linear and linear radiation. Hussain et al.^{##UREF##27##29##} computationally investigated the thermal radiation to find the HTR over a stretchy surface. Different related research^{##UREF##28##30##–##UREF##36##38##} in literature can be found. Arshad and Hassan^{##UREF##37##39##} studied the heat and mass transmission rate in a rotating permeable system using hybrid nanofluids.</p>", "<p id=\"Par42\">Nowadays, chemical reactions, thermal radiation, and the presence of heat source/sink are fundamental components in the study of HMT phenomena. In various engineering applications, the interplay of chemical reactions, thermal radiation, and heat source/sink mechanisms plays a pivotal role in shaping the thermal behavior of systems. Understanding the effects of chemical reactions and thermal radiation, along with heat source/sink interactions, is essential for optimizing processes in fields such as materials science and chemical engineering. Heidary et al.^{##UREF##38##40##} numerically investigated the magnetic field effect with forced convection in a duct for NF flow. Sheikholeslami and Rokni^{##UREF##39##41##} gave a review on the simulation for the HT phenomenon of nanoliquid in the existence of a magnetic field. Makinde and Mishra^{##UREF##40##42##} examined the MHD mixed convection with non-uniform viscosity Blasius flow inserted in a permeable medium incorporating the chemical reaction. Using the CR and heat source, a semi-analytical solution for MHD Jeffery fluid flow is provided by Nisar et al.^{##UREF##41##43##}. Mishra et al.^{##UREF##42##44##} explained the influence of nonlinear radiation and cross-diffusion effects on the flow of micropolar nanoliquid over a stretching sheet with an exponential heat source. Mehrizi et al.^{##UREF##43##45##} reported a new analysis of natural convection BL flow with variable wall temperature on a horizontal plate. Reddy et al.^{##UREF##44##46##} explored the HMT flow of NF at inclined plates with thermal radiation and magnetic fields under enhanced boundary conditions. Nayak et al.^{##UREF##45##47##} investigated the flow and HTR non-Newtonian fluid with hybrid nanoparticles by employing a magnetic field.</p>", "<p id=\"Par43\">The literature review conducted indicates a notable gap in research, as there has been no investigation into comparing different types of nanofluids over dual stretchable surfaces while factoring in the existence of an inclined magnetic field and accounting for viscous dissipation. Such applications involving nanofluids occur in advanced cooling systems, enhanced heat exchangers, biomedical devices, material processing, renewable energy, etc. Jena et al.^{##UREF##4##5##} considered only the temperature profile in their study but ignored the concentration profile. Jayavel et al.^{##UREF##25##27##} made their analysis over the wedge and cone but ignored the inclined magnetization. Pattanaik et al.^{##UREF##6##7##} examined the uniform heat source and ignored the chemical reaction. Gupta et al.^{##UREF##30##32##} used the kerosene oil for their investigations over exponentially SS. Arshad and Hassan^{##UREF##37##39##} deliberated hybrid nanofluids using different NPs. Singh et al.^{##UREF##16##18##} considered the non-uniform heat source but ignored the thermal radiation. Similarly, Pattanaik et al.^{##UREF##36##38##}, Mohanty et al.^{##UREF##29##31##}, and Parida^{##UREF##5##6##} presented their research in different aspects but none of these considered the inclined magnetic field. Based on the literature survey conducted above, the novelty of this study aims to provide a comparative analysis of different water-based NFs. These NFs, namely ; NF, HNF, are investigated concerning their HMT rates. This report is prepared for a dual stretching surface placed within a porous medium. Viscous dissipation, thermal radiation, chemical reaction, and most importantly inclined magnetic field are considered because they involve semiconductor manufacturing, solar energy, food processing, etc. The governing equalities are changed into the ODEs by employing a transformation and tackled a MATLAB by BVP-4c algorithm by setting the tolerance for solutions. The results are obtained for increasing values of different parameters involved in this research. This comparative analysis serves to provide insights into the central research queries outlined below:<list list-type=\"order\"><list-item><p id=\"Par44\">How does the rotation parameter affect the velocity, temperature, and concentration profile?</p></list-item><list-item><p id=\"Par45\">What is the influence of increasing behavior of mixed convection, stretching ratio, magnetic force, and inclination angle on velocity and temperature profile?</p></list-item><list-item><p id=\"Par46\">Does the increased thermal radiation and viscous dissipation reduce skin friction and enhance the HTR?</p></list-item><list-item><p id=\"Par47\">How does the chemical reaction affect the concentration profile and Sherwood number?</p></list-item><list-item><p id=\"Par48\">What do we get numerical outcomes for skin frictions along , Nusselt, and Sherwood numbers versus different parameters?</p></list-item></list></p>" ]

[]

[ "<title>Results and discussion</title>", "<p id=\"Par86\">The problem is formulated for HNF in the previous section. The authors obtained the results of the current problem separately for both NF and HNF and discussed them physically. The obtained influences of different constitutes by using the bvp4c algorithm at MATLAB are described in the following.</p>", "<title>Velocity profiles</title>", "<p id=\"Par87\">The influences of study parameters on velocities are discussed in this section. The influence of rotation on velocity profile when is presented in Fig. ##FIG##3##4##a. The graph displays the velocity profiles demonstrating a decrease in velocity as the rotation parameter increases for both NF and HNF cases. Initially, at and there is minimal alteration in the velocity profiles. However, a significant acceleration in the decay of these profiles is observed as the rotation parameter rises to and The main reason behind this is enhanced viscous dissipation that affects the velocity profile. Figure ##FIG##3##4##b represents the influence of the magnetic field on velocity . The magnetic parameter has a great influence on the velocity profile. In the non-existence of the magnetic field, the momentum BL looks similar but when it upsurges between a big change is noted due to the existing Lorentz force which decreases the fluid motion and consequently momentum BL decay. A wider momentum BL is noted for HNF as associated with NF. This is due to the generation of damping electromagnetic force which restricts the fluid's motion and results in a gradual reduction in velocity profile. Figure ##FIG##3##4##c depicts the impact of the angle of inclination 0 on velocity profile \n. The parameter at represents the magnetic force parallel to the and varies from to i.e., parallel to the <italic>y</italic>- As the inclination angle increases, the momentum BL decreases because Lorentz force increases gradually. The extended momentum BL is noted for HNF when and 90 whereas NF has smooth BL. A minimum flow for NF is observed when the inclination angle is parallel to the because greater interaction between the magnetic field and fluid increases flow resistance. The mixed convection parameter has a direct relation with velocity profile as presented in Fig. ##FIG##3##4##d and a higher velocity profile is observed for NF as associated with the HNF. This is owing to the driving forces associated with convection which typically increases the fluid’s velocity. Figure ##FIG##3##4##e shows that porous medium parameter has a negligible decreasing influence on velocity profile \n. The porosity acts as a flow impediment, and the drag force significantly reduces the velocity of the fluid. The stretching ratio parameter represents the effects on velocity profile in Fig. ##FIG##3##4##f . When the stretching rate along the increases as compared to the <italic>y</italic>-, the velocity momentum BL expands for both types of NFs.</p>", "<title>Temperature and concentration profiles</title>", "<p id=\"Par88\">The following Fig. ##FIG##4##5##a–h show the impression of different constraints on temperature and concentration profiles. The influence of magnetic parameters on temperature is represented in Fig. ##FIG##4##5##a and can be seen that the temperature increases when magnetic strength increases. The justification for this is that Lorentz force reduces the fluid motion and as a result, a maximum HT and a higher thermal BL are noted for HNF as compared to NF. Figure ##FIG##4##5##b indicates the effect of rotation on the temperature \n. When the rotation of fluids increases the temperature profile shows the same behavior. Rotation increases temperature transmission by promoting fluid mixing, reducing boundary layer thickness, and enhancing convective heat transfer due to the formation of vortices and turbulence, leading to improved thermal. In this figure low but consistent HTR is noted for HNF. The influence of thermal radiation on the temperature is shown in Fig. ##FIG##4##5##c . In the absence of the radiation parameter, a higher temperature BL is detected for both NFs. Thermal radiation typically decays temperature profiles by emitting heat energy from hotter regions to cooler surroundings, causing temperature gradients to diminish, resulting in a more uniform temperature distribution. The Eckert number characterizes the thermal energy conversion associated with the fluid’s motion. A higher Eckert number implies more kinetic energy, which promotes cooling, leading to a decrease in temperature gradients and a more uniform temperature profile. This phenomenon is presented in Fig. ##FIG##4##5##d However, we found that as viscous dissipation rises, the thermal BL gets thicker. The impact of mixed convection and CR is presented in Fig. ##FIG##4##5##e,f respectively. the mixed convection and chemical reactions decay concentration profiles due to enhanced fluid mixing from buoyancy and forced convection, leading to reduced concentration gradients and more uniform distribution. A higher concentration of BL is noted in the absence of mixed convection and CR for HNF as compared to NF which is presented in Fig. ##FIG##4##5##e,f for HNF. The rotation influence is represented in Fig. ##FIG##4##5##g . The rotation and concentration profile have a direct relation. As the rotation parameter increases the mass transfer rate also increases. Rotation increases the concentration profiles due to the centrifugal forces that drive fluid motion. The thermophoresis parameter effect on the concentration profile is shown in Fig. ##FIG##4##5##h . A wider concentration of BL is observed for NF as compared to HNF when the thermophoresis parameter increases. This is due to the inclusion of single and double NPs inclusion in the host fluid. So, HNF shows a consistent mass transfer rate in Fig. ##FIG##4##5##h.</p>", "<title>Numerical outcomes</title>", "<p id=\"Par89\">The numerical outputs for skin frictions , , Nusselt number , and Sherwood number are presented in this section. Table ##TAB##4##5## represents the obtained numerical results for skin frictions and for both nanofluids. A minimum skin friction is observed in the absence of rotation i.e. λ = 0 and increasing behavior is seen for increasing values of rotation parameter from to while an opposite behavior is observed for Increased porosity from reduces skin friction in porous media because higher permeability allows fluid to flow more easily through the medium, reducing the resistance to motion and minimizing the friction between the fluid and the porous structure. The stretching ratio is defined by the rate along the <italic>y</italic>- to the stretching rate <italic>x</italic>-. Increased stretching ratio increases skin friction in the context of flow over a solid surface. This occurs because a higher stretching ratio leads to increased shear stress. Reduced skin friction is followed in the deprivation of mixed convection and magnetic field and increasing behavior is noted when it increases. The angle of inclination has a great influence on skin friction. When the magnetic field is parallel to the <italic>x</italic>-, a maximum skin friction is noted while it decays when the angle of inclination increases between the range Minimum skin friction is noted when the magnetic field becomes parallel to the Table ##TAB##5##6## shows the influences of different constraints on Nusselt number and Sherwood number for both nanofluids. A higher HMT rate is noted when the angle of inclination for the magnetic field is parallel to the <italic>x</italic>- Increasing radiation parameter typically decreases the Nusselt and Sherwood numbers because radiative heat or mass transfer is a slower process compared to convection. As radiation becomes more significant, it diminishes the relative contribution of convection, leading to lower Nusselt and Sherwood numbers, indicating reduced HMTR and utmost Nusselt and Sherwood is seen in the absence of radiation, i.e. . Prandtl number and magnetic field have a direct relation and inverse relation with HMTR respectively because implies that thermal or mass diffusion is rapid relative to momentum diffusion and the existence of magnetic field suppresses fluid movement, disrupting convection resulting in reducing HMTR. Increasing values of the CR parameter and Lewis number decreases the Nusselt number while it increases the Sherwood number. CR consumes the temperature and concentration gradient and a higher Lewis number results in a more dominant effect on fluid behavior. Similar results are found for thermophoresis and Brownian motion factors corresponding to the Nusselt number and Sherwood number. As the viscous dissipation parameter increases between the HMT rate increases in both cases of used nanofluids because increased number indicates that the kinetic energy of the fluid is relatively higher than internal energy change.</p>" ]

[ "<title>Results and discussion</title>", "<p id=\"Par86\">The problem is formulated for HNF in the previous section. The authors obtained the results of the current problem separately for both NF and HNF and discussed them physically. The obtained influences of different constitutes by using the bvp4c algorithm at MATLAB are described in the following.</p>", "<title>Velocity profiles</title>", "<p id=\"Par87\">The influences of study parameters on velocities are discussed in this section. The influence of rotation on velocity profile when is presented in Fig. ##FIG##3##4##a. The graph displays the velocity profiles demonstrating a decrease in velocity as the rotation parameter increases for both NF and HNF cases. Initially, at and there is minimal alteration in the velocity profiles. However, a significant acceleration in the decay of these profiles is observed as the rotation parameter rises to and The main reason behind this is enhanced viscous dissipation that affects the velocity profile. Figure ##FIG##3##4##b represents the influence of the magnetic field on velocity . The magnetic parameter has a great influence on the velocity profile. In the non-existence of the magnetic field, the momentum BL looks similar but when it upsurges between a big change is noted due to the existing Lorentz force which decreases the fluid motion and consequently momentum BL decay. A wider momentum BL is noted for HNF as associated with NF. This is due to the generation of damping electromagnetic force which restricts the fluid's motion and results in a gradual reduction in velocity profile. Figure ##FIG##3##4##c depicts the impact of the angle of inclination 0 on velocity profile \n. The parameter at represents the magnetic force parallel to the and varies from to i.e., parallel to the <italic>y</italic>- As the inclination angle increases, the momentum BL decreases because Lorentz force increases gradually. The extended momentum BL is noted for HNF when and 90 whereas NF has smooth BL. A minimum flow for NF is observed when the inclination angle is parallel to the because greater interaction between the magnetic field and fluid increases flow resistance. The mixed convection parameter has a direct relation with velocity profile as presented in Fig. ##FIG##3##4##d and a higher velocity profile is observed for NF as associated with the HNF. This is owing to the driving forces associated with convection which typically increases the fluid’s velocity. Figure ##FIG##3##4##e shows that porous medium parameter has a negligible decreasing influence on velocity profile \n. The porosity acts as a flow impediment, and the drag force significantly reduces the velocity of the fluid. The stretching ratio parameter represents the effects on velocity profile in Fig. ##FIG##3##4##f . When the stretching rate along the increases as compared to the <italic>y</italic>-, the velocity momentum BL expands for both types of NFs.</p>", "<title>Temperature and concentration profiles</title>", "<p id=\"Par88\">The following Fig. ##FIG##4##5##a–h show the impression of different constraints on temperature and concentration profiles. The influence of magnetic parameters on temperature is represented in Fig. ##FIG##4##5##a and can be seen that the temperature increases when magnetic strength increases. The justification for this is that Lorentz force reduces the fluid motion and as a result, a maximum HT and a higher thermal BL are noted for HNF as compared to NF. Figure ##FIG##4##5##b indicates the effect of rotation on the temperature \n. When the rotation of fluids increases the temperature profile shows the same behavior. Rotation increases temperature transmission by promoting fluid mixing, reducing boundary layer thickness, and enhancing convective heat transfer due to the formation of vortices and turbulence, leading to improved thermal. In this figure low but consistent HTR is noted for HNF. The influence of thermal radiation on the temperature is shown in Fig. ##FIG##4##5##c . In the absence of the radiation parameter, a higher temperature BL is detected for both NFs. Thermal radiation typically decays temperature profiles by emitting heat energy from hotter regions to cooler surroundings, causing temperature gradients to diminish, resulting in a more uniform temperature distribution. The Eckert number characterizes the thermal energy conversion associated with the fluid’s motion. A higher Eckert number implies more kinetic energy, which promotes cooling, leading to a decrease in temperature gradients and a more uniform temperature profile. This phenomenon is presented in Fig. ##FIG##4##5##d However, we found that as viscous dissipation rises, the thermal BL gets thicker. The impact of mixed convection and CR is presented in Fig. ##FIG##4##5##e,f respectively. the mixed convection and chemical reactions decay concentration profiles due to enhanced fluid mixing from buoyancy and forced convection, leading to reduced concentration gradients and more uniform distribution. A higher concentration of BL is noted in the absence of mixed convection and CR for HNF as compared to NF which is presented in Fig. ##FIG##4##5##e,f for HNF. The rotation influence is represented in Fig. ##FIG##4##5##g . The rotation and concentration profile have a direct relation. As the rotation parameter increases the mass transfer rate also increases. Rotation increases the concentration profiles due to the centrifugal forces that drive fluid motion. The thermophoresis parameter effect on the concentration profile is shown in Fig. ##FIG##4##5##h . A wider concentration of BL is observed for NF as compared to HNF when the thermophoresis parameter increases. This is due to the inclusion of single and double NPs inclusion in the host fluid. So, HNF shows a consistent mass transfer rate in Fig. ##FIG##4##5##h.</p>", "<title>Numerical outcomes</title>", "<p id=\"Par89\">The numerical outputs for skin frictions , , Nusselt number , and Sherwood number are presented in this section. Table ##TAB##4##5## represents the obtained numerical results for skin frictions and for both nanofluids. A minimum skin friction is observed in the absence of rotation i.e. λ = 0 and increasing behavior is seen for increasing values of rotation parameter from to while an opposite behavior is observed for Increased porosity from reduces skin friction in porous media because higher permeability allows fluid to flow more easily through the medium, reducing the resistance to motion and minimizing the friction between the fluid and the porous structure. The stretching ratio is defined by the rate along the <italic>y</italic>- to the stretching rate <italic>x</italic>-. Increased stretching ratio increases skin friction in the context of flow over a solid surface. This occurs because a higher stretching ratio leads to increased shear stress. Reduced skin friction is followed in the deprivation of mixed convection and magnetic field and increasing behavior is noted when it increases. The angle of inclination has a great influence on skin friction. When the magnetic field is parallel to the <italic>x</italic>-, a maximum skin friction is noted while it decays when the angle of inclination increases between the range Minimum skin friction is noted when the magnetic field becomes parallel to the Table ##TAB##5##6## shows the influences of different constraints on Nusselt number and Sherwood number for both nanofluids. A higher HMT rate is noted when the angle of inclination for the magnetic field is parallel to the <italic>x</italic>- Increasing radiation parameter typically decreases the Nusselt and Sherwood numbers because radiative heat or mass transfer is a slower process compared to convection. As radiation becomes more significant, it diminishes the relative contribution of convection, leading to lower Nusselt and Sherwood numbers, indicating reduced HMTR and utmost Nusselt and Sherwood is seen in the absence of radiation, i.e. . Prandtl number and magnetic field have a direct relation and inverse relation with HMTR respectively because implies that thermal or mass diffusion is rapid relative to momentum diffusion and the existence of magnetic field suppresses fluid movement, disrupting convection resulting in reducing HMTR. Increasing values of the CR parameter and Lewis number decreases the Nusselt number while it increases the Sherwood number. CR consumes the temperature and concentration gradient and a higher Lewis number results in a more dominant effect on fluid behavior. Similar results are found for thermophoresis and Brownian motion factors corresponding to the Nusselt number and Sherwood number. As the viscous dissipation parameter increases between the HMT rate increases in both cases of used nanofluids because increased number indicates that the kinetic energy of the fluid is relatively higher than internal energy change.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par90\">In this present article, the authors discussed the heat and mass transfer rate of 3D rotating, incompressible NF and HNF fluid over the dual stretchable surface. The governing equations are transformed and tackled in MATLAB. We considered the inclined magnetic field, viscous dissipation, thermal radiation, and chemical reaction effects to provide a theoretical view of the study. The main findings that one needs to remember from this study are stated below:<list list-type=\"order\"><list-item><p id=\"Par91\">Increasing the rotation, magnetic force, and porosity of the SS decays the velocity profile while it increases by a rise in mixed convection and stretching ratio parameters.</p></list-item><list-item><p id=\"Par92\">The temperature profile increases by an increase in rotation and magnetic field parameters.</p></list-item><list-item><p id=\"Par93\">The concentration profile decreases under the increasing influence of mixed convection parameters, and thermophoresis parameters whereas it increases by raising the value of the rotation parameter.</p></list-item><list-item><p id=\"Par94\">A maximum and , and and minimum and , and is noted when i.e., angle of inclination is parallel to the for NF and HNF.</p></list-item><list-item><p id=\"Par95\">By increasing Eckert number i.e., the , and is noted for NF and HNF respectively.</p></list-item><list-item><p id=\"Par96\">When the chemical reaction parameter increases i.e., the Nusselt number and decreases, and Sherwood number and increases for NH and HNF respectively.</p></list-item><list-item><p id=\"Par97\">By changing the angle of inclination, the performance is noted at 8% for NF and 33% for HNF which proves the high heat transfer rate efficiency of HNF.</p></list-item></list></p>", "<p id=\"Par98\">The strength of this study lies in its comprehensive analysis of the three-dimensional mixed convection flow of nanofluid over a dual stretching sheet, considering influential factors such as viscous dissipation, Joule heating, and solar radiation. The practical relevance to solar energy systems adds significance to the findings. However, limitations include potential simplifications in assumptions, applicability restricted to similar geometries, assumptions about material properties, and the influence of numerical solution techniques, emphasizing the need for careful interpretation of results in specific contexts.</p>" ]

[ "<p id=\"Par1\">Heat and mass transfer rate by using nanofluids is a fundamental aspect of numerous industrial processes. Its importance extends to energy efficiency, product quality, safety, and environmental responsibility, making it a key consideration for industries seeking to improve their operations, reduce costs, and meet regulatory requirements. So, the principal objective of this research is to analyze the heat and mass transfer rate for three-dimensional magneto hydrodynamic nanoliquid movement with thermal radiation and chemical reaction over the dual stretchable surface in the existence of an inclined magnetization, and viscous dissipation. The flow is rotating with constant angular speed about the axis of rotation because such flows occur in the chemical processing industry and the governing equations of motion, energy, and concentration are changed to ODEs by transformation. The complex and highly nonlinear nature of these equations makes them impractical to solve analytically so tackled numerically at MATLAB. The obtained numerical results are validated with literature and presented through graphs and tables. Increasing the Eckert number from a higher Nusselt and Sherwood number was noted for the hybrid nanofluid. By changing the angle of inclination <italic>,</italic> the performance is noted at 8% for nanofluid and 33% for hybrid nanofluid. At the same time, performance of 0.5% and 2.0% are observed respectively. Additionally, as the angle of inclination increases the skin friction decreases and the chemical reaction rate increases the mass transmission rate.</p>", "<title>Subject terms</title>" ]

[ "<title>Problem formulation</title>", "<p id=\"Par49\">Consider a steady three-dimensional boundary layer, the MHD flow of a fluid over a dual stretching sheet within a porous medium, accompanied by a chemical reaction, thermal radiation, and the existence of a nonuniform heat source. The conceptual representation of the problem, inclusive of the flow design and coordinate system, is presented in Fig. ##FIG##0##1##. The horizontal direction is represented by the <italic>x</italic>- the upward direction by the<italic> z</italic>- and the y-axis is perpendicular to both axes. The fluid is undergoing a steady rotation at a constant speed denoted as around the<italic> z</italic>-. The surface is stretching along the<italic> x</italic>- with velocity and along the <italic>y</italic>- with velocity as shown. Inclined magnetic field with angle from the <italic>x</italic>- to the axis of rotation is working. By these assumptions, the flow conservation, momentum along the <italic>x</italic>-<italic>axis</italic>, and <italic>y</italic>-<italic>axis</italic>, temperature and concentration in the existence of joule heating, thermal radiation, and viscous dissipation equation are:</p>", "<p id=\"Par50\">Equation of continuity^{##UREF##46##48##}:</p>", "<p id=\"Par51\">Momentum equations along the and axis^{##UREF##46##48##}:</p>", "<p id=\"Par52\">Energy equation without relation^{##UREF##46##48##,##UREF##47##49##}:</p>", "<p id=\"Par53\">Concentration equation^{##UREF##47##49##}:</p>", "<p id=\"Par54\">The respective boundary conditions^{##UREF##46##48##} for the current problem are:</p>", "<p id=\"Par55\">Here —gravitational acceleration, —magnetic field, —temperature, —concentration, —ambient temperature, —radiative heat flux, —dynamic viscosity, —density, —mass diffusion, —temperature diffusion, —thermal conductivity, —specific heat, —electrical conductivity, —thermal volumetric coefficient, —the angle of inclination, are velocity components in respectively, the subscript represents the hybrid nanofluid.</p>", "<p id=\"Par56\">The specified boundary conditions for the fluid flow and thermal transport problem outline the physical behavior near and far from the solid surface. At the origin the prescribed velocities and denote a stretching wall, while enforces a no stretching. Temperature and concentration conditions and at the wall capture heat and mass transfer interactions. As the velocity components approach zero signifying a quiescent state, while temperature and concentration represent the free-stream values far from the surface. These conditions collectively provide interactions and asymptotic behavior of fluid flow, heat transfer, and mass transport in the given problem.</p>", "<p id=\"Par57\">There are numerous models in literature for characterizing the effective properties of NF and HNF. So, the thermophysical relations of NF and HNF are given in Tables ##TAB##0##1## and ##TAB##1##2## correspondingly. Table ##TAB##2##3## shows the thermophysical values for used NPs and base fluid. Table ##TAB##3##4## shows the comparison of literature and present outcomes.</p>", "<p id=\"Par58\">Here -volume fraction of NPs, subscripts are representing fluid, solid nanoparticles, nanofluid and hybrid nanofluid respectively.</p>", "<p id=\"Par59\">The term in the right side of Eq. (##FORMU##27##4##) presents the heat radiation effect. Utilizing the Rosseland approximation, the radiative heat flux is computed in the following:</p>", "<p id=\"Par60\">Here represents the Stefan–Boltzmann coefficient and represents the mean absorption constant. The radiation is optically thick considered. Considering that sufficiently small temperature difference in the flow, the term by employing the Taylor series as follows:</p>", "<p id=\"Par61\">Therefore, by abandoning higher-order terms above the first degree in we get.</p>", "<p id=\"Par62\">By using Eqs. (##FORMU##136##7##) and (##FORMU##140##8##)</p>", "<p id=\"Par63\">So, Eq. (##FORMU##27##4##) takes the following form:</p>", "<p id=\"Par64\">Similarity transformation:</p>", "<p id=\"Par65\">In the present problem, the following similarity transformations are taken to change the PDEs into ODEs.</p>", "<p id=\"Par66\">The differentiation is w.r.t The flow Eq. (##FORMU##21##1##) of mass conversation is satisfied identically by employing Eq. (##FORMU##145##12##). The Eqs. (##FORMU##24##2##,##FORMU##25##3##,##FORMU##28##5##) and Eq. (##FORMU##144##11##) for momentum, energy, and concentration will take the following form after using Eq. (##FORMU##145##12##) with boundary conditions:</p>", "<p id=\"Par67\">The non-dimensional quantities and are hybrid NPs relations (presented in Table ##TAB##1##2##), and and are defined as</p>", "<p id=\"Par68\">Here </p>", "<p id=\"Par69\">The modified boundary conditions are presented as follows:</p>", "<p id=\"Par70\">Here presents the dimensionless stretching ratio.</p>", "<p id=\"Par71\"><bold>Engineering parameters of interest</bold>:</p>", "<p id=\"Par72\">There are the following most important quantities regarding to engineering perspective.</p>", "<p id=\"Par73\">(A) Skin friction:</p>", "<p id=\"Par74\">The significant surface skin friction along the <italic>x</italic>- and <italic>y</italic>- are , defined as:</p>", "<p id=\"Par75\">The and indicate shear stress along the stretched wall <italic>x</italic>- and <italic>y</italic>- which is defined as:</p>", "<p id=\"Par76\">The dimensionless form of Eq. (##FORMU##168##20##) with the help of Eq. (##FORMU##150##16##) is:</p>", "<p id=\"Par77\">(B) Rate of heat and mass transfer:</p>", "<p id=\"Par78\">The HMT rates, expressed through Nusselt and Sherwood numbers are the following:</p>", "<p id=\"Par79\">By utilizing the temperature field, the thermal diffusion rate is characterized by the Nusselt number:</p>", "<p id=\"Par80\">By using the similarity transformation, the transformed form of Eq. (##FORMU##170##22##) is given below:</p>", "<p id=\"Par81\">By utilizing the concentration field, the mass transmission rate is characterized by the Sherwood number:</p>", "<p id=\"Par82\">By using the similarity transformation, the transformed form of Eq. (##FORMU##172##24##) is given below:</p>", "<title>Numerical solution</title>", "<p id=\"Par83\">This section provides the numerical solution methodology as presented in Fig. ##FIG##1##2## to get the solution of higher-order nondimensional ODEs. For this purpose, the bvp4c method is used to tackle the boundary value problem by transforming it into an initial value problem. The Fig. ##FIG##2##3## validates the code of the present problem. For this purpose, newly defined variables are as follows:</p>", "<p id=\"Par84\">The following form of equations is used in MATLAB to get the numerical solution.</p>", "<p id=\"Par85\">The transformed boundary conditions have been modified into the following form:</p>" ]

[ "<title>Acknowledgements</title>", "<p>The authors are thankful to the Deanship of Scientific Research, King Khalid University, Abha, Saudi Arabia, for financially supporting this work through the General Research Project under Grant No: RGP.1/435/44. This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444).</p>", "<title>Author contributions</title>", "<p>A.M. Galal: Supervision, Funding, Software. F.M. Alharbi: Data curation. Methodology. M. Arshad: Conceptualization, Writing- Original draft preparation, Writing- Reviewing and Editing. M.M. Alam: Funding, Software, Validation. T. Abdeljawad: Visualization, Funding. Q.M. Al-Mdallal: Formal analysis, Investigation.</p>", "<title>Dedication</title>", "<p>This manuscript is dedicated to author Mubashar Arshad on his 26th birthday.</p>", "<title>Data availability</title>", "<p>All data generated or analyzed during this study are included in this published article.</p>", "<title>Competing interests</title>", "<p id=\"Par99\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Figure 1</label><caption><p>Flow configuration of the problem.</p></caption></fig>", "<fig id=\"Fig2\"><label>Figure 2</label><caption><p>Flow chart for the numerical solution.</p></caption></fig>", "<fig id=\"Fig3\"><label>Figure 3</label><caption><p>Validation of code by velocity profile and .</p></caption></fig>", "<fig id=\"Fig4\"><label>Figure 4</label><caption><p>(<bold>a</bold>) Effect of on velocity . (<bold>b</bold>) Effect of on velocity . (<bold>c</bold>) Effect of on velocity . (<bold>d</bold>) Effect of on velocity . (<bold>e</bold>) Effect of on velocity . (<bold>f</bold>) Effect of on velocity .</p></caption></fig>", "<fig id=\"Fig5\"><label>Figure 5</label><caption><p>(<bold>a</bold>) Effect of on temperature . (<bold>b</bold>) Effect of on temperature . (<bold>c</bold>) Effect of on temperature r . (<bold>d</bold>) Effect of on temperature . (<bold>e</bold>) Effect of on concentration s . (<bold>f</bold>) Effect of on concentration s . (<bold>g</bold>) Effect of on concentration s . (<bold>h</bold>) Effect of on concentration s .</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Thermophysical relations of nanofluid.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Properties</th><th align=\"left\">Nanofluid relations^{##UREF##48##50##}</th></tr></thead><tbody><tr><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">Thermal expansion</td><td align=\"left\"></td></tr><tr><td align=\"left\">Electrical conductivity</td><td align=\"left\"></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Thermophysical relations of hybrid nanofluid.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Properties</th><th align=\"left\">Hybrid nanofluid relations^{##UREF##37##39##}</th></tr></thead><tbody><tr><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"><p></p><p><italic>Here </italic><italic>,</italic></p></td></tr><tr><td align=\"left\">Thermal expansion</td><td align=\"left\"></td></tr><tr><td align=\"left\">Electrical conductivity</td><td align=\"left\"></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Thermophysical properties of base fluid^{##UREF##49##51##} and nanoparticles.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Physical properties</th><th align=\"left\">Electrical conductivity</th><th align=\"left\">Density</th><th align=\"left\">Specific heat</th><th align=\"left\">Thermal conductivity</th><th align=\"left\">Thermal expansion</th></tr></thead><tbody><tr><td align=\"left\"></td><td char=\".\" align=\"char\">0.05</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td char=\".\" align=\"char\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td char=\".\" align=\"char\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Comparison of present outcomes with literature.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"></th><th align=\"left\" colspan=\"2\">Wang^{##UREF##50##52##}</th><th align=\"left\" colspan=\"2\">Present outcomes</th><th align=\"left\" colspan=\"2\">Nazar et al.^{##UREF##51##53##}</th></tr><tr><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th></tr></thead><tbody><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Numerical results for skin frictions along \n and when respectively.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"></th><th align=\"left\">Z</th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"> for NF</th><th align=\"left\"> for NF</th><th align=\"left\"> for HNF</th><th align=\"left\"> HNF</th></tr></thead><tbody><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\">0°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">30°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">60°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">90°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab6\"><label>Table 6</label><caption><p>Numerical results for Nusselt number and Sherwood number when respectively.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"></th><th align=\"left\"> for NF</th><th align=\"left\"> for NF</th><th align=\"left\"> for HNF</th><th align=\"left\"> HNF</th></tr></thead><tbody><tr><td align=\"left\">0°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">30°</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">60°</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">90°</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\">45°</td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr><tr><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td><td align=\"left\"></td></tr></tbody></table></table-wrap>" ]

[ "<inline-formula id=\"IEq1\"><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\upomega }^{*}$$\\end{document}</tex-math><mml:math id=\"M2\"><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">ω</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq2\"><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} 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id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}$$\\end{document}</tex-math><mml:math id=\"M8\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq5\"><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}$$\\end{document}</tex-math><mml:math id=\"M10\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Cu/{H}_{2}O$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mrow><mml:mi>C</mml:mi><mml:mi>u</mml:mi><mml:mo stretchy=\"false\">/</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>O</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$and Cu-A{l}_{2}{O}_{3}/{H}_{2}O$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:mrow><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mi>C</mml:mi><mml:mi>u</mml:mi><mml:mo>-</mml:mo><mml:mi>A</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>O</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo stretchy=\"false\">/</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>O</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq42\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${10}^{-6}$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq43\"><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$the x-axis$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq44\"><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$y-axis,$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq45\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis,$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:mrow><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq46\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis,$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:mrow><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq47\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\omega }^{*}$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:msup><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq48\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq49\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq50\"><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${U}_{w}=ax$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq51\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq52\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${V}_{w}=by$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq53\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${B}_{0}$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq54\"><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq55\"><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{\\partial \\widehat{u}}{\\partial x} + \\frac{\\partial \\widehat{v}}{\\partial y} + \\frac{\\partial \\widehat{w}}{\\partial z} = 0,$$\\end{document}</tex-math><mml:math id=\"M44\" display=\"block\"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq56\"><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x$$\\end{document}</tex-math><mml:math id=\"M46\"><mml:mi>x</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq57\"><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$y$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:mi>y</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\widehat{u}\\frac{\\partial \\widehat{u}}{\\partial x} + \\widehat{v} \\frac{\\partial \\widehat{u}}{\\partial y}+\\widehat{w} \\frac{\\partial \\widehat{u}}{\\partial z}-2{\\omega }^{*}\\widehat{v}=\\frac{{\\mu }_{hnf}}{{\\rho }_{hnf}}\\left(\\frac{{\\partial }^{2}\\widehat{u}}{{\\partial x}^{2}}+\\frac{{\\partial }^{2}\\widehat{u}}{{\\partial y}^{2}}+\\frac{{\\partial }^{2}\\widehat{u}}{{\\partial z}^{2}}\\right)+\\frac{{g}^{*}{\\left(\\rho {B}_{t}\\right)}_{hnf}}{{\\rho }_{hnf}}\\left(T-{T}_{\\infty }\\right)-\\frac{{\\sigma }_{hnf}}{{\\rho }_{hnf} }{{B}_{0}}^{2}{sin}^{2}\\left(\\alpha \\right)\\widehat{u}-\\frac{{\\mu }_{hnf}}{{\\rho }_{hnf} }\\frac{\\widehat{u}}{{k}_{o}},$$\\end{document}</tex-math><mml:math id=\"M50\" display=\"block\"><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:msup><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>-</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfrac><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:msub><mml:mi>k</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\widehat{u}\\frac{\\partial \\widehat{v}}{\\partial x} + \\widehat{v} \\frac{\\partial \\widehat{v}}{\\partial y}+\\widehat{w} \\frac{\\partial \\widehat{v}}{\\partial z}-2{\\omega }^{*}\\widehat{u}=\\frac{{\\mu }_{hnf}}{{\\rho }_{hnf}}\\left(\\frac{{\\partial }^{2}\\widehat{v}}{{\\partial x}^{2}}+\\frac{{\\partial }^{2}\\widehat{v}}{{\\partial y}^{2}}+\\frac{{\\partial }^{2}\\widehat{v}}{{\\partial z}^{2}}\\right)+\\frac{{g}^{*}{\\left({\\rho B}_{t}\\right)}_{hnf}}{{\\rho }_{hnf}}\\left(T-{T}_{\\infty }\\right)-\\frac{{\\sigma }_{hnf}}{{\\rho }_{hnf} }{{B}_{0}}^{2}{sin}^{2}\\left(\\alpha \\right)\\widehat{v}-\\frac{{\\mu }_{hnf}}{{\\rho }_{hnf} }\\frac{\\widehat{v}}{{k}_{o}},$$\\end{document}</tex-math><mml:math id=\"M52\" display=\"block\"><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:msup><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:msup><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>-</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfrac><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:msub><mml:mi>k</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq58\"><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}_{r}$$\\end{document}</tex-math><mml:math id=\"M54\"><mml:msub><mml:mi>q</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M55\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} &amp; \\widehat{u}\\frac{\\partial \\widehat{T}}{\\partial x} + \\widehat{v} \\frac{\\partial \\widehat{T}}{\\partial y}+\\widehat{w}\\frac{\\partial \\widehat{T}}{\\partial z}={\\alpha }_{hnf}\\left( \\frac{{\\partial }^{2}\\widehat{T}}{{\\partial x}^{2}}+\\frac{{\\partial }^{2}\\widehat{T}}{{\\partial y}^{2}}+\\frac{{\\partial }^{2}\\widehat{T}}{{\\partial z}^{2}}\\right)-\\frac{1}{{\\left({\\rho C}_{p}\\right)}_{hnf}}\\frac{\\partial {q}_{r}}{\\partial z}\\\\ &amp;\\quad+\\frac{{\\mu }_{hnf}}{{\\left({\\rho C}_{p}\\right)}_{hnf}}\\left[{\\left(\\frac{\\partial \\widehat{u}}{\\partial z}\\right)}^{2}+{\\left(\\frac{\\partial \\widehat{v}}{\\partial z}\\right)}^{2}\\right]+\\frac{{\\sigma }_{hnf}}{{\\left({\\rho C}_{p}\\right)}_{hnf} }{{B}_{0}}^{2}{sin}^{2}\\left(\\alpha \\right)\\left[{\\widehat{u}}^{2}+{\\widehat{v}}^{2}\\right]\\\\ &amp;\\quad+\\tau \\left(\\left[{D}_{B}\\left\\{\\frac{\\partial \\widehat{T}}{\\partial x}.\\frac{\\partial \\widehat{C}}{\\partial x}+\\frac{\\partial \\widehat{T}}{\\partial y}.\\frac{\\partial \\widehat{C}}{\\partial y}+\\frac{\\partial \\widehat{T}}{\\partial z}.\\frac{\\partial \\widehat{C}}{\\partial z}\\right\\}\\right]+\\frac{{D}_{T}}{{T}_{\\infty }}\\left\\{{\\left( \\frac{\\partial \\widehat{T}}{\\partial x}\\right)}^{2}+{\\left( \\frac{\\partial \\widehat{T}}{\\partial y}\\right)}^{2}+{\\left( \\frac{\\partial \\widehat{T}}{\\partial z}\\right)}^{2}\\right\\}\\right),\\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M56\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd/><mml:mtd columnalign=\"left\"><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mfenced><mml:mo>-</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:msub><mml:mi>q</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:msup><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mi>τ</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mfenced close=\"]\" open=\"[\"><mml:msub><mml:mi>D</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mfenced close=\"}\" open=\"{\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>D</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfrac><mml:mfenced close=\"}\" open=\"{\"><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\widehat{u}\\frac{\\partial \\widehat{C}}{\\partial x} + \\widehat{v} \\frac{\\partial \\widehat{C}}{\\partial y}+\\widehat{w}\\frac{\\partial \\widehat{C}}{\\partial z}={D}_{T}\\left( \\frac{{\\partial }^{2}\\widehat{C}}{{\\partial x}^{2}}+\\frac{{\\partial }^{2}\\widehat{C}}{{\\partial y}^{2}}+\\frac{{\\partial }^{2}\\widehat{C}}{{\\partial z}^{2}}\\right)+\\frac{{D}_{T}}{{D}_{\\infty }}\\left( \\frac{{\\partial }^{2}\\widehat{T}}{{\\partial x}^{2}}+\\frac{{\\partial }^{2}\\widehat{T}}{{\\partial y}^{2}}+\\frac{{\\partial }^{2}\\widehat{T}}{{\\partial z}^{2}}\\right)-{k}_{c}\\left(C-{C}_{\\infty }\\right).$$\\end{document}</tex-math><mml:math id=\"M58\" display=\"block\"><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>D</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>C</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{array}{c}\\widehat{u}={U}_{w}=ax, \\,\\widehat{v}={V}_{w}=by,\\, \\widehat{w}=0,\\, \\widehat{T}={\\widehat{T}}_{w},\\, \\widehat{C}={\\widehat{C}}_{w},\\, at\\, z=0 \\\\ \\widehat{u}\\to 0, \\,\\widehat{v}\\to 0,\\, \\widehat{T}\\to {\\widehat{T}}_{\\infty }, \\,\\widehat{C}\\to {\\widehat{C}}_{\\infty },\\, as\\, z\\to \\infty \\end{array}$$\\end{document}</tex-math><mml:math id=\"M60\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msub><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>w</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msub><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>w</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo stretchy=\"false\">→</mml:mo><mml:msub><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>∞</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo stretchy=\"false\">→</mml:mo><mml:msub><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>∞</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>z</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq59\"><alternatives><tex-math id=\"M61\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${g}^{*}$$\\end{document}</tex-math><mml:math id=\"M62\"><mml:msup><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq60\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${B}_{0}$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq61\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$T$$\\end{document}</tex-math><mml:math id=\"M66\"><mml:mi>T</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq62\"><alternatives><tex-math id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:mi>C</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq63\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${T}_{\\infty }$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq64\"><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}_{r}$$\\end{document}</tex-math><mml:math id=\"M72\"><mml:msub><mml:mi>q</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq65\"><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mu$$\\end{document}</tex-math><mml:math id=\"M74\"><mml:mi>μ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq66\"><alternatives><tex-math id=\"M75\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho$$\\end{document}</tex-math><mml:math id=\"M76\"><mml:mi>ρ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq67\"><alternatives><tex-math id=\"M77\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${D}_{{\\varvec{B}}}$$\\end{document}</tex-math><mml:math id=\"M78\"><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi mathvariant=\"bold-italic\">B</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq68\"><alternatives><tex-math id=\"M79\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${D}_{T}$$\\end{document}</tex-math><mml:math id=\"M80\"><mml:msub><mml:mi>D</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq69\"><alternatives><tex-math id=\"M81\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$k$$\\end{document}</tex-math><mml:math id=\"M82\"><mml:mi>k</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq70\"><alternatives><tex-math id=\"M83\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${C}_{p}$$\\end{document}</tex-math><mml:math id=\"M84\"><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq71\"><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\sigma$$\\end{document}</tex-math><mml:math id=\"M86\"><mml:mi>σ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq72\"><alternatives><tex-math id=\"M87\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${B}_{t}$$\\end{document}</tex-math><mml:math id=\"M88\"><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq73\"><alternatives><tex-math id=\"M89\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M90\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq74\"><alternatives><tex-math id=\"M91\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$u,v,w$$\\end{document}</tex-math><mml:math id=\"M92\"><mml:mrow><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq75\"><alternatives><tex-math id=\"M93\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x,y,z$$\\end{document}</tex-math><mml:math id=\"M94\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq76\"><alternatives><tex-math id=\"M95\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$hnf$$\\end{document}</tex-math><mml:math id=\"M96\"><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq77\"><alternatives><tex-math id=\"M97\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(z = 0),$$\\end{document}</tex-math><mml:math id=\"M98\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq78\"><alternatives><tex-math id=\"M99\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${U}_{w}$$\\end{document}</tex-math><mml:math id=\"M100\"><mml:msub><mml:mi>U</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq79\"><alternatives><tex-math id=\"M101\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${V}_{w}$$\\end{document}</tex-math><mml:math id=\"M102\"><mml:msub><mml:mi>V</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq80\"><alternatives><tex-math id=\"M103\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$w=0$$\\end{document}</tex-math><mml:math id=\"M104\"><mml:mrow><mml:mi>w</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq81\"><alternatives><tex-math id=\"M105\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(T)$$\\end{document}</tex-math><mml:math id=\"M106\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq82\"><alternatives><tex-math id=\"M107\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(C)$$\\end{document}</tex-math><mml:math id=\"M108\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>C</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq83\"><alternatives><tex-math id=\"M109\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${T}_{w}$$\\end{document}</tex-math><mml:math id=\"M110\"><mml:msub><mml:mi>T</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq84\"><alternatives><tex-math id=\"M111\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${C}_{w}$$\\end{document}</tex-math><mml:math id=\"M112\"><mml:msub><mml:mi>C</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq85\"><alternatives><tex-math id=\"M113\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$z\\to \\infty ,$$\\end{document}</tex-math><mml:math id=\"M114\"><mml:mrow><mml:mi>z</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>∞</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq86\"><alternatives><tex-math id=\"M115\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(u\\to 0,v\\to 0),$$\\end{document}</tex-math><mml:math id=\"M116\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>u</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq87\"><alternatives><tex-math id=\"M117\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$({T}_{\\infty },{ C}_{\\infty })$$\\end{document}</tex-math><mml:math id=\"M118\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq206\"><alternatives><tex-math id=\"M119\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\text{Density}}$$\\end{document}</tex-math><mml:math id=\"M120\"><mml:mtext>Density</mml:mtext></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq207\"><alternatives><tex-math id=\"M121\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\rho }_{nf}=(1-{(\\phi }_{1})){\\rho }_{f}+{\\phi }_{1}{\\rho }_{s1}, {G}_{1}=\\frac{{\\rho }_{nf}}{{\\rho }_{f}}$$\\end{document}</tex-math><mml:math id=\"M122\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ϕ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq208\"><alternatives><tex-math id=\"M123\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Dynamic viscosity}$$\\end{document}</tex-math><mml:math id=\"M124\"><mml:mrow><mml:mi mathvariant=\"normal\">Dynamic</mml:mi><mml:mi mathvariant=\"normal\">viscosity</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq209\"><alternatives><tex-math id=\"M125\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mu }_{nf}=\\frac{{\\mu }_{f}}{{[1-\\left({\\phi }_{1}\\right)]}^{5/2}}={K}_{1}$$\\end{document}</tex-math><mml:math id=\"M126\"><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mfenced><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mrow><mml:mn>5</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq210\"><alternatives><tex-math id=\"M127\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Heat capacity}$$\\end{document}</tex-math><mml:math id=\"M128\"><mml:mrow><mml:mi mathvariant=\"normal\">Heat</mml:mi><mml:mi mathvariant=\"normal\">capacity</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq211\"><alternatives><tex-math id=\"M129\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\left(\\rho {C}_{p}\\right)}_{nf}=\\left[1-\\left({\\phi }_{1}\\right)\\right]{\\left(\\rho {c}_{p}\\right)}_{f}+{{\\phi }_{1}(\\rho {c}_{p})}_{s1}, {G}_{2}=\\frac{{\\left(\\rho {C}_{p}\\right)}_{nf}}{{\\left(\\rho {C}_{p}\\right)}_{f}}$$\\end{document}</tex-math><mml:math id=\"M130\"><mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mfenced></mml:mfenced><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ρ</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq212\"><alternatives><tex-math id=\"M131\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Thermal conductivity}$$\\end{document}</tex-math><mml:math id=\"M132\"><mml:mrow><mml:mi mathvariant=\"normal\">Thermal</mml:mi><mml:mi mathvariant=\"normal\">conductivity</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq213\"><alternatives><tex-math id=\"M133\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{k}_{nf}}{{k}_{f}}=\\frac{{k}_{s1}+2{k}_{f}-2{\\phi }_{1}({k}_{f}-{k}_{s1})}{{k}_{s1}+2{k}_{f}+{\\phi }_{1}\\times ({k}_{f}-{k}_{s1})}, {G}_{3}=\\frac{{k}_{nf}}{{k}_{f}}$$\\end{document}</tex-math><mml:math id=\"M134\"><mml:mrow><mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq214\"><alternatives><tex-math id=\"M135\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\left(\\rho {B}_{t}\\right)}_{nf}=(1-{(\\phi }_{1})){\\rho {B}_{t}}_{f}+{\\phi }_{1}{\\rho {B}_{t}}_{s1}, {G}_{4}=\\frac{{\\left(\\rho {B}_{t}\\right)}_{nf}}{{\\left(\\rho {B}_{t}\\right)}_{f}}$$\\end{document}</tex-math><mml:math id=\"M136\"><mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ϕ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq215\"><alternatives><tex-math id=\"M137\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{\\sigma }_{nf}}{{\\sigma }_{f}}=1+\\frac{3\\left({\\sigma }_{s1}-{\\sigma }_{f}\\right)}{\\left({\\sigma }_{s1}+2{\\sigma }_{f}\\right)-\\left({\\sigma }_{s1}-{\\sigma }_{f}\\right){\\phi }_{1}}, {G}_{5}=\\frac{{\\sigma }_{nf}}{{\\sigma }_{f}}$$\\end{document}</tex-math><mml:math id=\"M138\"><mml:mrow><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>3</mml:mn><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfenced><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq216\"><alternatives><tex-math id=\"M139\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\text{Density}}$$\\end{document}</tex-math><mml:math id=\"M140\"><mml:mtext>Density</mml:mtext></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq217\"><alternatives><tex-math id=\"M141\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\rho }_{hnf}=(1-{(\\phi }_{1}+{\\phi }_{2})){\\rho }_{f}+{\\phi }_{1}{\\rho }_{s1}+{\\phi }_{2}{\\rho }_{s2}, {H}_{1}=\\frac{{\\rho }_{hnf}}{{\\rho }_{f}}$$\\end{document}</tex-math><mml:math id=\"M142\"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ϕ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>ρ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq218\"><alternatives><tex-math id=\"M143\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Dynamic viscosity}$$\\end{document}</tex-math><mml:math id=\"M144\"><mml:mrow><mml:mi mathvariant=\"normal\">Dynamic</mml:mi><mml:mi mathvariant=\"normal\">viscosity</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq219\"><alternatives><tex-math id=\"M145\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\mu }_{hnf}=\\frac{{\\mu }_{f}}{{[1-\\left({\\phi }_{1}+{\\phi }_{2}\\right)]}^{5/2}}={K}_{2}$$\\end{document}</tex-math><mml:math id=\"M146\"><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mfenced><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow><mml:mrow><mml:mn>5</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq220\"><alternatives><tex-math id=\"M147\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Heat capacity}$$\\end{document}</tex-math><mml:math id=\"M148\"><mml:mrow><mml:mi mathvariant=\"normal\">Heat</mml:mi><mml:mi mathvariant=\"normal\">capacity</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq221\"><alternatives><tex-math id=\"M149\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\left(\\rho {C}_{p}\\right)}_{hnf}=\\left[1-\\left({\\phi }_{1}+{\\phi }_{2}\\right)\\right]{\\left(\\rho {c}_{p}\\right)}_{f}+{{\\phi }_{1}(\\rho {c}_{p})}_{s1}+{{\\phi }_{2}(\\rho {c}_{p})}_{s2}, {H}_{2}=\\frac{{\\left(\\rho {C}_{p}\\right)}_{hnf}}{{\\left(\\rho {C}_{p}\\right)}_{f}}$$\\end{document}</tex-math><mml:math id=\"M150\"><mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mfenced></mml:mfenced><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ρ</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ρ</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq222\"><alternatives><tex-math id=\"M151\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Thermal conductivity}$$\\end{document}</tex-math><mml:math id=\"M152\"><mml:mrow><mml:mi mathvariant=\"normal\">Thermal</mml:mi><mml:mi mathvariant=\"normal\">conductivity</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq223\"><alternatives><tex-math id=\"M153\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{k}_{hnf}}{{k}_{nf}}=\\frac{{k}_{s2}+2\\times {k}_{nf}-2\\times {\\phi }_{2}\\times \\left({k}_{nf}-{k}_{s2}\\right)}{{k}_{s2}+2\\times {k}_{nf}+{\\phi }_{2}\\times \\left({k}_{nf}-{k}_{s2}\\right)},$$\\end{document}</tex-math><mml:math id=\"M154\"><mml:mrow><mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mfenced></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq224\"><alternatives><tex-math id=\"M155\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{k}_{nf}}{{k}_{f}}=\\frac{{k}_{s1}+2\\times {k}_{f}-2\\times {\\phi }_{1}\\times ({k}_{f}-{k}_{s1})}{{k}_{s1}+2\\times {k}_{f}+{\\phi }_{1}\\times ({k}_{f}-{k}_{s1})}$$\\end{document}</tex-math><mml:math id=\"M156\"><mml:mrow><mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">nf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq225\"><alternatives><tex-math id=\"M157\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${H}_{3}=\\frac{{k}_{hnf}}{{k}_{f}}$$\\end{document}</tex-math><mml:math id=\"M158\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq226\"><alternatives><tex-math id=\"M159\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\left(\\rho {B}_{t}\\right)}_{hnf}=(1-{(\\phi }_{1}+{\\phi }_{2})){\\left(\\rho {B}_{t}\\right)}_{f}+{\\phi }_{1}{\\left(\\rho {B}_{t}\\right)}_{s1}+{\\phi }_{2}{\\left(\\rho {B}_{t}\\right)}_{s2}, {H}_{4}=\\frac{{\\left(\\rho {B}_{t}\\right)}_{hnf}}{{\\left(\\rho {B}_{t}\\right)}_{f}}$$\\end{document}</tex-math><mml:math id=\"M160\"><mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ϕ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq227\"><alternatives><tex-math id=\"M161\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{\\sigma }_{hnf}}{{\\sigma }_{f}}=1+\\frac{3\\left[\\frac{{\\sigma }_{s1}{\\phi }_{1}-{\\sigma }_{s2}{\\phi }_{2}}{{\\sigma }_{f}}-{(\\phi }_{1}+{\\phi }_{2})\\right]}{\\left(2+\\frac{{\\sigma }_{s1}+{\\sigma }_{s2}}{{\\sigma }_{f}}\\right)-\\left[\\frac{{\\sigma }_{s1}{\\phi }_{1}-{\\sigma }_{s2}{\\phi }_{2}}{{\\sigma }_{f}}\\right]+{(\\phi }_{1}+{\\phi }_{2})}, {H}_{5}=\\frac{{\\sigma }_{hnf}}{{\\sigma }_{f}}$$\\end{document}</tex-math><mml:math id=\"M162\"><mml:mrow><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>3</mml:mn><mml:mfenced close=\"]\" open=\"[\"><mml:mfrac><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ϕ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mfrac><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>ϕ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq228\"><alternatives><tex-math id=\"M163\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\text{Water}}$$\\end{document}</tex-math><mml:math id=\"M164\"><mml:mtext>Water</mml:mtext></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq229\"><alternatives><tex-math id=\"M165\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$997$$\\end{document}</tex-math><mml:math id=\"M166\"><mml:mrow><mml:mn>997</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq230\"><alternatives><tex-math id=\"M167\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4179$$\\end{document}</tex-math><mml:math id=\"M168\"><mml:mrow><mml:mn>4179</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq231\"><alternatives><tex-math id=\"M169\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.614$$\\end{document}</tex-math><mml:math id=\"M170\"><mml:mrow><mml:mn>0.614</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq232\"><alternatives><tex-math id=\"M171\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$21\\times {10}^{-5}$$\\end{document}</tex-math><mml:math id=\"M172\"><mml:mrow><mml:mn>21</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq233\"><alternatives><tex-math id=\"M173\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Copper }\\left({{\\text{s}}}_{1}\\right)$$\\end{document}</tex-math><mml:math id=\"M174\"><mml:mrow><mml:mi mathvariant=\"normal\">Copper</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mtext>s</mml:mtext><mml:mn>1</mml:mn></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq234\"><alternatives><tex-math id=\"M175\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$5.96\\times {10}^{7}$$\\end{document}</tex-math><mml:math id=\"M176\"><mml:mrow><mml:mn>5.96</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mn>7</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq235\"><alternatives><tex-math id=\"M177\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8933$$\\end{document}</tex-math><mml:math id=\"M178\"><mml:mrow><mml:mn>8933</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq236\"><alternatives><tex-math id=\"M179\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$385$$\\end{document}</tex-math><mml:math id=\"M180\"><mml:mrow><mml:mn>385</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq237\"><alternatives><tex-math id=\"M181\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$400$$\\end{document}</tex-math><mml:math id=\"M182\"><mml:mrow><mml:mn>400</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq238\"><alternatives><tex-math id=\"M183\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.67\\times {10}^{-5}$$\\end{document}</tex-math><mml:math id=\"M184\"><mml:mrow><mml:mn>1.67</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq239\"><alternatives><tex-math id=\"M185\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Aluminum oxide }\\left({{\\text{s}}}_{2}\\right)$$\\end{document}</tex-math><mml:math id=\"M186\"><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">Aluminum</mml:mi><mml:mi mathvariant=\"normal\">oxide</mml:mi></mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mtext>s</mml:mtext><mml:mn>2</mml:mn></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq240\"><alternatives><tex-math id=\"M187\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.27\\times {10}^{-5}$$\\end{document}</tex-math><mml:math id=\"M188\"><mml:mrow><mml:mn>6.27</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq241\"><alternatives><tex-math id=\"M189\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3970$$\\end{document}</tex-math><mml:math id=\"M190\"><mml:mrow><mml:mn>3970</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq242\"><alternatives><tex-math id=\"M191\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$765$$\\end{document}</tex-math><mml:math id=\"M192\"><mml:mrow><mml:mn>765</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq243\"><alternatives><tex-math id=\"M193\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$40$$\\end{document}</tex-math><mml:math id=\"M194\"><mml:mrow><mml:mn>40</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq244\"><alternatives><tex-math id=\"M195\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.85\\times {10}^{-5}$$\\end{document}</tex-math><mml:math id=\"M196\"><mml:mrow><mml:mn>0.85</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq245\"><alternatives><tex-math id=\"M197\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda$$\\end{document}</tex-math><mml:math id=\"M198\"><mml:mi>λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq246\"><alternatives><tex-math id=\"M199\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}^{{\\prime}{\\prime}}(0)$$\\end{document}</tex-math><mml:math id=\"M200\"><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq247\"><alternatives><tex-math id=\"M201\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}^{\\prime}(0)$$\\end{document}</tex-math><mml:math id=\"M202\"><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq248\"><alternatives><tex-math id=\"M203\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}^{{\\prime}{\\prime}}\\left(0\\right)$$\\end{document}</tex-math><mml:math id=\"M204\"><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mn>0</mml:mn></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq249\"><alternatives><tex-math id=\"M205\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}^{\\prime}(0)$$\\end{document}</tex-math><mml:math id=\"M206\"><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq250\"><alternatives><tex-math id=\"M207\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}^{{\\prime}{\\prime}}(0)$$\\end{document}</tex-math><mml:math id=\"M208\"><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq251\"><alternatives><tex-math id=\"M209\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}^{\\prime}(0)$$\\end{document}</tex-math><mml:math id=\"M210\"><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq252\"><alternatives><tex-math id=\"M211\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.0$$\\end{document}</tex-math><mml:math id=\"M212\"><mml:mrow><mml:mn>0.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq253\"><alternatives><tex-math id=\"M213\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.0$$\\end{document}</tex-math><mml:math id=\"M214\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq254\"><alternatives><tex-math id=\"M215\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.0$$\\end{document}</tex-math><mml:math id=\"M216\"><mml:mrow><mml:mn>0.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq255\"><alternatives><tex-math id=\"M217\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.013$$\\end{document}</tex-math><mml:math id=\"M218\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.013</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq256\"><alternatives><tex-math id=\"M219\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.0$$\\end{document}</tex-math><mml:math id=\"M220\"><mml:mrow><mml:mn>0.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq257\"><alternatives><tex-math id=\"M221\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.0$$\\end{document}</tex-math><mml:math id=\"M222\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq258\"><alternatives><tex-math id=\"M223\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.0$$\\end{document}</tex-math><mml:math id=\"M224\"><mml:mrow><mml:mn>0.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq259\"><alternatives><tex-math id=\"M225\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M226\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq260\"><alternatives><tex-math id=\"M227\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.13$$\\end{document}</tex-math><mml:math id=\"M228\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.13</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq261\"><alternatives><tex-math id=\"M229\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.51$$\\end{document}</tex-math><mml:math id=\"M230\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.51</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq262\"><alternatives><tex-math id=\"M231\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.141$$\\end{document}</tex-math><mml:math id=\"M232\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.141</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq263\"><alternatives><tex-math id=\"M233\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.518$$\\end{document}</tex-math><mml:math id=\"M234\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.518</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq264\"><alternatives><tex-math id=\"M235\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.13$$\\end{document}</tex-math><mml:math id=\"M236\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.13</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq265\"><alternatives><tex-math id=\"M237\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.51$$\\end{document}</tex-math><mml:math id=\"M238\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.51</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq266\"><alternatives><tex-math id=\"M239\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.0$$\\end{document}</tex-math><mml:math id=\"M240\"><mml:mrow><mml:mn>1.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq267\"><alternatives><tex-math id=\"M241\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.32$$\\end{document}</tex-math><mml:math id=\"M242\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.32</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq268\"><alternatives><tex-math id=\"M243\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.83$$\\end{document}</tex-math><mml:math id=\"M244\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.83</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq269\"><alternatives><tex-math id=\"M245\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.332$$\\end{document}</tex-math><mml:math id=\"M246\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.332</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq270\"><alternatives><tex-math id=\"M247\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.831$$\\end{document}</tex-math><mml:math id=\"M248\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.831</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq271\"><alternatives><tex-math id=\"M249\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.32$$\\end{document}</tex-math><mml:math id=\"M250\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.32</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq272\"><alternatives><tex-math id=\"M251\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.83$$\\end{document}</tex-math><mml:math id=\"M252\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.83</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq273\"><alternatives><tex-math id=\"M253\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.0$$\\end{document}</tex-math><mml:math id=\"M254\"><mml:mrow><mml:mn>2.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq274\"><alternatives><tex-math id=\"M255\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.65$$\\end{document}</tex-math><mml:math id=\"M256\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.65</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq275\"><alternatives><tex-math id=\"M257\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.28$$\\end{document}</tex-math><mml:math id=\"M258\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.28</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq276\"><alternatives><tex-math id=\"M259\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.660$$\\end{document}</tex-math><mml:math id=\"M260\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.660</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq277\"><alternatives><tex-math id=\"M261\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.292$$\\end{document}</tex-math><mml:math id=\"M262\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.292</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq278\"><alternatives><tex-math id=\"M263\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.65$$\\end{document}</tex-math><mml:math id=\"M264\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.65</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq279\"><alternatives><tex-math id=\"M265\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.28$$\\end{document}</tex-math><mml:math id=\"M266\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.28</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq88\"><alternatives><tex-math id=\"M267\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\phi$$\\end{document}</tex-math><mml:math id=\"M268\"><mml:mi>ϕ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq89\"><alternatives><tex-math id=\"M269\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$f,s,nf,hnf$$\\end{document}</tex-math><mml:math id=\"M270\"><mml:mrow><mml:mi>f</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>f</mml:mi><mml:mo>,</mml:mo><mml:mi>h</mml:mi><mml:mi>n</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq90\"><alternatives><tex-math id=\"M271\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}_{r}$$\\end{document}</tex-math><mml:math id=\"M272\"><mml:msub><mml:mi>q</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M273\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}_{r}=-\\frac{4{\\sigma }^{*}}{3{k}_{1}}\\frac{{\\partial T}^{4}}{\\partial z}.$$\\end{document}</tex-math><mml:math id=\"M274\" display=\"block\"><mml:mrow><mml:msub><mml:mi>q</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>4</mml:mn><mml:msup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mfrac><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq91\"><alternatives><tex-math id=\"M275\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\sigma }^{*}$$\\end{document}</tex-math><mml:math id=\"M276\"><mml:msup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq92\"><alternatives><tex-math id=\"M277\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${k}_{1}$$\\end{document}</tex-math><mml:math id=\"M278\"><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq93\"><alternatives><tex-math id=\"M279\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${T}^{4}$$\\end{document}</tex-math><mml:math id=\"M280\"><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ8\"><label>8</label><alternatives><tex-math id=\"M281\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${T}^{4}={{T}^{4}}_{\\infty }+{4{T}^{3}}_{\\infty }\\left(T-{T}_{\\infty }\\right)+{6{T}^{2}}_{\\infty }{\\left(T-{T}_{\\infty }\\right)}^{2}+\\dots$$\\end{document}</tex-math><mml:math id=\"M282\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:mrow><mml:mi>∞</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mn>4</mml:mn><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow><mml:mi>∞</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mn>6</mml:mn><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mi>∞</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mo>⋯</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq94\"><alternatives><tex-math id=\"M283\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\left(T-{T}_{\\infty }\\right),$$\\end{document}</tex-math><mml:math id=\"M284\"><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ9\"><label>9</label><alternatives><tex-math id=\"M285\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${T}^{4}=4{{T}^{3}}_{\\infty }T-3{{T}^{4}}_{\\infty }.$$\\end{document}</tex-math><mml:math id=\"M286\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:msub><mml:mrow><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow><mml:mi>∞</mml:mi></mml:msub><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:mn>3</mml:mn><mml:msub><mml:mrow><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mn>4</mml:mn></mml:msup></mml:mrow><mml:mi>∞</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ10\"><label>10</label><alternatives><tex-math id=\"M287\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\frac{{\\partial q}_{r}}{\\partial z}=-\\frac{16{\\sigma }^{*}{{T}_{\\infty }}^{3}}{{3k}_{1}}\\frac{{\\partial }^{2}T}{{\\partial z}^{2}},$$\\end{document}</tex-math><mml:math id=\"M288\" display=\"block\"><mml:mrow><mml:mfrac><mml:msub><mml:mrow><mml:mi>∂</mml:mi><mml:mi>q</mml:mi></mml:mrow><mml:mi>r</mml:mi></mml:msub><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mn>16</mml:mn><mml:msup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow><mml:msub><mml:mrow><mml:mn>3</mml:mn><mml:mi>k</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub></mml:mfrac><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mi>T</mml:mi></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ11\"><label>11</label><alternatives><tex-math id=\"M289\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} &amp; \\widehat{u}\\frac{\\partial \\widehat{T}}{\\partial x} + \\widehat{v} \\frac{\\partial \\widehat{T}}{\\partial y}+\\widehat{w}\\frac{\\partial \\widehat{T}}{\\partial z}={\\alpha }_{hnf}\\left( \\frac{{\\partial }^{2}\\widehat{T}}{{\\partial x}^{2}}+\\frac{{\\partial }^{2}\\widehat{T}}{{\\partial y}^{2}}+\\frac{{\\partial }^{2}\\widehat{T}}{{\\partial z}^{2}}\\right)+\\frac{16{\\sigma }^{*}{{T}_{\\infty }}^{3}}{{3k}_{1}{\\left({\\rho C}_{p}\\right)}_{hnf}}\\frac{{\\partial }^{2}T}{{\\partial z}^{2}}\\\\ &amp; \\quad+\\frac{{\\mu }_{hnf}}{{\\left({\\rho C}_{p}\\right)}_{hnf}}\\left[{\\left(\\frac{\\partial \\widehat{u}}{\\partial z}\\right)}^{2}+{\\left(\\frac{\\partial \\widehat{v}}{\\partial z}\\right)}^{2}\\right]+\\frac{{\\sigma }_{hnf}}{{\\left({\\rho C}_{p}\\right)}_{hnf} }{{B}_{0}}^{2}{sin}^{2}\\left(\\alpha \\right)\\left[{\\widehat{u}}^{2}+{\\widehat{v}}^{2}\\right]\\\\ &amp; \\quad+\\tau \\left(\\left[{D}_{B}\\left\\{\\frac{\\partial \\widehat{T}}{\\partial x}.\\frac{\\partial \\widehat{C}}{\\partial x}+\\frac{\\partial \\widehat{T}}{\\partial y}.\\frac{\\partial \\widehat{C}}{\\partial y}+\\frac{\\partial \\widehat{T}}{\\partial z}.\\frac{\\partial \\widehat{C}}{\\partial z}\\right\\}\\right]+\\frac{{D}_{T}}{{T}_{\\infty }}\\left\\{{\\left( \\frac{\\partial \\widehat{T}}{\\partial x}\\right)}^{2}+{\\left( \\frac{\\partial \\widehat{T}}{\\partial y}\\right)}^{2}+{\\left( \\frac{\\partial \\widehat{T}}{\\partial z}\\right)}^{2}\\right\\}\\right),\\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M290\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd/><mml:mtd columnalign=\"left\"><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>16</mml:mn><mml:msup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mn>3</mml:mn><mml:mi>k</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mi>T</mml:mi></mml:mrow><mml:msup><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mfrac><mml:msup><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mo>+</mml:mo><mml:mi>τ</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mfenced close=\"]\" open=\"[\"><mml:msub><mml:mi>D</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mfenced close=\"}\" open=\"{\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mfenced><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>D</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfrac><mml:mfenced close=\"}\" open=\"{\"><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ12\"><label>12</label><alternatives><tex-math id=\"M291\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{array}{c}\\widehat{w}=\\sqrt{a{v}_{f} }\\left\\{p\\left(\\eta \\right)+q\\left(\\eta \\right)\\right\\}, \\,\\widehat{v}=ay{q}{\\prime}\\left(\\eta \\right),\\, \\widehat{u}=ax{p}^{\\prime}\\left(\\eta \\right), \\\\ \\eta =z\\sqrt{\\frac{a}{{v}_{f}}}, \\,s\\left(\\eta \\right)\\left({\\widehat{C}}_{o}-{\\widehat{C}}_{\\infty }\\right)=\\widehat{C}-{\\widehat{C}}_{\\infty },\\, r\\left(\\eta \\right)\\left({\\widehat{T}}_{o}-{T}_{\\infty }\\right)=\\widehat{T}-{\\widehat{T}}_{\\infty }.\\end{array}$$\\end{document}</tex-math><mml:math id=\"M292\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mover accent=\"true\"><mml:mi>w</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mi>a</mml:mi><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:msqrt><mml:mfenced close=\"}\" open=\"{\"><mml:mi>p</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mi>q</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mfenced><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>v</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mi>y</mml:mi><mml:mi>q</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mover accent=\"true\"><mml:mi>u</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mi>η</mml:mi><mml:mo>=</mml:mo><mml:mi>z</mml:mi><mml:msqrt><mml:mfrac><mml:mi>a</mml:mi><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac></mml:msqrt><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>s</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>o</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>-</mml:mo><mml:msub><mml:mover accent=\"true\"><mml:mi>C</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>∞</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>r</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>o</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mo>-</mml:mo><mml:msub><mml:mover accent=\"true\"><mml:mi>T</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover><mml:mi>∞</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq95\"><alternatives><tex-math id=\"M293\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\eta .$$\\end{document}</tex-math><mml:math id=\"M294\"><mml:mrow><mml:mi>η</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ13\"><label>13</label><alternatives><tex-math id=\"M295\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}^{{\\prime}{\\prime}{\\prime}}\\left(\\eta \\right)={H}_{1}*\\left\\{{{p}^{\\prime}\\left(\\eta \\right)}^{2}*\\left({p}^{\\prime}\\left(\\eta \\right)+{q}^{\\prime}\\left(\\eta \\right)\\right)-2* \\delta *{q}^{\\prime}\\left(\\eta \\right)+Z* {p}^{\\prime}\\left(\\eta \\right)-{\\epsilon }_{x}*r*{H}_{4}+{M}^{2}*{sin}^{2}\\left(\\alpha \\right)*{p}^{\\prime}*{H}_{5}\\right\\}*{K}_{2}$$\\end{document}</tex-math><mml:math id=\"M296\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\"}\" open=\"{\"><mml:msup><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mfenced><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>δ</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mi>Z</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mi>ϵ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>r</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ14\"><label>14</label><alternatives><tex-math id=\"M297\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}{\\mathrm{^{\\prime}}\\mathrm{^{\\prime}}\\mathrm{^{\\prime}}}\\left(\\eta \\right)={H}_{1}*\\left\\{{{q}{\\mathrm{^{\\prime}}}\\left(\\eta \\right)}^{2}\\left({p}{\\mathrm{^{\\prime}}}\\left(\\eta \\right)+{q}{\\mathrm{^{\\prime}}}\\left(\\eta \\right)\\right)-2*\\frac{\\lambda }{\\delta }* {p}{\\mathrm{^{\\prime}}}\\left(\\eta \\right)+Z* {q}{\\mathrm{^{\\prime}}}\\left(\\eta \\right)-{\\epsilon }_{y}*r*{H}_{4}+{M}^{2}*{sin}^{2}\\left(\\alpha \\right)*{q}{\\mathrm{^{\\prime}}}*{H}_{5}\\right\\}*{K}_{2}$$\\end{document}</tex-math><mml:math id=\"M298\" display=\"block\"><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\"}\" open=\"{\"><mml:msup><mml:mrow><mml:mi>q</mml:mi><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>p</mml:mi><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mi>q</mml:mi><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mfenced><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mrow/><mml:mo>∗</mml:mo><mml:mfrac><mml:mi>λ</mml:mi><mml:mi>δ</mml:mi></mml:mfrac><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>p</mml:mi><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mi>Z</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>q</mml:mi><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mi>ϵ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>r</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>q</mml:mi><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ15\"><label>15</label><alternatives><tex-math id=\"M299\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned}{r}^{{\\prime}{\\prime}} &amp; =-{\\left(1+\\frac{4}{3*{H}_{3}}*\\pi \\right)}^{-1}\\left[Pr*{H}_{2}*{r}^{\\prime}\\left(p\\left(\\eta \\right)+q\\left(\\eta \\right)\\right)+{r}^{\\prime}*{s}^{\\prime}*{N}_{b}+{{r}^{\\prime}}^{2}{N}_{t}\\right.\\\\ &amp; \\quad \\left.+\\left[{K}_{2}*Ec*\\left({{p}^{{\\prime}{\\prime}}}^{2}+{{q}^{{\\prime}{\\prime}}}^{2}\\right)+{H}_{5}*{M}^{2}*{sin}^{2}\\left(\\alpha \\right)*Ec*\\left({{p}^{\\prime}}^{2}+{{q}^{\\prime}}^{2}\\right)\\right]\\right]\\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M300\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:msup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mn>4</mml:mn><mml:mrow><mml:mn>3</mml:mn><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>π</mml:mi></mml:mfenced></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mfenced open=\"[\"><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>p</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mi>q</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mfenced><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:msup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mfenced close=\"]\"><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msup><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msup><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced></mml:mfenced></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ16\"><label>16</label><alternatives><tex-math id=\"M301\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${s}{\\mathrm{^{\\prime}}\\mathrm{^{\\prime}}}=Sc*\\left(\\left(p+q\\right)*{r}{\\mathrm{^{\\prime}}}+\\frac{{N}_{t}}{{N}_{b}}*{r}{\\mathrm{^{\\prime}}\\mathrm{^{\\prime}}}-s*{K}_{c}\\right)$$\\end{document}</tex-math><mml:math id=\"M302\" display=\"block\"><mml:mrow><mml:mi>s</mml:mi><mml:mrow><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mo>=</mml:mo><mml:mi>S</mml:mi><mml:mi>c</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mfenced close=\")\" open=\"(\"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>q</mml:mi></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>r</mml:mi><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:msub><mml:mi>N</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:mfrac><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>r</mml:mi><mml:mrow><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mo>-</mml:mo><mml:mi>s</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq96\"><alternatives><tex-math id=\"M303\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${H}_{1},{ H}_{2}, {H}_{3},{ H}_{4}{, H}_{5},$$\\end{document}</tex-math><mml:math id=\"M304\"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo>,</mml:mo><mml:mi>H</mml:mi></mml:mrow><mml:mn>5</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq97\"><alternatives><tex-math id=\"M305\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${K}_{2},$$\\end{document}</tex-math><mml:math id=\"M306\"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq98\"><alternatives><tex-math id=\"M307\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda ,\\delta , Z,\\epsilon , M, Pr, \\pi , Ec, Sc, {N}_{t},\\tau , {N}_{b},$$\\end{document}</tex-math><mml:math id=\"M308\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo>,</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>,</mml:mo><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>π</mml:mi><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mi>c</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq99\"><alternatives><tex-math id=\"M309\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${K}_{c}$$\\end{document}</tex-math><mml:math id=\"M310\"><mml:msub><mml:mi>K</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ17\"><label>17</label><alternatives><tex-math id=\"M311\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{array}{c}\\lambda =\\frac{{\\omega }^{*}}{a},\\delta =\\frac{y}{x}, Z=\\frac{{\\mu }_{hnf}}{{a{\\rho }_{hnf}k}_{o}},\\epsilon =\\frac{\\mathrm{ Gr}}{{{Re}_{x}}^{2}}, M= \\sqrt{\\frac{{\\sigma }_{f}{{B}_{0}}^{2}}{a{\\rho }_{f}}},\\\\ Pr=\\frac{{v}_{f}}{{k}_{f}}, \\pi =\\frac{4{\\sigma }^{*} {{T}_{\\infty }}^{3}}{{k}_{1} {k}_{f}}, Sc= \\frac{{D}_{B}}{{v}_{f}},\\tau =\\frac{{\\left(\\rho Cp\\right)}_{s}}{{\\left(\\rho Cp\\right)}_{f}},\\\\ Ec=\\frac{{{u}_{w}}^{2}}{{\\left(\\rho {C}_{p}\\right)}_{f}}\\frac{1}{\\left({T}_{w}-{T}_{\\infty }\\right)},{N}_{t}=\\frac{{\\left(\\rho Cp\\right)}_{s}{D}_{B}\\left({C}_{w}-{C}_{\\infty }\\right)}{{T}_{\\infty }{\\left(\\rho Cp\\right)}_{f} {v}_{f}},\\\\ {N}_{b}=\\frac{{\\left(\\rho Cp\\right)}_{s}{D}_{B}\\left({T}_{w}-{T}_{\\infty }\\right)}{{\\left(\\rho Cp\\right)}_{f} {v}_{f}},{K}_{c}=\\frac{{K}_{r}}{a}\\end{array}$$\\end{document}</tex-math><mml:math id=\"M312\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:msup><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mi>a</mml:mi></mml:mfrac><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mi>y</mml:mi><mml:mi>x</mml:mi></mml:mfrac><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>a</mml:mi><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:mi>k</mml:mi></mml:mrow><mml:mi>o</mml:mi></mml:msub></mml:mfrac><mml:mo>,</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mi mathvariant=\"normal\">Gr</mml:mi><mml:msup><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Re</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:msqrt><mml:mfrac><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msup><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:msub><mml:mi>ρ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:msqrt><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>,</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>4</mml:mn><mml:msup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>D</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>,</mml:mo><mml:mi>τ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:mfenced><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:mfenced><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:msup><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mfenced><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mfrac><mml:mn>1</mml:mn><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>T</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:mfenced><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>C</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:mfenced><mml:mi>f</mml:mi></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:msub><mml:mi>N</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:mfenced><mml:mi>s</mml:mi></mml:msub><mml:msub><mml:mi>D</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>T</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:mfenced><mml:mi>f</mml:mi></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>K</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mi>a</mml:mi></mml:mfrac></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq100\"><alternatives><tex-math id=\"M313\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\text{Gr}}=\\frac{{g}^{*}{\\left(\\rho {B}_{t}\\right)}_{hnf}}{{{v}_{f}}^{2}}\\left(T-{T}_{\\infty }\\right) {x}^{3}, {Re}_{x}=\\frac{{u}_{w}}{{v}_{f}}.$$\\end{document}</tex-math><mml:math id=\"M314\"><mml:mrow><mml:mtext>Gr</mml:mtext><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mrow/><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mi>ρ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfrac><mml:mfenced close=\")\" open=\"(\"><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Re</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>u</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ18\"><label>18</label><alternatives><tex-math id=\"M315\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{array}{c}at \\eta =0, \\,s=1,\\, r=1,\\, {q}^{\\prime}=\\gamma , \\,q=0,\\, {p}^{\\prime}=1, \\,p=0, \\\\ as \\eta \\to \\infty ,\\, s\\to 0,\\, r\\to 0, \\,{q}^{\\prime}\\to 0,\\, {p}{\\prime}\\to 0,\\end{array}$$\\end{document}</tex-math><mml:math id=\"M316\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>η</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>∞</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>s</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>r</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq101\"><alternatives><tex-math id=\"M317\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma =\\frac{b}{a}$$\\end{document}</tex-math><mml:math id=\"M318\"><mml:mrow><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mi>b</mml:mi><mml:mi>a</mml:mi></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq102\"><alternatives><tex-math id=\"M319\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M320\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq103\"><alternatives><tex-math id=\"M321\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M322\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq104\"><alternatives><tex-math id=\"M323\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x}$$\\end{document}</tex-math><mml:math id=\"M324\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq105\"><alternatives><tex-math id=\"M325\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{y}$$\\end{document}</tex-math><mml:math id=\"M326\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ19\"><label>19</label><alternatives><tex-math id=\"M327\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x}=\\frac{{\\tau }_{zx}}{{\\rho }_{f}{{u}_{w}}^{2}}, \\,{Cf}_{y}=\\frac{{\\tau }_{zy}}{{\\rho }_{f}{{v}_{w}}^{2}}$$\\end{document}</tex-math><mml:math id=\"M328\" display=\"block\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">zx</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msup><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">zy</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:msup><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq106\"><alternatives><tex-math id=\"M329\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\tau }_{zx}$$\\end{document}</tex-math><mml:math id=\"M330\"><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">zx</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq107\"><alternatives><tex-math id=\"M331\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\tau }_{zy}$$\\end{document}</tex-math><mml:math id=\"M332\"><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">zy</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq108\"><alternatives><tex-math id=\"M333\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M334\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq109\"><alternatives><tex-math id=\"M335\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M336\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ20\"><label>20</label><alternatives><tex-math id=\"M337\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\tau }_{zx}={\\mu }_{hnf}{\\left(\\frac{\\partial u}{\\partial z}+\\frac{\\partial w}{\\partial x}\\right)}_{z=0} , {\\tau }_{zy}={\\mu }_{hnf}{\\left(\\frac{\\partial v}{\\partial z}+\\frac{\\partial w}{\\partial y}\\right)}_{z=0}$$\\end{document}</tex-math><mml:math id=\"M338\" display=\"block\"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">zx</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:mfrac></mml:mfenced><mml:mrow><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">zy</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac></mml:mfenced><mml:mrow><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ21\"><label>21</label><alternatives><tex-math id=\"M339\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\left({Re}_{x}\\right)}^{1/2} C{f}_{x}=\\frac{{\\mu }_{hnf}}{{\\mu }_{f}} {p}^{{\\prime}{\\prime}}\\left(0\\right),\\, {\\left({Re}_{x}\\right)}^{1/2} C{f}_{y}=\\frac{{\\mu\\, }_{hnf}}{{\\mu }_{f}} {q}^{{\\prime}{\\prime}}\\left(0\\right),$$\\end{document}</tex-math><mml:math id=\"M340\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Re</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:mfenced></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mi>μ</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>μ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mn>0</mml:mn></mml:mfenced><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Re</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:mfenced></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:msub><mml:mrow><mml:mi>μ</mml:mi><mml:mspace width=\"0.166667em\"/></mml:mrow><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>μ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mfrac><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mn>0</mml:mn></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ22\"><label>22</label><alternatives><tex-math id=\"M341\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}=\\frac{x{q}_{w}}{{k}_{f}({T}_{w}-{T}_{\\infty })}, \\,{q}_{w}=-{k}_{hnf}{\\left(\\frac{\\partial T}{\\partial z}\\right)}_{z=0}+ {{(q}_{r})}_{w},$$\\end{document}</tex-math><mml:math id=\"M342\" display=\"block\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:msub><mml:mi>q</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>q</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant=\"italic\">hnf</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced><mml:mrow><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:msub><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>q</mml:mi></mml:mrow><mml:mi>r</mml:mi></mml:msub><mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow><mml:mi>w</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ23\"><label>23</label><alternatives><tex-math id=\"M343\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}=-\\left({B}_{3}+\\frac{4}{3}\\pi \\right){r}{\\prime}\\left(0\\right),$$\\end{document}</tex-math><mml:math id=\"M344\" display=\"block\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>B</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mn>4</mml:mn><mml:mn>3</mml:mn></mml:mfrac><mml:mi>π</mml:mi></mml:mfenced><mml:mi>r</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mn>0</mml:mn></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ24\"><label>24</label><alternatives><tex-math id=\"M345\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}=\\frac{x{q}_{m}}{{D}_{m}\\left({C}_{w}-{C}_{\\infty }\\right)}, {q}_{m}={D}_{m}{\\left(\\frac{\\partial C}{\\partial z}\\right)}_{z=0}$$\\end{document}</tex-math><mml:math id=\"M346\" display=\"block\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:msub><mml:mi>q</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>C</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:mfrac></mml:mfenced><mml:mrow><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ25\"><label>25</label><alternatives><tex-math id=\"M347\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}=-{s}{\\prime}\\left(0\\right).$$\\end{document}</tex-math><mml:math id=\"M348\" display=\"block\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi>s</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mn>0</mml:mn></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ26\"><label>26</label><alternatives><tex-math id=\"M349\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{gathered} z_{3}{\\prime} = p^{\\prime\\prime\\prime}, z_{3} = p^{\\prime\\prime}, z_{2} = p^{\\prime}, z_{1} = p, \\hfill \\\\ z_{6}{\\prime} = q^{\\prime\\prime\\prime}, z_{6} = q^{\\prime\\prime}, z_{5} = q^{\\prime}, z_{4} = q, \\hfill \\\\ z_{8}{\\prime} = r^{\\prime\\prime}, z_{8} = r^{\\prime}, z_{7} = r, \\hfill \\\\ z_{10}{\\prime} = s^{\\prime\\prime}, z_{10} = s^{\\prime}, z_{9} = s, \\hfill \\\\ \\end{gathered}$$\\end{document}</tex-math><mml:math id=\"M350\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>′</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mo>″</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>p</mml:mi><mml:mo>″</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>p</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:msub><mml:mi>z</mml:mi><mml:mn>6</mml:mn></mml:msub><mml:mo>′</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>q</mml:mi><mml:mrow><mml:mo>″</mml:mo><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>6</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>q</mml:mi><mml:mo>″</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>q</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi>q</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub><mml:mo>′</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>r</mml:mi><mml:mo>″</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>r</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>7</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:msub><mml:mi>z</mml:mi><mml:mn>10</mml:mn></mml:msub><mml:mo>′</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>s</mml:mi><mml:mo>″</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>10</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>s</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>9</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow/></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq633\"><alternatives><tex-math id=\"M351\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}^{\\prime}\\left(\\eta \\right)$$\\end{document}</tex-math><mml:math id=\"M352\"><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq634\"><alternatives><tex-math id=\"M353\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}^{\\prime}\\left(\\eta \\right)$$\\end{document}</tex-math><mml:math id=\"M354\"><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ27\"><label>27</label><alternatives><tex-math id=\"M355\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{1}}^{\\prime}={z}_{2}$$\\end{document}</tex-math><mml:math id=\"M356\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ28\"><label>28</label><alternatives><tex-math id=\"M357\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{2}}^{\\prime}={z}_{3}$$\\end{document}</tex-math><mml:math id=\"M358\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ29\"><label>29</label><alternatives><tex-math id=\"M359\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{3}}^{\\prime}={H}_{1}*\\left\\{\\left[{{z}_{2}}^{2}*\\left({z}_{1}+{z}_{4}\\right)\\right]-\\left[2* \\lambda *\\delta * {z}_{5}\\right]+\\left[Z*{z}_{2}\\right]-\\left[{\\epsilon }_{x}*{z}_{7}*{H}_{4}\\right]+\\left[{M}^{2}*{z}_{2}*{sin}^{2}\\left(\\alpha \\right)*{H}_{5}\\right]\\right\\}*{K}_{2}$$\\end{document}</tex-math><mml:math id=\"M360\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\"}\" open=\"{\"><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>z</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mfenced></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mn>2</mml:mn><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>λ</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>δ</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mi>Z</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:msub><mml:mi>ϵ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>7</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mfenced></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ30\"><label>30</label><alternatives><tex-math id=\"M361\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{4}}^{\\prime}={z}_{5}$$\\end{document}</tex-math><mml:math id=\"M362\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ31\"><label>31</label><alternatives><tex-math id=\"M363\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{5}}^{\\prime}{=z}_{6}$$\\end{document}</tex-math><mml:math id=\"M364\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:msub><mml:mrow><mml:mo>=</mml:mo><mml:mi>z</mml:mi></mml:mrow><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ32\"><label>32</label><alternatives><tex-math id=\"M365\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{6}}^{\\mathrm{{\\prime}}}={H}_{1}*\\left\\{\\left[{{z}_{5}}^{2}*\\left({z}_{1}+{z}_{4}\\right)\\right]-\\left[2*\\lambda *\\frac{1}{\\delta }* {z}_{2}\\right]+\\left[Z*{z}_{5}\\right]-\\left[{\\epsilon }_{y}*{z}_{7}*{H}_{4}\\right]+\\left[{M}^{2}*{sin}^{2}\\left(\\alpha \\right)*{z}_{5}*{H}_{5}\\right]\\right\\}*{K}_{2}$$\\end{document}</tex-math><mml:math id=\"M366\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\"}\" open=\"{\"><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>z</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mfenced></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mn>2</mml:mn><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>λ</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>δ</mml:mi></mml:mfrac><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mi>Z</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:msub><mml:mi>ϵ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>7</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mfenced></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ33\"><label>33</label><alternatives><tex-math id=\"M367\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{7}}^{\\prime}={z}_{8}$$\\end{document}</tex-math><mml:math id=\"M368\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>7</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ34\"><label>34</label><alternatives><tex-math id=\"M369\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned}{{z}_{8}}^{\\mathrm{^{\\prime}}} &amp; =-{\\left(1+\\frac{4}{3*{H}_{3}}*\\pi \\right)}^{-1}\\left[Pr*{H}_{2}*{z}_{8}\\left({z}_{1}+{z}_{4}\\right)+{z}_{8}*{z}_{10}*{N}_{b}+{{z}_{8}}^{2}{N}_{t}\\right.\\\\ &amp; \\quad \\left.+\\left[{K}_{2}*Ec*\\left({{z}_{3}}^{2}+{{z}_{6}}^{2}\\right)+{H}_{5}*{M}^{2}*{sin}^{2}\\left(\\alpha \\right)*Ec*\\left({{z}_{2}}^{2}+{{z}_{5}}^{2}\\right)\\right]\\right]\\end{aligned}$$\\end{document}</tex-math><mml:math id=\"M370\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign=\"right\"><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:mrow><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:msup></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mfrac><mml:mn>4</mml:mn><mml:mrow><mml:mn>3</mml:mn><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>π</mml:mi></mml:mfenced></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mfenced open=\"[\"><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>z</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>10</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"right\"><mml:mrow/></mml:mtd><mml:mtd columnalign=\"left\"><mml:mrow><mml:mspace width=\"1em\"/><mml:mfenced close=\"]\"><mml:mo>+</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"italic\">sin</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mfenced close=\")\" open=\"(\"><mml:mi>α</mml:mi></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mfenced></mml:mfenced></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ35\"><label>35</label><alternatives><tex-math id=\"M371\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{9}}^{\\prime}={z}_{10}$$\\end{document}</tex-math><mml:math id=\"M372\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>9</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>10</mml:mn></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ36\"><label>36</label><alternatives><tex-math id=\"M373\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{z}_{10}}^{\\mathrm{^{\\prime}}}= Sc*\\left(\\left(\\left({z}_{4}+{z}_{1}\\right)*{z}_{8}\\right)+\\left(\\left(\\frac{{N}_{t}}{{N}_{b}}\\right)*{{z}_{8}}^{\\mathrm{{\\prime}}}\\right)-\\left({z}_{10}*{K}_{c}\\right)\\right)$$\\end{document}</tex-math><mml:math id=\"M374\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>10</mml:mn></mml:msub></mml:mrow><mml:msup><mml:mrow/><mml:mo>′</mml:mo></mml:msup></mml:msup><mml:mo>=</mml:mo><mml:mi>S</mml:mi><mml:mi>c</mml:mi><mml:mrow/><mml:mo>∗</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mfenced close=\")\" open=\"(\"><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>z</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mfenced close=\")\" open=\"(\"><mml:mfrac><mml:msub><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:msub><mml:mi>N</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:mfrac></mml:mfenced><mml:mrow/><mml:mo>∗</mml:mo><mml:msup><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:mrow><mml:mo>′</mml:mo></mml:msup></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:msub><mml:mi>z</mml:mi><mml:mn>10</mml:mn></mml:msub><mml:mrow/><mml:mo>∗</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mfenced></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ37\"><label>37</label><alternatives><tex-math id=\"M375\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{array}{c}at \\eta =0,\\, {z}_{1}=0,\\, {z}_{2}=1,\\, {z}_{4}=0, \\,{z}_{5}=\\gamma , \\,{z}_{7}=1, \\\\ as\\, \\eta \\to \\infty ,\\, {z}_{2}\\to 0,\\, {z}_{5}\\to 0,\\, {z}_{7}\\to 0.\\end{array}$$\\end{document}</tex-math><mml:math id=\"M376\" display=\"block\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>η</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>7</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mrow/><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mspace width=\"0.166667em\"/><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>∞</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width=\"0.166667em\"/><mml:msub><mml:mi>z</mml:mi><mml:mn>7</mml:mn></mml:msub><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq110\"><alternatives><tex-math id=\"M377\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}\\left(\\eta \\right)$$\\end{document}</tex-math><mml:math id=\"M378\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq111\"><alternatives><tex-math id=\"M379\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Kc=Ec=0.5, Nt=Le=M=0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M380\"><mml:mrow><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq112\"><alternatives><tex-math id=\"M381\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}\\left(\\eta \\right),$$\\end{document}</tex-math><mml:math id=\"M382\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq113\"><alternatives><tex-math id=\"M383\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda$$\\end{document}</tex-math><mml:math id=\"M384\"><mml:mi>λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq114\"><alternatives><tex-math id=\"M385\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda =0$$\\end{document}</tex-math><mml:math id=\"M386\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq115\"><alternatives><tex-math id=\"M387\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda =1,$$\\end{document}</tex-math><mml:math id=\"M388\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq116\"><alternatives><tex-math id=\"M389\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda =2$$\\end{document}</tex-math><mml:math id=\"M390\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq117\"><alternatives><tex-math id=\"M391\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda =3.$$\\end{document}</tex-math><mml:math id=\"M392\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq118\"><alternatives><tex-math id=\"M393\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}{\\prime}\\left(\\eta \\right) \\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Kc=Ec=0.5, Nt=Le=\\lambda =0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M394\"><mml:mrow><mml:mi>q</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq119\"><alternatives><tex-math id=\"M395\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(M=0)$$\\end{document}</tex-math><mml:math id=\"M396\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq120\"><alternatives><tex-math id=\"M397\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1\\le M\\le 3,$$\\end{document}</tex-math><mml:math id=\"M398\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>M</mml:mi><mml:mo>≤</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq121\"><alternatives><tex-math id=\"M399\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^\\circ \\le \\alpha \\le 90^\\circ$$\\end{document}</tex-math><mml:math id=\"M400\"><mml:mrow><mml:msup><mml:mrow/><mml:mo>∘</mml:mo></mml:msup><mml:mo>≤</mml:mo><mml:mi>α</mml:mi><mml:mo>≤</mml:mo><mml:msup><mml:mn>90</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq122\"><alternatives><tex-math id=\"M401\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}\\left(\\eta \\right)$$\\end{document}</tex-math><mml:math id=\"M402\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq123\"><alternatives><tex-math id=\"M403\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Kc=Ec=0.5, Nt=Le=\\lambda =0.3, M=0.8$$\\end{document}</tex-math><mml:math id=\"M404\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq124\"><alternatives><tex-math id=\"M405\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0$$\\end{document}</tex-math><mml:math id=\"M406\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq125\"><alternatives><tex-math id=\"M407\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x-axis$$\\end{document}</tex-math><mml:math id=\"M408\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq126\"><alternatives><tex-math id=\"M409\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =0^\\circ$$\\end{document}</tex-math><mml:math id=\"M410\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>0</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq127\"><alternatives><tex-math id=\"M411\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =90^\\circ$$\\end{document}</tex-math><mml:math id=\"M412\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>90</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq128\"><alternatives><tex-math id=\"M413\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis.$$\\end{document}</tex-math><mml:math id=\"M414\"><mml:mrow><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq129\"><alternatives><tex-math id=\"M415\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha =30^\\circ , 45^\\circ$$\\end{document}</tex-math><mml:math id=\"M416\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>30</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq130\"><alternatives><tex-math id=\"M417\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$^\\circ$$\\end{document}</tex-math><mml:math id=\"M418\"><mml:msup><mml:mrow/><mml:mo>∘</mml:mo></mml:msup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq131\"><alternatives><tex-math id=\"M419\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$y-axis$$\\end{document}</tex-math><mml:math id=\"M420\"><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq132\"><alternatives><tex-math id=\"M421\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0\\le \\epsilon \\le 30$$\\end{document}</tex-math><mml:math id=\"M422\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>≤</mml:mo><mml:mn>30</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq133\"><alternatives><tex-math id=\"M423\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}\\left(\\eta \\right)$$\\end{document}</tex-math><mml:math id=\"M424\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq134\"><alternatives><tex-math id=\"M425\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\pi =Kc=Ec=0.5, Nt=Le=\\lambda =0.3, \\alpha =45^\\circ , M=3$$\\end{document}</tex-math><mml:math id=\"M426\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq135\"><alternatives><tex-math id=\"M427\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Z$$\\end{document}</tex-math><mml:math id=\"M428\"><mml:mi>Z</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq136\"><alternatives><tex-math id=\"M429\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}\\left(\\eta \\right)$$\\end{document}</tex-math><mml:math id=\"M430\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq137\"><alternatives><tex-math id=\"M431\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =\\epsilon =\\pi =Kc=Ec=0.5, Nt=Le=\\lambda =0.3, \\alpha =45^\\circ , M=0.8$$\\end{document}</tex-math><mml:math id=\"M432\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq138\"><alternatives><tex-math id=\"M433\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M434\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq139\"><alternatives><tex-math id=\"M435\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}{\\prime}\\left(\\eta \\right)$$\\end{document}</tex-math><mml:math id=\"M436\"><mml:mrow><mml:mi>q</mml:mi><mml:mo>′</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mi>η</mml:mi></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq140\"><alternatives><tex-math id=\"M437\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\lambda =Z=\\epsilon =\\pi =Kc=Ec=0.5, Nt=Le=0.3, \\alpha =45^\\circ , M=0.8$$\\end{document}</tex-math><mml:math id=\"M438\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq141\"><alternatives><tex-math id=\"M439\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x-axis$$\\end{document}</tex-math><mml:math id=\"M440\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq142\"><alternatives><tex-math id=\"M441\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M442\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq635\"><alternatives><tex-math id=\"M443\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda$$\\end{document}</tex-math><mml:math id=\"M444\"><mml:mi>λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq636\"><alternatives><tex-math id=\"M445\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}(\\eta )$$\\end{document}</tex-math><mml:math id=\"M446\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq637\"><alternatives><tex-math id=\"M447\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M$$\\end{document}</tex-math><mml:math id=\"M448\"><mml:mi>M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq638\"><alternatives><tex-math id=\"M449\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}{\\prime}(\\eta )$$\\end{document}</tex-math><mml:math id=\"M450\"><mml:mrow><mml:mi>q</mml:mi><mml:mo>′</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq639\"><alternatives><tex-math id=\"M451\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M452\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq640\"><alternatives><tex-math id=\"M453\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}(\\eta )$$\\end{document}</tex-math><mml:math id=\"M454\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq641\"><alternatives><tex-math id=\"M455\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon$$\\end{document}</tex-math><mml:math id=\"M456\"><mml:mi>ϵ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq642\"><alternatives><tex-math id=\"M457\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}{\\prime}(\\eta )$$\\end{document}</tex-math><mml:math id=\"M458\"><mml:mrow><mml:mi>q</mml:mi><mml:mo>′</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq643\"><alternatives><tex-math id=\"M459\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Z$$\\end{document}</tex-math><mml:math id=\"M460\"><mml:mi>Z</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq644\"><alternatives><tex-math id=\"M461\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${p}{\\prime}(\\eta )$$\\end{document}</tex-math><mml:math id=\"M462\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>′</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq645\"><alternatives><tex-math id=\"M463\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda$$\\end{document}</tex-math><mml:math id=\"M464\"><mml:mi>λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq646\"><alternatives><tex-math id=\"M465\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${q}{\\prime}(\\eta )$$\\end{document}</tex-math><mml:math id=\"M466\"><mml:mrow><mml:mi>q</mml:mi><mml:mo>′</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq143\"><alternatives><tex-math id=\"M467\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r(\\eta )$$\\end{document}</tex-math><mml:math id=\"M468\"><mml:mrow><mml:mi>r</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq144\"><alternatives><tex-math id=\"M469\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Kc=Ec=0.5, Nt=Le=\\lambda =0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M470\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq145\"><alternatives><tex-math id=\"M471\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\eta )$$\\end{document}</tex-math><mml:math id=\"M472\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq146\"><alternatives><tex-math id=\"M473\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, M=0.3, Z=\\epsilon =\\pi =Kc=Ec=0.5,Nt=Le=\\lambda =0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M474\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq147\"><alternatives><tex-math id=\"M475\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r(\\eta )$$\\end{document}</tex-math><mml:math id=\"M476\"><mml:mrow><mml:mi>r</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq148\"><alternatives><tex-math id=\"M477\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, M=03, \\gamma =Z=\\epsilon =Kc=Ec=0.5, Nt=Le=\\lambda =0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M478\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>03</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq149\"><alternatives><tex-math id=\"M479\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Kc=0.5,Nt=Le=\\lambda =0.3, \\alpha =45^\\circ , M=03.$$\\end{document}</tex-math><mml:math id=\"M480\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>03</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq150\"><alternatives><tex-math id=\"M481\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{When }Nb=0.1, M=08, \\delta =0.8, \\gamma =Z=\\pi =Kc=Ec=0.5, Nt=Le=\\lambda =0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M482\"><mml:mrow><mml:mi mathvariant=\"normal\">When</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>08</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq151\"><alternatives><tex-math id=\"M483\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Ec=0.5, Nt=Le=\\lambda =0.3, M=08, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M484\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>08</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq152\"><alternatives><tex-math id=\"M485\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Kc=Ec=0.5, Nt=Le=M=0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M486\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq153\"><alternatives><tex-math id=\"M487\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{when }Nb=0.1,\\delta =0.8, \\gamma =Z=\\epsilon =\\pi =Kc=Ec=0.5, M=08, Le=\\lambda =0.3, \\alpha =45^\\circ$$\\end{document}</tex-math><mml:math id=\"M488\"><mml:mrow><mml:mi mathvariant=\"normal\">when</mml:mi><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>08</mml:mn><mml:mo>,</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn>45</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq647\"><alternatives><tex-math id=\"M489\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M$$\\end{document}</tex-math><mml:math id=\"M490\"><mml:mi>M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq648\"><alternatives><tex-math id=\"M491\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r(\\eta )$$\\end{document}</tex-math><mml:math id=\"M492\"><mml:mrow><mml:mi>r</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq649\"><alternatives><tex-math id=\"M493\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda$$\\end{document}</tex-math><mml:math id=\"M494\"><mml:mi>λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq650\"><alternatives><tex-math id=\"M495\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r(\\eta )$$\\end{document}</tex-math><mml:math id=\"M496\"><mml:mrow><mml:mi>r</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq651\"><alternatives><tex-math id=\"M497\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\pi$$\\end{document}</tex-math><mml:math id=\"M498\"><mml:mi>π</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq652\"><alternatives><tex-math id=\"M499\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\eta )$$\\end{document}</tex-math><mml:math id=\"M500\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq653\"><alternatives><tex-math id=\"M501\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Ec$$\\end{document}</tex-math><mml:math id=\"M502\"><mml:mrow><mml:mi mathvariant=\"italic\">Ec</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq654\"><alternatives><tex-math id=\"M503\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r(\\eta )$$\\end{document}</tex-math><mml:math id=\"M504\"><mml:mrow><mml:mi>r</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq655\"><alternatives><tex-math id=\"M505\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon$$\\end{document}</tex-math><mml:math id=\"M506\"><mml:mi>ϵ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq656\"><alternatives><tex-math id=\"M507\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\eta )$$\\end{document}</tex-math><mml:math id=\"M508\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq657\"><alternatives><tex-math id=\"M509\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Kc$$\\end{document}</tex-math><mml:math id=\"M510\"><mml:mrow><mml:mi mathvariant=\"italic\">Kc</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq658\"><alternatives><tex-math id=\"M511\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\eta )$$\\end{document}</tex-math><mml:math id=\"M512\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq659\"><alternatives><tex-math id=\"M513\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda$$\\end{document}</tex-math><mml:math id=\"M514\"><mml:mi>λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq660\"><alternatives><tex-math id=\"M515\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\eta )$$\\end{document}</tex-math><mml:math id=\"M516\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq661\"><alternatives><tex-math id=\"M517\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Nt$$\\end{document}</tex-math><mml:math id=\"M518\"><mml:mrow><mml:mi mathvariant=\"italic\">Nt</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq662\"><alternatives><tex-math id=\"M519\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(\\eta )$$\\end{document}</tex-math><mml:math id=\"M520\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq154\"><alternatives><tex-math id=\"M521\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x}$$\\end{document}</tex-math><mml:math id=\"M522\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq155\"><alternatives><tex-math id=\"M523\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{y}$$\\end{document}</tex-math><mml:math id=\"M524\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq156\"><alternatives><tex-math id=\"M525\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}$$\\end{document}</tex-math><mml:math id=\"M526\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq157\"><alternatives><tex-math id=\"M527\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}$$\\end{document}</tex-math><mml:math id=\"M528\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq158\"><alternatives><tex-math id=\"M529\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x}$$\\end{document}</tex-math><mml:math id=\"M530\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq159\"><alternatives><tex-math id=\"M531\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{y}$$\\end{document}</tex-math><mml:math id=\"M532\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq160\"><alternatives><tex-math id=\"M533\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x}$$\\end{document}</tex-math><mml:math id=\"M534\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq161\"><alternatives><tex-math id=\"M535\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda =1$$\\end{document}</tex-math><mml:math id=\"M536\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq162\"><alternatives><tex-math id=\"M537\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda =2,$$\\end{document}</tex-math><mml:math id=\"M538\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq163\"><alternatives><tex-math id=\"M539\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{y}.$$\\end{document}</tex-math><mml:math id=\"M540\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq164\"><alternatives><tex-math id=\"M541\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10\\le Z\\le 30$$\\end{document}</tex-math><mml:math id=\"M542\"><mml:mrow><mml:mn>10</mml:mn><mml:mo>≤</mml:mo><mml:mi>Z</mml:mi><mml:mo>≤</mml:mo><mml:mn>30</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq165\"><alternatives><tex-math id=\"M543\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M544\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq166\"><alternatives><tex-math id=\"M545\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M546\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq167\"><alternatives><tex-math id=\"M547\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.9\\le \\gamma \\le 1.1$$\\end{document}</tex-math><mml:math id=\"M548\"><mml:mrow><mml:mn>0.9</mml:mn><mml:mo>≤</mml:mo><mml:mi>γ</mml:mi><mml:mo>≤</mml:mo><mml:mn>1.1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq168\"><alternatives><tex-math id=\"M549\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis$$\\end{document}</tex-math><mml:math id=\"M550\"><mml:mrow><mml:mi mathvariant=\"italic\">axis</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq169\"><alternatives><tex-math id=\"M551\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x}$$\\end{document}</tex-math><mml:math id=\"M552\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq170\"><alternatives><tex-math id=\"M553\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0\\le \\alpha \\le 90.$$\\end{document}</tex-math><mml:math id=\"M554\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>α</mml:mi><mml:mo>≤</mml:mo><mml:mn>90</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq171\"><alternatives><tex-math id=\"M555\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$y-axis.$$\\end{document}</tex-math><mml:math id=\"M556\"><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq172\"><alternatives><tex-math id=\"M557\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}$$\\end{document}</tex-math><mml:math id=\"M558\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq173\"><alternatives><tex-math id=\"M559\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}$$\\end{document}</tex-math><mml:math id=\"M560\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq174\"><alternatives><tex-math id=\"M561\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$axis.$$\\end{document}</tex-math><mml:math id=\"M562\"><mml:mrow><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq175\"><alternatives><tex-math id=\"M563\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0\\le \\pi \\le 4$$\\end{document}</tex-math><mml:math id=\"M564\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>π</mml:mi><mml:mo>≤</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq176\"><alternatives><tex-math id=\"M565\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\pi =0$$\\end{document}</tex-math><mml:math id=\"M566\"><mml:mrow><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq177\"><alternatives><tex-math id=\"M567\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$7.2\\le Pr\\le 9.2$$\\end{document}</tex-math><mml:math id=\"M568\"><mml:mrow><mml:mn>7.2</mml:mn><mml:mo>≤</mml:mo><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mo>≤</mml:mo><mml:mn>9.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq178\"><alternatives><tex-math id=\"M569\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0\\le M\\le 15$$\\end{document}</tex-math><mml:math id=\"M570\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>M</mml:mi><mml:mo>≤</mml:mo><mml:mn>15</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq179\"><alternatives><tex-math id=\"M571\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Pr$$\\end{document}</tex-math><mml:math id=\"M572\"><mml:mrow><mml:mi mathvariant=\"italic\">Pr</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq180\"><alternatives><tex-math id=\"M573\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0\\le Kc\\le 4$$\\end{document}</tex-math><mml:math id=\"M574\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>≤</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq181\"><alternatives><tex-math id=\"M575\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10\\le Le\\le 20$$\\end{document}</tex-math><mml:math id=\"M576\"><mml:mrow><mml:mn>10</mml:mn><mml:mo>≤</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>≤</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq182\"><alternatives><tex-math id=\"M577\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0\\le {N}_{t}\\le 6$$\\end{document}</tex-math><mml:math id=\"M578\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq183\"><alternatives><tex-math id=\"M579\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5 \\le {N}_{b}\\le 1.5$$\\end{document}</tex-math><mml:math id=\"M580\"><mml:mrow><mml:mn>0.5</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq184\"><alternatives><tex-math id=\"M581\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$5\\le Ec\\le 15$$\\end{document}</tex-math><mml:math id=\"M582\"><mml:mrow><mml:mn>5</mml:mn><mml:mo>≤</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>≤</mml:mo><mml:mn>15</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq185\"><alternatives><tex-math id=\"M583\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Ec$$\\end{document}</tex-math><mml:math id=\"M584\"><mml:mrow><mml:mi mathvariant=\"italic\">Ec</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq280\"><alternatives><tex-math id=\"M585\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x-axis$$\\end{document}</tex-math><mml:math id=\"M586\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq281\"><alternatives><tex-math id=\"M587\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C{f}_{x}$$\\end{document}</tex-math><mml:math id=\"M588\"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq282\"><alternatives><tex-math id=\"M589\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$y-axis C{f}_{y}$$\\end{document}</tex-math><mml:math id=\"M590\"><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq283\"><alternatives><tex-math id=\"M591\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\pi =0.7, Pr=6.2, M=0.8, Le=0.6, Nt=0.3, Ec=0.5, Nb=0.2$$\\end{document}</tex-math><mml:math id=\"M592\"><mml:mrow><mml:mi>π</mml:mi><mml:mo>=</mml:mo><mml:mn>0.7</mml:mn><mml:mo>,</mml:mo><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>6.2</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn><mml:mo>,</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mn>0.6</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq284\"><alternatives><tex-math id=\"M593\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda$$\\end{document}</tex-math><mml:math id=\"M594\"><mml:mi>λ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq285\"><alternatives><tex-math id=\"M595\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}</tex-math><mml:math id=\"M596\"><mml:mi>γ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq286\"><alternatives><tex-math id=\"M597\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\epsilon$$\\end{document}</tex-math><mml:math id=\"M598\"><mml:mi>ϵ</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq287\"><alternatives><tex-math id=\"M599\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M$$\\end{document}</tex-math><mml:math id=\"M600\"><mml:mi>M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq288\"><alternatives><tex-math id=\"M601\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M602\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq289\"><alternatives><tex-math id=\"M603\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C{f}_{x}$$\\end{document}</tex-math><mml:math id=\"M604\"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq290\"><alternatives><tex-math id=\"M605\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C{f}_{y}$$\\end{document}</tex-math><mml:math id=\"M606\"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq291\"><alternatives><tex-math id=\"M607\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C{f}_{x}$$\\end{document}</tex-math><mml:math id=\"M608\"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq292\"><alternatives><tex-math id=\"M609\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C{f}_{y}for$$\\end{document}</tex-math><mml:math id=\"M610\"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>f</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mi>f</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq293\"><alternatives><tex-math id=\"M611\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.0$$\\end{document}</tex-math><mml:math id=\"M612\"><mml:mrow><mml:mn>0.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq294\"><alternatives><tex-math id=\"M613\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M614\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq295\"><alternatives><tex-math id=\"M615\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M616\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq296\"><alternatives><tex-math id=\"M617\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math 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id=\"M635\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.95226$$\\end{document}</tex-math><mml:math id=\"M636\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.95226</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq306\"><alternatives><tex-math id=\"M637\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.84510$$\\end{document}</tex-math><mml:math 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id=\"M645\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.86364$$\\end{document}</tex-math><mml:math id=\"M646\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.86364</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq311\"><alternatives><tex-math id=\"M647\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.30971$$\\end{document}</tex-math><mml:math 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id=\"M659\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-4.28186$$\\end{document}</tex-math><mml:math id=\"M660\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>4.28186</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq318\"><alternatives><tex-math id=\"M661\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.23697$$\\end{document}</tex-math><mml:math id=\"M662\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.23697</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq319\"><alternatives><tex-math id=\"M663\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-4.37705$$\\end{document}</tex-math><mml:math id=\"M664\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>4.37705</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq320\"><alternatives><tex-math id=\"M665\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.25723$$\\end{document}</tex-math><mml:math id=\"M666\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.25723</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq321\"><alternatives><tex-math id=\"M667\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$20$$\\end{document}</tex-math><mml:math id=\"M668\"><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq322\"><alternatives><tex-math id=\"M669\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-5.83925$$\\end{document}</tex-math><mml:math id=\"M670\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>5.83925</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq323\"><alternatives><tex-math id=\"M671\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.98470$$\\end{document}</tex-math><mml:math id=\"M672\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.98470</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq324\"><alternatives><tex-math id=\"M673\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-5.48274$$\\end{document}</tex-math><mml:math id=\"M674\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>5.48274</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq325\"><alternatives><tex-math id=\"M675\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.79401$$\\end{document}</tex-math><mml:math id=\"M676\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.79401</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq326\"><alternatives><tex-math id=\"M677\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$30$$\\end{document}</tex-math><mml:math id=\"M678\"><mml:mrow><mml:mn>30</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq327\"><alternatives><tex-math 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id=\"M689\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M690\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq333\"><alternatives><tex-math id=\"M691\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.9$$\\end{document}</tex-math><mml:math 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id=\"M699\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.00135$$\\end{document}</tex-math><mml:math id=\"M700\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.00135</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq338\"><alternatives><tex-math id=\"M701\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.95067$$\\end{document}</tex-math><mml:math 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id=\"M709\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.20911$$\\end{document}</tex-math><mml:math id=\"M710\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.20911</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq343\"><alternatives><tex-math id=\"M711\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.94398$$\\end{document}</tex-math><mml:math 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id=\"M719\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.42367$$\\end{document}</tex-math><mml:math id=\"M720\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.42367</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq348\"><alternatives><tex-math id=\"M721\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.93726$$\\end{document}</tex-math><mml:math id=\"M722\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.93726</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq349\"><alternatives><tex-math id=\"M723\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-3.42038$$\\end{document}</tex-math><mml:math id=\"M724\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>3.42038</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq350\"><alternatives><tex-math id=\"M725\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M726\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq351\"><alternatives><tex-math id=\"M727\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M728\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq352\"><alternatives><tex-math id=\"M729\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M730\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq353\"><alternatives><tex-math id=\"M731\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.0$$\\end{document}</tex-math><mml:math id=\"M732\"><mml:mrow><mml:mn>0.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq354\"><alternatives><tex-math id=\"M733\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M734\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq355\"><alternatives><tex-math id=\"M735\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.12530$$\\end{document}</tex-math><mml:math 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id=\"M787\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-17.8269$$\\end{document}</tex-math><mml:math id=\"M788\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>17.8269</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq382\"><alternatives><tex-math id=\"M789\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-8.93220$$\\end{document}</tex-math><mml:math 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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-19.4546$$\\end{document}</tex-math><mml:math id=\"M794\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>19.4546</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq385\"><alternatives><tex-math id=\"M795\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-9.75085$$\\end{document}</tex-math><mml:math id=\"M796\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>9.75085</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq386\"><alternatives><tex-math id=\"M797\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-35.6205$$\\end{document}</tex-math><mml:math id=\"M798\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>35.6205</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq387\"><alternatives><tex-math id=\"M799\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-17.8196$$\\end{document}</tex-math><mml:math 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id=\"M811\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.36554$$\\end{document}</tex-math><mml:math id=\"M812\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.36554</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq394\"><alternatives><tex-math id=\"M813\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.11913$$\\end{document}</tex-math><mml:math 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id=\"M831\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-3.02022$$\\end{document}</tex-math><mml:math id=\"M832\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>3.02022</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq404\"><alternatives><tex-math id=\"M833\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.63860$$\\end{document}</tex-math><mml:math 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id=\"M841\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.91633$$\\end{document}</tex-math><mml:math id=\"M842\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.91633</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq409\"><alternatives><tex-math id=\"M843\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.51397$$\\end{document}</tex-math><mml:math id=\"M844\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.51397</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq410\"><alternatives><tex-math id=\"M845\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.48003$$\\end{document}</tex-math><mml:math id=\"M846\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.48003</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq411\"><alternatives><tex-math id=\"M847\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-4.14240$$\\end{document}</tex-math><mml:math id=\"M848\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>4.14240</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq412\"><alternatives><tex-math id=\"M849\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.16088$$\\end{document}</tex-math><mml:math id=\"M850\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.16088</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq413\"><alternatives><tex-math id=\"M851\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}$$\\end{document}</tex-math><mml:math id=\"M852\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq414\"><alternatives><tex-math id=\"M853\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}$$\\end{document}</tex-math><mml:math id=\"M854\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq415\"><alternatives><tex-math id=\"M855\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda =0.5, Z=0.7, \\gamma =0.5, \\epsilon =0.3, M=0.8$$\\end{document}</tex-math><mml:math id=\"M856\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>0.7</mml:mn><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mi>ϵ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>,</mml:mo><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq416\"><alternatives><tex-math id=\"M857\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha$$\\end{document}</tex-math><mml:math id=\"M858\"><mml:mi>α</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq417\"><alternatives><tex-math id=\"M859\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\pi$$\\end{document}</tex-math><mml:math id=\"M860\"><mml:mi>π</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq418\"><alternatives><tex-math id=\"M861\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Pr$$\\end{document}</tex-math><mml:math id=\"M862\"><mml:mrow><mml:mi mathvariant=\"italic\">Pr</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq419\"><alternatives><tex-math id=\"M863\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$M$$\\end{document}</tex-math><mml:math id=\"M864\"><mml:mi>M</mml:mi></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq420\"><alternatives><tex-math id=\"M865\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Kc$$\\end{document}</tex-math><mml:math id=\"M866\"><mml:mrow><mml:mi mathvariant=\"italic\">Kc</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq421\"><alternatives><tex-math id=\"M867\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Le$$\\end{document}</tex-math><mml:math id=\"M868\"><mml:mrow><mml:mi mathvariant=\"italic\">Le</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq422\"><alternatives><tex-math id=\"M869\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Nt$$\\end{document}</tex-math><mml:math id=\"M870\"><mml:mrow><mml:mi mathvariant=\"italic\">Nt</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq423\"><alternatives><tex-math id=\"M871\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Ec$$\\end{document}</tex-math><mml:math id=\"M872\"><mml:mrow><mml:mi mathvariant=\"italic\">Ec</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq424\"><alternatives><tex-math id=\"M873\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Nb$$\\end{document}</tex-math><mml:math id=\"M874\"><mml:mrow><mml:mi mathvariant=\"italic\">Nb</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq425\"><alternatives><tex-math id=\"M875\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}$$\\end{document}</tex-math><mml:math id=\"M876\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq426\"><alternatives><tex-math id=\"M877\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}$$\\end{document}</tex-math><mml:math id=\"M878\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq427\"><alternatives><tex-math id=\"M879\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}$$\\end{document}</tex-math><mml:math id=\"M880\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq428\"><alternatives><tex-math id=\"M881\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x}for$$\\end{document}</tex-math><mml:math id=\"M882\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mi>f</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq429\"><alternatives><tex-math id=\"M883\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M884\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq430\"><alternatives><tex-math id=\"M885\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M886\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq431\"><alternatives><tex-math id=\"M887\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M888\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq432\"><alternatives><tex-math id=\"M889\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M890\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq433\"><alternatives><tex-math id=\"M891\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M892\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq434\"><alternatives><tex-math id=\"M893\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M894\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq435\"><alternatives><tex-math id=\"M895\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M896\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq436\"><alternatives><tex-math id=\"M897\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M898\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq437\"><alternatives><tex-math id=\"M899\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3.00058$$\\end{document}</tex-math><mml:math id=\"M900\"><mml:mrow><mml:mn>3.00058</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq438\"><alternatives><tex-math id=\"M901\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.72922$$\\end{document}</tex-math><mml:math id=\"M902\"><mml:mrow><mml:mn>1.72922</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq439\"><alternatives><tex-math id=\"M903\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4.36870$$\\end{document}</tex-math><mml:math id=\"M904\"><mml:mrow><mml:mn>4.36870</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq440\"><alternatives><tex-math id=\"M905\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.74389$$\\end{document}</tex-math><mml:math id=\"M906\"><mml:mrow><mml:mn>1.74389</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq441\"><alternatives><tex-math id=\"M907\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.74390$$\\end{document}</tex-math><mml:math id=\"M908\"><mml:mrow><mml:mn>2.74390</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq442\"><alternatives><tex-math id=\"M909\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.71586$$\\end{document}</tex-math><mml:math id=\"M910\"><mml:mrow><mml:mn>1.71586</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq443\"><alternatives><tex-math id=\"M911\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3.04228$$\\end{document}</tex-math><mml:math id=\"M912\"><mml:mrow><mml:mn>3.04228</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq444\"><alternatives><tex-math id=\"M913\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.68995$$\\end{document}</tex-math><mml:math id=\"M914\"><mml:mrow><mml:mn>1.68995</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq445\"><alternatives><tex-math id=\"M915\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.52236$$\\end{document}</tex-math><mml:math id=\"M916\"><mml:mrow><mml:mn>2.52236</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq446\"><alternatives><tex-math id=\"M917\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.70378$$\\end{document}</tex-math><mml:math id=\"M918\"><mml:mrow><mml:mn>1.70378</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq447\"><alternatives><tex-math id=\"M919\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.14219$$\\end{document}</tex-math><mml:math id=\"M920\"><mml:mrow><mml:mn>2.14219</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq448\"><alternatives><tex-math id=\"M921\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.65535$$\\end{document}</tex-math><mml:math id=\"M922\"><mml:mrow><mml:mn>1.65535</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq449\"><alternatives><tex-math id=\"M923\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.32647$$\\end{document}</tex-math><mml:math id=\"M924\"><mml:mrow><mml:mn>2.32647</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq450\"><alternatives><tex-math id=\"M925\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.69307$$\\end{document}</tex-math><mml:math id=\"M926\"><mml:mrow><mml:mn>1.69307</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq451\"><alternatives><tex-math id=\"M927\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.42823$$\\end{document}</tex-math><mml:math id=\"M928\"><mml:mrow><mml:mn>1.42823</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq452\"><alternatives><tex-math id=\"M929\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.62959$$\\end{document}</tex-math><mml:math id=\"M930\"><mml:mrow><mml:mn>1.62959</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq453\"><alternatives><tex-math id=\"M931\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.14992$$\\end{document}</tex-math><mml:math id=\"M932\"><mml:mrow><mml:mn>2.14992</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq454\"><alternatives><tex-math id=\"M933\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.68352$$\\end{document}</tex-math><mml:math id=\"M934\"><mml:mrow><mml:mn>1.68352</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq455\"><alternatives><tex-math id=\"M935\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.82732$$\\end{document}</tex-math><mml:math id=\"M936\"><mml:mrow><mml:mn>0.82732</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq456\"><alternatives><tex-math id=\"M937\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.60887$$\\end{document}</tex-math><mml:math id=\"M938\"><mml:mrow><mml:mn>1.60887</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq457\"><alternatives><tex-math id=\"M939\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$00$$\\end{document}</tex-math><mml:math id=\"M940\"><mml:mrow><mml:mn>00</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq458\"><alternatives><tex-math id=\"M941\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M942\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq459\"><alternatives><tex-math id=\"M943\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M944\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq460\"><alternatives><tex-math id=\"M945\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M946\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq461\"><alternatives><tex-math id=\"M947\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M948\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq462\"><alternatives><tex-math id=\"M949\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M950\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq463\"><alternatives><tex-math id=\"M951\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M952\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq464\"><alternatives><tex-math id=\"M953\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M954\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq465\"><alternatives><tex-math id=\"M955\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10.1829$$\\end{document}</tex-math><mml:math id=\"M956\"><mml:mrow><mml:mn>10.1829</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq466\"><alternatives><tex-math id=\"M957\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.72429$$\\end{document}</tex-math><mml:math id=\"M958\"><mml:mrow><mml:mn>1.72429</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq467\"><alternatives><tex-math id=\"M959\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.59213$$\\end{document}</tex-math><mml:math id=\"M960\"><mml:mrow><mml:mn>6.59213</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq468\"><alternatives><tex-math id=\"M961\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.66263$$\\end{document}</tex-math><mml:math id=\"M962\"><mml:mrow><mml:mn>1.66263</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq469\"><alternatives><tex-math id=\"M963\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$02$$\\end{document}</tex-math><mml:math id=\"M964\"><mml:mrow><mml:mn>02</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq470\"><alternatives><tex-math id=\"M965\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$5.60675$$\\end{document}</tex-math><mml:math id=\"M966\"><mml:mrow><mml:mn>5.60675</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq471\"><alternatives><tex-math id=\"M967\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.68505$$\\end{document}</tex-math><mml:math id=\"M968\"><mml:mrow><mml:mn>1.68505</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq472\"><alternatives><tex-math id=\"M969\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4.41799$$\\end{document}</tex-math><mml:math id=\"M970\"><mml:mrow><mml:mn>4.41799</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq473\"><alternatives><tex-math id=\"M971\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.64535$$\\end{document}</tex-math><mml:math id=\"M972\"><mml:mrow><mml:mn>1.64535</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq474\"><alternatives><tex-math id=\"M973\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$04$$\\end{document}</tex-math><mml:math id=\"M974\"><mml:mrow><mml:mn>04</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq475\"><alternatives><tex-math id=\"M975\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4.05846$$\\end{document}</tex-math><mml:math id=\"M976\"><mml:mrow><mml:mn>4.05846</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq476\"><alternatives><tex-math id=\"M977\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.67249$$\\end{document}</tex-math><mml:math id=\"M978\"><mml:mrow><mml:mn>1.67249</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq477\"><alternatives><tex-math id=\"M979\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3.37044$$\\end{document}</tex-math><mml:math id=\"M980\"><mml:mrow><mml:mn>3.37044</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq478\"><alternatives><tex-math id=\"M981\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.63681$$\\end{document}</tex-math><mml:math id=\"M982\"><mml:mrow><mml:mn>1.63681</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq479\"><alternatives><tex-math id=\"M983\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M984\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq480\"><alternatives><tex-math id=\"M985\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$7.2$$\\end{document}</tex-math><mml:math id=\"M986\"><mml:mrow><mml:mn>7.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq481\"><alternatives><tex-math id=\"M987\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M988\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq482\"><alternatives><tex-math id=\"M989\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M990\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq483\"><alternatives><tex-math id=\"M991\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M992\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq484\"><alternatives><tex-math id=\"M993\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M994\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq485\"><alternatives><tex-math id=\"M995\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M996\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq486\"><alternatives><tex-math id=\"M997\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M998\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq487\"><alternatives><tex-math id=\"M999\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.74899$$\\end{document}</tex-math><mml:math id=\"M1000\"><mml:mrow><mml:mn>2.74899</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq488\"><alternatives><tex-math id=\"M1001\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.70996$$\\end{document}</tex-math><mml:math id=\"M1002\"><mml:mrow><mml:mn>1.70996</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq489\"><alternatives><tex-math id=\"M1003\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.14219$$\\end{document}</tex-math><mml:math id=\"M1004\"><mml:mrow><mml:mn>2.14219</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq490\"><alternatives><tex-math id=\"M1005\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.65535$$\\end{document}</tex-math><mml:math id=\"M1006\"><mml:mrow><mml:mn>1.65535</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq491\"><alternatives><tex-math id=\"M1007\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$8.2$$\\end{document}</tex-math><mml:math id=\"M1008\"><mml:mrow><mml:mn>8.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq492\"><alternatives><tex-math id=\"M1009\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.98656$$\\end{document}</tex-math><mml:math id=\"M1010\"><mml:mrow><mml:mn>2.98656</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq493\"><alternatives><tex-math id=\"M1011\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.71649$$\\end{document}</tex-math><mml:math id=\"M1012\"><mml:mrow><mml:mn>1.71649</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq494\"><alternatives><tex-math id=\"M1013\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.44237$$\\end{document}</tex-math><mml:math id=\"M1014\"><mml:mrow><mml:mn>2.44237</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq495\"><alternatives><tex-math id=\"M1015\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.66191$$\\end{document}</tex-math><mml:math id=\"M1016\"><mml:mrow><mml:mn>1.66191</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq496\"><alternatives><tex-math id=\"M1017\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$9.2$$\\end{document}</tex-math><mml:math id=\"M1018\"><mml:mrow><mml:mn>9.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq497\"><alternatives><tex-math id=\"M1019\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3.21141$$\\end{document}</tex-math><mml:math id=\"M1020\"><mml:mrow><mml:mn>3.21141</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq498\"><alternatives><tex-math id=\"M1021\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.72272$$\\end{document}</tex-math><mml:math id=\"M1022\"><mml:mrow><mml:mn>1.72272</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq499\"><alternatives><tex-math id=\"M1023\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.75913$$\\end{document}</tex-math><mml:math id=\"M1024\"><mml:mrow><mml:mn>2.75913</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq500\"><alternatives><tex-math id=\"M1025\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.66886$$\\end{document}</tex-math><mml:math id=\"M1026\"><mml:mrow><mml:mn>1.66886</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq501\"><alternatives><tex-math id=\"M1027\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M1028\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq502\"><alternatives><tex-math id=\"M1029\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M1030\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq503\"><alternatives><tex-math id=\"M1031\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$00$$\\end{document}</tex-math><mml:math id=\"M1032\"><mml:mrow><mml:mn>00</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq504\"><alternatives><tex-math id=\"M1033\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M1034\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq505\"><alternatives><tex-math id=\"M1035\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M1036\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq506\"><alternatives><tex-math id=\"M1037\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M1038\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq507\"><alternatives><tex-math id=\"M1039\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M1040\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq508\"><alternatives><tex-math id=\"M1041\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M1042\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq509\"><alternatives><tex-math id=\"M1043\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3.00058$$\\end{document}</tex-math><mml:math id=\"M1044\"><mml:mrow><mml:mn>3.00058</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq510\"><alternatives><tex-math id=\"M1045\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.72922$$\\end{document}</tex-math><mml:math id=\"M1046\"><mml:mrow><mml:mn>1.72922</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq511\"><alternatives><tex-math id=\"M1047\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4.36870$$\\end{document}</tex-math><mml:math id=\"M1048\"><mml:mrow><mml:mn>4.36870</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq512\"><alternatives><tex-math id=\"M1049\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.74389$$\\end{document}</tex-math><mml:math id=\"M1050\"><mml:mrow><mml:mn>1.74389</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq513\"><alternatives><tex-math id=\"M1051\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$05$$\\end{document}</tex-math><mml:math id=\"M1052\"><mml:mrow><mml:mn>05</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq514\"><alternatives><tex-math id=\"M1053\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-2.2238$$\\end{document}</tex-math><mml:math id=\"M1054\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>2.2238</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq515\"><alternatives><tex-math id=\"M1055\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.48799$$\\end{document}</tex-math><mml:math id=\"M1056\"><mml:mrow><mml:mn>1.48799</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq516\"><alternatives><tex-math id=\"M1057\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-11.973$$\\end{document}</tex-math><mml:math id=\"M1058\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>11.973</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq517\"><alternatives><tex-math id=\"M1059\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.25456$$\\end{document}</tex-math><mml:math id=\"M1060\"><mml:mrow><mml:mn>1.25456</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq518\"><alternatives><tex-math id=\"M1061\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10$$\\end{document}</tex-math><mml:math id=\"M1062\"><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq519\"><alternatives><tex-math id=\"M1063\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-6.6810$$\\end{document}</tex-math><mml:math id=\"M1064\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>6.6810</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq520\"><alternatives><tex-math id=\"M1065\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.33243$$\\end{document}</tex-math><mml:math id=\"M1066\"><mml:mrow><mml:mn>1.33243</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq521\"><alternatives><tex-math id=\"M1067\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-26.824$$\\end{document}</tex-math><mml:math id=\"M1068\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>26.824</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq522\"><alternatives><tex-math id=\"M1069\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.903258$$\\end{document}</tex-math><mml:math id=\"M1070\"><mml:mrow><mml:mn>0.903258</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq523\"><alternatives><tex-math id=\"M1071\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M1072\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq524\"><alternatives><tex-math id=\"M1073\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M1074\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq525\"><alternatives><tex-math id=\"M1075\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M1076\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq526\"><alternatives><tex-math id=\"M1077\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$00$$\\end{document}</tex-math><mml:math id=\"M1078\"><mml:mrow><mml:mn>00</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq527\"><alternatives><tex-math id=\"M1079\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M1080\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq528\"><alternatives><tex-math id=\"M1081\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M1082\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq529\"><alternatives><tex-math id=\"M1083\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M1084\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq530\"><alternatives><tex-math id=\"M1085\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M1086\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq531\"><alternatives><tex-math id=\"M1087\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.62898$$\\end{document}</tex-math><mml:math id=\"M1088\"><mml:mrow><mml:mn>2.62898</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq532\"><alternatives><tex-math id=\"M1089\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.58260$$\\end{document}</tex-math><mml:math id=\"M1090\"><mml:mrow><mml:mn>0.58260</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq533\"><alternatives><tex-math id=\"M1091\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.29389$$\\end{document}</tex-math><mml:math id=\"M1092\"><mml:mrow><mml:mn>2.29389</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq534\"><alternatives><tex-math id=\"M1093\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.504837$$\\end{document}</tex-math><mml:math id=\"M1094\"><mml:mrow><mml:mn>0.504837</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq535\"><alternatives><tex-math id=\"M1095\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$02$$\\end{document}</tex-math><mml:math id=\"M1096\"><mml:mrow><mml:mn>02</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq536\"><alternatives><tex-math id=\"M1097\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.49564$$\\end{document}</tex-math><mml:math id=\"M1098\"><mml:mrow><mml:mn>2.49564</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq537\"><alternatives><tex-math id=\"M1099\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.16376$$\\end{document}</tex-math><mml:math id=\"M1100\"><mml:mrow><mml:mn>2.16376</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq538\"><alternatives><tex-math id=\"M1101\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.10901$$\\end{document}</tex-math><mml:math id=\"M1102\"><mml:mrow><mml:mn>2.10901</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq539\"><alternatives><tex-math id=\"M1103\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.123040$$\\end{document}</tex-math><mml:math id=\"M1104\"><mml:mrow><mml:mn>2.123040</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq540\"><alternatives><tex-math id=\"M1105\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$04$$\\end{document}</tex-math><mml:math id=\"M1106\"><mml:mrow><mml:mn>04</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq541\"><alternatives><tex-math id=\"M1107\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.43024$$\\end{document}</tex-math><mml:math id=\"M1108\"><mml:mrow><mml:mn>2.43024</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq542\"><alternatives><tex-math id=\"M1109\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4.10204$$\\end{document}</tex-math><mml:math id=\"M1110\"><mml:mrow><mml:mn>4.10204</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq543\"><alternatives><tex-math id=\"M1111\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.03810$$\\end{document}</tex-math><mml:math id=\"M1112\"><mml:mrow><mml:mn>2.03810</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq544\"><alternatives><tex-math id=\"M1113\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4.07362$$\\end{document}</tex-math><mml:math id=\"M1114\"><mml:mrow><mml:mn>4.07362</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq545\"><alternatives><tex-math id=\"M1115\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M1116\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq546\"><alternatives><tex-math id=\"M1117\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M1118\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq547\"><alternatives><tex-math id=\"M1119\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M1120\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq548\"><alternatives><tex-math id=\"M1121\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M1122\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq549\"><alternatives><tex-math id=\"M1123\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10$$\\end{document}</tex-math><mml:math id=\"M1124\"><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq550\"><alternatives><tex-math id=\"M1125\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M1126\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq551\"><alternatives><tex-math id=\"M1127\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M1128\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq552\"><alternatives><tex-math id=\"M1129\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M1130\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq553\"><alternatives><tex-math id=\"M1131\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.46683$$\\end{document}</tex-math><mml:math id=\"M1132\"><mml:mrow><mml:mn>2.46683</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq554\"><alternatives><tex-math id=\"M1133\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.51915$$\\end{document}</tex-math><mml:math id=\"M1134\"><mml:mrow><mml:mn>2.51915</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq555\"><alternatives><tex-math id=\"M1135\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.07947$$\\end{document}</tex-math><mml:math id=\"M1136\"><mml:mrow><mml:mn>2.07947</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq556\"><alternatives><tex-math id=\"M1137\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.41901$$\\end{document}</tex-math><mml:math id=\"M1138\"><mml:mrow><mml:mn>2.41901</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq557\"><alternatives><tex-math id=\"M1139\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$15$$\\end{document}</tex-math><mml:math id=\"M1140\"><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq558\"><alternatives><tex-math id=\"M1141\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.45546$$\\end{document}</tex-math><mml:math id=\"M1142\"><mml:mrow><mml:mn>2.45546</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq559\"><alternatives><tex-math id=\"M1143\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.75390$$\\end{document}</tex-math><mml:math id=\"M1144\"><mml:mrow><mml:mn>2.75390</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq560\"><alternatives><tex-math id=\"M1145\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.06659$$\\end{document}</tex-math><mml:math id=\"M1146\"><mml:mrow><mml:mn>2.06659</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq561\"><alternatives><tex-math id=\"M1147\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.64903$$\\end{document}</tex-math><mml:math id=\"M1148\"><mml:mrow><mml:mn>2.64903</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq562\"><alternatives><tex-math id=\"M1149\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$20$$\\end{document}</tex-math><mml:math id=\"M1150\"><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq563\"><alternatives><tex-math id=\"M1151\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.44728$$\\end{document}</tex-math><mml:math id=\"M1152\"><mml:mrow><mml:mn>2.44728</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq564\"><alternatives><tex-math id=\"M1153\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.94512$$\\end{document}</tex-math><mml:math id=\"M1154\"><mml:mrow><mml:mn>2.94512</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq565\"><alternatives><tex-math id=\"M1155\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.05751$$\\end{document}</tex-math><mml:math id=\"M1156\"><mml:mrow><mml:mn>2.05751</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq566\"><alternatives><tex-math id=\"M1157\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.83747$$\\end{document}</tex-math><mml:math id=\"M1158\"><mml:mrow><mml:mn>2.83747</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq567\"><alternatives><tex-math id=\"M1159\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M1160\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq568\"><alternatives><tex-math id=\"M1161\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M1162\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq569\"><alternatives><tex-math id=\"M1163\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M1164\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq570\"><alternatives><tex-math id=\"M1165\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M1166\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq571\"><alternatives><tex-math id=\"M1167\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M1168\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq572\"><alternatives><tex-math id=\"M1169\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$00$$\\end{document}</tex-math><mml:math id=\"M1170\"><mml:mrow><mml:mn>00</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq573\"><alternatives><tex-math id=\"M1171\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M1172\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq574\"><alternatives><tex-math id=\"M1173\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M1174\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq575\"><alternatives><tex-math id=\"M1175\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.98666$$\\end{document}</tex-math><mml:math id=\"M1176\"><mml:mrow><mml:mn>2.98666</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq576\"><alternatives><tex-math id=\"M1177\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.64205$$\\end{document}</tex-math><mml:math id=\"M1178\"><mml:mrow><mml:mn>1.64205</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq577\"><alternatives><tex-math id=\"M1179\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.77205$$\\end{document}</tex-math><mml:math id=\"M1180\"><mml:mrow><mml:mn>2.77205</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq578\"><alternatives><tex-math id=\"M1181\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.61567$$\\end{document}</tex-math><mml:math id=\"M1182\"><mml:mrow><mml:mn>1.61567</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq579\"><alternatives><tex-math id=\"M1183\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$03$$\\end{document}</tex-math><mml:math id=\"M1184\"><mml:mrow><mml:mn>03</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq580\"><alternatives><tex-math id=\"M1185\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.487884$$\\end{document}</tex-math><mml:math id=\"M1186\"><mml:mrow><mml:mn>0.487884</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq581\"><alternatives><tex-math id=\"M1187\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.66930$$\\end{document}</tex-math><mml:math id=\"M1188\"><mml:mrow><mml:mn>1.66930</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq582\"><alternatives><tex-math id=\"M1189\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.2628$$\\end{document}</tex-math><mml:math id=\"M1190\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.2628</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq583\"><alternatives><tex-math id=\"M1191\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.46950$$\\end{document}</tex-math><mml:math id=\"M1192\"><mml:mrow><mml:mn>1.46950</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq584\"><alternatives><tex-math id=\"M1193\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$06$$\\end{document}</tex-math><mml:math id=\"M1194\"><mml:mrow><mml:mn>06</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq585\"><alternatives><tex-math id=\"M1195\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.060626$$\\end{document}</tex-math><mml:math id=\"M1196\"><mml:mrow><mml:mn>0.060626</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq586\"><alternatives><tex-math id=\"M1197\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.45236$$\\end{document}</tex-math><mml:math id=\"M1198\"><mml:mrow><mml:mn>1.45236</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq587\"><alternatives><tex-math id=\"M1199\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.6053$$\\end{document}</tex-math><mml:math id=\"M1200\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.6053</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq588\"><alternatives><tex-math id=\"M1201\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.16859$$\\end{document}</tex-math><mml:math id=\"M1202\"><mml:mrow><mml:mn>1.16859</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq589\"><alternatives><tex-math id=\"M1203\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M1204\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq590\"><alternatives><tex-math id=\"M1205\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M1206\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq591\"><alternatives><tex-math id=\"M1207\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M1208\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq592\"><alternatives><tex-math id=\"M1209\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M1210\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq593\"><alternatives><tex-math id=\"M1211\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M1212\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq594\"><alternatives><tex-math id=\"M1213\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M1214\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq595\"><alternatives><tex-math id=\"M1215\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$05$$\\end{document}</tex-math><mml:math id=\"M1216\"><mml:mrow><mml:mn>05</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq596\"><alternatives><tex-math id=\"M1217\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.2$$\\end{document}</tex-math><mml:math id=\"M1218\"><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq597\"><alternatives><tex-math id=\"M1219\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.268410$$\\end{document}</tex-math><mml:math id=\"M1220\"><mml:mrow><mml:mn>6.268410</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq598\"><alternatives><tex-math id=\"M1221\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.80742$$\\end{document}</tex-math><mml:math id=\"M1222\"><mml:mrow><mml:mn>1.80742</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq599\"><alternatives><tex-math id=\"M1223\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$11.6602$$\\end{document}</tex-math><mml:math id=\"M1224\"><mml:mrow><mml:mn>11.6602</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq600\"><alternatives><tex-math id=\"M1225\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.86675$$\\end{document}</tex-math><mml:math id=\"M1226\"><mml:mrow><mml:mn>1.86675</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq601\"><alternatives><tex-math id=\"M1227\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10$$\\end{document}</tex-math><mml:math id=\"M1228\"><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq602\"><alternatives><tex-math id=\"M1229\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$10.26151$$\\end{document}</tex-math><mml:math id=\"M1230\"><mml:mrow><mml:mn>10.26151</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq603\"><alternatives><tex-math id=\"M1231\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.91756$$\\end{document}</tex-math><mml:math id=\"M1232\"><mml:mrow><mml:mn>1.91756</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq604\"><alternatives><tex-math id=\"M1233\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$20.8553$$\\end{document}</tex-math><mml:math id=\"M1234\"><mml:mrow><mml:mn>20.8553</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq605\"><alternatives><tex-math id=\"M1235\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.07063$$\\end{document}</tex-math><mml:math id=\"M1236\"><mml:mrow><mml:mn>2.07063</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq606\"><alternatives><tex-math id=\"M1237\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$15$$\\end{document}</tex-math><mml:math id=\"M1238\"><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq607\"><alternatives><tex-math id=\"M1239\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$18.72051$$\\end{document}</tex-math><mml:math id=\"M1240\"><mml:mrow><mml:mn>18.72051</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq608\"><alternatives><tex-math id=\"M1241\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.13910$$\\end{document}</tex-math><mml:math id=\"M1242\"><mml:mrow><mml:mn>2.13910</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq609\"><alternatives><tex-math id=\"M1243\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$28.9276$$\\end{document}</tex-math><mml:math id=\"M1244\"><mml:mrow><mml:mn>28.9276</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq610\"><alternatives><tex-math id=\"M1245\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.24937$$\\end{document}</tex-math><mml:math id=\"M1246\"><mml:mrow><mml:mn>2.24937</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq611\"><alternatives><tex-math id=\"M1247\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.7$$\\end{document}</tex-math><mml:math id=\"M1248\"><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq612\"><alternatives><tex-math id=\"M1249\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$6.2$$\\end{document}</tex-math><mml:math id=\"M1250\"><mml:mrow><mml:mn>6.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq613\"><alternatives><tex-math id=\"M1251\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.8$$\\end{document}</tex-math><mml:math id=\"M1252\"><mml:mrow><mml:mn>0.8</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq614\"><alternatives><tex-math id=\"M1253\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M1254\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq615\"><alternatives><tex-math id=\"M1255\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.6$$\\end{document}</tex-math><mml:math id=\"M1256\"><mml:mrow><mml:mn>0.6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq616\"><alternatives><tex-math id=\"M1257\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.3$$\\end{document}</tex-math><mml:math id=\"M1258\"><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq617\"><alternatives><tex-math id=\"M1259\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M1260\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq618\"><alternatives><tex-math id=\"M1261\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.5$$\\end{document}</tex-math><mml:math id=\"M1262\"><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq619\"><alternatives><tex-math id=\"M1263\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.513160$$\\end{document}</tex-math><mml:math id=\"M1264\"><mml:mrow><mml:mn>2.513160</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq620\"><alternatives><tex-math id=\"M1265\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.79520$$\\end{document}</tex-math><mml:math id=\"M1266\"><mml:mrow><mml:mn>1.79520</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq621\"><alternatives><tex-math id=\"M1267\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.13120$$\\end{document}</tex-math><mml:math id=\"M1268\"><mml:mrow><mml:mn>2.13120</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq622\"><alternatives><tex-math id=\"M1269\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.71391$$\\end{document}</tex-math><mml:math id=\"M1270\"><mml:mrow><mml:mn>1.71391</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq623\"><alternatives><tex-math id=\"M1271\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.0$$\\end{document}</tex-math><mml:math id=\"M1272\"><mml:mrow><mml:mn>1.0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq624\"><alternatives><tex-math id=\"M1273\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.497920$$\\end{document}</tex-math><mml:math id=\"M1274\"><mml:mrow><mml:mn>2.497920</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq625\"><alternatives><tex-math id=\"M1275\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.94580$$\\end{document}</tex-math><mml:math id=\"M1276\"><mml:mrow><mml:mn>1.94580</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq626\"><alternatives><tex-math id=\"M1277\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.11298$$\\end{document}</tex-math><mml:math id=\"M1278\"><mml:mrow><mml:mn>2.11298</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq627\"><alternatives><tex-math id=\"M1279\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.80989$$\\end{document}</tex-math><mml:math id=\"M1280\"><mml:mrow><mml:mn>1.80989</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq628\"><alternatives><tex-math id=\"M1281\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.5$$\\end{document}</tex-math><mml:math id=\"M1282\"><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq629\"><alternatives><tex-math id=\"M1283\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.482801$$\\end{document}</tex-math><mml:math id=\"M1284\"><mml:mrow><mml:mn>2.482801</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq630\"><alternatives><tex-math id=\"M1285\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.09423$$\\end{document}</tex-math><mml:math id=\"M1286\"><mml:mrow><mml:mn>2.09423</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq631\"><alternatives><tex-math id=\"M1287\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.09489$$\\end{document}</tex-math><mml:math id=\"M1288\"><mml:mrow><mml:mn>2.09489</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq632\"><alternatives><tex-math id=\"M1289\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.90382$$\\end{document}</tex-math><mml:math id=\"M1290\"><mml:mrow><mml:mn>1.90382</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq186\"><alternatives><tex-math id=\"M1291\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$r(\\eta )$$\\end{document}</tex-math><mml:math id=\"M1292\"><mml:mrow><mml:mi>r</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>η</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq187\"><alternatives><tex-math id=\"M1293\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x }=3.00$$\\end{document}</tex-math><mml:math id=\"M1294\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>3.00</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq188\"><alternatives><tex-math id=\"M1295\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$4.36$$\\end{document}</tex-math><mml:math id=\"M1296\"><mml:mrow><mml:mn>4.36</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq189\"><alternatives><tex-math id=\"M1297\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x }=1.72$$\\end{document}</tex-math><mml:math id=\"M1298\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.72</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq190\"><alternatives><tex-math id=\"M1299\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1.74,$$\\end{document}</tex-math><mml:math id=\"M1300\"><mml:mrow><mml:mn>1.74</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq191\"><alternatives><tex-math id=\"M1301\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x }=-1.36$$\\end{document}</tex-math><mml:math id=\"M1302\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>1.36</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq192\"><alternatives><tex-math id=\"M1303\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-1.16$$\\end{document}</tex-math><mml:math id=\"M1304\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.16</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq193\"><alternatives><tex-math id=\"M1305\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{y}=-1.11$$\\end{document}</tex-math><mml:math id=\"M1306\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Cf</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>1.11</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq194\"><alternatives><tex-math id=\"M1307\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$-0.95$$\\end{document}</tex-math><mml:math id=\"M1308\"><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.95</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq195\"><alternatives><tex-math id=\"M1309\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha ={0}^{0}$$\\end{document}</tex-math><mml:math id=\"M1310\"><mml:mrow><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mn>0</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq196\"><alternatives><tex-math id=\"M1311\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$x-axis,$$\\end{document}</tex-math><mml:math id=\"M1312\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq197\"><alternatives><tex-math id=\"M1313\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$5\\le Ec\\le 10,$$\\end{document}</tex-math><mml:math id=\"M1314\"><mml:mrow><mml:mn>5</mml:mn><mml:mo>≤</mml:mo><mml:mi>E</mml:mi><mml:mi>c</mml:mi><mml:mo>≤</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq198\"><alternatives><tex-math id=\"M1315\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x }=18.7, 28.9$$\\end{document}</tex-math><mml:math id=\"M1316\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>18.7</mml:mn><mml:mo>,</mml:mo><mml:mn>28.9</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq199\"><alternatives><tex-math id=\"M1317\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Sh}_{x }=2.1, 2.2$$\\end{document}</tex-math><mml:math id=\"M1318\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2.1</mml:mn><mml:mo>,</mml:mo><mml:mn>2.2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq200\"><alternatives><tex-math id=\"M1319\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0\\le Kc\\le 4,$$\\end{document}</tex-math><mml:math id=\"M1320\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>K</mml:mi><mml:mi>c</mml:mi><mml:mo>≤</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq201\"><alternatives><tex-math id=\"M1321\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.62\\le {Nu}_{x }\\le 2.43$$\\end{document}</tex-math><mml:math id=\"M1322\"><mml:mrow><mml:mn>2.62</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mn>2.43</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq202\"><alternatives><tex-math id=\"M1323\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2.29\\le {Nu}_{x }\\le 2.03$$\\end{document}</tex-math><mml:math id=\"M1324\"><mml:mrow><mml:mn>2.29</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mn>2.03</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq203\"><alternatives><tex-math id=\"M1325\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${0.58\\le Sh}_{x }\\le 4.10$$\\end{document}</tex-math><mml:math id=\"M1326\"><mml:mrow><mml:msub><mml:mrow><mml:mn>0.58</mml:mn><mml:mo>≤</mml:mo><mml:mi>S</mml:mi><mml:mi>h</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mn>4.10</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq204\"><alternatives><tex-math id=\"M1327\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0.50\\le {Sh}_{x }\\le 4.07$$\\end{document}</tex-math><mml:math id=\"M1328\"><mml:mrow><mml:mn>0.50</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Sh</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mn>4.07</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq205\"><alternatives><tex-math id=\"M1329\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x}$$\\end{document}</tex-math><mml:math id=\"M1330\"><mml:msub><mml:mrow><mml:mi mathvariant=\"italic\">Nu</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:math></alternatives></inline-formula>" ]

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{ "acronym": [ "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\omega }^{*}$$\\end{document}ω∗", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${C}_{p}$$\\end{document}Cp", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\phi }_{1},{\\phi }_{2}$$\\end{document}ϕ1,ϕ2", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${G}_{1}, {G}_{2},{G}_{3}, {G}_{4}$$\\end{document}G1,G2,G3,G4", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$T,C$$\\end{document}T,C", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Z$$\\end{document}Z", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$a,b$$\\end{document}a,b", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} 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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\uplambda$$\\end{document}λ", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\rho$$\\end{document}ρ", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\gamma$$\\end{document}γ", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$k$$\\end{document}k", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Nu}_{x},{Sh}_{x}$$\\end{document}Nux,Shx", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\eta$$\\end{document}η", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$u,v$$\\end{document}u,v, w", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${Cf}_{x}, {Cf}_{y}$$\\end{document}Cfx,Cfy", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} 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[ "<title>Introduction</title>", "<p id=\"Par2\">The impacts of climate change are causing significant social, economic and ecological disruptions to global systems of farming and food production (IPCC ##UREF##17##2022##). These climate changes challenges are prompting the need for well prepared and resilient farming and food systems that are adaptive and minimise risks of global food insecurity (Chriest and Niles ##UREF##4##2018##; Janssens et al. ##UREF##19##2020##). The development of farm resilience and preparedness requires transformative thinking and adaptive management to facilitate the behaviour change needed to transform farm systems (Colloff et al. ##UREF##6##2021##; Pahl-Wostl ##UREF##27##2006##; Park et al. ##UREF##29##2012##). The viability and continuity of Australian farming businesses depends on the transformative processes to prepare resilient farming systems that minimise the risk of climate change (Rickards and Howden ##UREF##36##2012##).</p>", "<p id=\"Par3\">Australian farmers co-exist with the beneficial and adverse consequences of the natural environment as they interact with natural meteorological processes (Renaud et al. ##UREF##35##2010##). This necessitates a human environmental systems (HES) approach to building systems capability and reconciling accelerating risk arising from climate change, landscape, and socio-economic interactions (Scholz et al. ##UREF##40##2011##b). These interactions potentially amplify the human, economic and landscape costs and risks of future adverse consequences (Mozumder et al. ##UREF##25##2009##). Risk is the likelihood of the benefits of farming in certain geo-climatic locations as a proportion of the costs arising from exposure to adverse climate consequences (Paton and Buergelt ##UREF##32##2017##). Without managed adaptation the costs of farming in certain geo-climatic environments may exceed the likelihood of benefits. Therefore, unless farmers are ready to build resilience, and adaptively manage these risks, the viable continuity of farming in these locations may not be sustained.</p>", "<p id=\"Par4\">Building farm resilience is an important precursor for how well farming systems in Australia adapt to the demands of climate change stressors (Asghari et al. ##UREF##1##2021##; Bardsley et al. ##UREF##2##2018##). The model of stress resistance and resilience over time accounts for these co-occurring adaptation and resilience processes (Norris et al. ##REF##18157631##2008##). This model suggests that farms with more management capability and resource sufficiency will self-organise and adapt, whilst restoring systems from post-stressor states of transient dysfunction (i.e., climate disruption). By studying cohorts of farmers that have learnt to prepare resilient systems by adapting to situational and extreme climate stressors, knowledge is constructed of how these farmers think, prioritise, and strategically manage these as learning processes (Gorddard et al. ##UREF##16##2016##; Paton and Buergelt ##UREF##31##2019##).</p>", "<p id=\"Par5\">Climate and environmental science have developed models that accounts for adaptation to the external conditions of climate change, as pathway processes of <italic>action</italic>-<italic>learning-decision cycles</italic> (Wise et al. ##UREF##42##2014##). The development of these models has applications of generalising descriptions of the phenomenon and specifying the elements and conditions that influence the processes. The Adaptation Action Cycles model of adaptation reflects how farmers interchangeably use <italic>incremental</italic> and <italic>transformation</italic> processes to adapt to the stressors of climate change (Park et al. ##UREF##29##2012##). Park et al. (##UREF##29##2012##) recognised that the <italic>incremental</italic> and <italic>transformative</italic> adaptation of farm systems were based on learning and cognitive processes. Farming systems were improved by thinking strategically, reframing, and questioning assumptions. Whereas, farms were <italic>transformed</italic>, by altering worldviews and structural context leading to a <italic>different</italic> system (Park et al. ##UREF##29##2012##). The reframing and normalisation of <italic>incremental</italic> and <italic>transformative</italic> as <italic>better</italic> and <italic>different</italic> were also important symbolic learning processes for changing the behaviours of disaster preparedness (O’Connell et al. ##UREF##26##2020##). The Transformative Adaptation Research Alliance (TARA) research framework further elaborated adaptation models by recognising the efficacy of contextual variables in <italic>transforming</italic> human systems (Colloff et al. ##UREF##7##2017##). Furthermore, the HES framework incorporated triple loop learning processes within a multi-level systems context (Pahl-Wostl ##UREF##28##2009##; Scholz et al. ##UREF##39##2011##a). This framework may better explain decision processes of adaptation within a systems context. This evolving conceptual understanding of adaptation necessitates further research of elements and processes that transmit and regulate adaptation and integrates models of resilience and preparedness processes.</p>", "<p id=\"Par6\">Farm preparedness refers to adaptive adjustments that give farming systems protective agency and resilience to effectively respond to changing patterns and extremes events of climate change (Paton et al. ##UREF##33##2014##). The efficacy of business continuity as a preparedness management strategy had limited exposure in farm (James ##UREF##18##2020##), and disaster preparedness (Sawalha ##UREF##38##2021##) literature. Some exemplary Australian farmers are building farm resilience and developing systems of adaptive management the integrate <italic>differen</italic>t and <italic>better</italic> adaptive practices (Bardsley et al. ##UREF##2##2018##). Pahl-Wostl (##UREF##27##2006##) defines adaptive management as on-going systematic processes of learning, refining and reorganising management processes, strategies and practices. For instance, Bardsley et al. (##UREF##2##2018##) identified adaptive management and innovation as contributing to farm viability and business continuity. Lockwood et al. (##UREF##22##2015##) and Raymond et al. (##UREF##34##2015##) recognised that farm management competencies and change orientation were essential adaptation capacities. Literature on CCA has developed a generalised understanding of adaptive capacities in exemplar farmers. These farmers exhibit well-connected farmer informational networks, high degrees of environmental awareness, local knowledge, and strategic thinking and planning management capabilities (Marshall et al. ##UREF##23##2016##; Marshall et al. ##UREF##24##2012##).</p>", "<p id=\"Par7\">The role of financial resources and preparedness behaviours was underrepresented in CCA research.,</p>", "<p id=\"Par8\">The purpose of this study was to explore the farm management processes of resilience, and preparedness as an adaptive learning response to the stressors of climate change in an understudied farmer cohort. The study informs processes of adaptive farm management and resilience building that ensures business viability and continuity and reduced risk. The development of the transactional maps extends the theoretical understanding of resilience, transformation, and behavioural learning processes and factors that transmit and regulate farm adaptation. The maps have potential for identifying points of influence for leveraging farm resilience building and strengthening farmer preparedness.</p>" ]

[ "<title>Methods</title>", "<title>Design</title>", "<p id=\"Par9\">This qualitative priority study was part of a multiphase mixed methods program of research. The purpose of this study was to answer what/ how research question and generate theories (i.e., enhancement), and examine exemplar cases (i.e., initiation) (Creamer ##UREF##10##2018##). We applied the Human Environmental Systems multi-level framework (Scholz et al. ##UREF##39##2011##a), the functional and constructivist interpretive lens (Creswell and Poth ##UREF##11##2017##), and grounded theory methodology (GT) (Corbin and Strauss ##UREF##9##2015##) to data collection and analysis. Ethics approval for this study was obtained through the Human Research Ethics Committee at Charles Darwin University (H19096). The data was collected from farmer interviews and artifact documents of specific farmer interviews retrieved from a media and organisational websites, according to GT iterative and theoretical sampling, and analysis processes (Corbin and Strauss ##UREF##9##2015##).</p>", "<title>Sampling and Recruitment</title>", "<p id=\"Par10\">The sample frame consisted of farmers in the eastern states of Australia (i.e., NSW, Victoria, SA, Queensland). The qualitative purposive approach was used to sample a cohort of farmers using positive deviance criteria (Pascale et al. ##UREF##30##2010##). The selection criteria for this cohort were that farmers had transformed their farming systems as a learning and behavioural response to anticipated and actual stressors of extreme climatic conditions. Participants were initially recruited by the executive officer of Farmers for Climate Action, in accordance with the positive deviance criteria. Subsequent participants were recruited via a snowball technique as a means of theoretical sampling. The theoretical sampling selected participants from various farm sectors, climatic zones, and specific climate extremes with purpose of further developing emerging GT concept and category codes.</p>", "<title>Participants and Collection</title>", "<p id=\"Par11\">Twenty two participants were interviewed, consisting of 16 men and 6 women. All participants were located in eastern Australian states and represented diverse mixed cropping and livestock farm sectors (See Table ##TAB##0##1##).</p>", "<p id=\"Par12\">All participants were interviewed between March 2020 and June 2021. On-farm interviews and data collection were paused between April 2020 and April 2021 due to the COVID-19 restrictions and recommenced in May 2021. During the COVID-19 pandemic restrictions, interviews were conducted via telephone and the Zoom web-platform. Participants interviews were guided by the episodic interview technique (Flick ##UREF##15##2009##) and by a question guide that outlined the direction of the interview. The interview questions had focus on participant experiences of climate change and interactions with the landscape, business, production, and humans. The interviews lasted an average of 90 min and were audio recorded. The recordings from interviews were transcribed in accordance with the transcription protocol. Secondary situational maps of the farming systems and memo data was generated and included in the data analysis (Clarke ##UREF##5##2003##; Corbin and Strauss ##UREF##9##2015##).</p>", "<title>Data Analysis</title>", "<p id=\"Par13\">The Corbin and Strauss (##UREF##9##2015##) procedures were used to analyse the data and build the theoretical model. The ATLAS.ti 9 (Evers and Silver ##UREF##13##2014##) data analysis software was used for data management and tracking the frequency that concepts were referred to in the data (references) as an indicator of concept importance. The data was systematically analysed using a three-step iterative coding scheme of open, axial, and selective coding (Corbin and Strauss ##UREF##9##2015##), in conjunction with constant comparison, theoretical sampling, and memo writing. The theoretical sampling was an emergent process of collecting different forms of data (e.g., situational maps, memos) and data from farmers exposed to challenging conditions (i.e., climate change) and across different farm sectors. Corbin and Strauss (##UREF##9##2015##) contend that challenging conditions are more likely to reveal adaptive processes embedded in the data. Data collection was finalised at the point of saturation, the point of data sufficiency with no new concepts emerging.</p>", "<p id=\"Par14\">In the open coding process the interview transcripts, artefact documents, memos, and situational maps were conceptually labelled. Then, the emerging concepts were constantly compared for similarities and differences and integrated into higher order concept groups (i.e., tentative categories). The higher order concept groups of <italic>better</italic> and <italic>different</italic> forms of adaptation were coded in accordance with the composite set of criteria derived from Triple loop learning (Pahl-Wostl ##UREF##28##2009##) and Park et al. (##UREF##29##2012##), that distinguished <italic>incremental</italic> (i.e., <italic>better</italic>) as systems improvement, and <italic>transformative</italic> (i.e., <italic>different</italic>) as systems change. The analysis identified adaptation levers as influential factors that contribute or facilitate farmer adaptation to perceived or actual climate change by adoption of <italic>better</italic> and <italic>different</italic> thinking, behaviour, management regimes, practices, and strategies.</p>", "<p id=\"Par15\">The data was organised via concept groups causal, situational, and intervening conditions, and strategies (action-interaction), and consequences. Situational maps were constructed from the analysis as shown in Fig. ##FIG##2##3## to illustrate the context conditions. Clarke (##UREF##5##2003##) argues that situational maps act as units of analysis and better represents the actors, actants and discursive elements of the situational context than the Corbin and Strauss (##UREF##8##1990##) contextual matrix. The twofold axial coding process identified hierarchical category components of sub-category and respective properties and dimensions. Next, the various categories were assigned to the scheme groups and linkages assigned according to the emergent relationship (e.g., transmitting, regulating, interacting). Selective coding was final coding procedure of defining and refining the specifics of each category and creating explanations for respective categories that reflected the data. Lastly, models were created that reflected the elements and relationships of the adaptation processes.</p>" ]

[ "<title>Results</title>", "<p id=\"Par16\">Grounded Theory analysis yielded two core categories and three sets of adaptation processes. The core categories were ‘Dancing with uncertainty’ and ‘Sustaining viable continuity’. The processes were (1) framing changing climate uncertainty, (2) managing farm resilience, and (3) pathways of farmer adaptation. The processes led to the development of two transactional maps (i) Transactional maps of farm continuity; and (ii) Transactional map of cyclic adaptation.</p>", "<title>Process 1: Framing the Effects of Climate Change</title>", "<p id=\"Par17\">This section explores how this cohort of interviewees from diverse geo-locations and farm sectors have common experiences of changes to windows and potential for plant and animal growth that result from changes in climate phenomena. The findings in Table ##TAB##1##2## shows the categories, subcategories and sets of properties of ‘Changing climate uncertainty’ category as ‘Shifting variability patterns and ‘Emerging variability extremes’. These shifting climate patterns and extremes were framed by interviewees as the effects on growing windows and the potential for productive output (i.e., ‘Growing potential’). The elements of climate, and competition (i.e., weeds, pathogens), and management strategy variables contributed to the growing potential of crops and animals within the farming system. The findings in Fig. ##FIG##2##3##, maps these elements and their interactions with the elements of the farming system.</p>", "<title>Effects of shifting climate patterns</title>", "<p id=\"Par18\">Interviewees identified emerging shifts in variability patterns of rainfall and temperature that were both extreme and unprecedented:</p>", "<p id=\"Par20\">Alongside these extreme unprecedented events interviewees described a regular truncated growing season due to rainfall switching-off during the critical plant growing phase:</p>", "<p id=\"Par22\">In response, interviewees identified processes for managing and adapting to the non-growing season rainfall episodes that occurred as intense hot dry season rainfall events outside the usual growing window.</p>", "<title>Impacts of emerging variability extremes</title>", "<p id=\"Par24\">The Emerging variability extremes subcategory was highly represented by droughts, heatwaves, floods, and bushfire events. Interviewees recounted the intensity of life-threatening impacts of large scale, out of control, cropping zone fires:</p>", "<p id=\"Par26\">Alongside this were the increasing frequency and severity of heatwaves:</p>", "<p id=\"Par28\">Interviewees described the life threating flooding impacts of fast storm occurrences:</p>", "<p id=\"Par30\">Consequently, interviewees view the effects on the land of flooding and rising sea-levels as farm viability hazard risks:</p>", "<title>Process 2: Managing Farm Resilience</title>", "<p id=\"Par32\">This section explores the management of adaptation and resilience processes, as responses to the changing climate that ensure the viability and continuity of the farm. These interviewees continually repositioned the farm system as a reciprocal management response to the uncertain climate, as reflected by the ‘Dancing with uncertainty’ core category. The second core category of ‘Sustaining viable continuity’ reflects that interviewees sustain the continuity and viability of the farming landscape, family social identity, and business in the context of climate change challenges. The findings in Table ##TAB##2##3## outlines the ‘Managing business directions’ and ‘Building resource capability’ categories, and subcategories that represent the management and resource adaptation processes.</p>", "<title>Managing business directions</title>", "<p id=\"Par33\">The category of ‘Managing business directions’ shows that interviewees are strategically managing the direction and position of the business system to accommodate social, macro-economic, and climate risk uncertainty. Strategic management regulated the recasting of the farming system through the agency of adopting <italic>better</italic> and <italic>different</italic> forms of adaptation.</p>", "<title>Managing business strategy</title>", "<p id=\"Par34\">Interviewees identified the strategic value of creating a business model that accommodated the localised adaptive demands of the changing climate:</p>", "<p id=\"Par36\">Interviewees described the rationale for creating a <italic>different</italic> and simplified business model:</p>", "<p id=\"Par38\">Consequently, interviewees preserved the core business in times of drought extremes to sustain the continuity of the farm:</p>", "<p id=\"Par40\">Interviewees identified the strategic necessity of planning adaptive business and operational readiness to accommodate the changing rainfall distribution patterns:</p>", "<p id=\"Par42\">Interviewees planned and managed livestock resource systems to accommodate extreme climate events:</p>", "<p id=\"Par44\">Consequently, the platform of cloud-based software enabled monitoring and tactical planning in sustaining the dynamic balance between landscape carrying capacity and stocking rate:</p>", "<p id=\"Par46\">Interviewees identified the necessity of managing risk to protect business viability against the increasing uncertainty of climate variability:</p>", "<p id=\"Par48\">Consequently, business strategies were packaged as adaptive levers for managing continuity risks. Strategies ranged from geographic relocation and property spread to enterprise diversification, altering scale, and flexible substitution:</p>", "<p id=\"Par50\">Interviewees recasted systems of management to accommodate the integration of <italic>different</italic> strategic approaches. Consequently, well organised management systems were an adaptive lever and incorporated effective sets of strategies that led to cohesive performance overtime:</p>", "<title>Managing farm transformation</title>", "<p id=\"Par52\">Interviewees identified variants of managing farm transformations with make-over processes, aimed at strengthening farm resilience and future preparedness. The farm make-over represents the purposeful creation of <italic>better</italic> and <italic>different</italic> farm structures, business and production functions, and management processes. These changes were accomplished through cycles of adaptation and learning that varied in complexity, time, and degree of systems change.</p>", "<p id=\"Par53\">Interviewees described singular makeovers as one-time change, such as developing <italic>different</italic> bred types and sheep husbandry management that created a <italic>different</italic> flock genotype and <italic>better</italic> wool quality and ease of management:</p>", "<p id=\"Par55\">Interviewees described other make-overs as an evolving series of improvments to the system that together created the step of forming a <italic>different</italic> system:</p>", "<p id=\"Par57\">Interviewees commonly used project based make-overs in the form of self-contained developments. Projects, such as building livestock containments, structurally created <italic>different systems</italic>. Consequently<italic>, different</italic> management regimes led to <italic>better</italic> protective ground cover:</p>", "<p id=\"Par59\">Some interviewees devised makeovers as series of sequential projects that evolved overtime:</p>", "<p id=\"Par61\">Other interviewees devised concurrent make-over projects to create a different farming system. These complex projects simultaneously created <italic>different</italic> landscape and infrastructure structural elements. Consequently<italic>, different</italic> management regimes and productivity functions led to <italic>better</italic> landcape and productivity outputs:</p>", "<p id=\"Par63\">One interviewee described the bold move of creating a <italic>different</italic> farming system by relocating the farm business and operations to another geographical location. Consequently, risks of heat stress risk and irrigation water allocation shortfalls were averted:</p>", "<title>Managing farm efficiency</title>", "<p id=\"Par65\">This subcategory of ‘Managing farm efficiency’ conveys that farmers are managing the tactics of operational routines that enables the efficient functioning of adaptation processes.</p>", "<p id=\"Par66\">Farmers identified that learning and problem solving were essential management processes for integrating farm ‘makeovers’ into the system throughout multiple cycles of adaptation:</p>", "<p id=\"Par68\">Interviewees described learning and problem solving processes of identifying the weakest point in the system that needed fixing.</p>", "<p id=\"Par70\">Interviewees decribed the value of collborative learning and problem solving processes. Consequently, complex biota processes were explained with application to other crops:</p>", "<title>Building resource capability</title>", "<title>Developing capital resources</title>", "<p id=\"Par72\">This subcategory category of ‘Building resource capability’ conveys that farmers are growing the scale, capability, and resilience of the farm through the agency of adopting <italic>better</italic> and <italic>different</italic> forms of farm resources to match the adaptive demands of the system.</p>", "<p id=\"Par73\">Interviewees described the strategic value of growing and looking after property resources. In response, property signified wealth, enabled economies of business scale, and was buffer to better accommodate the adaptive demands of the changing climate:</p>", "<p id=\"Par75\">Interviewees described the strategic development of <italic>different</italic> infrastructure resources to minimise risks of the rising sea level and intense rainfall episodes. Consequently, the landscape was protected, and <italic>better</italic> growing conditions were created:</p>", "<title>Sustaining operating resources</title>", "<p id=\"Par77\">Interviewees identified the adaptive response of optimising equipment capability and scale. Consequently, operational effectiveness and timeliness accommodated the adaptive demands of the changing climate:</p>", "<p id=\"Par79\">Interviewees described the adaptive response of creating a different flock genotype. In response, livestock potential and scale were matched to the adaptive demands of the changing climate, that led to enhanced productivity and operational effectiveness:</p>", "<title>Developing human capital</title>", "<p id=\"Par81\">Interviewees identified the importance of developing the resilience of human capital. They described the underdevelopment of metal resilience. Consequently, insufficient resilience meant that farmers were underprepared to handle the on-going stressors and challenges of farm adversities:</p>", "<title>Managing financial resources</title>", "<p id=\"Par83\">This subcategory conveys that farmers are managing the ability of the farm business to sustain viability and continuity despite adaptive demand variability.</p>", "<p id=\"Par84\">Interviewees identified differing forms of financial reserves to buffer from variability in the changing climate. Farmers descibed the use of equity to fund drought induced revenue short-falls:</p>", "<p id=\"Par86\">Other interviewees created farm management deposits as an adaptive financial response. Consequently, deposits were withdrawn to buffer short-falls in revenue:</p>", "<p id=\"Par88\">Interviewees identified diverse approaches to financing growth in farm capabilities. They described the reinvestment of profits to develop future productivity and reduce risk arising from the adaptive demands of the changing climate:</p>", "<title>Transactional map of resilient farm continuity</title>", "<p id=\"Par90\">Analysis developed the transactional map illustrated in Fig. ##FIG##0##1## to represent how resilience processes of managing farm resources and the adaptation cycle (steps 1–6) processes work together. The core category of ‘Creating viable continuity’ suggests that farmers stay in business overtime through the astute management of the adaptation cycle, building human and landscape capital, and financial resource accumulation. In the map, resources act as capital (i.e., landscape, human, economic), with beneficial or adverse consequences of the adaptation cycle adding (e.g., profits, property acquisition) or withdrawing (e.g., income and property losses) from the resources. The points of management leverage in the map are business modelling, corrective management systems, farm problem solving, healing the landscape, and ‘farm make-overs’ for strengthening landscape, social, and productive performance, and continuity. Furthermore, the map shows that certain events and learning experiences (i.e., ‘emerging game changer’) are the catalysts to the sequence of socio-cognitive processing, decision-making (i.e., ‘adopting game changers’), and undertaking adaptive farm make-overs (i.e., innovations) in functions within the farming system, structures and processes.</p>", "<title>Process 3: Adaptation Pathways Processes</title>", "<p id=\"Par91\">Analysis developed a cyclic map of adaptation processes that accounts for key elements and pathway processes of <italic>better</italic> and <italic>different</italic>. The elements of the map, shown in Table ##TAB##3##4## represent casual, situational and intervening conditions, action strategies and consequence categories.</p>", "<title>Pathway processes of <italic>better</italic> and <italic>different</italic></title>", "<p id=\"Par92\">The map found that incremental (i.e., <italic>better</italic>) and transformative (i.e., <italic>different</italic>) adaptation outcomes are incubated at the thinking stage with a sequence of deciding and acting steps. Analysis found six adaptation pathway processes of <italic>better</italic> and <italic>different</italic>: thinking-deciding, deciding-acting, acting-consequences, managing-strategies, managing-landscape, and managing resources.</p>", "<title>Thinking-deciding</title>", "<p id=\"Par93\">The process of <italic>better</italic> thinking incorporated questioning assumptions that result in having more control in decisions:</p>", "<p id=\"Par95\">Interviewees identified that conceiving ideas <italic>differently</italic> involved a different set of world-views about managing the farm system:</p>", "<title>Deciding-acting</title>", "<p id=\"Par97\">The process of <italic>better</italic> decision making involved actions that optimised business outcomes:</p>", "<p id=\"Par99\">Interviewees identified deciding <italic>differently</italic> involved a different set of world-views and structural changes to the farm management system:</p>", "<title>Acting-consequences</title>", "<p id=\"Par101\">Interviewees identified that transformative consequences were the outcome of <italic>different</italic> action strategies:</p>", "<title>Managing-strategies</title>", "<p id=\"Par103\">Interviewees identified integrating <italic>better</italic> and <italic>different</italic> forms of management and the selective application of strategies:</p>", "<title>Managing-landscape</title>", "<p id=\"Par105\">Interviewees identified that a <italic>different</italic> landscape management regime restored healthy functioning in the landscape:</p>", "<title>Managing-resources</title>", "<p id=\"Par107\">Interviewees identified that <italic>different</italic> resource management produced structural changes to the farm management system:</p>", "<p id=\"Par109\">The <italic>transformation</italic> of drainage management and pumping resources boosted crop yields and protected the viability of the fragile landscape.</p>", "<title>Transactional map of cyclic adaptation</title>", "<p id=\"Par110\">The step-wise process and conditions that influence adaptation are illustrated in Fig. ##FIG##1##2##. The cycle has six transmission steps that are regulated by intervening conditions. The cycle has multi-level applications at the personal, family, community, and farm business and production level. The cycle starts with a farm being impacted by the changing climate that create (1) farm consequences (crop losses), and the subsequent growing windows, growing season and landscape potential. Subsequently, adaptation cycles produce beneficial consequences (e.g., profits, well-being), and improve farm structures and functions that prepare the farm for future risk. Farmers learn by assessing and gathering feedback (2) throughout the cyclic process. Primary learning from feedback is derived from assessing impacts and anticipating future effects of climate change. Feedback learning is integrated into all the intelligence that farmers selectively gather (3). Farmers seek and are presented with multiple sources of farm data and external sources of information and influence (e.g., peers, groups, advisors, media). Then the socio-cognitive processing occurs (4), by interpreting the intelligence and level of risk, and then selectively thinking about adaptive solutions to problems arising from the original consequences. The efficacy of mental processing depends on influences of socio-cognitive factors.</p>", "<p id=\"Par111\">The decision step (5) is a goal-directed form of mentally processing options, choices, and strategies. The goal is to minimise ‘states of transient dysfunction’ (Norris et al. ##REF##18157631##2008##) and adapt to the changed environment. Decision options are formed and selected. Strategies to achieve goals are informed and influenced by farmer preferences and sources of intelligence. The application of action strategies (4) gives the decision goals tangible form. Action strategies and the growing windows determine the growing potential. That in turn produces consequences. The intervening conditions of management and farm resources regulate actions strategies and growing potential and landscape potential.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par112\">The study explored how processes of resilience and adaptation are managed as preparedness and learning responses to climate change in an understudied cohort of farmers. A critical finding was that management, resources, and behavioural learning regulated resilience and adaptation as integrated and self-righting processes, in response to anticipated and actual stressors of climate change.</p>", "<title>Mapping Resilient Farm Continuity</title>", "<p id=\"Par113\">The map of farm resilience identified that the management of resource capabilities and sufficiency, and the corrective actions of adaptation cycles were integrated self-righting processes that ensured farm viability and continuity. These findings extend the Paton et al. (##UREF##33##2014##) and Norris et al. (##REF##18157631##2008##) explanation of resilience processes by explaining interactions with cyclic adaptation and management processes. At the business level, the management of innovative business models were found to strategically position the farm system while capturing the benefits and minimising losses of evolving climatic conditions. These business models and plans were identified as strategic precursors for transforming the functioning and direction of business and production systems. This is similar to the suggestions of Robertson and Murray-Prior (##UREF##37##2016##), that farm viability was better achieved by transforming the business. Similarly, Kingwell et al. (##UREF##21##2020##), suggested that the management of business strategy was vital for sustaining profitable farming systems. This study furthers these claims by adding knowledge of the transformative and management pathway processes of building the resilience of the farm business and resources, needed for stronger farm profits and viability.</p>", "<p id=\"Par114\">The farm system was continually repositioned in step with the changing climate as core resilience and adaptive management strategy to sustain control and business continuity. This finding is consistent with the Wise et al. (##UREF##42##2014##) principle of ‘adaptive pathways’. Furthermore, this farm cohort developed adaptive management systems (i.e., regimes) and integrated these with the development of business and farming practice transformation. These finding add to the Pahl-Wostl (##UREF##27##2006##) explanation of ‘learning to manage’ by explaining how farmers were learning and integrating intel from multiple feedback loops throughout short (i.e., tactical) and longer (i.e., strategic) cycles of adaptation. These farmers prioritised the management of natural resources (e.g., soil, water), whilst weighing competing family and economic interests of farm production. These finding are similar to (Everest ##UREF##12##2020##), that indicated the importance of managing the soil, water, and agroforestry natural resources as adaptation responses to climate change.</p>", "<p id=\"Par115\">The findings suggest that the managed accrual of property and financial resources and development of farm resources (e.g., landscape, people, infrastructure, plant, livestock), strengthened farm resilience and assured viability and business continuity. This is consistent with the Norris et al. (##REF##18157631##2008##) concept of transient dysfunction that robust resource sufficiency (i.e., productive scale, wealth) minimised disruptive stressor consequences. The findings highlight that farmers managed portfolios of insurance and self-managed strategies to reduce the financial risk of climate uncertainty. They transferred hazard risks to insurers for fire and hail. According to Khuu and Juerg Weber (##UREF##20##2013##), there are limited multi-peril tools for transferring production risks of climate change in Australia. Farmers self-managed downturns in revenue with buffer funds, used short term debt by drawing on equity in properties, and developed property portfolios and/or farm productivity with surplus revenue. These self-reliant strategies for managing financial disruptions of climate change will increasingly be essential for ensuring business continuity.</p>", "<p id=\"Par116\">The findings suggest that farm systems and resources (e.g., landscape, people, infrastructure, plant, livestock) were transformed and improved as preparedness and reactive responses to anticipated and actual climate change stressors. These farm developments (i.e., make-overs) followed a sequence of catalyst events, change incubation, and the integration of adaptive initiatives into the farm system that were regulated by adaptive management. There was a paucity of CCA literature on farmer processes of integrating adaptive initiatives into farming systems. Farm makeovers occurred by integrating multiple domains of self, landscape functioning, infrastructure, equipment technology, and managerial and practice strategies. Adverse hazard and financial conditions often triggered reactive responses, resulting in evolving and larger scale projects of redeveloping the farm. Preparedness responses ranged from one off projects to serial projects that were designed to accommodate future adaptive demands. The catalyst of these responses was autonomous agency (e.g., values), sources of influence (e.g., trusted advisor, peers, groups), and experiential learning and knowledge exchange (e.g., groups).</p>", "<p id=\"Par117\">The acknowledgement of insufficient attention given to developing the resilience of human capital in the farmer sector was a concerning finding. Several farmer studies validate problems of stress and distress arising from climate change (Fleming et al. ##UREF##14##2015##; Hogan et al. ##REF##23924885##2013##; Wheeler et al. ##UREF##41##2018##). The findings that farmers were less inclined to prioritise the importance of building psychological capabilities compared with farm productivity represents a systemic vulnerability. This has the potential to amplify as the frequencies and severity of adverse climate events accelerates. Yet, research programs aimed at building the resilience in the triad of people, landscapes and businesses were underrepresented in agricultural literature.</p>", "<title>Mapping Adaptation Pathways Processes</title>", "<p id=\"Par118\">The findings critically identify a comprehensive map of adaptation as a cyclic learning process with a series of incremental and transformative pathway steps (i.e., <italic>better</italic> and <italic>different</italic>). These dual pathways of <italic>better</italic> and <italic>different</italic> were identified as thinking, deciding, acting, and managing strategies, landscape and resources. This transaction map elaborates those developed by climate science (e.g., dual pathway cycle (Park et al. ##UREF##29##2012##), pathways of decision cycles (Wise et al. ##UREF##42##2014##)), and environmental science frameworks (e.g., HES (Scholz et al. ##UREF##39##2011##a)). Firstly, the transaction map illustrates the conditions that interact with the cyclic processes. These conditions include casual (e.g., growing windows, landscape potential, socio-ecological influence), situational (e.g., macro-risk uncertainty), regulating (e.g., property and financial resources), and socio-cognitive precursors (e.g., values, education) that were not specifically identified in prior models. The findings of Everest (##UREF##12##2020##) identified socio-economic factors, such as land size and education, that had similarity as the influential contributors to the adaptation responses in this cohort of farmers. Secondly, the socio-cognitive agency and consequences variables, and the regulating processes of feedback learning were important inclusions in the map.</p>", "<p id=\"Par119\">The transactional adaptation process accommodates reactive and preparedness responses across multiple scales (i.e., individual, business, community) resulting from stressors and changes in the external environment. Therefore, the cyclic process accounts for stressor induced states of transient dysfunction and resilience processes as described by Norris et al. (##REF##18157631##2008##). The adaptive cycles of problem solving and corrective action, identified by these farmers was consistent with the pathways model of action learning cycles conceptualised by Wise et al. (##UREF##42##2014##). In this study, farmers thought outside the box and created <italic>different</italic> farming systems by synthesising principles and techniques. This transactional map has diagnostic utility for identifying variables at various levels of the system, that have the most potency for strengthening responses at each step of the adaptation cycle. These findings make an important contribution to the broader need for models that articulate farmer decision-making, that are integral in ensuring adaptation to agricultural challenges and opportunities related to climate change (Adelhart Toorop et al., ##UREF##0##2020##). Further research is needed to identify various factors that have the most efficacy as levers in strengthening various stages and levels of adaptive responses.</p>", "<title>Framing Effects of Climate Change</title>", "<p id=\"Par120\">The findings uniquely identify that the changing climate was framed as effects on growing windows and the growth potential of plants and animals. The language frames of growing windows were used to demarcate temporal and climate limits of active plant growth (e.g., crops, pastures). Farmers also framed growth potential to account for beneficial and adverse effects of climate change (e.g., floods, fire, hail, heat stress), growth competition factors (e.g., weeds, pathogen), and growth enhancing factors (e.g., fertilisers). The force field approach has value for identifying which of these beneficial and adverse variables have efficacy for improving growth potential (Burnes and Cooke ##UREF##3##2012##). This cohort of farmers experienced instability in growing season patterns of rainfall and temperature, whilst climate variability extremes were amplified. The frame of climate variability had continued application to these climate change phenomena due the use of learnt interpretive frames. Farmers acknowledged that these chronic phenomena had little hope of restoration, and likely to last indefinitely. However, disruptions faced by well-prepared farmers due to climate change consequences were fewer, they adapted more readily, and sustained viable businesses and continuity of farm systems.</p>", "<title>Implications of These Findings</title>", "<p id=\"Par121\">The findings of the current study have several implications for theory, management, and policy. The study adds to theorical knowledge by developing conceptual maps that capture the interdependent processes of resilience and adaptation. Resilience arises from the management of resources interacting with cyclic processes of transformation, learning and corrective action. The adaptation map illustrates the processes of thinking, deciding, acting and managing that accounts for transformational and incremental forms of adaptation. Furthermore, the map accounts for the precursors of adaptation and interacting factors that transmit and regulate the processes.</p>", "<p id=\"Par122\">The study adds to the knowledge of farm business and management systems. We identified that farm businesses need to be strategically positioned and managed to keep in step with adaptive demands of evolving climate change. The strategic design and management of business models were precursors to transforming business and production systems, and pivotal to capturing the benefits of, and minimising losses of, evolving climatic conditions. The strategic management and viability of all balance sheet assets, including financial, human and natural resources, were markers of resilient farming systems. Farm resilience is crucial for the adaptive preparedness required for counteracting the uncertainty of climate disruptions, through re-positioning of farm businesses. Furthermore, transformative forms of adaptation were often triggered by disruption, implying that salient threats to business continuity motivated adaptive behaviours, in this particular cohort of innovative farmers. Farm make-overs occurred as evolving, scalable, developmental projects that restored and protected landscape functions, improved productivity, and improved management practices. These projects were mediated by experiential learning and active change management, regulated by self and collective efficacy within supportive cultural environments. The study further adds to knowledge that the changing climate can be framed as effects on growing windows and the growth potential of plants and animals. These have management applications as indictors of climate change by tracking changes in growing windows and evaluating changes to growth potential.</p>", "<p id=\"Par123\">Based on the findings, it is recommended that policy makers place greater emphasis on creating policy frameworks that foster adaptation and preparedness. These should emphasise specific programs that build strategic business and financial management capabilities, and psychological resilience.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par125\">This study provides comprehensive maps of managing resilience and adaptation processes, by this specific cohort of farmers. These maps provide important detail about the pathways and variables that are key to the self-righting processes of preparedness and resilience. The findings emphasise that the viability of farm businesses and continuity of the farming system depend on thinking and managing differently. Although previous studies have suggested some of these key adaptation mechanisms, such as the dual pathway model, our map provides a range of contextual conditions and potential transmission and regulating variables. These elements offer policy makers useful information about points of leverage to consider when working with farmers in co-creating programs aimed at broadening the scope of adoption and rate of farmer adaptation.</p>" ]

[ "<p id=\"Par1\">The uncertainty of climate change is a significant challenge prompting Australian farmers to create different thinking and different management systems that ensure sustained farm business viability and continuity, particularly in extreme environments. The purpose of this study was to explore the conditions and adaptive processes for managing farm resilience and cyclic adaptation pathways, in response to climate change. A positive deviance sample of farmers was interviewed, and data was collected from a cohort of twenty-two climate change innovators across Eastern Australia. Grounded theory analysis of data identified three processes and two transactional maps of climate change adaptation, in this under studied farmer cohort. The development of the transactional maps found the resilience and preparedness processes as adaptive learning responses to the stressors of climate change. The processes of managing the business and resources were identified as markers of preparedness and resilience that ensured business viability and continuity. Farmers prepared for climate change through transforming make-over processes as an adaptive learning response to climate challenges. Mapping the cycle of adaptation identified the processes of socio-cognitive agency, learning from feedback and consequences, and contextual variables as critical elements of adaptation. The intervening socio-ecological processes of intelligence gathering and influencing, and socio-cognitive precursors, were found to regulate the adaptation cycle. The cycle was found to have both incremental and transformative transmission processes, and intervening processes of climate and contextual variables. The changing patterns and extremes of climate change were found to impact the growing season, and its potential, as unique variables that demand farm adaptation. Ultimately, this study identified potential points of influence for leveraging preparedness behaviours.</p>", "<title>Keywords</title>" ]

[ "<title>Limitations</title>", "<p id=\"Par124\">The maps do not set out to define a generalised set of outcomes produced by the composite model, rather forms a starting point from which to direct future research. The various types of farms that are represented by the data have adapted and developed resilience and preparedness, which attests to their viable continuity. The farm sectors represented by farmers in the study may not reflect other farm sectors and the interactions between management, resources and situational context.</p>" ]

[ "<title>Appendix</title>", "<p id=\"Par127\">Fig. ##FIG##2##3##</p>", "<title>Author Contributions</title>", "<p>DM wrote the main manuscript text. All authors reviewed the manuscript.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by CAUL and its Member Institutions.</p>", "<title>Compliance with Ethical Standards</title>", "<title>Conflict of Interest</title>", "<p id=\"Par126\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Transactional map of resilient farm continuity. The figure represents the resilience processes of managing farm resources. The transactional map shows the processes and pathways of the resilience and adaptation cycle (steps numbered 1–6). The cycle starts with a farm being impacted by the changing climate that (1) create farm consequences. This is followed the adaptation response sequence of (2) gathering feedback and learning, then (3) gathering intelligence or influencing behaviour. This leads to (4) farmer agency that allows socio-cognitive processing, then (5) to farm decisions, and then (6) applying action strategies that generate further consequences (1), and ongoing cycles of corrective processes. The map focuses on the regulating and transmitting processes between the management and resource elements in the cycle. The map accommodates reactive and proactive forms of adaptation and steps of <italic>better</italic> and <italic>different</italic> forms of thinking, deciding, acting and managing as dual learning pathways (red), i.e. transformative and incremental</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Transactional map of cyclic adaptation. The transactional map shows the processes and pathways of the adaptation cycle (steps numbered 1–6). The cycle starts with a farm being impacted by the changing climate that create (1) farm consequences. This is followed the adaptation response sequence - (2) gathering feedback and learning, then (3) gathering intelligence or influencing behaviour. This leads to (4) farmer agency that allows socio-cognitive processing, then (5) to farm decisions, and then (6) applying action strategies that generate further consequences (1), and ongoing cycles of corrective processes. The process is regulated by intervening management and resource conditions. This map accommodates reactive and proactive forms of adaptation and steps of <italic>better</italic> and <italic>different</italic> forms thinking, deciding, acting and managing as with dual learning pathways (red), incremental and transformational</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Situational farming systems map. The situational map represents the of the processes and interactions of the biophysical and social ecological elements within the farming system. The map shows the relationships between the elements of farm business, growing system, climate, and actors, actants and discourse within the system</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Participant demographics</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>State</th><th/><th>Farm sector</th><th/><th>Age</th><th/><th>Gender</th><th/></tr></thead><tbody><tr><td>NSW</td><td>10</td><td>Sheep</td><td>1</td><td>20–30</td><td>0</td><td>Women</td><td>6</td></tr><tr><td>Victoria</td><td>4</td><td>Cattle</td><td>7</td><td>30–40</td><td>0</td><td>Men</td><td>16</td></tr><tr><td>Queensland</td><td>3</td><td>Sheep-cattle</td><td>1</td><td>40–50</td><td>7</td><td/><td/></tr><tr><td>South Australia</td><td>5</td><td>Crop-sheep</td><td>7</td><td>50–60</td><td>11</td><td/><td/></tr><tr><td/><td/><td>Crop</td><td>4</td><td>60–70</td><td>3</td><td/><td/></tr><tr><td/><td/><td>Dairy</td><td>1</td><td>70–80</td><td>1</td><td/><td/></tr><tr><td/><td/><td>Sugar</td><td>1</td><td/><td/><td/><td/></tr><tr><td>Total</td><td>22</td><td/><td>22</td><td/><td>22</td><td/><td>22</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Changing climate effects on growth windows and potential: categories and subcategories</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Categories</th><th>Subcategories</th><th>Properties</th></tr></thead><tbody><tr><td>Changing climate uncertainty</td><td>Shifting variability patterns</td><td>Changing distribution</td></tr><tr><td/><td/><td>Changing seasonal amounts</td></tr><tr><td/><td/><td>Changing reliability</td></tr><tr><td/><td>Emerging variability extremes</td><td>Intensifying climate conditions</td></tr><tr><td/><td/><td>Creating hazard impacts</td></tr><tr><td>Shifting growing windows</td><td>Growing potential hazards</td><td/></tr><tr><td/><td>Growing season patterns</td><td/></tr><tr><td/><td>Locating growing geo-climate</td><td/></tr><tr><td>Creating growing potential</td><td>Growing potential competition</td><td/></tr><tr><td/><td>Manipulating growing strategies</td><td/></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Managing adaptation and resilience: categories and subcategories</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Categories</th><th>Subcategories</th></tr></thead><tbody><tr><td>Managing business directions</td><td>Building resource capability</td></tr><tr><td>Managing business strategy</td><td>Building human capital</td></tr><tr><td>Managing farm transformation</td><td>Building financial resources</td></tr><tr><td>Managing farm efficiency</td><td>Developing capital resources</td></tr><tr><td/><td>Sustaining operating resources</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Adaptation pathway connected elements</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th colspan=\"2\">Conditions</th><th colspan=\"2\">Adaptation pathway processes</th></tr></thead><tbody><tr><td>Casual</td><td>Changing climate uncertainty</td><td>Pathway categories</td><td>Creating growing potential</td></tr><tr><td/><td>Growing season potential</td><td/><td>Gathering feedback learning</td></tr><tr><td/><td>Healing landscape potential</td><td/><td>Gathering intel selectively</td></tr><tr><td>Contextual</td><td>Shaping uncertain macro-risk</td><td/><td>Directing socio-cognitive agency</td></tr><tr><td/><td/><td/><td>Creating farm decisions</td></tr><tr><td/><td/><td>Action-strategies</td><td>Applying action strategies</td></tr><tr><td>Intervening</td><td>Managing business directions</td><td>Consequences</td><td>Creating farm consequences</td></tr><tr><td/><td>Building resource capability</td><td>Core categories</td><td>Dancing with uncertainty</td></tr><tr><td/><td>Collaborating business team</td><td/><td>Creating viable continuity</td></tr><tr><td/><td>Creating self-determined autonomy</td><td/><td/></tr></tbody></table></table-wrap>" ]

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[ "<disp-quote><p id=\"Par19\"><italic>We had 42 degrees… it’s not a dry heat here…this wasn’t high humidity… we had a 70-knot westerly blowing for three days … I’ve never seen that before… we didn’t have any rain through those three years of winter…That’s never happened before… we had two winters without any frost that’s never happened before. These are subtle. (Cattle farmer, CE Qld)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par21\"><italic>Our biggest growing period is October, but what’s been happening is that the rain’s been cutting out in September. (Cattle farmer, NE Vic.)</italic></p></disp-quote>", "<disp-quote><p id=\"Par23\"><italic>Get massive dumps of rain that last for one month, then it will leave us for 4 to 5 months at a time, so we’ve basically set our grazing business up to harvest that rainfall event. (Mixed farmer, CW NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par25\"><italic>[fire storm] …Like a really big round bale just rolling towards his house… it was making an awful noise… when this thing hit the house, the house just exploded…So if you were in the wrong place at the wrong time. (Cropping district, SA)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par27\"><italic>The number of hot days in Northern Victoria over 42 degrees…1980s there was one day and the nineties…about five days… early two thousands it was 10 days…2010 to 2020, it was up to 16 to 25 days in heading towards forty. (Dairy farmer, Vic.)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par29\"><italic>I’ve noticed with our creek… floods are getting higher over time…had a storm here that lasted for 14</italic> <italic>h…we’re breaking records over time….more extreme events as time goes on … and the water came up into the second story….15</italic> <italic>min to get out of the place. It eclipsed the last record in 1990 by 4.6 metres…totally engulfed our sons house, I was a bit in denial… It’s just unbelievable. (Cattle farmer, Queensland)</italic></p></disp-quote>", "<disp-quote><p id=\"Par31\"><italic>[rainfall]… events where we didn’t really get a big flood…water stayed there for fourteen days…the ability to drain the property in a hurry is crucial. That’s, the main hazard we’re dealing with…we’ve got to deal with the flooding…biggest risk factor is sea level rise. (Sugar-cane farmer, N NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par35\"><italic>Modelling of my farm is done to get water [heavy rainfall episodes] off and, in the dry times retain moisture. (Sugar-cane farmer NNSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par37\"><italic>‘I wanted to go back to a simplified farming and not have the complexity of rations and feed systems and irrigation and heat in Northern Victoria [relocated to Southern Victoria]’ (Dairy farmer, Victoria)</italic></p></disp-quote>", "<disp-quote><p id=\"Par39\"><italic>Like a formula one racing car driver, … make a bad decision…miss a corner, you can tumble…still be safe and sound in your shell…. parts of your business that you can drop off, …. and you’re going to be there to rebuild … plugin options to go on…business model that fits in with climate variability that matches stocking rate to carrying capacity. (Sheep-cattle farmer, SW NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par41\"><italic>Restructured business around that rainfall uncertainty, rather than planning around traditional wet seasons…success planning around individual rainfall events regardless of the time of the year they come</italic>. <italic>(Mixed farmer CW NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par43\"><italic>[planned] business within our core breeding stock…25 to 30% of our total stock, because if its anymore than that [in dry years], we’re going to have to sell our core breeders … got to map out all these options and these plug in options to rebuild up to a hundred percent or 120%, depending on the season. (Sheep-cattle farmer, SW NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par45\"><italic>We use an outside consultant…who provides some input through MaiaGrazing, by using a cloud based product…cause we have just bought some stock…so we put together a feed budget to work out if we might have excess. (Sheep-cattle farmer, SW NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par47\"><italic>How do you manage what everybody calls risk, I call variability…things aren’t always good, or they aren’t always bad, they’re somewhere in between, the climate component of that fits in there really well. (Grain farmer, SA)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par49\"><italic>[climate change] increased the risk obviously… put out lot of money with cropping…we reduced the cropping, reduced back 50% or less, and the sheep which are more consistent….now that they’re worth something. (Mixed farmer, SE NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par51\"><italic>When you get summer storms, which we’re getting more of, so we’re trying to keep as much stubble as we can [minimise run-off]…graze our stubbles briefly…if there’s not enough pasture cover, we often lock them up [sheep]…try and keep 70% ground cover. We cut silage in the good years and stick underground, so we feed that out to sheep in confinement yards with our silage heaps next door…use the silage to feed the ewes…gives more room for the lambs on the lucerne. (Mixed farmer, SE NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par54\"><italic>Move to something that’s shorn twice a year to manage the vegetation issues…there is less dust in them and less vegetable matter… don’t need to treat for lice or fly..they just don’t get into them with that skin type. (Sheep farmer, Riverina NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par56\"><italic>Cropping systems evolved by packaging strategies such as optimising ground cover, summer weed control, soil moisture testing, calendar based early planting, press wheel creating good seed soil contact and water harvesting contours, and varieties with temperature sensitive flowering. (Cropping farmers, SA)</italic></p></disp-quote>", "<disp-quote><p id=\"Par58\"><italic>We’ve invested in drought lots…got three of those confinements, so we can nearly lock up all our ewes and confine them for short periods of time…if there’s not enough cover. (Mixed farmer, SE NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par60\"><italic>‘I’ve gone from trees [tree corridors] to sheep [different genetics- breed type] restablishing perennial pastures [different grazing management]. I tend to get really focused on one thing…so now I think probably soil is probably going to be my thing… tend to focus on things, ‘get that going, get that going’ and meanwhile everything else is going, keeps going’ (Sheep farmer, Riverina NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par62\"><italic>We refenced the property…from two and a half thousand acres in a paddock …refenced those into five or six paddocks. There was 30,000</italic> <italic>acres…massive electric fencing and rewatering…did trial [large mob rotational grazing system]…realized that what we were seeing was working perfectly’ (Sheep-cattle farmer SE NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par64\"><italic>Crystal clear in my mind that for me to keep milking cows, it wasn’t going to be there and we had to move…get a farm that was secure, rain fed, didn’t rely on irrigation, and nine years out of ten…going to have a good season…pretty much the criteria. (Dairy farmer, Vic.)</italic></p></disp-quote>", "<disp-quote><p id=\"Par67\"><italic>The integration of the different system of grazing management was an on-going problem solving and adjustment over many decision cycles… finding the stocking rate that matched the carrying capacity, and livestock type to match the plant type [C3, C4], and discovering the optimum mobs size, plant leaf area as a signal to move on and best pasture rest periods. (Sheep cattle farmer, SW NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par69\"><italic>We had to find this weakest link and you work on your weakest link. So if your weakest link is no grass or no water or not enough fences…your weakest link goes higher up the scale…process of elimination…we went out and learnt about it…we made a plan. (Cattle farmer, SE NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par71\"><italic>Working with NSW Ag senior soil person and a PhD ….[explain sequeration processes]…it’s that carbon and nitrogen ratio, and activating microbes.. a symbiotic relationship, the plant takes it in carbon through the leave, it takes it down and changes carbon nutrients …..exudates from the roots of the sugar cane…works for soybeans….sprayed the soybeans with another product..it doubled the production of beans. (Sugar-cane farmer, N NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par74\"><italic>Our biggest capital investment that we have is our land…need to critically look after our land…our biggest risk. If we don’t look after our land, it’s no longer the income producing asset once it was, we’ve let us and our business down. (Sheep-cattle farmer, SW NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par76\"><italic>We’d laser levelled the whole farm for drainage…[increasing drainage pumping capacity.. this one we’ll be able to deal with four inches 150</italic> <italic>mm rainfall per day … pump in twenty-four hours, at the moment its taking a couple of days. (Sugar cane farmer, NNSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par78\"><italic>Recently got into precision ag….they develop a prescription for us…their IT bloke..gets the information from our agronomist…do comprehensive soil tests of each zone…paddock is divided into zones….works out what fertilizer rate goes on different zones, so the fertilizer rate changes….variable rate fertilizer… all done automatically…five, six years now. (Cropping-sheep farmer, SE NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par80\"><italic>Started to change them into dual-purpose animal… lifted weaning percentage from 90% to 130%. …17 micron as lambs, 20 micron as adults, fine wool merinos, .. twinning conception to round 65, 70%… joined 400 ewe lambs at six and a half months old… two thirds of those have conceived and 20% have got twins…come from, 75% lambing, wrinkly getting fly struck classic merinos to what we’ve got now, shorn twice a year.. it’s quite, quite amazing… a huge turnaround. (Sheep farmer, Riverina NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par82\"><italic>So how do you define resilience…..I’d argue [many farmers] are still leaving something on the table, in terms of our ability…to be socially strong in the face of adversity… the game that we’re involved in…an incredibly difficult one… we face stresses all the time…how do we handle that? …really important part of what we do…mental resilience in the face of adversity, is a thing that we don’t necessarily handle very well…all at different stages with that process. (Grain farmer, Mid-North SA)</italic></p></disp-quote>", "<disp-quote><p id=\"Par85\"><italic>‘We have the market rate facility… gives us 18 months worth of funding … try to remain flexible within our program…sell off some stock if you think you need to, and know which stock that you would need to sell’ (Cattle farmer, NE Vic.)</italic></p></disp-quote>", "<disp-quote><p id=\"Par87\"><italic>We’ve got a bit of money invested with a financial advisor…instead of paying tax, you put the money into FMD [farm management deposits]… and I’ll pull some of that out this year because production was a bit low. (Sugar cane farmer, NE NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par89\"><italic>After we had a really good year…we did really well. I looked at doing a FMD [farm management deposit]…decided to invest [surplus revenue] back into our pastures… figured if I could grow more grass, and improve my soil nutrient levels…would pay me back over a few years. So that was my choice. (Cattle farmer, NE Vic.)</italic></p></disp-quote>", "<disp-quote><p id=\"Par94\"><italic>Let’s keep making decisions where we have got control and let’s not worry about things we don’t have control over. But lets keep making sure we understand and make decisions, good decisions, where possible around the areas that we can control. (Sheep-cattle farmer, SW NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par96\"><italic>If we want genuine biodiversity, we’ve got to put in place, a diversity of management that might be a diversity of species of animals, a diversity of classes of animals and a diversity of grazing times of grazing intensity. (Sheep-cattle farmer, SW NSW</italic>).</p></disp-quote>", "<disp-quote><p id=\"Par98\"><italic>You’ve got to make sure you make decisions that don’t have too much of a negative impact on your business… you’ve got to keep that intact… if you can articulate …we’re gonna be selling down stock and you might have a stock agent saying it’s the wrong time to sell…. if you can adequately explain how you arrived at the decision, why you arrived at the decision. (Sheep-cattle farmer, SW NSW</italic>).</p></disp-quote>", "<disp-quote><p id=\"Par100\"><italic>Then this is a big deal, decided …not putting any crop in, like this is mad because we were getting rain…normal autumn… I didn’t even sow anything…I just parked the machinery in the shed…and that year I think I might one of the best, like profit margins, I’d ever made. (Riverina NSW sheep farmer)</italic></p></disp-quote>", "<disp-quote><p id=\"Par102\"><italic>Work I’ve been doing … for the last 20 years..been able to build the to soil carbon by 3%… capturing around nine tons per hectare per year…spray [crop residue] with five kilograms of urea after harvest… changes the carbon to nitrogen balance…but not to stop the microbes working… if you don’t have a microbial population, you don’t grow crops. (Sugar-cane farmer, N NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par104\"><italic>Able to communicate, monitor, this is going this direction,…how do we turn it around if it is going in the wrong direction. What do we need to do? …so all those questions, normally a diversity of management can resolve a lot of those issues. In any given landscape, there’s areas that are doing well and areas that are doing poorly…give it a diversity of management and over time you cater for a diversity of soil types, landscape types. (Sheep-cattle farmer, SW NSW)</italic>.</p></disp-quote>", "<disp-quote><p id=\"Par106\"><italic>We’ve got 50 tonne of sulphuric acid per hectare oxidized in the landscape…We’re keeping acid down… it’s an ecosystem service…[developed drainage-land management system]…something we had to do to stay in business…now accepted as world’s best practice for growing sugar cane in acid sulphate soils. (Sugar-cane farmer, N NSW)</italic></p></disp-quote>", "<disp-quote><p id=\"Par108\"><italic>Because I’ve got the pumps, my average was higher in the wet years than anybody else…..it was probably 40 [district average], I was 60, at the moment its 115…[cane yield. (Sugar-cane farmer, N NSW)</italic>.</p></disp-quote>" ]

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[ "<title>Introduction</title>", "<p id=\"Par12\">To achieve long-term training adaptations to strength exercise, repair of muscle damage, and restructuring of muscle tissue after acute exercise is essential (Damas et al. ##REF##29282529##2018##). These processes are tightly regulated by a controlled and coordinated inflammatory response, of which cytokines are one of the main mediators (Freidenreich and Volek ##REF##22876721##2012##; Pedersen and Hoffman-Goetz ##REF##10893431##2000##). Generally, from previous research it is known that a local inflammatory response is generated immediately after muscle loading occurs and pro-inflammatory cytokines, such as interleukin 1 beta (IL-1β), interleukin 1 alpha (IL-1α), IL-6 and tumour necrosis factor alpha (TNF-α) are released to initiate muscle remodulation processes (Peake et al. ##REF##25826432##2015##). However, to avoid an excessive pro-inflammatory response, anti-inflammatory cytokines such as interleukin 1 receptor antagonist (IL-1ra), IL-10, IL-4 and tumour growth factor beta (TGF-β) are released further on in the repair process (Petersen and Pedersen ##REF##15772055##2005##).</p>", "<p id=\"Par13\">While the general inflammatory response seems to be well characterised in men (Ihalainen et al. ##REF##25145982##2014##; Izquierdo et al. ##REF##19649649##2009##; Suzuki et al. ##REF##32962110##2020##), less is known on the extent of which hormonal fluctuations in women may impact these responses, especially following acute strength exercise. Inflammatory responses in women distinctly vary to men; for example, evidence suggests that women produce higher levels of antibodies and a larger secretion of inflammatory mediators to external pathogens (Klein and Flanagan ##REF##27546235##2016##). Likely this is at least in part due to differences in sex hormones, with women experiencing regular fluctuations of the sex hormones oestrogen and progesterone throughout the menstrual cycle. The receptors of these hormones are expressed on a variety of immune cells, therefore, indicating that oestrogen and progesterone also play a role in regulating inflammatory responses and the secretion of cytokines from these cells (Kovats ##UREF##3##2015##; Straub ##REF##17640948##2007##). In the early follicular phase, low oestrogen concentrations and progesterone concentrations may provoke a pro-inflammatory environment, as these have been shown to induce T helper type 1 (Th1) responses and the release of cytokines, such as IL-1β and TNF-α (Salem ##REF##15032646##2004##; Whitcomb et al. ##REF##24581581##2014##). In contrast, high oestrogen concentrations, as experienced during the late follicular phase and luteal phase, have been discussed to have a protective effect on inflammatory responses and lead to a stronger T helper type 2 (Th2) response (Klein and Flanagan ##REF##27546235##2016##; Straub ##REF##17640948##2007##). Therefore, it is likely that hormonal fluctuations may influence the inflammatory response to strength exercise.</p>", "<p id=\"Par14\">The use of oral contraceptives further adds complication to understanding the influence of hormonal fluctuations in women on the inflammatory responses to strength exercise. Women using oral contraceptives do not experience naturally cycling hormonal concentrations, as circulating hormone concentrations are determined by exogenous hormones. In the active pill phase, endogenous oestrogen and progesterone concentrations are suppressed by the daily dose of exogenous hormones. During the pill-free interval, there is a withdrawal of exogenous oestrogen and progesterone, which lead to slight increase of endogenous oestrogen concentrations throughout this phase, however, concentrations of oestrogen and progesterone remain low (De Leo et al. ##REF##27307386##2016##). Independent of performing strength exercise, studies have shown oral contraceptives to have an effect on the resting inflammatory status of women. For example, an increased concentration of IL-6 and TNF-α was found in the pill-free interval of young women using oral contraceptives compared to naturally cycling women (Eagan et al. ##REF##34138651##2021##; Hinton et al. ##REF##24259996##2006##), indicating a chronic effect of oral contraceptive use beyond the acute daily dose of exogenous hormones. Furthermore, increased concentrations of high-sensitive C-reactive protein (hs-CRP) and markers of oxidative stress were found in oral contraceptive users, indicating a status of low-grade inflammation in these women (Cauci et al. ##REF##27084393##2017##, ##UREF##1##2021##; Quinn et al. ##REF##34106325##2021##), which has been speculated to predispose oral contraceptive users to a stronger exercise-induced inflammatory response. In the context of exercise, differences in the inflammatory response after acute cycling exercise (90 min at 65% of peak power) have been shown (Timmons et al. ##REF##15879167##2005##). In this study, women using oral contraceptives showed a reduced IL-6 response in the low hormone phase compared to women in the follicular phase of a natural menstrual cycle. However, research on inflammatory responses in oral contraceptive users and naturally cycling women is limited and results have also been contradictory in some cases, potentially also due to limited control, definition and verification of the cycle phases and oral contraceptives investigated. Furthermore, how the response to acute strength exercise compares, largely remains to be investigated.</p>", "<p id=\"Par15\">As the number of female participants in sports has been rising in recent years and further approximately 50% of female athletes are using oral contraceptives (Martin et al. ##REF##29283683##2018##), better characterising the inflammatory response to strength exercise in women is vital. Therefore, the aim of this study was to analyse a number of cytokines (IL-1β, IL-1ra, IL-6, IL-8 and IL-10), which have previously been shown to respond to acute exercise and play a role in regulating muscular regeneration (Peake et al. ##REF##25826432##2015##; Pedersen and Hoffman-Goetz ##REF##10893431##2000##), in response to acute strength exercise between naturally cycling women and women using oral contraceptives. To enable comparison between these groups, women were either tested in the early follicular phase of the menstrual cycle, where oestradiol and progesterone concentrations are generally low, or in the pill-free interval, where there is no acute intake of exogenous hormones.</p>" ]

[ "<title>Methods</title>", "<title>Experimental design</title>", "<p id=\"Par16\">The study is a secondary analysis of a previous study investigating the effects of acute strength exercise in naturally cycling women (MC) and oral contraceptive users (OC) on steroid hormones and the tryptophan metabolism (Umlauff et al. ##REF##33555830##2021##). The study consisted of a maximal strength test and a strength training session in the low-hormone phase in the first days of the respective cycle, i.e., in the early follicular phase of the MC group and the pill-free interval of the OC group (see Fig. ##FIG##0##1##). The menstrual cycle phase was determined by the onset of menstrual bleeding. Firstly, the one-repetition maximum (1RM) of participants in the deep back squat was determined with a maximal strength test. This test was performed on days 1–3 after the onset of menstruation (MC) or the withdrawal bleed (OC). After 48 to 72 h recovery, a strength training session was performed. This was performed between days 3–6 of the respective cycle. The strength training session consisted of a warm-up on a cycle ergometer and 4 × 10 repetitions at 70% 1RM in the deep back squat. Blood sampling and explosive strength testing was performed before (pre), directly after (post) and 24 h after the training session (post₂₄). Participants arrived in a fasted state and rested on a chair for 5 min before the first blood sampling. They then proceeded to have a light breakfast at least 15 min prior to starting the warm-up. Similarly, participants also arrived in a fasted stated for the post₂₄ testing. Testing was performed at similar times of the day (± 1 h) and participants were instructed to refrain from alcohol and any intense physical activity at least 24 h prior to testing.</p>", "<title>Participants</title>", "<p id=\"Par17\">Twenty-four healthy women with strength training experience, defined by 1RM in the back-squat between 0.8 and 1.5-times body mass and at least two strength training sessions per week for a minimum of two years, originally participated in the study. Three women using contraceptives had to be excluded due to timing of testing, insufficient maximal strength (1RM &lt; 0.8 × body mass) and abnormal cortisol levels, therefore, 21 women were included in the final analysis. Women belonged to either one of two groups: (1) a group (MC; <italic>n</italic> = 13, age: 24 ± 4 years, weekly strength training: 4.3 ± 1.7 h) with a regular natural menstrual cycle (± 2 days) and no use of oral contraceptives (last use &gt; 8 months) or (2) a contraceptive group (OC; <italic>n</italic> = 8, age: 22 ± 3 years, weekly strength training: 4.5 ± 1.9 h) with the regular use (&gt; 9 months) of a monophasic combined pill (21 + 7 intake scheme with 30 µg ethinyloestradiol + 20 µg chlormadinone or dienogest). Smokers, women experiencing menstrual cycle irregularities (&gt; ± 2 days) or amenorrhea in the last 12 months or women using emergency contraceptives or other hormone-affecting medication in the last 3 months were excluded from participating in this study. Before commencing with the study, all participants were informed of possible risks and provided written consent. The study was approved by the German Sport University Institutional Review Board (020/2019) and also conducted in accordance with the Declaration of Helsinki and its later amendments. Recruitment and testing were performed by different study personnel, therefore the person performing data analysis was blinded.</p>", "<title>Procedures</title>", "<p id=\"Par18\"><italic>Maximal strength testing</italic> To determine the 1RM of participants in the back squat, a maximal strength test was performed using a Smith Machine (Gym80 international GmbH, Gelsenkirchen, Germany). For the warm-up, 5 min cycling on a cycle ergometer (1.5 W kg⁻¹), unweighted squat exercise and six repetitions with a guided 22 kg bar were performed. Thereafter, the 1RM was determined using a force–velocity based approach. Participants were asked to descend their hips below their knees and rest periods between sets were standardised to 2 min. A more detailed description of testing and participant characteristics can be found in Umlauff et al. ##REF##33555830##2021##.</p>", "<p id=\"Par19\"><italic>Explosive strength testing</italic> Indices of neuromuscular fatigue were assessed by using an explosive strength protocol, which consisted of three repetitions at 60% 1RM. Participants were instructed to perform a slow and controlled eccentric phase and the following concentric phase explosively and as fast as possible. Mean propulsive velocity (MPV) was recorded for each repetition using T-FORCE Dynamic Measurement System (ERGOTECH Consulting, S.L., Pamplona, Spain) and averaged for each sampling timepoint.</p>", "<p id=\"Par20\"><italic>Strength training session.</italic> Between day 3 and 6 of the cycle, a strength training session was performed using a Smith Machine. A similar warm-up to maximal strength testing was performed, which was followed by 4 × 10 repetitions at 70% 1RM in the back squat with 2 min rest between sets. This protocol was based on a protocol (3 × 12 repetitions at 70% 1RM), which had previously been shown to produce a marked physiological response in men (Pareja-Blanco et al. ##REF##26970332##2017##). As women show increased time to task failure and faster neuromuscular recovery, we modified the protocol to include 4 sets and in pilot testing found this to be sufficient (Hunter ##REF##19550202##2009##). Participants performed the exercise with constant velocity in both concentric and eccentric phases and a two-second pause between each repetition. Study personnel provided assistance, if participants were unable to perform the concentric phase of the squat, so that all participants had an identical number of repetitions.</p>", "<p id=\"Par21\"><italic>Blood sampling and analysis</italic> Blood samples were collected from the antecubital vein into heparin-coated serum containers, for pre and post₂₄ after 5 min of rest in a sitting position and post directly after testing ended. After clotting for 10 min, samples were centrifuged at 1900 g for 10 min. Serum was aliquoted and stored at -80 °C for further analysis. Cytokine concentrations were measured by enzyme-linked immunosorbent assay (ELISA) for IL-1β (<italic>IL-1beta Human ELISA Kit, BMS224-2</italic>, <italic>Invitrogen, ThermoFisher Scientific, Massachusetts, USA)</italic>, IL-1ra (<italic>IL1RA Human ELISA Kit, KAC1181</italic>, <italic>Invitrogen, ThermoFisher Scientific, Massachusetts, USA)</italic>, IL-6 (<italic>IL-6 High Sensitivity Human ELISA Kit, BMS213HS, Invitrogen, ThermoFisher Scientific, Massachusetts, USA</italic>), IL-8 (<italic>High Sensitive ELISA Kit for IL-8, HEA080Hu, Cloud Clone Corp., Katy, USA)</italic> and IL-10 (<italic>IL-10 High Sensitivity Human ELISA Kit, BMS215HS, Invitrogen, ThermoFisher Scientific, Massachusetts, USA</italic>). Samples were analysed in duplicate. The intra-assay CV were as follows: IL-1β—5.0%, IL-1ra—6.5%, IL-6—6.2%, IL-8—8.8%, IL-10—6.4%. One data point for IL-1β and two data points for IL-6 were outside the sensitivity limits, so the corresponding participants were not included in the analysis for the respective cytokines. Oestradiol and cortisol were analysed previously (Umlauff et al. ##REF##33555830##2021##).</p>", "<title>Statistical analysis</title>", "<p id=\"Par22\">An a-priori power analysis was performed for the original study using G*Power 3 with an expected medium effect size of 0.3, alpha = 0.5 and power = 0.8 and projected a participant number of <italic>n</italic> = 20 (Umlauff et al. ##REF##33555830##2021##). Data were analysed using SPSS version 29.0 (SPSS, IBM Statistics, New York, US). Firstly, normality and homoscedasticity were checked by using the Shapiro–Wilk Test and visually inspecting residual histograms, residual plots and Q-Q plots. A log-transformation was used to achieve normality for non-normally distributed data (IL-1β, IL-6). Baseline differences were analysed by using a two-tailed independent t-tests. For time and interaction effects, a mixed repeated measure analysis of variance (ANOVA) was performed with Bonferroni correction for post-hoc tests. Measurement timepoints for the cytokines were defined as within-group variables (i.e., pre, post and post₂₄) and the group (OC, MC) was defined as the between-group variable. Effect sizes for main effects of the ANOVA are reported as partial η² and for the comparison between time-points Hedges g was calculated. To assess associations between the parameters (oestradiol, cortisol, IL-1β, IL-1ra, IL-6, IL-8, IL-10 and MPV) across all conditions Spearman’s rank correlation coefficient was calculated. For all tests, statistical significance was accepted at <italic>p</italic> ≤ 0.05. All data are presented as mean ± standard deviation (SD). For absolute concentrations of oestradiol, cortisol and cytokines 95% confidence intervals (CI) were also calculated.</p>" ]

[ "<title>Results</title>", "<title>Participant characteristics</title>", "<p id=\"Par24\">Participants did not differ in age, height, weight, BMI, 1RM or training experience (Table ##TAB##0##1##, all p &gt; 0.05).</p>", "<title>Cytokines</title>", "<p id=\"Par25\">Concentrations of cytokines throughout the strength training sessions are presented in Table ##TAB##1##2##. There were no baseline differences for all cytokines between the MC and OC group (p &gt; 0.05). For IL-1ra, there was a main effect for time in the OC group only (<italic>p</italic> = 0.027, <italic>η</italic>² = 0.174). In the OC group, concentrations of IL-1ra increased by + 51.1 ± 59.4% from pre to post (<italic>p</italic> = 0.189, <italic>g</italic> = 0.693) and statistically decreased by -20.5 ± 13.5% from post to post₂₄ (p = 0.011, <italic>g</italic> = 1.348) (Fig. ##FIG##1##2##C). There were no statistical changes in the MC group (all p &gt; 0.05) and there was no main interaction effect (<italic>p</italic> = 0.360, <italic>η</italic>² = 0.052). For IL-1β, there was no main effect for time (<italic>p</italic> = 0.216, <italic>η</italic>² = 0.084), however there was an interaction effect (<italic>p</italic> = 0.038, <italic>η</italic>² = 0.200). At post₂₄ concentrations of IL-1β were statistically lower in the OC group compared to MC (<italic>p</italic> = 0.05, <italic>η</italic>² = 0.193). The OC group showed a main effect for time (<italic>p</italic> = 0.033, <italic>η</italic>² = 0.435), with concentrations of IL-1β not statistically changed from pre to post (<italic>p</italic> = 1.000) but statistically decreased by – 39.6 ± 23.0% from post to post₂₄ (<italic>p</italic> = 0.044, <italic>g</italic> = 0.971) (Fig. ##FIG##1##2##B). There was no main effect for IL-6 for time (<italic>p</italic> = 0.599, <italic>η</italic>² = 0.030) or group (<italic>p</italic> = 0.723, <italic>η</italic>² = 0.019) (Fig. ##FIG##1##2##D). Similarly, for IL-10 there was no main effect for time (<italic>p</italic> = 0.489, <italic>η</italic>² = 0.039) or group (<italic>p</italic> = 0.269, <italic>η</italic>² = 0.070) (Fig. ##FIG##1##2##F). For IL-8, there was a main effect for time across both groups (<italic>p</italic> &lt; 0.001, <italic>η</italic>² = 0.358) but no interaction effect (p = 0.921, η² = 0.004). Concentrations of IL-8 statistically increased by + 66.6 ± 96.3% from post to post₂₄ across both groups (<italic>p</italic> = 0.004).</p>", "<title>Explosive strength, oestradiol and cortisol</title>", "<p id=\"Par26\">Detailed results for these parameters have previously been published (Umlauff et al. ##REF##33555830##2021##). Briefly, there were no statistical baseline differences between groups for oestradiol (<italic>p</italic> = 0.083) and MPV (<italic>p</italic> = 0.068). Cortisol concentrations at baseline were statistically increased in the OC compared to the MC group (<italic>p</italic> &lt; 0.001, <italic>η</italic>² = 0.759). Oestradiol concentrations are in line with the early follicular phase of the MC group. MPV and oestradiol did not statistically change throughout the intervention (oestradiol: <italic>p</italic> = 0.307, <italic>η</italic>² = 0.060, MPV: <italic>p</italic> = 0.075, <italic>η</italic>² = 0.127) and there were no between group differences. Cortisol showed a main effect for time (<italic>p</italic> = 0.002, <italic>η</italic>² = 0.325) but no interaction effect (<italic>p</italic> = 0.570, <italic>η</italic>² = 0.024).</p>", "<title>Pooled associations between cytokines, oestradiol, cortisol and explosive strength</title>", "<p id=\"Par27\">There were no associations between cytokine concentrations and 1RM, oestradiol, and cortisol concentrations (<italic>p</italic> &gt; 0.05). However, there were some associations between single cytokines. At post and post₂₄ there was an association between concentrations of IL-10 and IL-6 (<italic>r</italic> = 0.487, <italic>p</italic> = 0.004, <italic>r</italic> = 0.651, <italic>p</italic> = 0.003, respectively) across all subjects. Additionally, at post₂₄, changes in IL-10 were associated with changes in IL-1β (<italic>r</italic> = 0.472, <italic>p</italic> = 0.041) and IL-1ra (<italic>r</italic> = 0.514, <italic>p</italic> = 0.02) and changes in IL-8 were associated with changes in IL-1ra (<italic>r</italic> = – 0.495, <italic>p</italic> = 0.018).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par28\">The aim of this study was to compare the response of cytokines to acute strength exercise between naturally cycling women in the early follicular phase and oral contraceptive users in the pill-free interval. At baseline, we found no differences between these groups in any of the cytokines. In response to strength exercise, IL-6 and IL-10 remained unaltered in the two groups. For IL-8, similar responses were found across both groups, with concentrations increasing from post to post₂₄. On the other hand, IL-1β and IL-1ra showed differential regulation between groups, with concentrations of IL-1β and IL-1ra decreasing only in the OC group from post to post₂₄. IL-1β also showed a statistical between group difference, with concentrations differing statistically at post₂₄.</p>", "<p id=\"Par29\">When looking at baseline differences of cytokines, results from previous studies have been conflicting. Some studies have proposed a reduction of inflammatory status with OC use, for example through reductions of neutrophils and IL-8 (Giraldo et al. ##REF##18401558##2008##), while others have found an increased inflammatory status with higher concentrations of CRP and TNF-α (Cauci et al. ##REF##27084393##2017##; Rickenlund et al. ##REF##15769986##2005##). However, comparison between studies is difficult, as pill and cycle phases are often not described or accounted for. Nevertheless, some well-controlled studies exist. In contrast to our results, two studies found IL-6 concentrations to be decreased in the pill-free interval compared to the early follicular phase (Eagan et al. ##REF##34138651##2021##; Souter et al. ##REF##15866588##2005##), while we found no difference between the pill-free interval and the early follicular phase in this study. Participants in these studies were described only as healthy, whereas participants in this current study were resistance trained and participating in regular physical activity. As regular exercise promotes an anti-inflammatory environment, this may be an explanation for the lack of difference between the two groups in our study. Similarly, Larsen et al. (##REF##32038307##2020##) found no difference in any cytokines, including IL-6, between naturally cycling elite athletes and those using oral contraceptives, although menstrual cycle phases were mixed (Larsen et al. ##REF##32038307##2020##). For the other cytokines, there are less well controlled studies comparing baseline concentrations between OC users and naturally cycling women. Giraldo et al. (##REF##18401558##2008##) showed decreased IL-8 concentrations in OC users compared to naturally cycling women (Giraldo et al. ##REF##18401558##2008##), while others found no difference (Larsen et al. ##REF##29769824##2018##; Welsh et al. ##REF##18371109##2008##). For IL-1β, IL-1ra, and IL-10, studies have shown no baseline differences, which is in line with our results (Cullup et al. ##REF##15270852##2004##; Michel et al. ##REF##25763784##2015##; Sikora et al. ##REF##26315533##2015##).</p>", "<p id=\"Par30\">Furthermore, the lack of information regarding the composition of the oral contraceptive used also limits interpretation of previous results, as the spectrum of synthetic progestins vary in their effects regarding estrogenic, androgenic and progestogenic activity, possibly masking unambiguous results. Although the effect of different progestins in oral contraceptives has not yet been investigated on cytokines, studies have for example shown differing effects on adipokines (Di Carlo et al. ##REF##21645895##2011##; El-Haggar and Mostafa ##REF##25539793##2015##) and natural killer cells (Auerbach et al. ##REF##12095495##2002##), dependent on the composition of the oral contraceptive. Therefore, different synthetic progestins could influence the release of cytokines differently. However, the oral contraceptives used in the present study were limited to formulations containing chlormadinone acetate or dienogest as the progestin component only. Both have strong antiandrogenic and low to no estrogenic activity (Bouchard ##UREF##0##2005##; Prez-Campos ##REF##20394455##2010##), therefore allowing for a clearer interpretation of the results.</p>", "<p id=\"Par31\">Changes in cytokines in response to the strength exercise were mainly seen 24 h after exercise, in the recovery period. However, only certain cytokines were regulated and a difference in regulation between OC users and naturally cycling women was found for IL-1β and IL-1ra only. In contrast, after a three-stage cycling trial (total exercise duration: 52.5 min), no statistical change was detected in IL-1β and IL-1ra concentrations and no difference was found between OC users and naturally cycling women (Larsen et al. ##REF##29769824##2018##). However, blood was only sampled directly post exercise in the aforementioned study, while in this current study changes were mainly found 24-h post exercise. More specifically, in this study, while not statistically significant but showing an intermediate effect (<italic>g</italic> = 0.693), OC users showed an increase in IL-1ra directly after strength exercise (post: + 51 ± 59%) and also showed a statistical decrease at post₂₄ with a concurrent decrease in IL-1β. These two cytokines are antagonistic in their activity, with IL-1β being released in response to muscle damage to facilitate a pro-inflammatory response for muscle repair. IL-1ra has anti-inflammatory activity and can decrease IL-1β activity (J. E. Sims and Smith ##REF##20081871##2010##). Therefore, it could be hypothesised that the antagonistic properties of IL-1ra are responsible for the significant decrease in IL-1β in OC users at post₂₄. However, statistical associations were not found between IL-1ra and IL-1β (i.e., no significant correlations at any timepoints or in any group) and therefore are not able to support this interaction.</p>", "<p id=\"Par32\">Regarding endogenous oestradiol concentrations, no differences were found between groups and concentrations were low, which is in line with previous findings. However, when looking at the groups separately, MC participants in the early follicular phase are experiencing the lowest hormone concentrations of the cycle. In contrast, it is known that in OC users, endogenous concentrations of oestradiol increase slightly throughout the pill-free interval, as exogenous hormones are not suppressing the release of endogenous oestrogen in the pill-free interval. Therefore, while objectively endogenous concentrations were similar, OC users and MC users are experiencing the highest and lowest concentrations of their cycle, respectively. This could partly explain the differing response between the two groups in IL-1β and IL-1ra. Indeed, oestrogen has been shown to reduce the mRNA synthesis and secretion of IL-1β and IL-1ra in monocytes in in vitro experiments (Morishita et al. ##REF##10440637##1999##; Polan et al. ##REF##2584355##1989##) and also postmenopausal women treated with oestrogen replacement therapy show a reduction in IL-1β and IL-1ra (Pacifici et al. ##REF##8077304##1993##). Furthermore, high oestrogen and progesterone concentrations have also been found to suppress the release of IL-6 and IL-1ß, while low oestrogens concentrations can stimulate this release (Klein and Flanagan ##REF##27546235##2016##; Straub ##REF##17640948##2007##). Therefore, there may be a differing dependency on endogenous oestrogen concentrations as well as chronic oestrogen exposure between oral contraceptive users and naturally cycling women (Campesi et al. ##REF##22284681##2012##). This could be an explanation for the decrease of IL-1β and IL-1ra after 24 h in response to exercise in the OC group only, but it is speculative and further investigations are necessary. Similarly, changes in oestrogen receptor sensitivity or binding proteins should be investigated. For example it is known that oral contraceptive users show increased concentrations of sex-hormone binding globulin (Wiegratz et al. ##REF##12521654##2003##), which has been shown to have an inverse relationship with pro-inflammatory cytokines and anti-inflammatory effects on adipocytes and macrophages (Maggio et al. ##REF##21239514##2011##; Yamazaki et al. ##REF##30046278##2018##). However, to assess this was beyond the scope of this study.</p>", "<p id=\"Par33\">Interestingly, both groups showed a similar response to the strength exercise in IL-8, which increased by + 67 ± 96% 24 h after the strength exercise. IL-8 can be transiently released in small concentrations by working muscles, however, in response to exercise, it is mainly released due to a systemic release of pro-inflammatory cytokines (Hoffmann et al. ##REF##12429706##2002##). IL-8 shows inflammatory and chemokine properties in attracting neutrophils to sites of muscle damage (Pedersen et al. ##REF##17347387##2007##). However, IL-8 has previously been found to be released after extensive endurance exercise or eccentric exercise and not commonly after strength exercise (Chan et al. ##UREF##2##2004##; Henson et al. ##REF##10949003##2000##), where muscle damage is more likely to occur. We did not assess any markers of muscle damage, however, the testing protocol did not induce reductions in explosive strength performance (i.e., a surrogate of neuromuscular fatigue). Nevertheless, as both groups show a similar increase, it can be postulated that this response to exercise is not modulated by oral contraceptive use, when compared to the early follicular phase.</p>", "<p id=\"Par34\">The lack of reductions in explosive strength performance suggest that the protocol did not induce a measurable level of neuromuscular fatigue, unlike it was previously shown to in men (Pareja-Blanco et al. ##REF##26970332##2017##). In line with this, women have been shown to have an increased time to task failure, as well as faster recovery of neuromuscular function compared to men (Hunter ##REF##19550202##2009##). Therefore, it can be speculated that for certain cytokine responses the volume of the strength protocol was possibly not high enough to induce a marked response. This may somewhat explain, why we did not see any responses or between group differences in IL-6, which shows a stronger released with increasing intensity but especially with increasing duration of exercise (Pedersen and Febbraio ##REF##18923185##2008##). This is also in contrast to a study by Timmons et al. (##REF##15879167##2005##) showing a lower IL-6 response in the pill-free interval of oral contraceptive users compared to the follicular phase of the menstrual cycle (Timmons et al. ##REF##15879167##2005##). However, it has to be mentioned, that exercise mode was very different (90 min continuous cycling at 65% VO₂max), which makes a direct comparison difficult. Nevertheless, we found exercise-induced responses in some cytokines (IL-1β, IL-1ra and IL-8) and differences in responses between groups. Therefore, the exercise protocol induced an inflammatory response despite the lack of reductions in explosive strength. Whether a more intense and longer exercise protocol may induce a stronger inflammatory response and greater differences between groups cannot be ultimately concluded and remains to be investigated.</p>", "<p id=\"Par35\">Importantly, in this study, we only assessed the acute response to strength exercise and therefore, the consequences, if any, of this differential regulation of IL-1β and IL-1ra between naturally cycling women and oral contraceptive users on neuromuscular adaptations, such as hypertrophy need to be further investigated. For example, Hansen et al. (##REF##19883384##2011##) found a lower myofibrillar synthesis rate in OC users with a low androgenic pill compared to naturally cycling women (Hansen et al. ##REF##19883384##2011##), while Dalgaard et al. found a trend (p = 0.06) towards a larger increase in muscle mass in OC users with similar low androgenic pills (Dalgaard et al. ##REF##30723415##2019##). Ihalainen et al. (##REF##31186194##2019##) showed higher concentrations of hs-CRP in hormonal contraceptive users after 10 weeks of combined strength and endurance training, along with smaller gains in lean body mass compared to naturally cycling women, suggesting that inflammation may be linked to smaller muscular adaptations in response to training (Ihalainen et al. ##REF##31186194##2019##). Therefore, results have been conflicting and the involvement of inflammatory parameters in muscle adaptation in longitudinal training studies in this setting largely remains to be investigated.</p>", "<p id=\"Par36\">In conclusion, IL-1β and IL-1ra showed a differential regulation in response to acute strength exercise between oral contraceptive users and naturally cycling women, with concentrations of both cytokines decreasing 24 h post exercise in the OC group only. IL-6 and IL-10 did not change over time and also showed no between group differences, while IL-8 increased across both groups 24 h post exercise. Therefore, it is proposed that the long-term use of oral contraceptives chronically affect the response of certain cytokines, like IL-1β and IL-1ra, even when testing in the pill-free interval of oral contraceptive users. This disparate regulation highlights the fact that research should not be investigating inflammatory status per se but instead view inflammatory processes differentially. It remains to be further analysed, how these inflammatory responses change throughout the full menstrual cycle, when variations in hormonal concentrations increase. Additionally, the exact physiology behind these differences and long-term implications for adaptations to strength exercise remain to be investigated.</p>" ]

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[ "<p>Communicated by Fabio fischetti.</p>", "<title>Purpose</title>", "<p id=\"Par1\">Cytokines are released as part of an inflammatory reaction in response to strength exercise to initiate muscle repair and morphological adaptations. Whether hormonal fluctuations induced by the menstrual cycle or oral contraceptives affect inflammatory responses to strength exercise remains unknown. Therefore, we aimed to compare the response of cytokines after acute strength exercise in naturally menstruating women and oral contraceptive users.</p>", "<title>Methods</title>", "<p id=\"Par2\">Naturally menstruating women (MC, <italic>n</italic> = 13, 24 ± 4 years, weekly strength training: 4.3 ± 1.7 h) and women using a monophasic combined pill (&gt; 9 months) (OC, <italic>n</italic> = 8, 22 ± 3 years, weekly strength training: 4.5 ± 1.9 h) were recruited. A one-repetition-maximum (1RM) test and strength exercise in the squat (4 × 10 repetitions, 70%1RM) was performed in the early follicular phase or pill free interval. Concentrations of oestradiol, IL-1β, IL-1ra, IL-6, IL-8, and IL-10 were assessed before (pre), directly after (post) and 24 h after (post₂₄) strength exercise.</p>", "<title>Results</title>", "<p id=\"Par3\">IL-1ra increased from pre to post (+ 51.1 ± 59.4%, <italic>p</italic> = 0.189) and statistically decreased from post to post₂₄ (– 20.5 ± 13.5%, <italic>p</italic> = 0.011) only in OC. Additionally, IL-1β statistically decreased from post to post₂₄ (– 39.6 ± 23.0%, <italic>p</italic> = 0.044) only in OC. There was an interaction effect for IL-1β (<italic>p</italic> = 0.038) and concentrations were statistically decreased at post₂₄ in OC compared to MC (<italic>p</italic> = 0.05). IL-8 increased across both groups from post to post₂₄ (+ 66.6 ± 96.3%, <italic>p</italic> = 0.004).</p>", "<title>Conclusion</title>", "<p id=\"Par4\">We showed a differential regulation of IL-1β and IL-1ra between OC users in the pill-free interval and naturally cycling women 24 h after strength exercise, while there was no effect on other cytokines. Whether this is associated with previously shown compromised morphological adaptations remains to be investigated.</p>", "<title>Keywords</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>" ]

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[ "<title>Author contributions</title>", "<p>Conceptualization: HLN, LU, MS; methodology: HLN, LU; formal analysis and investigation: HLN, MS, WB; writing–original draft preparation: HLN; writing–review and editing: WB, MS, LU; supervision: WB, MS.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL. No third-party funding was received for the submitted work.</p>", "<title>Data availability</title>", "<p>The data generated and analysed during the current study are available from the corresponding author on reasonable request.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par37\">The authors declare that there are no competing interests relevant to the content of this article.</p>", "<title>Ethics approval</title>", "<p id=\"Par38\">This study was performed in line with the principles of the Declaration of Helsinki and its later amendments. Approval was granted by the Ethics Committee of the German Sport University Cologne (020/2019).</p>", "<title>Consent to participate</title>", "<p id=\"Par39\">Informed consent was obtained from all individual participants included in the study.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Timing of testing in the natural menstrual cycle and oral contraceptive intake (exemplary data modified from Sims and Heather (##REF##30051938##2018##). Testing was performed in the early follicular phase or pill-free interval of the respective cycle. 1RM = one-repetition maximum in the back squat</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Baseline concentrations at pre of all cytokines (<bold>A</bold>) and fold change from baseline values for IL-1β (<bold>B</bold>), IL-1ra (<bold>C</bold>), IL-6 (D), IL-8 (<bold>E</bold>) and IL-10 (<bold>F</bold>). For IL-1β analysis was performed for <italic>n</italic> = 20 (MC: 13, OC: 7) and for IL-6 <italic>n</italic> = 19 (MC:11, OC: 8). Data are shown as mean ± SD, with black dots showing individual values</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Characteristics of the menstrual cycle (MC) and oral contraceptive (OC) group</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">MC</th><th align=\"left\">OC</th></tr></thead><tbody><tr><td align=\"left\">Age (yrs)</td><td align=\"left\">24 ± 4</td><td align=\"left\">22 ± 3</td></tr><tr><td align=\"left\">BMI (kg m⁻²)</td><td align=\"left\">22.4 ± 2.6</td><td align=\"left\">21.5 ± 1.8</td></tr><tr><td align=\"left\">1RM (kg kg bodyweight⁻¹)</td><td align=\"left\">1.1 ± 0.2</td><td align=\"left\">1.1 ± 0.1</td></tr><tr><td align=\"left\">Weekly strength training (h week⁻¹)</td><td align=\"left\">4.3 ± 1.7</td><td align=\"left\">4.5 ± 1.9</td></tr><tr><td align=\"left\">Day of cycle tested</td><td align=\"left\">5 ± 0.7 (4—6)</td><td align=\"left\">4 ± 0.8 (3—5)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Concentrations of cytokines, oestradiol and cortisol</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\" colspan=\"3\">MC</th><th align=\"left\" colspan=\"3\">OC</th></tr><tr><th align=\"left\">Variable</th><th align=\"left\">Pre</th><th align=\"left\">Post</th><th align=\"left\">Post₂₄</th><th align=\"left\">Pre</th><th align=\"left\">Post</th><th align=\"left\">Post₂₄</th></tr></thead><tbody><tr><td align=\"left\">Oestradiol (pg ml⁻¹)</td><td align=\"left\">29.7 ± 13.6 [21.4; 37.9]</td><td align=\"left\">23.8 ± 9.1 [18.4; 29.3]</td><td align=\"left\">28.6 ± 19.6 [16.8; 40.5]</td><td align=\"left\">18.7 ± 12.7 [8.1; 29.4]</td><td align=\"left\">15.7 ± 8.7 [8.4; 22.9]</td><td align=\"left\">17.3 ± 7.8 [10.8;23.8]</td></tr><tr><td align=\"left\">Cortisol (ng ml⁻¹)</td><td align=\"left\">248.6 ± 62.1^† [211.1; 286.2]</td><td align=\"left\">205.8 ± 66.4^# [165.5; 245.8]</td><td align=\"left\">210.4 ± 72.1 [166.9; 254.0]</td><td align=\"left\">490.4 ± 80.7^† [422.9; 557,9]</td><td align=\"left\">435.7 ± 92.4^# [358.4; 513.0]</td><td align=\"left\">451.6 ± 81.8 [383.3; 520.0]</td></tr><tr><td align=\"left\">IL-1β (pg ml⁻¹)</td><td align=\"left\">3.5 ± 2.8 [1.8; 5.2]</td><td align=\"left\">3.5 ± 2.6 [2.0; 5.1]</td><td align=\"left\">3.5 ± 2.2^† [2.2; 4.8]</td><td align=\"left\">3.6 ± 1.8 [1.9; 5.3]</td><td align=\"left\">4.0 ± 2.7 [1.5; 6.5]</td><td align=\"left\">2.6 ± 1.9<bold>*</bold>^{<bold>,</bold> †} [0.8; 4.3]</td></tr><tr><td align=\"left\">IL-1ra (pg ml⁻¹)</td><td align=\"left\">59.6 ± 31.6 [40.4; 78.7]</td><td align=\"left\">63.0 ± 20.2 [50.0; 75.2]</td><td align=\"left\">52.3 ± 39.0 [28.7; 75.9]</td><td align=\"left\">46.0 ± 23.9 [26.0; 66.0]</td><td align=\"left\">65.9 ± 35.4 [36.3; 95.5]</td><td align=\"left\">45.3 ± 27.8<bold>* </bold>[22.1; 68.6]</td></tr><tr><td align=\"left\">IL-6 (pg ml⁻¹)</td><td align=\"left\">1.4 ± 1.1 [0.6; 2.2]</td><td align=\"left\">1.9 ± 1.7 [0.7; 3.0]</td><td align=\"left\">1.3 ± 0.7 [0.9; 1.8]</td><td align=\"left\">1.6 ± 1.2 [0.6; 2.6]</td><td align=\"left\">1.4 ± 1.0 [0.6; 2.2]</td><td align=\"left\">1.5 ± 1.1 [0.6; 2.5]</td></tr><tr><td align=\"left\">IL-8 (pg ml⁻¹)</td><td align=\"left\">1.1 ± 0.5 [0.8; 1.4]</td><td align=\"left\">1.1 ± 0.4 [0.8; 1.3]</td><td align=\"left\">1.7 ± 0.9<bold>* </bold>[1.2; 2.3]</td><td align=\"left\">1.6 ± 0.8 [1.0; 2.3]</td><td align=\"left\">1.6 ± 0.6 [1.1; 2.1]</td><td align=\"left\">2.2 ± 0.9 [1.4; 3.0]</td></tr><tr><td align=\"left\">IL-10 (pg ml⁻¹)</td><td align=\"left\">1.4 ± 0.5 [1.1; 1.6]</td><td align=\"left\">1.3 ± 0.6 [1.1; 1.7]</td><td align=\"left\">1.5 ± 0.8 [0.9; 1.9]</td><td align=\"left\">2.2 ± 1.8 [0.6; 3.8]</td><td align=\"left\">2.0 ± 0.1.9 [0.2; 3.7]</td><td align=\"left\">1.8 ± 1.6 [0.3; 3.3]</td></tr></tbody></table></table-wrap>" ]

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[ "<table-wrap-foot><p>Data are presented as mean ± SD. For day of cycle tested, the range is also presented.</p></table-wrap-foot>", "<table-wrap-foot><p>Data are given as mean ± SD [95% Confidence Interval]</p><p>*Statistical change from post to post₂₄</p><p>^#Statistical change from pre to post</p><p>^†Statistical difference between groups</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"421_2023_5275_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"421_2023_5275_Fig2_HTML\" id=\"MO2\"/>" ]

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{ "acronym": [ "1RM", "IL", "IL-1ra", "OC", "MC", "Th1/2", "TNF-α" ], "definition": [ "One-repetition maximum", "Interleukin", "Interleukin-1 receptor antagonist", "Oral contraceptive", "Menstrual cycle", "T helper type 1/2 response", "Tumour necrosis factor alpha" ] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Global unrestrained urbanization alters urban natural ecosystems and landscape structure and increases the share of impermeable surfaces in cities (Mullaney et al. ##UREF##52##2015##; Senes et al. ##UREF##70##2021##). This greatly leads to modification and disruption of the urban hydrological cycle, resulting in increased magnitude of surface water runoff and local flooding (Xu et al. ##UREF##87##2013##; Qian and Eslamian ##UREF##62##2022##). This issue is further accelerated by the extreme weather events due to global climate change in cities (Kumar et al. ##UREF##39##2022##; Muyambo et al. ##UREF##54##2023##). Consequently, not only does excessive stormwater runoff increase, but also the capability of cities to deal with these challenges diminishes (McGrane ##UREF##48##2016##; Janke et al. ##REF##28756675##2017##; Zhou et al. ##UREF##90##2021##). Urban stormwater can seriously affect ecosystems, built environment, people, and property (Beck et al. ##UREF##8##2016##; Subramanian ##UREF##73##2017##).</p>", "<p id=\"Par3\">Traditional stormwater management approaches (gray infrastructure) are often inadequate and unsustainable to mitigate the current and future impacts and are also expensive to construct and maintain (US EPA ##UREF##79##2017##; Lu and Wang ##UREF##44##2021##). This has led to a demand for alternative and complementary cost-effective and sustainable approaches, primarily involving urban green infrastructure (UGI) (Wang et al. ##UREF##83##2008##; Carlyle-Moses et al. ##UREF##11##2020##; Hamel and Tan ##UREF##24##2022##). This highlights the importance of providing hydrologic ecosystem services (HES) by UGI in general and provision of runoff reduction by urban trees (RRES) in particular to mitigate stormwater issues. Urban trees facilitate HES and interact with the urban hydrologic cycle (Szota et al. ##UREF##75##2018##; Van Stan et al. ##UREF##81##2020##). The HES can decrease flow rate, peak runoff, and flooding hazards (Xiao and McPherson ##UREF##86##2002##; Kermavnar and Vilhar ##UREF##37##2017##). Previous studies have shown the positive effects of UGI, specifically urban trees, on surface runoff (Asadian and Weiler ##UREF##4##2009##; Inkiläinen et al. ##UREF##32##2013##; Li et al. ##UREF##42##2020##; Liu et al. ##UREF##43##2020##).</p>", "<p id=\"Par4\">The sustainability of HES is disturbed by urban landscape modification (Qiu and Turner ##UREF##63##2015##; Duarte et al. ##UREF##17##2018##; Metzger et al. ##REF##34328874##2021##). Hydrological characteristics of a given area, including but not limited to water flow, are more influenced by landscape structure (shape or form) (Uuemaa et al. ##UREF##80##2007##). Changes in the urban spatial landscape structure alter ecological (ecosystem) functions, processes, and flow patterns (Mitchell et al. ##UREF##50##2013##; Muleta and Biru ##REF##30673908##2019##). This, in turn, substantially alters the capability of urban ecosystems to provide various ecosystem services (ES), either positively or negatively (Chen et al. ##UREF##13##2021##; Yohannes et al. ##REF##34328959##2021##). It is crucial to the regulating ES, particularly HES, as their supply, demand, and flow are explicitly linked to the movement and flow of the matter across urban landscapes (Eigenbrod ##UREF##19##2016##; Xia et al. ##REF##34153752##2021##).</p>", "<p id=\"Par5\">Increasing evidence, including theories (Mitchell et al. ##UREF##51##2015a##), meta-analysis (Mitchell et al. ##UREF##50##2013##; Duarte et al. ##UREF##17##2018##), conceptual frameworks (Inkoom et al. ##UREF##33##2018##), and case studies (Syrbe and Walz ##UREF##74##2012##; Kim and Park ##UREF##38##2016##; Duflot et al. ##UREF##18##2017##) has highlighted the impact of landscape structures on different ES, mainly in natural contexts. However, our understanding in this area is still in its early stages, and for many ES, how different aspects of landscape structures (most) affect their provision has not yet been well understood empirically (Lamy et al. ##UREF##40##2016##; Herrero-Jáuregui et al. ##UREF##25##2019##; Tran et al. ##REF##34863745##2022##). These relations in cities are even more unclear due to the high complexity and heterogeneity (LaPoint et al. ##UREF##41##2015##; Grafius et al. ##UREF##22##2016##) and the lack of empirical studies (Dobbs et al. ##UREF##16##2014##; Grafius et al. ##REF##31258244##2018##). Therefore, overcoming this critical knowledge gap in urban areas is essential.</p>", "<p id=\"Par6\">Understanding what features of urban landscape structure affect the provision of ES, especially HES, substantially improves the landscape management knowledge and practices for sustainable ES provision (Breuste et al. ##UREF##9##2013##; Mitchell et al. ##REF##25716547##2015b##). Based on the shape-function relationship, the patch’s geometrical and morphometric shape features (landscape structure) affect the landscape function regarding water flow (Amiri et al. ##UREF##0##2019##; With ##UREF##85##2019##). Landscape structural patterns are a dominant element of landscape structure (Karimi et al. ##UREF##36##2021##). It is considered a useful lever to affect the movement, flow, interaction, and provision of HES (Rieb and Bennett ##UREF##65##2020##). Although landscape structure is expected to significantly influence the provision of HES, it has not been widely studied in the urban context. Previous studies have appreciated the effects of urban landscape structure on some aspects of stormwater management through HES, including sediment erosion, flood control, peak runoff, freshwater supply, and surface and groundwater quality (Qiu and Turner ##UREF##63##2015##; Kim and Park ##UREF##38##2016##; Grafius et al. ##REF##31258244##2018##; Inkoom et al. ##UREF##33##2018##; Metzger et al. ##REF##34328874##2021##; Luo et al. ##UREF##45##2022##). Also, the impacts of LULC changes on runoff reduction ES have been acknowledged using landscape metrics (Zhang et al. ##UREF##89##2015##; Li et al. ##UREF##42##2020##). These studies primarily concentrated on mitigating runoff through ES provided by various LULC classes, specifically UGI, and relied on empirical models and runoff reduction coefficients from prior research to estimate the capacity of UGI to reduce runoff. However, an overlooked aspect in these studies is investigating the effects of landscape structural patterns on RRES. The existing literature highlights a gap in scientific understanding and empirical evidence concerning the relations between multiple measures of landscape structural patterns and provision of RRES, which is essential for developing ES-based landscape management tools to sustain RRES. To address this gap, this paper aims to analyze the role of urban landscape structure in the provision of RRES by analyzing the relations between landscape structural patterns and RRES in Tabriz, Iran. This city faces frequent heavy stormwater runoff and floods due to rapid urbanization, local climate and topography conditions, and global climate change, leading to severe flooding in densely inhabited areas (Mahmood Zadeh et al. ##UREF##46##2015##; Yazdani et al. ##UREF##88##2018##). Consequently, Tabriz was selected as the case study for scientific and practical purposes.</p>", "<p id=\"Par7\">This paper seeks to empirically understand how RRES responds to the multiple measures of landscape structural pattern. The specific objectives were to (1) quantify the capacity of urban trees for runoff reduction, (2) quantify the measures of urban landscape structural pattern of LULC classes using landscape shape metrics, and (3) analyze the relations between the several measures of urban landscape structural pattern and the provision of RRES. The findings spur our understanding of how landscape structural pattern can influence the provision of RRES and help improve ES-based landscape management guidance to sustain RRES and more effectively manage stormwater runoff in cities.</p>" ]

[ "<title>Materials and Methods</title>", "<title>Study Area</title>", "<p id=\"Par8\">This study was conducted in Tabriz, the largest city in northwest Iran (Fig. ##FIG##0##1##). It has a population of about 1.56 million people and a 243 km² area (Statistical Center of Iran ##UREF##72##2016##). Tabriz has a mountainous topography (Asakereh and Akbarzadeh ##UREF##5##2017##), with a cold and semi-arid climate (Ghazi and Jeihouni ##UREF##21##2022##). The annual mean precipitation is 311.1 mm, with ~77.07 days experiencing rainfall of 1.0 mm or more (rainy days). The rainfall period is about 7.5 months, from 17 October to 1 June, with April having the highest average rainfall of 23 mm and August having the lowest average rainfall of 3 mm (IMO ##UREF##31##2022##). The rainfall pattern observed in Tabriz exhibits characteristics similar to that of the Mediterranean type (Jani1 et al. ##UREF##34##2013##). However, global climate change has affected the seasonal precipitation patterns, resulting in more intense rainfall events (Sanikhani et al. ##UREF##69##2014##; Sadeqi and Dinpashoh ##UREF##68##2019##). Tabriz faces a significant flood risk, with approximately 50% of its residents vulnerable to floods (Yazdani et al. ##UREF##88##2018##). The historical data showed that Tabriz had experienced about 42 cases of urban flooding from 1954 to 2009, resulting in significant human and economic losses (Soleimani-Alyar et al. ##UREF##71##2016##). Over the past century, rapid urban development and landscape changes have led to an increased share of impervious surfaces at the expense of decreasing green spaces (pervious surfaces) (Rahimi ##UREF##64##2016##).</p>", "<title>Data Sources</title>", "<p id=\"Par9\">The administrative map and the initial LULC map for 2020 (scale 1:25000 and minimum mapping unit of 1 m) were obtained from the municipality of Tabriz. Hourly precipitation data of the synoptic station of Tabriz for a complete calendar year was received from the Iran Meteorological Organization (IMO ##UREF##31##2022##). Other meteorological data for executing the i-Tree Eco model were automatically retrieved from the archived NOAA database (Hirabayashi and Endreny ##UREF##27##2016##). Urban tree structural data were collected through the fieldwork.</p>", "<title>Methods</title>", "<p id=\"Par10\">This study was carried out based on Fig. ##FIG##1##2##. The overall methodological approach of this study includes three main steps:</p>", "<title>Assessing the Provision of RRES</title>", "<p id=\"Par11\">To assess the provision of RRES, i-Tree tools were applied due to being one of the most appropriate, robust, fast, and process-based models to estimate RRES (Hirabayashi ##UREF##26##2013##; US EPA ##UREF##79##2017##; Nowak ##UREF##57##2021##). The i-Tree Eco model, exclusively developed for the U.S., was adapted for the study area by providing location information and hourly precipitation data to the i-Tree Database, following the protocol (i-Tree Eco International Projects ##UREF##28##2016##). The submitted data underwent a rigorous evaluation process by the U.S. Forest Service and was subsequently incorporated into the i-Tree Eco software. Subsequently, the recently appended location (Tabriz) was integrated into the subsequent versions of i-Tree Eco.</p>", "<p id=\"Par12\">The required structural data for trees, including total height, live crown height, height to crown base, crown width, missing and health, species, tree cover, and diameter at breast height (DBH), were collected from 325 standard plots (with a radius of 11.34 m) through fieldwork during the leaf-on season following the manuals (i-Tree Eco User Manual ##UREF##29##2016##; i-Tree Field Guide ##UREF##30##2016##). Furthermore, the detailed data was collected for each plot, encompassing its precise geographical location and exact central coordinates, the proportion of the plot that was accessible and surveyed by the field crew, the percentage of the plot area covered by trees and shrubs, the quantity of space suitable for tree planting, identification of the reference objects from the plot center, the specific land use type within each plot, and the classification of ground cover types observed within each plot.</p>", "<p id=\"Par13\">The sample size was chosen to balance data uncertainty, time constraints, limited resources, and costs for the field survey and achieve a standard error of approximately 10% for the entire city (Nowak et al. ##UREF##56##2008##). A unique methodological approach was employed to clarify the variations in RRES provision across the city. The plots were pre-stratified randomly among the LULC classes within the ten administrative districts to bring the multiple elements of RRES to each district and identify how the RRES provision varies across the districts. This approach was applied to obtain reliable observation data for further regression analysis of the relationship between landscape metrics and RRES provision (Fig. ##FIG##5##6##). Therefore, the initial LULC map was reclassified into six LULC classes (agricultural land, residential area, green infrastructure, commercial/transportation/institutional (CTI), open space and water body) according to the ten administrative districts (Fig. ##FIG##2##3##). Then the plots were pre-stratified based on LULC classes and randomly distributed among the LULC classes and urban districts using Create Random Points tool in ArcMap 10.8.2 (Fig. ##FIG##0##1##).</p>", "<p id=\"Par14\">Based on the field data, the i-Tree Eco model estimated the structural characteristics of the urban tree population. Using the structural traits of trees (including tree species, total tree height, tree height to crown base, crown width, and missing and total tree cover) along with location information and precipitation data, the RRES was calculated using the <italic>Hydrology Effects of Trees module</italic> in i-Tree Eco for the entire city and each LULC class and district. This module estimates the various components of RRES, including rainfall interception, storage, transpiration, and evaporation, contributing to runoff reduction (Wang et al. ##UREF##83##2008##; Hirabayashi ##UREF##26##2013##; Nowak ##UREF##57##2021##). The modified Rutter methodology was utilized to simulate the process of interception (Nowak ##UREF##57##2021##). Moreover, evaporation was simulated according to the research of Deardorff (##UREF##15##1978##) and Noilhan and Planton (##UREF##55##1989##). These estimates are process-based, meaning each process is simulated separately before being linked to other processes (Hirabayashi ##UREF##26##2013##; Nowak ##UREF##57##2021##). To assess the impact of urban trees on runoff, the module assumes two scenarios: the actual (current tree conditions) and hypothetical (without trees in the same area) scenarios. For both scenarios, hourly precipitation, interception, evaporation, transpiration, and potential evapotranspiration processes are simulated first, followed by the volume of annual surface runoff. The difference in generated surface runoff between the scenarios determines the annual net RRES. Due to the effects of trees by intercepting, storing, and evaporating rainwater, the actual scenario generates less runoff than the hypothetical one. The net avoided runoff is further summarized for each tree, species, and stratum. The methods and equations are detailed in Hirabayashi (##UREF##26##2013##) and Hirabayashi and Endreny (##UREF##27##2016##).</p>", "<title>Analyzing the Urban Landscape Structural Pattern</title>", "<p id=\"Par15\">To analyze the urban landscape structural pattern, the metrics related to the landscape structure of LULC classes were calculated using FRAGSTATS 4.0. The equations, ranges, and a short description of each landscape metric are summarized in Table ##TAB##0##1##.</p>", "<title>Analyzing the Relationships Between the Landscape Structural Pattern and the Provision of RRES</title>", "<p id=\"Par16\">To model the relationship between landscape structure-related metrics and the provision of RRES, stepwise regression analysis was conducted using IBM SPSS 19 software. Stepwise regression analysis is the automated computational process using forward and backward selection techniques to obtain the optimal regression (Thatcher ##UREF##77##2021##). The model omits irrelevant variables and secures that independent variables are not correlated (Johnsson ##UREF##35##1992##; Thatcher ##UREF##77##2021##). Consequently, the landscape metrics were entered into the model as independent variables, while RRES was a dependent variable. P ≤ 0.05 and P ≥ 0.100 were applied to the entry and exclusion criteria. The model outlines which landscape metrics would better explain the RRES provision. This brought about the equation to estimate the RRES:where <italic>y</italic>_{<italic>i</italic>} is the total annual RRES () in the study area, <italic>x</italic>₁…<italic>x</italic>_{<italic>n</italic>-1} are the landscape structure-related metrics (PARA, SHP, FRAC. RCC and CI), <italic>β</italic>₁…<italic>β</italic>_{<italic>n</italic>-1} are the coefficients of city landscape metrics retained with P ≤ 0.05, is a constant of the model with P ≤ 0.05 and is the error for the annual RRES.</p>", "<p id=\"Par17\">The variation inflation factor (VIF) was also applied to assess the intervariable collinearity of the models obtained, where VIF &lt; 10 states a lack of collinearity (Chatterjee and Hadi ##UREF##12##2013##). Scatter plots of observed versus predicted values of the total annual RRES were used to evaluate the goodness of fit for each model.</p>" ]

[ "<title>Results</title>", "<title>Urban Tree Structure and the Corresponding RRES</title>", "<p id=\"Par18\">The results showed that there were 1,927,566 trees (with a standard error of 12.3%), with a tree cover of 9.4% in the study area. Accordingly, they provided 8,373.04 km² of leaf area (LA). Total LA was greatest for open spaces, followed by residential areas and GI. However, the GI, residential area and open space classes had the highest tree density, respectively (Fig. ##FIG##3##4##).</p>", "<p id=\"Par19\">Among the administrative districts, the highest number of trees was observed in D6 (District 6), followed by D5 and D3. The total tree density was 79.33 trees ha⁻¹, with the highest value in D10 (105 trees ha⁻¹) (Table ##TAB##1##2##).</p>", "<p id=\"Par20\">The results indicated that the trees reduced 196,854.15 m³ of runoff annually. Open spaces and agricultural land had the highest and lowest contribution to RRES, respectively. The majority of runoff (82%) was reduced by open spaces, residential areas, and GI at a total of 16,1425 m³ per year. This pattern is likely due to the different structural characteristics of urban trees in each LULC class (Fig. ##FIG##3##4##). GI class had the highest runoff reduction efficiency (40.51 m³ha⁻¹yr⁻¹), followed by residential areas, open spaces, agricultural land, and CTI (Fig. ##FIG##4##5a##).</p>", "<p id=\"Par21\">The capacities of the different districts for runoff reduction indicated that D6 obtained the highest runoff reduction ratio (average of 28%). Districts 6, 5 and 7 were responsible for approximately half (51.1%) of total runoff reduction in the study area (Table ##TAB##2##3##). The results showed that districts’ runoff reduction efficiency (RRE) varies: D10 and D9 had the highest RRE with 10.16 and 6.92 (m³ha⁻¹yr⁻¹), respectively. The potential reason is that D10 and D9 have the greatest and lowest leaf area and tree number per hectare, respectively (Table ##TAB##1##2##).</p>", "<title>Landscape Structural Pattern of LULC Classes</title>", "<p id=\"Par22\">Descriptive statistics, including mean, maximum, minimum, standard division, and variance, were calculated for all patches (LULC classes) within districts (Table ##TAB##3##4## and Appendix 1).</p>", "<p id=\"Par23\">The results indicated that the LULC classes have different values of landscape structure-related metrics. The landscape metrics showed different maximum and minimum values, suggesting they all have unique insights to provide. The mean of <italic>SHP</italic> and <italic>FRAC</italic> for all patches was greater than 1, which means relative irregular, complex and convoluted patch shapes of LULC classes. All LULC patches had complex shapes because the relevant <italic>PARA</italic> values were high, indicating a deviation from the isodiametric shapes (larger edge for a given area). The <italic>CI</italic> results indicated that agricultural land had the highest patch connectedness (CI = 0.84), while the open space had the lowest patch contiguity (CI = 0.16). In total, the landscape metrics indicate that the LULC patches of the study area tended to be almost complex shapes.</p>", "<title>The Linkage Between Landscape Structural Pattern and RRES</title>", "<p id=\"Par24\">Multiple linear regression models were developed, explaining the RRES through landscape structure-related metrics measurements (Eqs. (##FORMU##19##2## to ##FORMU##24##7##)). Other statistics for these models can be found in Table ##TAB##4##5##. The one-by-one relationships between observed and predicted RRES using landscape metrics are shown in Fig. ##FIG##5##6##.where <italic>RRES</italic> is the annual runoff reduction provided by urban trees, <italic>RCC</italic> represents mean related circumscribing circle index for a given class of the LULC, <italic>SHP</italic> is the mean shape index for a given LULC type, <italic>R</italic> is the residential class, <italic>A</italic> is the agriculture class, <italic>CTI</italic> is the commercial/transportation/institutional class, and <italic>Ln</italic> represents natural logarithm.</p>", "<p id=\"Par25\">The stepwise regression modeling results indicated the structural pattern’s effects on the annual RRES. The relationships between the RRES and landscape metrics were highly significant (0.889 ≤ <italic>r</italic>² ≤ 0.983) (Table ##TAB##4##5##). The results suggested that the total RRES could be predicted using the means of the two landscape metrics: the related circumscribing circle (0.889 ≤ <italic>r</italic>² ≤ 0.954), and the shape index (<italic>r</italic>² = 0.983) (Table ##TAB##4##5##), indicating these indexes explain 88.9 to 98.3% of the variation of RRES across the study area. Stepwise regression modeling determined the relevance of only four LULC classes, including residential areas, CTI, agricultural land, and GI (Eqs. ##FORMU##19##2## to ##FORMU##24##7##). Furthermore, <italic>PARA</italic>, <italic>FRA</italic>, and <italic>CI</italic> indexes were not observed in the developed models.</p>", "<p id=\"Par26\">Table ##TAB##4##5## shows that the mean <italic>RCC</italic> indices of the residential and CTI patches (Eq. ##FORMU##19##2##) statistically explain 95.3 % of the overall variations in the measures of RRES. The total RRES had a negative relationship with the associated related circumscribing circle index of CTI patches (<italic>CTI</italic>_{<italic>RCC</italic>}) (Eq. ##FORMU##19##2##), showing that the lower the CTI_RCC (i.e., the less narrow elongated the CTI patches are), the higher the RRES. It signifies that convoluting the shape of the CTI patches due to an increase in the RCC index would contribute to providing RRES in the city rather than elongation. Furthermore, the mean <italic>RCC</italic> for the residential area was positively correlated with the RRES. According to the <italic>RCC</italic> definition, the more narrow the elongated residential patches are, the greater the RRES in the city. This suggests that relatively narrow and elongated residential patches would play an important role in the RRES compared to relatively convoluted patches.</p>", "<p id=\"Par27\">About 89% of the total variations in the RRES (Eqs. 3 and 4) were explained by the value of the <italic>RCC</italic> index of agricultural patches in the absence of any other metrics of LULC patches. Therefore, if the <italic>A</italic>_{<italic>RCC</italic>} Increases in the city, the RRES will increase significantly. This indicates that the RRES is influenced by agricultural area when the patches are more narrow and elongated in the city.</p>", "<p id=\"Par28\">About 98% of the total variations in RRES (Eqs. 6 and 7) were significantly explained by a combination of the <italic>GI</italic>_{<italic>SHP</italic>} and <italic>A</italic>_{<italic>SHP</italic>} Hence, the shape index of GI and agricultural patches substantially affects RRES. According to the level of the model, the overall complexity of GI and agriculture patches may significantly explain the variations in RRES. Therefore, an increase in the shape index of the GI and agricultural patches (<italic>GI</italic>_{<italic>SHP</italic>} and <italic>A</italic>_{<italic>SHP</italic>}) in the city could increase the RRES due to the higher shape irregularity of the GI and agricultural patches. Accordingly, only the modification of GI and agricultural land into square or nearly square (i.e., regularly shaped) patches would likely decrease the RRES throughout the city. The function can be deduced from the shape index of green infrastructure (<italic>GI</italic>_{<italic>SHP</italic>}) and agriculture (<italic>A</italic>_{<italic>SHP</italic>}) patches in the city’s landscape (Eqs. 6 and 7).</p>", "<p id=\"Par29\">Moreover, using VIF, the intervariable collinearity of the models was assessed (Table ##TAB##4##5##). All models had VIFs smaller than 1.4, indicating a lack of collinearity.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par30\">Urban trees are recommended as an effective and complementary measure to alleviate the problem of urban stormwater runoff, improving urban sustainability (Mullaney et al. ##UREF##52##2015##; US EPA ##UREF##79##2017##; Lu and Wang ##UREF##44##2021##). To properly understand and utilize the capacity of urban trees for runoff mitigation, it is vital to obtain precise and reliable estimates of RRES. This work attempted to quantify the contributions of urban trees to runoff mitigation at the urban scale in Tabriz, Iran. The results indicated that urban trees are effective in mitigating runoff. They can reduce 196.85 × 10³ m³ of stormwater runoff annually. Different runoff reduction capacities have been observed due to the various urban LULC classes. The open spaces had shown the highest runoff reduction (Fig. ##FIG##3##4##). A potential reason is that open spaces tend to have the highest share of area (45.4%) in general and more leaf area and tree number in particular.</p>", "<p id=\"Par31\">On the other hand, as regards runoff reduction efficiency (Fig. ##FIG##4##5, a##), GI, which covers the lowest area in the city (3.1%), has the highest efficiency due to the greatest leaf area per hectare and tree density (456 tree ha⁻¹). This is also true for urban districts; the more tree density the district has, the more RRES was observed. This conclusion is reinforced by the fact that leaf area is one of the most important factors in runoff reduction process by urban trees (Nowak ##UREF##57##2021##). So, runoff reduction efficiency provides a better understanding of the potential of each LULC type and district in runoff reduction. Knowledge of the runoff reduction capacity of urban trees within LULC classes in different urban districts can contribute to proper management as local municipalities manage each district independently.</p>", "<p id=\"Par32\">The effect of the GI and agricultural land in this study agrees with previous studies (Pace and Sales ##UREF##60##2012##; Mikulanis ##UREF##49##2014##; Nowak et al. ##UREF##58##2017##), identifying green spaces as the main source of runoff reduction. The comparison of urban tree traits and RRES across the cities (Table ##TAB##5##6##) indicates that Tabriz has a somewhat near-the-average tree number; however, the tree cover ranks among the lowest, exceeding only Phoenix, implying its trees are quite small and young. Estimated annual runoff reduction efficiency has ranged from 8.04 to 71.52 m³ per tree, within which Tabriz has the lowest value. Although tree characteristics may be the primary contributor to this low efficiency, as 78 % of the existing trees are not large enough to produce significant runoff reduction, the effects of rainfall (amount, duration, and pattern) could not be ignored on runoff reduction (Nytch et al. ##UREF##59##2019##). Despite the modest RRE in the study area, such a reduction in surface runoff can have considerable environmental benefits in addition to the significant reduction in stormwater management costs.</p>", "<p id=\"Par33\">The usefulness of the ES concept for landscape and ecosystem management depends on our knowledge of links between landscape structure and ES provision (Mitchell et al. ##UREF##50##2013##). Since HES provision can be either directly or indirectly affected by landscape structure (Chen et al. ##UREF##13##2021##; Yohannes et al. ##REF##34328959##2021##), improving our knowledge of the interactions between landscape structure and RRES provision by integrating the concepts of landscape ecology and ES into urban hydrology helps effectively manage urban landscapes and resiliently maintain and enhance the sustainability of HES supply (Mitchell et al. ##UREF##50##2013##; Francis et al. ##UREF##20##2022##; Tran et al. ##REF##34863745##2022##). However, the empirical understanding of how landscape structure impacts RRES provision remains limited. This gap limits our ability to manage urban landscape effectively for RRES. To bridge this gap, this study assessed the impacts of landscape structural patterns, particularly the shape of LULC patches, on RRES provision. The findings provided direct evidence that the shape of urban LULC patches significantly influences RRES capacity. This is consistent with previous studies demonstrating the importance of landscape structure in providing HES (Zhang et al. ##UREF##89##2015##; Li et al. ##UREF##42##2020##).</p>", "<p id=\"Par34\">In doing so, we emphasize how LULC patches’ shape can mediate the RRES supply. To sum up the findings, it is noteworthy that only two of the five studied landscape structure-related metrics (shape and related circumscription circle metrics) have resulted in reliable models for predicting the provision of RRES. The results indicate that <italic>SHP</italic> and <italic>RCC</italic> metrics are the influential determinants of RRES and could be applied in RRES assessment. This is consistent with those of the previous study, which analyzed the links between flooding phenomena with landscape metrics on a larger scale using the same landscape metrics (Amiri et al. ##UREF##1##2018##).</p>", "<p id=\"Par35\">The finding showed that the <italic>RCC</italic> metric for agricultural patches could be applied to develop the RRES prediction model. However, applying the RRES prediction models, which are based on the <italic>RCC</italic> metric for residential areas and CTI, could provide more reliable estimations to their users. Moreover, it is noteworthy that the more elongated the shape of the residential and agricultural patches, the greater the supply of RRES. Therefore, expanding agricultural and residential patches may only improve the capacity of trees to mitigate runoff if they have more elongated and narrower shapes, but an extended CTI with a more convoluted shape would be advantageous. However, regularity or irregularity in the shape of the GI and agricultural patches, specifically the degree by which their patches deviate from an iso-diametric shape as reflected by differences in shape index, was observed to be significantly related to the extent of RRES. The results showed that increasing the degree of shape irregularity in the GI and agricultural patches improves their contribution to runoff mitigation.</p>", "<p id=\"Par36\">Even though the previous works (e.g., Buckland et al. ##UREF##10##2020##; Rogers et al. ##UREF##66##2015##; Watson et al. ##UREF##84##2017##) have demonstrated that urban trees in green spaces have a considerable impact on stormwater runoff; the results of this study suggest that, in addition to current GI cover, the shape of the GI patches should also be considered.</p>", "<p id=\"Par37\">Our approach can help to understand the RRES provisioning mechanism better and provides useful information for the urban decision support system to improve the sustainable functionality of the landscape. We have found a strong influence of the structural pattern on RRES. While some of the relationships between landscape structure and HES have been outlined in previous research (Dobbs et al. ##UREF##16##2014##; Grafius et al. ##REF##31258244##2018##; Karimi et al. ##UREF##36##2021##), this work expands our understanding of the influence of landscape structural pattern on the RRES.</p>", "<p id=\"Par38\">The results showed evidence of support for the role of landscape structure in maintaining the RRES in urbanized areas now and into the future. Understanding the impacts of the structural pattern on ES is a significant research goal that provides a foundation for alternative landscape management, planning, and restoration strategies (Turner et al. ##UREF##78##2013##). These findings can contribute to improving urban landscape planning and management with respect to sustainable urban runoff reduction. This helps to cover the necessity of carrying out ES assessment in parallel with and according to the urban landscape planning process (Grunewald and Bastian ##UREF##23##2015##).</p>", "<p id=\"Par39\">Assessing the impacts of different urban landscape plans on multiple dimensions particularly ES, is crucial for establishing optimal landscape strategies (Termorshuizen and Opdam ##UREF##76##2009##; Francis et al. ##UREF##20##2022##). Through integrating the i-Tree Eco measurements with conventional landscape structure metrics analyses, this research provides an explicit landscape metrics-based tool to describe variations in the RRES capacity. This provides a potential approach to evaluate the response of RRES to changes in the urban landscape structural pattern. Urban decision-makers and planners can use it to establish optimal spatial policies and assess the impacts of their landscape strategies on the capacity of tree to provide RRES. In fact, once the urban land use strategies are defined, the obtained regression models could be an easy-to-use way to rapidly and iteratively assess whether the proposed strategies will result in positive or negative changes in RRES. This helps to identify how to change the landscape to improve the RRES provision and is in line with the critical elopement of landscape planning which aims to maintain the functions of the landscape and ecosystem (Grunewald and Bastian ##UREF##23##2015##).</p>", "<p id=\"Par40\">This study helps to link ES assessment and urban landscape planning, which initially have different focuses (Grunewald and Bastian ##UREF##23##2015##). We try to bridge a gap in the field of integrating ES into landscape ecology and spatial planning, which can ease dialog with different practitioners and decision-makers. Despite the growing body of literature on ES, it has not been fully integrated into urban landscape planning and decision-making (Anna Hermann et al. ##UREF##3##2011##). Some of the main questions that need to be answered are 1) how can the relationships between ES and landscape characteristics be quantified and modeled? and 2) what is the effect of landscape features on ES? (de Groot et al. ##UREF##14##2010##). One approach to cover these challenging questions is better understanding the interrelations between LULC and ES (Verburg et al. ##UREF##82##2009##). This study tries to answer these questions and aims to integrate the ES concept into urban landscape management, planning and decision-making by analyzing the interactions between RRES and structural characteristics of LULC. Integrating landscape concepts into ES helps the ES framework to convey the complex relationships of socio-ecological systems and resolve its operational gaps (Angelstam et al. ##UREF##2##2019##).</p>", "<p id=\"Par41\">This paper also helps to cover one of the main research directions of the \"ES at the landscape scale\" (Müller et al. ##UREF##53##2010##) by providing a suitable methodology to apply ES at the landscape scale and integrating ES in landscape analysis. This study contributes to the existing body of literature (Bastian ##UREF##7##2001##; Syrbe and Walz ##UREF##74##2012##; Babí Almenar et al. ##UREF##6##2018##), which advocate expanding the landscape ecology paradigm and highlighting the necessity for making an appropriate foundation for the resolution of urban planning subjects through analyzing the linkage between landscape structure and ES.</p>", "<p id=\"Par42\">Although using the i-Tree Eco model to estimate RRES offers distinct benefits, including utilizing locally gathered field data, process-based hydrology estimations and modeling, and eco-hydrology of trees, it also has uncertainties and limitations. These drawbacks stem from simplifying (sub)surface hydrology to reflect the effects of urban trees, excluding of changing amounts of impervious cover, dismissing the impacts of the various spatial configuration of trees or other LULC types and applying default soil and hydrologic parameters (Hirabayashi ##UREF##26##2013##; Nowak ##UREF##57##2021##). Future research is required to help overcome these uncertainties and limitations.</p>", "<p id=\"Par43\">Another limitation of this study is that it has focused on analyzing the effects of landscape structural patterns in an urban area with the varying terrain and topographic and hydrologic gradients, which might be considered to identify the impact of these variables.</p>", "<p id=\"Par44\">To improve the knowledge of how landscape structure influences HES, future works are needed to consider additional biophysical, cultural, and social drivers at different spatial and temporal scales, as these factors determine ES distribution (Eigenbrod ##UREF##19##2016##). Further attempts are needed to study the impacts of landscape structure on multiple ES at once (ES bundles) and other dimensions of the ES delivery process. Comprehensive scenario analysis of future changes in rainfall, tree characteristics, landscape structure, LULC, and subsequently in RRES is required for long-term sustainable urban planning. Furthermore, analysis of the impacts of the other aspects of landscape, such as composition and connectivity on RRES using other landscape metrics can be considered in additional research.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par45\">This paper provides the empirical basis to evaluate the hypothesis that urban landscape structural pattern impacts the REES provision. First, we provided the theoretical fundaments that suggest the landscape structure would affect the supply of HES and how common research concentrates on the links between landscape structure and HES. Second, by developing a new approach, we brought empirical evidence of how urban landscape structure affects RRES, which is required to manage and model RRES provision across urban landscapes accurately.</p>", "<p id=\"Par46\">The idea for this work was due to the absence of empirical evidence on the relationship between landscape structure and RRES. This paper provided an explicit location-based estimation tool based on landscape metrics to describe variations in the RRES.</p>", "<p id=\"Par47\">This study revealed the significant influence of the spatial shape of landscape on RRES and showed linear responses of the RRES to landscape metrics: shape and related circumscribing circle. Specifically, consistent with the shape-function relationship principle, we argue that the landscape structural pattern will significantly mediate the provision of RRES.</p>", "<p id=\"Par48\">Our approach made it possible to predict the effects of changes in landscape structure on providing RRES. The findings have indicated that a change in the shape of the LULC due to the alteration of the structural attributes and landscape metrics of the LULC would cause a change in the runoff reduction capacity of trees as a process.</p>", "<p id=\"Par49\">The findings would help urban environmental managers and policymakers better understand the importance of landscape structure when thinking about improving runoff mitigation capacity and, consequently, establishing proper LULC strategies through optimizing landscape metrics that result in positive changes in the supply of RRES. The landscape structure metrics could be served as capable and cost-effective indicators to assess RRES and monitor changes in RRES provision produced by several urban plans, such as a masterplan.</p>", "<p id=\"Par50\">This work provides practical information for urban spatial planning by incorporating ES concept and landscape ecological perspective. The results could improve urban plans by considering landscape structure in the RRES supply.</p>", "<p id=\"Par51\">This research helps to overcome the lack of a coherent and integrated approach to ES assessment at the level of methods. The findings contributed to an evolving body of knowledge on the relationship between landscape structure and ES provision and help to incorporate landscape structure into ES framework. The findings help to pave the way for expanding the urban landscape ecology paradigm and provide an appropriate foundation for the resolution of urban planning subjects through analyzing the linkage between landscape structure and RRES.</p>", "<p id=\"Par52\">We suggest that this work may give a flexible approach with the potential to advance the application of the ES concept in practice for sustainable urban stormwater management and help to improve current tools and approaches. As the ES concept is increasingly integrated into urban decision-making and planning processes, this research contributes to a better understanding of the provision of ES on the landscape scale.</p>", "<p id=\"Par53\">Expanding the approach to other cities and ES can illuminate and improve the capacity to identify ecological value in terms of ES provision and emphasize ES’s essential structural factors specific to each landscape.</p>" ]

[ "<p id=\"Par1\">Urban stormwater runoff has posed significant challenges in the face of urbanization and climate change, emphasizing the importance of trees in providing runoff reduction ecosystem services (RRES). However, the sustainability of RRES can be disturbed by urban landscape modification. Understanding the impact of landscape structure on RRES is crucial to manage urban landscapes effectively to sustain supply of RRES. So, this study developed a new approach that analyzes the relationship between the landscape structural pattern and the RRES in Tabriz, Iran. The provision of RRES was estimated using the i-Tree Eco model. Landscape structure-related metrics of land use and cover (LULC) were derived using FRAGSTATS to quantify the landscape structure. Stepwise regression analysis was used to assess the relationship between landscape structure metrics and the provision of RRES. The results indicated that throughout the city, the trees prevented 196854.15 m³ of runoff annually. Regression models (<italic>p</italic> ≤ 0.05) suggested that the provision of RRES could be predicted using the measures of the related circumscribing circle metric (0.889 ≤ <italic>r</italic>^{<italic>2</italic>} ≤ 0.954) and the shape index (<italic>r</italic>^{<italic>2</italic>} = 0.983) of LULC patches. The findings also revealed that the regularity or regularity of the given LULC patches’ shape could impact the patches’ functions, which, in turn, affects the provision of RRES. The landscape metrics can serve as proxies to predict the capacity of trees for potential RRES using the obtained regression models. This helps to allocate suitable LULC through optimizing landscape metrics and management guidance to sustain RRES.</p>", "<title>Keywords</title>" ]

[]

[ "<title>Appendix 1 The landscape structure-related metrics distribution statistics for LULC classes within each district</title>", "<p id=\"Par57\">\n\n</p>", "<title>Author contributions</title>", "<p id=\"Par54\">This research was funded by IDUB grant under the increased by 2% subsidy for the University of Lodz, which took part in the competition under the “The Excellence Initiative – Research University” Program for the year 2021. Conceptualization:Vahid Amini Parsa, Jakub Kronenberg, Bahman Jabbarian Amiri; Methodology: Vahid Amini Parsa, Mustafa Nur Istanbuly, Bahman Jabbarian Amiri; Software: Vahid Amini Parsa, Mustafa Nur Istanbuly; Data curation: Vahid Amini Parsa; Formal analysis and investigation: Vahid Amini Parsa, Mustafa Nur Istanbuly; Visualization: Vahid Amini Parsa; Writing - Original draft preparation: Vahid Amini Parsa; Writing - Reviewing &amp; editing: Vahid Amini Parsa, Jakub Kronenberg, Alessio Russo, Bahman Jabbarian Amiri; Supervision: Jakub Kronenberg, Bahman Jabbarian Amiri; Validation: Jakub Kronenberg, Bahman Jabbarian Amiri</p>", "<title>Funding</title>", "<p id=\"Par55\">This research was funded by IDUB grant under the increased by 2% subsidy for the University of Lodz, which took part in the competition under the “The Excellence Initiative – Research University” Program for the year 2021.</p>", "<title>Compliance with ethical standards</title>", "<title>Conflict of interest</title>", "<p id=\"Par56\">The authors declare no competing interest.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Location of the studied area, LULC classes, administrative districts, and sample plots. D1-D10 are urban districts</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Summary of the methodological process</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Area (%) of LULC types within each urban district (D1 (District 1) to D10 (District 10))</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Comparison of urban trees’ structural traits and the runoff reduction among the LULC classes</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Runoff reduction efficiency (RRE) between the LULC classes (a) and districts (b). D1-D10 are urban districts</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Predicted vs. observed values (m³yr⁻¹) for RRES models using different landscape structure-related metrics</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>The detailed explanation of landscape structure-related metrics (Mcgarigal and Marks ##UREF##47##1994##; Rutledge ##UREF##67##2003##)</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Landscape metrics</th><th>Symbol</th><th colspan=\"2\">Equation</th><th>Range</th><th>Description</th></tr></thead><tbody><tr><td>Perimeter-Area Ratio</td><td><italic>PARA</italic></td><td></td><td>(1)</td><td></td><td>Measures the extent of shape complexity without standardization to the simple Euclidean shape.</td></tr><tr><td>Shape Index</td><td><italic>SHP</italic></td><td></td><td>(2)</td><td></td><td>Compares the complexity of the patch shape to the standard shape (square) of the same size.</td></tr><tr><td>Fractal Dimension Index</td><td><italic>FRAC</italic></td><td></td><td>(3)</td><td></td><td>Reflects the degree of patch shape complexity</td></tr><tr><td>Related Circumscribing Circle</td><td><italic>RCC</italic></td><td></td><td>(4)</td><td></td><td>Measures the overall patch elongation</td></tr><tr><td>Contiguity Index</td><td><italic>CI</italic></td><td></td><td>(5)</td><td></td><td>Measures the spatial contiguity of cells in the grid cell patches (patch boundary configuration and patch shape)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Tree population summary by urban districts</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Urban districts</th><th>Number of Trees</th><th>Percentage of Population</th><th>Tree Density (number ha⁻¹)</th><th>Leaf Area (km²)</th><th>Leaf Area per hectare (km² ha⁻¹)</th></tr></thead><tbody><tr><td>D1</td><td>141,550.00</td><td>7.34</td><td>91.77</td><td>601.49</td><td>0.3899</td></tr><tr><td>D2</td><td>205,958.00</td><td>10.68</td><td>99.33</td><td>859.67</td><td>0.4146</td></tr><tr><td>D3</td><td>232,665.00</td><td>12.07</td><td>83.62</td><td>961.09</td><td>0.3454</td></tr><tr><td>D4</td><td>196,119.00</td><td>10.17</td><td>79.77</td><td>848.67</td><td>0.3452</td></tr><tr><td>D5</td><td>238,648.00</td><td>12.38</td><td>75.59</td><td>1,098.14</td><td>0.3478</td></tr><tr><td>D6</td><td>490,798.00</td><td>25.46</td><td>68.56</td><td>2,189.08</td><td>0.3058</td></tr><tr><td>D7</td><td>229,349.00</td><td>11.90</td><td>79.44</td><td>991.74</td><td>0.3435</td></tr><tr><td>D8</td><td>32,822.00</td><td>1.70</td><td>85.75</td><td>131.69</td><td>0.3441</td></tr><tr><td>D9</td><td>49,333.00</td><td>2.56</td><td>61.32</td><td>237.00</td><td>0.2946</td></tr><tr><td>D10</td><td>110,324.00</td><td>5.72</td><td>104.94</td><td>454.46</td><td>0.4323</td></tr><tr><td>Total</td><td>1,927,566.00</td><td>100.00</td><td>79.33</td><td>8,373.04</td><td>0.3446</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>RRES by urban trees and its hydrological components within the urban districts</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Urban Districts</th><th>Potential Evapotranspiration (m³yr⁻¹)</th><th>Evaporation (m³yr⁻¹)</th><th>Transpiration (m³yr⁻¹)</th><th>Water Intercepted (m³yr⁻¹)</th><th>Runoff Reduction (m³yr⁻¹)</th></tr></thead><tbody><tr><td>D1</td><td>950,925.46</td><td>77,479.02</td><td>395,132.67</td><td>77,796.61</td><td>14,141.27</td></tr><tr><td>D2</td><td>1,359,103.38</td><td>110,736.34</td><td>564,740.53</td><td>111,190.24</td><td>20,211.31</td></tr><tr><td>D3</td><td>1,519,439.43</td><td>123,800.12</td><td>631,364.07</td><td>124,307.57</td><td>22,595.68</td></tr><tr><td>D4</td><td>1,341,711.12</td><td>109,319.26</td><td>557,513.63</td><td>109,767.35</td><td>19,952.67</td></tr><tr><td>D5</td><td>1,736,116.24</td><td>141,454.40</td><td>721,398.56</td><td>142,034.22</td><td>25,817.89</td></tr><tr><td>D6</td><td>3,460,841.69</td><td>281,980.71</td><td>1,438,063.97</td><td>283,136.53</td><td>51,466.38</td></tr><tr><td>D7</td><td>1,567,898.50</td><td>127,748.44</td><td>651,499.99</td><td>128,272.08</td><td>23,316.31</td></tr><tr><td>D8</td><td>208,196.68</td><td>16,963.34</td><td>86,510.79</td><td>17,032.88</td><td>3,096.11</td></tr><tr><td>D9</td><td>374,684.20</td><td>30,528.33</td><td>155,690.40</td><td>30,653.46</td><td>5,571.95</td></tr><tr><td>D10</td><td>718,481.64</td><td>58,540.08</td><td>298,546.61</td><td>58,780.04</td><td>10,684.58</td></tr><tr><td>Total</td><td>13,237,398.33</td><td>1,078,550.05</td><td>5,500,461.22</td><td>1,082,970.97</td><td>196,854.15</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Descriptive statistics of landscape structure-related metrics</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"2\">Landscape Metrics</th><th rowspan=\"2\">Descriptive Statistics</th><th colspan=\"5\">LULC Classes</th></tr><tr><th>CTI</th><th>Agricultural land</th><th>Green infrastructure</th><th>Residential area</th><th>Open space</th></tr></thead><tbody><tr><td rowspan=\"5\"><italic>RCC</italic></td><td>Mean</td><td>0.48</td><td>0.53</td><td>0.60</td><td>0.56</td><td>0.44</td></tr><tr><td>Max.</td><td>0.53</td><td>0.62</td><td>0.74</td><td>0.59</td><td>0.52</td></tr><tr><td>Min.</td><td>0.41</td><td>0.43</td><td>0.43</td><td>0.53</td><td>0.37</td></tr><tr><td>Std.</td><td>0.04</td><td>0.06</td><td>0.10</td><td>0.02</td><td>0.06</td></tr><tr><td>Var.</td><td>0.00</td><td>0.00</td><td>0.01</td><td>0.00</td><td>0.00</td></tr><tr><td rowspan=\"5\"><italic>CI</italic></td><td>Mean</td><td>0.45</td><td>0.84</td><td>0.48</td><td>0.73</td><td>0.16</td></tr><tr><td>Max.</td><td>0.64</td><td>0.94</td><td>0.77</td><td>0.80</td><td>0.18</td></tr><tr><td>Min.</td><td>0.27</td><td>0.75</td><td>0.31</td><td>0.66</td><td>0.12</td></tr><tr><td>Std.</td><td>0.13</td><td>0.06</td><td>0.15</td><td>0.04</td><td>0.02</td></tr><tr><td>Var.</td><td>0.02</td><td>0.00</td><td>0.02</td><td>0.00</td><td>0.00</td></tr><tr><td rowspan=\"5\"><italic>FRAC</italic></td><td>Mean</td><td>1.08</td><td>1.09</td><td>1.15</td><td>1.13</td><td>1.11</td></tr><tr><td>Max.</td><td>1.10</td><td>1.11</td><td>1.20</td><td>1.14</td><td>1.15</td></tr><tr><td>Min.</td><td>1.07</td><td>1.05</td><td>1.12</td><td>1.11</td><td>1.08</td></tr><tr><td>Std.</td><td>0.01</td><td>0.02</td><td>0.03</td><td>0.01</td><td>0.02</td></tr><tr><td>Var.</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td rowspan=\"5\"><italic>PARA</italic></td><td>Mean</td><td>6,750.39</td><td>1,903.17</td><td>6,432.22</td><td>3,258.64</td><td>10,738.80</td></tr><tr><td>Max.</td><td>9,118.51</td><td>3,133.51</td><td>8,802.72</td><td>4,119.78</td><td>11,383.50</td></tr><tr><td>Min.</td><td>4,342.77</td><td>735.05</td><td>2,717.19</td><td>2,325.06</td><td>10,310.91</td></tr><tr><td>Std.</td><td>1,704.02</td><td>782.88</td><td>2,155.84</td><td>566.97</td><td>359.81</td></tr><tr><td>Var.</td><td>2,903,692.45</td><td>612,894.67</td><td>4,647,648.30</td><td>321,457.01</td><td>129,460.41</td></tr><tr><td rowspan=\"5\"><italic>SHP</italic></td><td>Mean</td><td>1.21</td><td>1.52</td><td>1.63</td><td>1.69</td><td>1.33</td></tr><tr><td>Max.</td><td>1.37</td><td>1.74</td><td>1.92</td><td>1.91</td><td>1.51</td></tr><tr><td>Min.</td><td>1.12</td><td>1.12</td><td>1.48</td><td>1.46</td><td>1.22</td></tr><tr><td>Std.</td><td>0.08</td><td>0.20</td><td>0.14</td><td>0.15</td><td>0.10</td></tr><tr><td>Var.</td><td>0.01</td><td>0.04</td><td>0.02</td><td>0.02</td><td>0.01</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Statistics of regression models for the RRES using different landscape metrics</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th colspan=\"2\">Model</th><th colspan=\"3\">Coefficients</th><th rowspan=\"2\"><italic>r</italic>^{<italic>2</italic>}</th><th rowspan=\"2\"><italic>t</italic></th><th rowspan=\"2\"><italic>p</italic> value</th><th colspan=\"2\">Collinearity Statistics</th></tr><tr><th>Number</th><th>Variable</th><th><italic>B</italic></th><th>Standard Error</th><th>Beta</th><th>Tolerance</th><th>VIF</th></tr></thead><tbody><tr><td rowspan=\"3\">Eq. (##FORMU##19##2##)</td><td>Constant</td><td>−601,952.09</td><td>81,629.93</td><td/><td rowspan=\"3\">0.953</td><td>−7.374</td><td>0.005</td><td/><td/></tr><tr><td><italic>R</italic>_{<italic>RCC</italic>}</td><td>1,224,265.12</td><td>157,767.55</td><td>1.102</td><td>7.760</td><td>0.004</td><td>0.782</td><td>1.279</td></tr><tr><td><italic>CTI</italic>_{<italic>RCC</italic>}</td><td>−147,837.09</td><td>46,013.46</td><td>−0.456</td><td>−3.213</td><td>0.049</td><td>0.782</td><td>1.279</td></tr><tr><td rowspan=\"2\">Eq. (##FORMU##20##3##)</td><td>Constant</td><td>−0.05</td><td>1.73</td><td/><td rowspan=\"2\">0.889</td><td>−0.028</td><td>0.979</td><td/><td/></tr><tr><td><italic>A</italic>_{<italic>RCC</italic>}</td><td>18.79</td><td>3.32</td><td>0.943</td><td>5.666</td><td>0.005</td><td>1.000</td><td>1.000</td></tr><tr><td rowspan=\"2\">Eq. (##FORMU##21##4##)</td><td>Constant</td><td>15.88</td><td>1.09</td><td/><td rowspan=\"2\">0.891</td><td>14.532</td><td>0.000</td><td/><td/></tr><tr><td><italic>Ln</italic>(<italic>A</italic>_{<italic>RCC</italic>})</td><td>9.36</td><td>1.64</td><td>0.944</td><td>5.714</td><td>0.005</td><td>1.000</td><td>1.000</td></tr><tr><td rowspan=\"3\">Eq. (##FORMU##22##5##)</td><td>Constant</td><td>372,044.53</td><td>45,599.48</td><td/><td rowspan=\"3\">0.954</td><td>8.159</td><td>0.004</td><td/><td/></tr><tr><td><italic>Ln</italic>(<italic>R</italic>_{<italic>RCC</italic>})</td><td>711,165.57</td><td>90,408.06</td><td>1.118</td><td>7.866</td><td>0.004</td><td>0.758</td><td>1.319</td></tr><tr><td><italic>Ln</italic>(<italic>CTI</italic>_{<italic>RCC</italic>})</td><td>−71,587.56</td><td>21,505.89</td><td>−0.473</td><td>−3.329</td><td>0.045</td><td>0.758</td><td>1.319</td></tr><tr><td rowspan=\"3\">Eq. (##FORMU##23##6##)</td><td>Constant</td><td>−135,890.44</td><td>12,629.30</td><td/><td rowspan=\"3\">0.983</td><td>−10.760</td><td>0.002</td><td/><td/></tr><tr><td><italic>GI</italic>_{<italic>SHP</italic>}</td><td>71,403.05</td><td>8,972.72</td><td>0.698</td><td>7.958</td><td>0.004</td><td>0.750</td><td>1.333</td></tr><tr><td><italic>A</italic>_{<italic>SHP</italic>}</td><td>29,249.77</td><td>5,881.56</td><td>0.436</td><td>4.973</td><td>0.016</td><td>0.750</td><td>1.333</td></tr><tr><td rowspan=\"3\">Eq. (##FORMU##24##7##)</td><td>Constant</td><td>−51,322.51</td><td>6,197.89</td><td/><td rowspan=\"3\">0.983</td><td>−8.281</td><td>0.004</td><td/><td/></tr><tr><td><italic>Ln</italic>(<italic>GI</italic>_{<italic>SHP</italic>})</td><td>123,069.29</td><td>14,622.22</td><td>0.710</td><td>8.417</td><td>0.004</td><td>0.782</td><td>1.279</td></tr><tr><td><italic>Ln</italic>(<italic>A</italic>_{<italic>SHP</italic>})</td><td>40,982.88</td><td>7,945.54</td><td>0.435</td><td>5.158</td><td>0.014</td><td>0.782</td><td>1.279</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab6\"><label>Table 6</label><caption><p>Annual runoff reduction and trees for different cities</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"2\">City</th><th colspan=\"3\">Tree</th><th colspan=\"3\">Runoff reduction</th><th rowspan=\"2\">References</th></tr><tr><th>Number (million)</th><th>Cover (%)</th><th>Number per hectare</th><th>(m³ yr⁻¹)</th><th>(m³ tree⁻¹ yr⁻¹)</th><th>Efficiency (m³ ha⁻¹ yr⁻¹)</th></tr></thead><tbody><tr><td>Mesquite, U.S</td><td>2.09</td><td>24.4</td><td>174.7</td><td>855,858.00</td><td>0.409</td><td>71.52</td><td>(Pace and Sales ##UREF##60##2012##)</td></tr><tr><td>Houston, U.S</td><td>33.27</td><td>18.4</td><td>205.09</td><td>4,898,814.00</td><td>0.147</td><td>31.5</td><td>(Nowak et al. ##UREF##58##2017##)</td></tr><tr><td>Phoenix, Arizona, US</td><td>3.17</td><td>9</td><td>31.8</td><td>2,596,655.00</td><td>0.82</td><td>26.07</td><td>(Mikulanis ##UREF##49##2014##)</td></tr><tr><td>Plano, U.S</td><td>1.69</td><td>16.4</td><td>90.93</td><td>189,401.00</td><td>0.112</td><td>10.16</td><td>(PARD ##UREF##61##2014##)</td></tr><tr><td>London, UK</td><td>8.42</td><td>14</td><td>53</td><td>3,413,471.00</td><td>0.405</td><td>21.40</td><td>(Rogers et al. ##UREF##66##2015##)</td></tr><tr><td>Newport City, UK</td><td>0.26</td><td>12</td><td>54</td><td>87,900.00</td><td>0.338</td><td>18.10</td><td>(Buckland et al. ##UREF##10##2020##)</td></tr><tr><td>Oldham, UK</td><td>0.47</td><td>12</td><td>33</td><td>202,680.00</td><td>0.434</td><td>14.47</td><td>(Watson et al. ##UREF##84##2017##)</td></tr><tr><td>Tabriz, Iran</td><td>1.93</td><td>9.4</td><td>79.3</td><td>196,854.00</td><td>0.10</td><td>8.04</td><td>(this study)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Taba\"><table frame=\"hsides\" rules=\"groups\"><thead><tr><th rowspan=\"3\">Urban districts</th><th colspan=\"25\">Landscape metrics</th></tr><tr><th colspan=\"5\">\n<italic>CRC</italic>\n</th><th colspan=\"5\">\n<italic>CI</italic>\n</th><th colspan=\"5\">\n<italic>FRAC</italic>\n</th><th colspan=\"5\">\n<italic>PARA</italic>\n</th><th colspan=\"5\">\n<italic>SHP</italic>\n</th></tr><tr><th>CTI</th><th>Agricultural land</th><th>GI</th><th>Residential area</th><th>Open space</th><th>CTI</th><th>Agricultural land</th><th>GI</th><th>Residential area</th><th>Open space</th><th>CTI</th><th>Agricultural land</th><th>GI</th><th>Residential area</th><th>Open space</th><th>CTI</th><th>Agricultural land</th><th>GI</th><th>Residential area</th><th>Open space</th><th>CTI</th><th>Agricultural land</th><th>GI</th><th>Residential area</th><th>Open space</th></tr></thead><tbody><tr><td>D1</td><td>0.47</td><td>0.57</td><td>0.64</td><td>0.53</td><td>0.38</td><td>0.35</td><td>0.94</td><td>0.31</td><td>0.73</td><td>0.12</td><td>1.08</td><td>1.10</td><td>1.19</td><td>1.12</td><td>1.10</td><td>8,033.30</td><td>735.05</td><td>8,746.02</td><td>3,298.51</td><td>11,383.50</td><td>1.16</td><td>1.61</td><td>1.72</td><td>1.68</td><td>1.26</td></tr><tr><td>D2</td><td>0.51</td><td>0.54</td><td>0.43</td><td>0.57</td><td>0.37</td><td>0.48</td><td>0.89</td><td>0.34</td><td>0.80</td><td>0.15</td><td>1.08</td><td>1.09</td><td>1.12</td><td>1.11</td><td>1.08</td><td>6,204.21</td><td>1,250.72</td><td>8,802.72</td><td>2,325.06</td><td>10,797.28</td><td>1.18</td><td>1.50</td><td>1.52</td><td>1.54</td><td>1.25</td></tr><tr><td>D3</td><td>0.47</td><td>0.62</td><td>0.62</td><td>0.56</td><td>0.40</td><td>0.38</td><td>0.90</td><td>0.60</td><td>0.71</td><td>0.15</td><td>1.07</td><td>1.11</td><td>1.14</td><td>1.13</td><td>1.09</td><td>7,578.55</td><td>1,274.98</td><td>4,608.95</td><td>3,422.23</td><td>10,634.94</td><td>1.14</td><td>1.63</td><td>1.61</td><td>1.75</td><td>1.22</td></tr><tr><td>D4</td><td>0.41</td><td>0.53</td><td>0.57</td><td>0.55</td><td>0.45</td><td>0.29</td><td>0.84</td><td>0.52</td><td>0.66</td><td>0.15</td><td>1.07</td><td>1.10</td><td>1.12</td><td>1.14</td><td>1.12</td><td>8,939.97</td><td>1,937.47</td><td>5,693.92</td><td>4,119.78</td><td>10,951.68</td><td>1.12</td><td>1.69</td><td>1.50</td><td>1.86</td><td>1.32</td></tr><tr><td>D5</td><td>0.52</td><td>0.51</td><td>0.58</td><td>0.57</td><td>0.46</td><td>0.59</td><td>0.81</td><td>0.43</td><td>0.76</td><td>0.18</td><td>1.09</td><td>1.08</td><td>1.17</td><td>1.12</td><td>1.13</td><td>5,008.45</td><td>2,359.80</td><td>7,489.43</td><td>2,863.24</td><td>10,619.74</td><td>1.27</td><td>1.54</td><td>1.65</td><td>1.53</td><td>1.48</td></tr><tr><td>D6</td><td>0.49</td><td>0.58</td><td>0.74</td><td>0.59</td><td>0.52</td><td>0.50</td><td>0.75</td><td>0.55</td><td>0.67</td><td>0.18</td><td>1.08</td><td>1.11</td><td>1.20</td><td>1.13</td><td>1.14</td><td>6,078.83</td><td>3,133.51</td><td>5,177.65</td><td>3,986.69</td><td>10,310.91</td><td>1.21</td><td>1.74</td><td>1.92</td><td>1.68</td><td>1.41</td></tr><tr><td>D7</td><td>0.49</td><td>0.57</td><td>0.65</td><td>0.57</td><td>0.47</td><td>0.40</td><td>0.90</td><td>0.77</td><td>0.70</td><td>0.17</td><td>1.09</td><td>1.10</td><td>1.13</td><td>1.13</td><td>1.12</td><td>7,318.64</td><td>1,158.45</td><td>2,717.19</td><td>3,677.71</td><td>10,462.75</td><td>1.19</td><td>1.61</td><td>1.70</td><td>1.66</td><td>1.35</td></tr><tr><td>D8</td><td>0.53</td><td>0.43</td><td>0.71</td><td>0.56</td><td>0.44</td><td>0.59</td><td>0.77</td><td>0.47</td><td>0.76</td><td>0.18</td><td>1.10</td><td>1.07</td><td>1.17</td><td>1.13</td><td>1.10</td><td>4,880.62</td><td>2,745.88</td><td>5,870.29</td><td>2,848.75</td><td>10,360.38</td><td>1.29</td><td>1.23</td><td>1.48</td><td>1.83</td><td>1.30</td></tr><tr><td>D9</td><td>0.51</td><td>0.45</td><td/><td>0.53</td><td>0.51</td><td>0.64</td><td>0.80</td><td/><td>0.77</td><td>0.17</td><td>1.09</td><td>1.09</td><td/><td>1.11</td><td>1.15</td><td>4,342.77</td><td>2,487.10</td><td/><td>2,787.89</td><td>10,619.09</td><td>1.37</td><td>1.51</td><td/><td>1.46</td><td>1.51</td></tr><tr><td>D10</td><td>0.43</td><td>0.51</td><td>0.47</td><td>0.56</td><td>0.38</td><td>0.27</td><td>0.82</td><td>0.32</td><td>0.73</td><td>0.13</td><td>1.08</td><td>1.05</td><td>1.14</td><td>1.14</td><td>1.10</td><td>9,118.51</td><td>1,948.72</td><td>8,783.82</td><td>3,256.55</td><td>11,247.70</td><td>1.13</td><td>1.12</td><td>1.58</td><td>1.91</td><td>1.23</td></tr></tbody></table></table-wrap>" ]

[ "<inline-formula id=\"IEq1\"><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$PARA = \\frac{{p_{ij}}}{{a_{ij}}}$$\\end{document}</tex-math><mml:math id=\"M2\"><mml:mrow><mml:mi>P</mml:mi><mml:mi>A</mml:mi><mml:mi>R</mml:mi><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq2\"><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$PARA &gt; 0$$\\end{document}</tex-math><mml:math id=\"M4\"><mml:mrow><mml:mi>P</mml:mi><mml:mi>A</mml:mi><mml:mi>R</mml:mi><mml:mi>A</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq3\"><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SHP = \\frac{{0.25\\,p_{ij}}}{{\\sqrt {a_{ij}} }}$$\\end{document}</tex-math><mml:math id=\"M6\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>H</mml:mi><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>0.25</mml:mn><mml:mspace width=\"0.25em\"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msqrt><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq4\"><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$SHP \\ge 1$$\\end{document}</tex-math><mml:math id=\"M8\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>H</mml:mi><mml:mi>P</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq5\"><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$FRAC = \\frac{{2\\,\\ln \\left( {0.25\\,p_{ij}} \\right)}}{{\\ln a_{ij}}}$$\\end{document}</tex-math><mml:math id=\"M10\"><mml:mrow><mml:mi>F</mml:mi><mml:mi>R</mml:mi><mml:mi>A</mml:mi><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mspace width=\"0.25em\"/><mml:mo>ln</mml:mo><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mn>0.25</mml:mn><mml:mspace width=\"0.25em\"/><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mo>ln</mml:mo><mml:mspace width=\"0.25em\"/><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq6\"><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$1 \\le FRAC \\le 2$$\\end{document}</tex-math><mml:math id=\"M12\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>F</mml:mi><mml:mi>R</mml:mi><mml:mi>A</mml:mi><mml:mi>C</mml:mi><mml:mo>≤</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq7\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RCC = 1 - \\left[ {\\frac{{a_{ij}}}{{a_{ij}^s}}} \\right]$$\\end{document}</tex-math><mml:math id=\"M14\"><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq8\"><alternatives><tex-math id=\"M15\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0 \\le RCC \\le 1$$\\end{document}</tex-math><mml:math id=\"M16\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq9\"><alternatives><tex-math id=\"M17\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$CI = \\frac{{\\left[ {\\frac{{\\mathop {\\sum}\\nolimits_{r = 1}^z {c_{ijr}} }}{{a_{ij}^ \\ast }}} \\right] - 1}}{{v - 1}}$$\\end{document}</tex-math><mml:math id=\"M18\"><mml:mrow><mml:mi>C</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mfenced close=\"]\" open=\"[\"><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>v</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq10\"><alternatives><tex-math id=\"M19\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$0 \\le CI \\le 1$$\\end{document}</tex-math><mml:math id=\"M20\"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>C</mml:mi><mml:mi>I</mml:mi><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq11\"><alternatives><tex-math id=\"M21\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{\\boldsymbol{p}}}}_{{{{\\boldsymbol{ij}}}}}$$\\end{document}</tex-math><mml:math id=\"M22\"><mml:msub><mml:mrow><mml:mi mathvariant=\"bold-italic\">p</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold-italic\">ij</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq12\"><alternatives><tex-math id=\"M23\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{\\boldsymbol{a}}}}_{{{{\\boldsymbol{ij}}}}}$$\\end{document}</tex-math><mml:math id=\"M24\"><mml:msub><mml:mrow><mml:mi mathvariant=\"bold-italic\">a</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold-italic\">ij</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq13\"><alternatives><tex-math id=\"M25\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{\\boldsymbol{c}}}}_{{{{\\boldsymbol{ijr}}}}}$$\\end{document}</tex-math><mml:math id=\"M26\"><mml:msub><mml:mrow><mml:mi mathvariant=\"bold-italic\">c</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold-italic\">ijr</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq14\"><alternatives><tex-math id=\"M27\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{\\boldsymbol{a}}}}_{{{{\\boldsymbol{ij}}}}}^ \\ast$$\\end{document}</tex-math><mml:math id=\"M28\"><mml:msubsup><mml:mrow><mml:mi mathvariant=\"bold-italic\">a</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold-italic\">ij</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq15\"><alternatives><tex-math id=\"M29\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${{{\\boldsymbol{v}}}}$$\\end{document}</tex-math><mml:math id=\"M30\"><mml:mi mathvariant=\"bold-italic\">v</mml:mi></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M31\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$y_i = \\beta _0 + \\beta _1x_1 + \\beta _2x_2 + \\cdots + \\beta _{n - 1}x_{n - 1} + \\varepsilon _i$$\\end{document}</tex-math><mml:math id=\"M32\"><mml:mrow><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>⋯</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<inline-formula id=\"IEq16\"><alternatives><tex-math id=\"M33\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m^3/yr$$\\end{document}</tex-math><mml:math id=\"M34\"><mml:mrow><mml:msup><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mi>y</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq17\"><alternatives><tex-math id=\"M35\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\beta _0$$\\end{document}</tex-math><mml:math id=\"M36\"><mml:msub><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq18\"><alternatives><tex-math id=\"M37\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\varepsilon _i$$\\end{document}</tex-math><mml:math id=\"M38\"><mml:msub><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M39\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RRES = - 601952.094 + 1224265.115\\,R_{RCC} - 147837.089\\,CTI_{RCC}$$\\end{document}</tex-math><mml:math id=\"M40\"><mml:mrow><mml:mi>R</mml:mi><mml:mi>R</mml:mi><mml:mi>E</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>601952.094</mml:mn><mml:mo>+</mml:mo><mml:mn>1224265.115</mml:mn><mml:mspace width=\"0.25em\"/><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>147837.089</mml:mn><mml:mspace width=\"0.25em\"/><mml:mi>C</mml:mi><mml:mi>T</mml:mi><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M41\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Ln\\,RRES = - 0.048 + 18.791\\,A_{RCC}$$\\end{document}</tex-math><mml:math id=\"M42\"><mml:mrow><mml:mi>L</mml:mi><mml:mi>n</mml:mi><mml:mspace width=\"0.25em\"/><mml:mi>R</mml:mi><mml:mi>R</mml:mi><mml:mi>E</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>0.048</mml:mn><mml:mo>+</mml:mo><mml:mn>18.791</mml:mn><mml:mspace width=\"0.25em\"/><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M43\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$Ln\\,RRES = 15.879 + 9.361\\,Ln\\left( {A_{RCC}} \\right)$$\\end{document}</tex-math><mml:math id=\"M44\"><mml:mrow><mml:mi>L</mml:mi><mml:mi>n</mml:mi><mml:mspace width=\"0.25em\"/><mml:mi>R</mml:mi><mml:mi>R</mml:mi><mml:mi>E</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>15.879</mml:mn><mml:mo>+</mml:mo><mml:mn>9.361</mml:mn><mml:mspace width=\"0.25em\"/><mml:mi>L</mml:mi><mml:mi>n</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M45\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RRES = 372044.529 + 711165.569\\,Ln\\left( {R_{RCC}} \\right) - 71587.563\\,Ln\\left( {CTI_{RCC}} \\right)$$\\end{document}</tex-math><mml:math id=\"M46\"><mml:mrow><mml:mi>R</mml:mi><mml:mi>R</mml:mi><mml:mi>E</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>372044.529</mml:mn><mml:mo>+</mml:mo><mml:mn>711165.569</mml:mn><mml:mspace width=\"0.25em\"/><mml:mi>L</mml:mi><mml:mi>n</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>−</mml:mo><mml:mn>71587.563</mml:mn><mml:mspace width=\"0.25em\"/><mml:mi>L</mml:mi><mml:mi>n</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi>C</mml:mi><mml:mi>T</mml:mi><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ6\"><label>6</label><alternatives><tex-math id=\"M47\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RRES = - 135890.437 + 71403.049\\,GI_{SHP} + 29249.765\\,A_{SHP}$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:mrow><mml:mi>R</mml:mi><mml:mi>R</mml:mi><mml:mi>E</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>135890.437</mml:mn><mml:mo>+</mml:mo><mml:mn>71403.049</mml:mn><mml:mspace width=\"0.25em\"/><mml:mi>G</mml:mi><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi><mml:mi>H</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>29249.765</mml:mn><mml:mspace width=\"0.25em\"/><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi><mml:mi>H</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ7\"><label>7</label><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$RRES = - 51322.510 + 123069.289\\,Ln\\left( {GI_{SHP}} \\right) + 40982.882\\,Ln\\left( {A_{SHP}} \\right)$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:mrow><mml:mi>R</mml:mi><mml:mi>R</mml:mi><mml:mi>E</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>51322.510</mml:mn><mml:mo>+</mml:mo><mml:mn>123069.289</mml:mn><mml:mspace 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[ "<table-wrap-foot><p> : perimeter (<italic>m</italic>) of patch ij, : area (<italic>m</italic>²) of patch ij: area (<italic>m</italic>²) of the smallest circumscribing circle around patch ij, : contiguity value for pixel r in patch ij, : area of patch ij in terms of the number of cells, : sum of the values in a 3-by-3 cell template (13 in this case).</p></table-wrap-foot>", "<table-wrap-foot><p><italic>Max.</italic> Maximum, <italic>Min.</italic> Minimum, <italic>Std.</italic> Standard division, <italic>Var.</italic> Variance.</p></table-wrap-foot>", "<table-wrap-foot><p><italic>CTI</italic> Commercial/ Transportation /institutional, <italic>GI</italic> Green infrastructure.</p></table-wrap-foot>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Internal representations of space are used to process stimuli located around an individual’s body (Aggius-Vella et al. ##REF##32898519##2020a##; see Serino ##REF##30685486##2019## for a review). Peripersonal space, referring to the space in front of us, is defined as the portion of space surrounding our body where objects can be grasped and we can interact with the environment (e.g., Rizzolatti et al. ##REF##9235632##1997##). Not surprisingly, the extent of the individual peripersonal space is debatable and can be modulated by different context and interactions with the environment (Sambo et al. ##REF##22973016##2012a##; Serino ##REF##30685486##2019##).</p>", "<p id=\"Par3\">Some authors suggested that a crucial aspect of PPS is related to arm length (e.g., Longo and Lourenco ##REF##17256162##2007##) and different findings indicate that the transition between peripersonal and extrapersonal space is not clearly defined (de Vignemont and Iannetti ##REF##25448854##2015##; Bufacchi and Iannetti ##REF##30337061##2018##) depending on tool use and type of stimuli (Hunley and Lourenco ##REF##29985555##2018##; Longo and Lourenco ##REF##16243365##2006##; Longo et al. ##REF##25446963##2015##; Maravita and Iriki ##REF##15588812##2004##; Canzoneri et al. ##REF##23028516##2012##; Ferri et al. ##REF##25744869##2015##). However, stimuli presented within the peripersonal space can also trigger different responses depending on their perceived nature and whether they are positioned in close proximity to the body (e.g., Spaccasassi et al. ##UREF##6##2019##), an area known as the ‘Defensive Peri-Personal Space’ <italic>(</italic>DPPS). This is an area within the peripersonal space that represents a ‘safety margin’ surrounding the body (e.g., Graziano and Cooke ##REF##16277998##2006## p. 845; Sambo and Iannetti ##REF##23986256##2013##; de Vignemont and Iannetti ##REF##25448854##2015##). A fascinating aspect about DPPS is the flexibility of its boundaries and how the magnitude of our response can be modulated by the perceived proximity of stimuli entering this area (e.g., Sambo et al. ##REF##22090460##2012b##).</p>", "<p id=\"Par4\">A series of elegant studies refined the DPPS looking at the magnitude of hand-blink reflex (see Bufacchi and Iannetti ##REF##30337061##2018## for a review), which is a subcortical reflex elicited by the electrical stimulation of the median nerve on the internal part of the wrist. The electrical stimulation tends to induce a rapid blink response, which is maximised when the hand enters the DPPS and is close to the face (far-near effect; Bufacchi et al. ##UREF##2##2015##). The authors delimited a bubble-shaped area around the face representing the DPPS where the magnitude of the reflexive response was more intense (see also Versace et al. ##REF##32573801##2020##, ##UREF##7##2021##). This finding suggests that knowing the location of the hand via proprioceptive information has an impact on a brainstem reflex response. This top–down process is even more evident in a series of studies by Sambo et al. (##REF##22973016##2012a##; see also Bufacchi and Iannetti ##REF##30337061##2018##) where the blink response was modulated by adding or removing a ‘protective’ screen between the participant’s hand and face. These studies also pointed out how the boundaries of this defensive area are malleable, without clear in-or-out zone, and can be affected by a variety of factors (e.g., valence of stimuli) in addition to proximity to the body (Bufacchi and Iannetti ##REF##30337061##2018##).</p>", "<p id=\"Par5\">Surprisingly, very little is known about the peripersonal space behind us (back space) and a few studies have attempted to investigate this portion of the space (e.g., Graziano et al. ##REF##9989407##1999##; Kóbor et al. ##REF##16516383##2006##; Cocchini et al. ##REF##16934381##2007##; Zampini et al. ##REF##17291546##2007##; Occelli et al. ##REF##20621120##2011##; Noel et al. ##REF##26231086##2015##; Aggius-Vella et al. ##REF##29925849##2018##; Aggius-Vella et al. ##REF##31358878##2019##; Aggius-Vella et al. ##REF##32898519##2020a##,##REF##32286362##b##; Aggius-Vella et al. ##REF##35220107##2022##; see also Vallar et al. ##REF##7735887##1995##; Farnè &amp; Làdavas ##REF##12419126##2002##; Viaud-Delmon et al. ##REF##17702039##2007##; Kerkhoff et al. ##REF##16256151##2006## for studies with clinical population). By means of the hand-blink-reflex paradigm, Bufacchi et al. (##UREF##2##2015##) did not observe a significantly stronger blink response once the hand was positioned on the back of the head compared to front positions. However, unlike the front space, the rear space is not seen and acoustic stimuli may play a crucial role in the spatial representation of the rear space (Graziano et al. ##REF##9989407##1999##). In fact, adopting an audio-tactile stimulation, Noel et al. (##REF##26231086##2015##) observed that subjective perception of the back space could be modulated during a full-body illusion paradigm. Aggius-Vella et al. (##REF##29925849##2018##) adopted an auditory bisection paradigm to compare participants’ performance on front and back space. The authors concluded that the lack of vision and limited movement in the back space would be responsible for a poorer representation of the back space compared to the front space.</p>", "<p id=\"Par6\">Taken together, these findings suggest that the (defensive) peripersonal space is malleable with no discrete boundaries and it should not be considered a single space but rather as various peripersonal fields modulated by a multitude of factors (Bufacchi and Iannetti ##REF##30337061##2018##). However, although extensive studies have been devoted to exploring the front space, the possible interaction of top–down and bottom–up mechanisms is still unclear, especially for the rear space.</p>", "<p id=\"Par7\">Blinking is a broad response that can be elicited by a multitude of stimuli, including sounds (Esteban ##REF##10093816##1999##; Grosse and Brown ##REF##12750424##2003##; Carlsen et al. ##REF##20466020##2011##; Brown et al. ##REF##1884184##1991##). Since the source of sounds, unlike somatosensory stimuli, is not constrained by the extension of the arm, acoustic stimulation can offer suitable means to explore spatial representation of the back space. Therefore, the scope of this study was to evaluate individuals’ spatial representation for back space compared to front space in an ambiguous environment that offered some degree of uncertainty in terms of both distance and front–back egocentric location of sound sources. In particular, we aimed to consider back space representation by looking at verbal responses about localization of sound sources and blink reflex comparing stimuli in the front–back egocentric space.</p>" ]

[ "<title>Methods and procedure</title>", "<title>Participants</title>", "<p id=\"Par8\">A priori sample size calculation for behavioural phase (see later) of the study was conducted with G*Power for a 2 × 2 repeated-measures ANOVA (effect size of 0.3; power of 0.8; α of 0.05), which suggested a minimum sample size of 26. A group of 30 healthy volunteers (19 women) with no neurological or psychiatric history entered the study. Their average age was 24.8 (SD = 3.0; range 20–30) with, on average, 18.0 years of formal education (SD = 1.86; range 12–23). According to the Oldfield Questionnaire (Oldfield ##REF##5146491##1971##) score, 3 participants were classified as left-handed and 27 were right-handed. All participants reported normal hearing and right-ear dominance.</p>", "<p id=\"Par9\">Because of the experimental setting described below, an important inclusion criterion was no evidence of claustrophobia <xref ref-type=\"fn\" rid=\"Fn1\">1</xref>. The study was approved by Goldsmiths Ethics Committee and participants gave written informed consent before taking part in the study.</p>", "<title>Sound localization task</title>", "<p id=\"Par10\">Each participant sat blindfolded at the centre of an anechoic and soundproof booth of 150 × 160 cm. Two speakers were placed at fixed distances, one directly in front and one behind the participant. Acoustic stimuli were sent from a PC placed outside the soundproof booth and connected via cable with the speakers. Examiners controlled the entire experiment from outside the soundproof room. Acoustic stimuli were developed with Goldwave (digital audio editing software) and consisted of 20 white noise bursts. To render the sound localisation more challenging, the sound pressure was constantly held at 75 dB at ear level and the sound duration was 200 ms. These parameters were selected following a pilot study showing that performance was not at ceiling. The inter-stimulus interval was randomly selected amongst three possible intervals of 5, 10, or 15 s.</p>", "<p id=\"Par11\">The experiment was divided in two blocks of 10 sounds, 5 sounds coming from the front speaker (Front condition) and 5 coming from the back speaker (Back condition). Both speakers were located at 90 cm from the floor (approximately at the height of the participants’ head). Back and Front conditions were randomly presented within each block. In one block, the speakers were located 50 cm from the participant (within reaching space; namely Close condition in our study). In the other block, the speakers were located 1 m from the participant (outside reaching space; namely Far condition in our study; see Fig. ##FIG##0##1##). The order of the two blocks was counterbalanced across participants. After each block, there was an interval of approximately 5 min during which the participants, with their eyes closed, were carefully guided outside the soundproof room to allow repositioning of the speakers for the next block. Participants were not informed about the change of location of the speakers nor about the number of possible locations. The ambiguity of the sound localization permitted to opt for a block design to allow direct comparisons of back and front sound sources at the same distance; it also minimises sound reflections by minimising the number of objects with hard surfaces (i.e., speakers) in the room.</p>", "<p id=\"Par12\"><underline>Behavioural data</underline>: Participants were instructed to sit as still as possible and pay attention to brief sounds that were played at different intervals from different positions. Soon after each sound, they provided verbal responses about the location of the sound source (saying “back” or “front”; <italic>perceived location</italic>) and then its distance (<italic>perceived distance</italic>) expressed in their preferred metric (these responses were then all transformed in cm for the analyses). Their verbal responses were audio recorded for later analysis. Importantly, since participants were instructed to keep their eyes closed before entering the testing room and during the entire duration of the experiment, they had no information about the real size of the soundproof room. The sound localisation task lasted about 9 min (approx. 2 min per each block, plus 5 min to reposition the speakers for block 2).</p>", "<p id=\"Par13\">Considering the behavioural data, we aim to explain a) the subjectively perceived location and distance of the sound source and b) the accuracy of participants’ perceived location and distance judgments. As independent variables, we use the actual location (back vs. front) and actual distance (near vs. far). In addition, we test whether perceived, instead of actual, location is a better predictor for perceived distance. This could provide insight into how subjective location and distance judgements are linked.</p>", "<p id=\"Par14\"><underline>Electromyographical data</underline>: For 26 participants, we also recorded the electromyographic (EMG) activity of the orbicularis oculi muscle bilaterally to measure the blink reflexes in response to the acoustic stimuli. EMG was recorded using two pairs of surface electrodes with the active electrode over the mid lower eyelid and the reference electrode placed laterally to the outer canthus (interelectrode distance 1 cm). The ground electrode was placed on the mastoid. Before positioning the electrodes, skin was accurately scrubbed to reduce skin impedance (Blumenthal et al. ##REF##15720576##2005##). Signals were recorded through a custom-made surface EMG acquisition system performing amplification and digitization at a sampling frequency of 1200 Hz with 24-bit resolution, and saved for offline analysis. A program created with C +  + was designed to synchronise stimuli delivery and EMG data collection. The design of the amplifier removes the DC component with a time constant of 0.1 s. The ADC dynamic was 50 mV due to front-end gain, ADC reference voltage was actually 2.5 V (headroom was ± 2.5 V). Electrodes were positioned before the start of the first block and remained in place for the entire duration of the experiment.</p>", "<p id=\"Par15\">EMG raw signals were bandpass filtered (200–400 Hz, fourth-order Butterworth filter) and cleaned from power line interference (50 Hz notch filter, fourth-order Butterworth). Signal quality was assessed through visual analysis in the time-domain of single blink responses and bad trials (i.e., high levels of noise artifacts or failure of detecting spontaneous blinks) were rejected. For each subject and trial, EMG responses were averaged bilaterally given the symmetrical nature of elicited blinking (Esteban ##REF##10093816##1999##; Blumenthal et al. ##REF##8913523##1996##).</p>", "<p id=\"Par16\">For each trial, we identified the onset and the peak of a blink reflex. The former was identified after signal rectification as the first point exceeding 2 standard deviations of the EMG baseline mean (identified as data in 200 ms before the stimulus delivery; Hodges and Bang ##UREF##4##1996##); the latter was identified as the peak value in a time window between the delivered stimulus and 200 ms after it (Blumenthal et al. ##REF##15720576##2005##).</p>", "<p id=\"Par17\">EMG responses were then quantified in terms of (i) Onset Latency (latency between the start of each stimulus and blinking onset; (ii) Peak Latency (latency between the start of the stimulus and the peak of blinking; (iii) Peak amplitude. The aforementioned metrics are indeed retained the most representative in quantifying the response to a blinking stimulus from electromyographic signals (Blumenthal et al. ##REF##15720576##2005##; Blumenthal ##REF##8913523##1996##; Berg and Balaban ##UREF##1##1999##; van Boxtel ##REF##20688130##2010##).</p>" ]

[ "<title>Results</title>", "<title>Behavioural data</title>", "<title>Data pre-processing and analysis strategy</title>", "<p id=\"Par18\">All 30 participants completed the Sound localization task for a total of 600 trials across all four conditions. Participants’ responses about distance, originally expressed in their preferred metric, were all converted in the same metric (cm). Individuals’ overall mean estimation of distances across conditions was calculated and two participants (n. 16 and 30) were excluded as their responses were more than 2 SDs<xref ref-type=\"fn\" rid=\"Fn2\">2</xref> (i.e., 2.72 and 3.34, respectively) from the group mean. A third participant (n. 7) was excluded as she did not provide any response in the Far condition. Therefore, analyses were conducted on the remaining 27 participants for a total of 540 trials across all conditions. Of these, 66 trials (12% across all four conditions with a number of excluded trials ranging from 11 to 22 out of 135 per condition; the median of valid trials per participant was 95% ranging from 55 to 100%) could not be considered for further analysis as they were associated with invalid responses for localization or estimated distance (e.g., “Left”, “Above”, “I don’t know” or there was no response). Therefore, final analyses were conducted on 474 trials across both distance conditions (i.e., 236 for Close and 238 for Far) and across both spatial locations (234 for Front and 240 for Back). Values of d’ were computed at the aggregate level for Close and Far conditions. To by-pass the problem of ceiling or floor effects for some cells, we followed the replacement of data method adopted as in the previous studies (e.g., Baddeley et al. ##REF##10536087##1999##; Brazzelli et al. ##REF##7890820##1994##; Guilford ##UREF##3##1954##). The average d’ for the Close condition was 0.75 (SD = 1.29), while it was 0.65 (SD = 1.49) for the Far condition; a t test did not show a significant difference between conditions (<italic>p</italic> = 0.423). Overall, 60.55% of the perceived location responses were correct; a one-sample t test analysis indicated that this performance was significantly above chance level (<italic>t</italic> = 26.943; <italic>p</italic> &lt; 0.001). Perceived locations for all conditions are reported in Table ##TAB##0##1##.</p>", "<p id=\"Par20\">The distribution of distance responses was heavily skewed (skewness = 2.78, see figure in the supplementary material), and therefore, distance responses were log-transformed.</p>", "<p id=\"Par21\">Location accuracy was scored as a binary variable (0 = incorrect, 1 = correct) and distance accuracy was computed as <italic>|r – a|/a</italic>, where <italic>r</italic> is the distance response in cm and <italic>a</italic> represents the actual distance (50 cm or 100 cm).</p>", "<p id=\"Par22\">All analyses were implemented using mixed effect models using the lmer() function (using a Gaussian error distribution) and the glmer() function (using a binomial error distribution) from the R package lme4. For each analysis, we computed four models that had identical fixed effects (i.e., location and distance and independent variables) but varied in their random effects structure from simple random intercepts for participants to the maximal random effect structure also containing random slopes for both experimental factors (Barr et al. ##UREF##0##2013##). In particular, we tested models with only random intercepts across participants, models with uncorrelated and correlated random effects for intercepts and slopes for actual location and models with random participant intercepts, and random slopes for actual location and actual distance. These four models differing in their random effect structure were compared on the Bayesian Information Criterion (BIC) and using a likelihood ratio Chi-square test. Once the random effect structure with the best fit to the data was chosen, the fixed effects of this model were then analysed with a type III sum-of-squares (ANOVA) Wald test. In addition, partial <italic>R</italic>² effect sizes are calculated for each fixed effect predictor by refitting the final model using penalised maximum likelihood (via the glmmPQL() function from the R package MASS) and subsequently applying the r2beta() function from the r2glmm package. Further information is provided in the supplementary material file.<list list-type=\"simple\"><list-item><label>(i)</label><p id=\"Par23\">Modelling perceived location and perceived distance responses</p><p id=\"Par24\">For modelling perceived location and perceived distance, the models with random participant intercepts and correlated random slopes for actual locations directions each had the best fit (see supplementary material to see model formulae and model comparison results). For the model using perceived location as a dependent variable, Table ##TAB##1##2## and the model summary in Fig. ##FIG##1##2## indicate that the participant response \"front\" is significantly associated with front being the actual location but also with the sound coming from the far distance (100 cm).</p><p id=\"Par25\">In contrast, the model using perceived distance as a dependent variable shows that neither actual location, actual distance nor their interaction influences participant responses significantly. That being said, the effect of actual stimulus direction is approaching the usual significance level and stimuli sounding in the back are perceived as more distant (but <italic>p</italic> = 0.071; see Table ##TAB##2##3##). This trend is also visible in Fig. ##FIG##2##3##, as well as the wide confidence intervals around the point estimates.</p><p id=\"Par26\">Replacing actual stimulus location with perceived stimulus location as a predictor does not improve the modelling of perceived distance judgements. The model with perceived stimulus location as predictor has a BIC = 939, while the model with actual stimulus location has a better BIC = 928. Thus, the accuracy of (log) distance judgements is best modelled with actual location.</p></list-item><list-item><label>(ii)</label><p id=\"Par27\">Modelling the accuracy of location and distance responses</p><p id=\"Par28\">Across all participants, the percentage of accurate responses for perceived location (as ‘front’ or ‘back’) of the sounds was 60.55% (287/474) of which: 60.7% (142/234) for stimuli in the Front, 60.4% (145/240) for stimuli in the Back, 62.7% (148/236) for Close stimuli, and 58.4% (139/238) for Far stimuli. When modelling the accuracy of the perceived location with mixed-effects models (using a binomial error distribution), a model with random intercepts for participants and correlated random slopes for location had the best fit. The summaries of the model tests in Table ##TAB##3##4##A and B, as well as the corresponding plot (Fig. ##FIG##3##4##), show that the main effects of actual direction or actual distance do not influence the accuracy of participants’ perceived \nlocation, but their interaction does. Stimuli presented at a close distance at the back of the participants are judged most accurately. Stimuli presented from the front and at a far distance are most difficult to judge.</p><p id=\"Par29\">The means and standard deviations of perceived distance accuracy for each experimental condition are given in Table ##TAB##4##5##. Because accuracy values are expressed relative to the target distance, this allows for an interpretation in terms of percentage distance from the actual distance of the sound source. Participant perceived distance is much more accurate (about 15%) for near sounds.</p><p id=\"Par30\">When modelling perceived distance, a model with random intercepts for participants and correlated random slopes (across directions and locations) has the best fit. The model-based effects plot in Fig. ##FIG##4##5## and the model summary in Table ##TAB##5##6## show that only the actual distance—not the direction or their interaction—influence participant responses significantly.</p></list-item></list></p>", "<title>EMG data</title>", "<p id=\"Par31\">After data pre-processing, as described in the Method section, we quantified/measured the EMG response on 122 trials in terms of (i) Onset Latency, (ii) Peak Latency, and (iii) Peak amplitude. Out of these three variables, only the Peak Amplitude had a distribution that was substantially skewed and required a log-transformation.<list list-type=\"bullet\"><list-item><p>Modelling peak amplitude</p></list-item></list></p>", "<p>Means and standard deviations for all three dependent variables derived EMG responses are given in Table ##TAB##6##7## and illustrated in Fig. ##FIG##5##6##.</p>", "<p id=\"Par34\">Peak amplitude is best modelled with only random intercepts for participants. However, none of the fixed effect predictors makes a significant contribution towards explaining the EMG peak as Table ##TAB##7##8## shows.</p>", "<p id=\"Par35\">Model fit increases when actual stimulus location (BIC = 272) is replaced with perceived stimulus location (BIC = 268) and perceived stimulus location becomes a significant model predictor as Table ##TAB##8##9## shows.</p>", "<p id=\"Par36\">This implies that the EMG peak is better modelled with perceived as opposed to actual location of the sound source.</p>", "<p id=\"Par37\">For modelling the latency between stimulus onset and EMG amplitude peak, a random effect model with random intercepts and random slopes for locations has the best model fit. However, none of the fixed effect predictors reaches the common significance levels in the model. When replacing actual stimulus location with perceived stimulus location, a model fit in terms of the BIC is obtained, but predictors in the resulting model still have non-significant coefficients as Table ##TAB##9##10## shows.</p>", "<p id=\"Par38\">A similar picture emerges when the latency between stimulus onset and onset of the EMG amplitude is modelled as a dependent variable. A model with only random intercepts for participants has the closest fit, but neither actual sound location nor actual distance has a significant model coefficient (see Table ##TAB##10##11##). However, when actual sound location is replaced with perceived sound location, model fit increases and perceived location approaches the common significance level (see Table ##TAB##10##11##).</p>", "<p id=\"Par39\">Finally, a further analysis considering blink magnitude as a predictive factor did not show a significant contribution (<italic>p</italic> = 0.1991) and a very low effect was associated with it (R2 = 0.003).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par40\">Studies evaluating the peripersonal space have indicated that the front space is not uniformly represented and that stimuli presented closer to the body may trigger stronger responses as they fall in a defensive graded field (Bufacchi and Iannetti ##REF##30337061##2018##). However, much less is known about the rear space where accurate location of stimuli, sounds in particular, would be crucial from an evolutionary perspective (Kolarik et al. ##REF##26590050##2016##). By means of a sound localization paradigm, our study aimed to establish whether participants hold a different spatial representation for front and back space and whether acoustic stimuli at different distances from the body could trigger stronger (defensive) blink responses.</p>", "<p id=\"Par41\">A natural methodological limitation to evaluate spatial representation with sounds at various distances is sound reverberation and the difference of the sound level reaching the individual’s ear (Zahorik and Wightman ##REF##11135648##2001##), which is “the most reliable auditory distance cue” available to participants (Aggius-Vella et al. ##REF##35220107##2022##; p. 4). To enhance some degree of uncertainty about localisation, the study was run in a soundproof environment and the sound loudness was maintained constant at the level of the participant’s ear. Clearly, some minor differences amongst the perceived sounds could have guided, at least in part, the participants’ response about location. Indeed, the localisation task proved to be rather challenging, with an overall localisation accuracy above chance of 60%, comparable for both front and back stimuli; an ambiguity that became crucial for further analyses. Importantly, the lack of significant difference between front and back discrimination suggests that our participants did not show an overall response bias for either position.</p>", "<p id=\"Par42\">The first set of analyses with behavioural data was conducted considering the effect of actual location and distance of acoustic stimuli on subjective evaluation of location and perceived distance of the stimuli. Findings indicated that participants’ perceived location (front vs back) of sounds was influenced by the actual location and distance of the stimuli, but we also observed a significant tendency to perceive stimuli originated in more distant locations as coming from the front. It seems, therefore, that participants tended to correctly locate the source (front vs back) of the sounds above chance level, but their more frequent front–back discrimination error was to misallocate distant back sounds to the front space. This type of error trend may have mitigated possible effects during the distance estimation of the stimuli as an incorrect location of a stimulus will inevitably affect all spatial references, making distance judgments meaningless. Thus, it was crucial to take into account the accuracy of perceived location in a second set of analyses.</p>", "<p id=\"Par43\">When the accuracy for the perceived location of stimuli was considered in the mixed effect models, we observed an interaction between actual location and actual distance. The interaction suggested that participants were more accurate in locating back sounds in the close condition and more accurate in locating front stimuli in the far condition. Sounds in the far back condition tended to be misallocated in the front space. It is important to note that, overall, participants’ perceived distance of sounds was about 15% more accurate for close stimuli than far stimuli. This result may be due, at least in part, to a general underestimation of distances in auditory representation for sounds located at the edge or beyond the reaching space (e.g., Zahorik et al. ##UREF##8##2005##; Kearney et al. ##UREF##5##2012##), though this aspect is still not well understood (Kolarik et al. ##REF##26590050##2016##).</p>", "<p id=\"Par44\">Taking these findings together, it seems that stimuli perceived as close to the body, regardless of their actual location, were more likely to be allocated in the back space and their distance was generally estimated accurately. On the contrary, stimuli perceived as distant, regardless of their actual location, were more likely to be subjectively allocated in the front and their distance considerably underestimated, as if the front space was compressed. The perceived distance of the sounds is not per se important, but its relationship with the subjective front or back space is interesting.</p>", "<p id=\"Par45\">Based on studies recording blink responses for stimuli located in the front space (e.g., Graziano and Cooke ##REF##16277998##2006##; Bufacchi and Iannetti ##REF##30337061##2018##), we would expect that stimuli perceived as close to the body would induce stronger blink responses than stimuli perceived as distant. However, little is known about the back space and a recent study by Bufacchi et al. (##UREF##2##2015##) did not observe the expected strong (defensive) blink reflex when the hand was positioned on the back of the head. This may be due to the fact that the back space is rarely explored with the hand and acoustic stimuli seem more informative for it. Considering our EMG data, we did not find a significant impact of actual location. Like our behavioural findings, the blink responses were better explained by perceived location rather than actual location. In other words, the actual location or distance of sounds did not lead to different blink responses. We only observed a modulation of the blink response when the perceived location of stimuli was considered.</p>", "<p id=\"Par46\">At this point, it is important to note that the verbal (location and distance) responses inevitably occurred after the fast process linked to blink reflex; therefore, these findings indicate that the mechanisms also underling the blink reflex may have guided, possibly unconsciously, the participant’s front–back discrimination and verbal response. In particular, we recorded higher peak amplitudes in response to stimuli that were later verbally localised in the front. This implies that the participants tended to locate those stimuli that caused a more intense blink response in the front space. It is unclear what determined a different strength of the blink response in the first place and we do not exclude that more complex mechanisms may play a role. For example, the sound level may have not been perfectly equivalent across conditions as the shape of the pinna or minimal movements of the head may have played a role in this. Other factors may have enhanced reflex responses (Kolarik et al. ##REF##26590050##2016##) as blink responses did not add predictive value to determine sound location per se. It is more likely that common factors underlying reflex responses and spatial location may have interacted and guided the final behaviour. It seems, therefore, that participants’ responses, clearly dominated by auditory sensory information, can be further modulated by an interaction of top–down processes (e.g., Bufacchi and Iannetti ##REF##30337061##2018##; Versace et al. ##REF##32573801##2020##; ##UREF##7##2021##) and additional bottom–up mechanisms, which dictate blink response magnitude. Within the ‘defensive graded field’ framework (Bufacchi et al. ##UREF##2##2015##; Bufacchi and Iannetti ##REF##30337061##2018##), we could speculate that a strong blink reflex may be associated with a more threatening situation (Versace et al. ##UREF##7##2021##), which in turn requires more attention and an individual may ‘prefer’ to represent it in the front space. Perrott et al. (##REF##2216648##1990##) claimed that the primary function of sound localization consists of providing information to allow individuals to move their eyes and “bring the fovea into line with an acoustically active object” (p. 214). It is indeed very common to turn our head (and body) toward a stimulus that may represent a potential threat or that requires more attention. In doing this, the egocentric front–back environment is completely and continuously reshaped and the stimulus is ‘moved’ in the front representational space supported by additional modalities (in particular vision; Aggius-Vella et al. ##REF##35220107##2022##). Even if our participants were blindfolded, the alignment of auditory and visual spatial representations is constantly updated (Lewald ##REF##23178211##2013##; Kolarik et al. ##REF##26590050##2016##). In line with the hypothesised ‘supremacy’ of front space also for auditory representation, Aggius-Vella et al. (##REF##35220107##2022##) found that sighted people were more accurate than blind people in localising sounds in the front space, suggesting that visual experience plays a crucial role in accurately representing auditory spatial representation for the front space. In this case, we may expect that stimuli requiring increasing attentional resources, such as those signalling a potential ongoing threat, may be represented in the front space where spatial organization is also refined by vision and it overlaps with the hand-action area.</p>", "<title>Limitations and alternative explanations</title>", "<p id=\"Par47\">A very different outcome may be expected for stimuli well outside the peripersonal space where any potential threats are much less salient. Our ‘relatively’ far condition was probably just outside the reaching space (Kolarik et al. ##REF##26590050##2016##) and we could not investigate the far extrapersonal condition due to the size constraint of the soundproof booth. Similarly, our ‘relatively’ close condition was just within the reaching areas and stimuli even closer to the face, and well inside the ‘defensive graded field’, could trigger more intense responses. Future studies may attempt to by-pass this limitation using advanced acoustic methods to mimic different distances on headphones. Moreover, the block design did not lead to a ceiling performance and both location and distance evaluations of the sound source proved to be challenging. However, it would be interesting to run a similar study with multiple sources in larger soundproof rooms to better refine the representation of egocentric space. Finally, future studies may aim to systematically manipulate, within the same experiment, top–down and bottom–up processes by providing information about the actual front–back position of the stimuli in advance (top–down) and manipulating the sound intensity at the same distance (bottom–up). To this aim, it would be interesting to mimic the hand-blink-reflex paradigms where proprioceptive information provides the actual location of their stimulated body part. With acoustic stimuli, top–down information could be manipulated by providing congruent and incongruent information about the egocentric location (front or back) of the acoustic source. Manipulation of these factors may provide further interesting information on sound localization and, more crucial to our study, a more detailed representation of egocentric space.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par48\">In line with the current literature, our findings underlined the crucial role of top–down processes that lead individuals to locate and respond to stimuli in different locations around the body, including the back space. We also suggest that bottom–up mechanisms, common to the blink reflex and additional to those directly linked to acoustic sensory information, can also play a crucial role on later and higher cognitive decisions, offering a more complex scenario where higher cognitive processes and physiological responses concur to create the final subjective representation of the peripersonal space.</p>" ]

[ "<p>Communicated by Francesco Lacquaniti.</p>", "<p id=\"Par1\">Previous studies have identified a ‘defensive graded field’ in the peripersonal front space where potential threatening stimuli induce stronger blink responses, mainly modulated by top–down mechanisms, which include various factors, such as proximity to the body, stimulus valence, and social cues. However, very little is known about the mechanisms responsible for representation of the back space and the possible role of bottom–up information. By means of acoustic stimuli, we evaluated individuals’ representation for front and back space in an ambiguous environment that offered some degree of uncertainty in terms of both distance (close vs. far) and front–back egocentric location of sound sources. We aimed to consider verbal responses about localization of sound sources and EMG data on blink reflex. Results suggested that stimulus distance evaluations were better explained by subjective front–back discrimination, rather than real position. Moreover, blink response data were also better explained by subjective front–back discrimination. Taken together, these findings suggest that the mechanisms that dictate blink response magnitude might also affect sound localization (possible bottom–up mechanism), probably interacting with top–down mechanisms that modulate stimuli location and distance. These findings are interpreted within the defensive peripersonal framework, suggesting a close relationship between bottom–up and top–down mechanisms on spatial representation.</p>", "<title>Keywords</title>" ]

[]

[ "<title>Acknowledgements</title>", "<p>The authors are grateful to Mr. Rob Davies for building the EMG equipment and synchronising the stimuli presentation. We are also grateful to Prof. Lauren Stewart for allowing us to use the soundproof booth and to Mr. Andrea Defilippi for proofreading the manuscript.</p>", "<title>Author contributions</title>", "<p>GC, DM, CN, and RP conceived the study and designed the experiment. CN and RP collected the data; LV, GC, EJ, and ET screened and pre-analysed EMG data for final analyses; DM ran main statistical analyses on all data and wrote the results section; GC wrote the manuscript. All authors provided significant contribution to the revision of the manuscript.</p>", "<title>Data availability</title>", "<p>Data accessibility: Supplementary material, anonymized data and scripts for the analyses\nare publicly available at <ext-link ext-link-type=\"uri\" xlink:href=\"https://osf.io/8vmq6/\">https://osf.io/8vmq6/</ext-link>.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par49\">The authors have no conflict of interest.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Schematic representation of the setting for each condition and timeline of the paradigm. Paradigm outline not to scale. The time allowed for responses ranged from 5 to 15 s, randomly</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Perceived location for back and front stimuli by experimental conditions (actual location and actual distance)</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Distance evaluation for back and front stimuli</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Back–Front location accuracy for Close (50) and Far (100) stimuli</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Distance accuracy ratio for Close (50) and Far (100) stimuli</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Samples of sEMG blink reflex data (<bold>a</bold>) for Front Close (<bold>b</bold>) and Far (<bold>c</bold>) and for Back Close (<bold>d</bold>) and Far (<bold>e</bold>) conditions</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Perceived location for actual locations and distances</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Actual location</th><th align=\"left\">Actual distance</th><th align=\"left\">Perceived location</th><th align=\"left\"><italic>N</italic></th><th align=\"left\">%</th></tr></thead><tbody><tr><td align=\"left\"><bold>Back</bold></td><td align=\"left\"><bold>50</bold></td><td align=\"left\"><bold>Back</bold></td><td align=\"left\"><bold>78</bold></td><td align=\"left\"><bold>67.2</bold></td></tr><tr><td align=\"left\">Back</td><td align=\"left\">50</td><td align=\"left\">Front</td><td align=\"left\">38</td><td align=\"left\">32.8</td></tr><tr><td align=\"left\"><bold>Back</bold></td><td align=\"left\"><bold>100</bold></td><td align=\"left\"><bold>Back</bold></td><td align=\"left\"><bold>67</bold></td><td align=\"left\"><bold>54</bold></td></tr><tr><td align=\"left\">Back</td><td align=\"left\">100</td><td align=\"left\">Front</td><td align=\"left\">57</td><td align=\"left\">46</td></tr><tr><td align=\"left\"><italic>Total back</italic></td><td align=\"left\"><italic>240</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Front</td><td align=\"left\">50</td><td align=\"left\">Back</td><td align=\"left\">50</td><td align=\"left\">41.7</td></tr><tr><td align=\"left\"><bold>Front</bold></td><td align=\"left\"><bold>50</bold></td><td align=\"left\"><bold>Front</bold></td><td align=\"left\"><bold>70</bold></td><td align=\"left\"><bold>58</bold></td></tr><tr><td align=\"left\">Front</td><td align=\"left\">100</td><td align=\"left\">Back</td><td align=\"left\">42</td><td align=\"left\">36.8</td></tr><tr><td align=\"left\"><bold>Front</bold></td><td align=\"left\"><bold>100</bold></td><td align=\"left\"><bold>Front</bold></td><td align=\"left\"><bold>72</bold></td><td align=\"left\"><bold>63.2</bold></td></tr><tr><td align=\"left\"><italic>Total front</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"><italic>234</italic></td><td align=\"left\"/></tr><tr><td align=\"left\"><italic>Total (back &amp; front)</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"><italic>474</italic></td><td align=\"left\"/></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Analysis of deviance table (Type III Wald Chi-squared tests) for perceived location</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"2\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Response: perceived location</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">0.0088</td><td align=\"left\">1</td><td align=\"left\">0.92530</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance _categorical</td><td align=\"left\">13.1265</td><td align=\"left\">1</td><td align=\"left\"><bold>0.00029</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual location</td><td align=\"left\">6.2126</td><td align=\"left\">1</td><td align=\"left\"><bold>0.01268</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance _categorical:Actual Location</td><td align=\"left\">1.9981</td><td align=\"left\">1</td><td align=\"left\">0.15749</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\">R²</th><th align=\"left\" colspan=\"2\">95% Conf. interval</th></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Effect</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.069</td><td align=\"left\">0.029</td><td align=\"left\">0.139</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual location1</td><td align=\"left\">0.039</td><td align=\"left\">0.007</td><td align=\"left\">0.092</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Actual distance_catigorical1</td><td align=\"left\">0.030</td><td align=\"left\">0.004</td><td align=\"left\">0.079</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Actual distance_categorical1: Actual Location1</td><td align=\"left\">0.004</td><td align=\"left\">0.000</td><td align=\"left\">0.032</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Analysis of deviance table (Type III Wald Chi-squared tests) for perceived distance</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Response: Log_perceived_distance</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">411.6023</td><td align=\"left\">1</td><td align=\"left\"><bold>0.00001</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_catergorical</td><td align=\"left\">0.5960</td><td align=\"left\">1</td><td align=\"left\">0.44011</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual location</td><td align=\"left\">3.2647</td><td align=\"left\">1</td><td align=\"left\">0.07079</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical:Actual location</td><td align=\"left\">0.0223</td><td align=\"left\">1</td><td align=\"left\">0.88140</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"><italic>R</italic>²</th><th align=\"left\">95% Conf. Interval</th><th align=\"left\"/></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Effect</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.029</td><td align=\"left\">0.007</td><td align=\"left\">0.085</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Actual location1</td><td align=\"left\">0.027</td><td align=\"left\">0.003</td><td align=\"left\">0.074</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual distance_categorical 1</td><td align=\"left\">0.002</td><td align=\"left\">0.000</td><td align=\"left\">0.024</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Actual location_categorical: Actual location1</td><td align=\"left\">0.000</td><td align=\"left\">0.000</td><td align=\"left\">0.017</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p><bold>A</bold> Analysis of deviance table (Type III Wald Chi-squared tests) for accuracy of perceived location, and <bold>B</bold> model coefficient estimates and significance tests of fixed effects</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\">(<bold>A</bold>)</td><td align=\"left\"><italic>Response: accuracy</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">6.2128</td><td align=\"left\">1</td><td align=\"left\"><bold>0.01268</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical</td><td align=\"left\">1.9982</td><td align=\"left\">1</td><td align=\"left\">0.15749</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual location</td><td align=\"left\">0.0088</td><td align=\"left\">1</td><td align=\"left\">0.92529</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical: actual location</td><td align=\"left\">13.1268</td><td align=\"left\">1</td><td align=\"left\"><bold>0.00029</bold></td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\">R²</th><th align=\"left\" colspan=\"2\">95% Conf. Interval</th></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Effect</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.034</td><td align=\"left\">0.010</td><td align=\"left\">0.093</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Actual distance_categorical: actual location</td><td align=\"left\">0.030</td><td align=\"left\">0.004</td><td align=\"left\">0.079</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual distance_categorical</td><td align=\"left\">0.004</td><td align=\"left\">0.000</td><td align=\"left\">0.032</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Actual location</td><td align=\"left\">0.000</td><td align=\"left\">0.000</td><td align=\"left\">0.017</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\">SE</th><th align=\"left\">z</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\">(B)</td><td align=\"left\"><italic>Beta</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">(Intercept)</td><td align=\"left\">1.4621</td><td align=\"left\">0.5866</td><td align=\"left\">2.493</td><td align=\"left\"><bold>0.01268</bold></td></tr><tr><td align=\"left\">Actual distance_categorical (close)</td><td align=\"left\">0.3509</td><td align=\"left\">0.2483</td><td align=\"left\">1.414</td><td align=\"left\">0.15749</td></tr><tr><td align=\"left\">Actual location (back)</td><td align=\"left\">-0.1396</td><td align=\"left\">1.4887</td><td align=\"left\">-0.094</td><td align=\"left\">0.92529</td></tr><tr><td align=\"left\">Actual distance_categorical (close):</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Actual_location (back)</td><td align=\"left\">0.8966</td><td align=\"left\">0.2475</td><td align=\"left\">3.623</td><td align=\"left\"><bold>0.00029</bold></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab5\"><label>Table 5</label><caption><p>Means and SDs of perceived distance accuracy for each condition</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Actual distance</th><th align=\"left\">Actual location</th><th align=\"left\">Mean</th><th align=\"left\">SD</th></tr></thead><tbody><tr><td align=\"left\">50</td><td align=\"left\">Back</td><td char=\".\" align=\"char\">0.63</td><td char=\".\" align=\"char\">0.27</td></tr><tr><td align=\"left\">100</td><td align=\"left\">Back</td><td char=\".\" align=\"char\">0.77</td><td char=\".\" align=\"char\">0.20</td></tr><tr><td align=\"left\">50</td><td align=\"left\">Front</td><td char=\".\" align=\"char\">0.65</td><td char=\".\" align=\"char\">0.28</td></tr><tr><td align=\"left\">100</td><td align=\"left\">Front</td><td char=\".\" align=\"char\">0.800</td><td char=\".\" align=\"char\">0.14</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab6\"><label>Table 6</label><caption><p>Analysis of deviance table (Type III Wald Chi-squared tests) for distance accuracy</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Response:distance accuracy ratio</th><th align=\"left\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">753.8365</td><td align=\"left\">1</td><td align=\"left\"><bold>0.0001</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical</td><td align=\"left\">23.7161</td><td align=\"left\">1</td><td align=\"left\"><bold>0.0001</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual location</td><td align=\"left\">0.4545</td><td align=\"left\">1</td><td align=\"left\">0.50020</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical: actual location</td><td align=\"left\">1.3009</td><td align=\"left\">1</td><td align=\"left\">0.25410</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\">Effect</th><th align=\"left\" rowspan=\"2\">R²</th><th align=\"left\" colspan=\"2\">95% Conf. interval</th></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.196</td><td align=\"left\">0.128</td><td align=\"left\">0.281</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Actual distance_categorical: actual location</td><td align=\"left\">0.19</td><td align=\"left\">0.119</td><td align=\"left\">0.271</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual distance_categorical</td><td align=\"left\">0.008</td><td align=\"left\">0.000</td><td align=\"left\">0.04</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Actual location</td><td align=\"left\">0.003</td><td align=\"left\">0.000</td><td align=\"left\">0.029</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab7\"><label>Table 7</label><caption><p>Means and SDs of EMG log-transformation data</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">EMG measures</th><th align=\"left\">Mean</th><th align=\"left\">SD</th></tr></thead><tbody><tr><td align=\"left\">Peak amplitude</td><td char=\".\" align=\"char\">5.67</td><td char=\".\" align=\"char\">0.74</td></tr><tr><td align=\"left\">Peak latency</td><td char=\".\" align=\"char\">0.43</td><td char=\".\" align=\"char\">0.07</td></tr><tr><td align=\"left\">Onset latency</td><td char=\".\" align=\"char\">0.34</td><td char=\".\" align=\"char\">0.13</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab8\"><label>Table 8</label><caption><p>Analysis of deviance table (Type III Wald Chi-squared tests) for peak amplitude</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Response: peak amplitude</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">855.8569</td><td align=\"left\">1</td><td align=\"left\"><bold>0.0001</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical</td><td align=\"left\">23.9455</td><td align=\"left\">1</td><td align=\"left\">0.1631</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual location</td><td align=\"left\">0.243</td><td align=\"left\">1</td><td align=\"left\">0.2654</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical: actual location</td><td align=\"left\">1.4708</td><td align=\"left\">1</td><td align=\"left\">0.2252</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\">R²</th><th align=\"left\" colspan=\"2\">95% Conf. Interval</th></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Effec</italic>t</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.053</td><td align=\"left\">0.011</td><td align=\"left\">0.194</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Actual Distance_categorical100</td><td align=\"left\">0.049</td><td align=\"left\">0.001</td><td align=\"left\">0.165</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual Distance_categorical100: actual locationF</td><td align=\"left\">0.014</td><td align=\"left\">0.000</td><td align=\"left\">0.098</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Actual locationF</td><td align=\"left\">0.011</td><td align=\"left\">0.000</td><td align=\"left\">0.092</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab9\"><label>Table 9</label><caption><p>Analysis of deviance table (Type III Wald chi-squared tests) for peak amplitude</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Response: peak amplitude</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">876.1267</td><td align=\"left\">1</td><td align=\"left\"><bold>0.0001</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical</td><td align=\"left\">1.1404</td><td align=\"left\">1</td><td align=\"left\">0.2856</td></tr><tr><td align=\"left\"/><td align=\"left\">Perceived location</td><td align=\"left\">4.3102</td><td align=\"left\">1</td><td align=\"left\"><bold>0.0379</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical: perceived location</td><td align=\"left\">0.318</td><td align=\"left\">1</td><td align=\"left\">0.5728</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\">R²</th><th align=\"left\" colspan=\"2\">95% Conf. Interval</th></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Effect</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.166</td><td align=\"left\">0.067</td><td align=\"left\">0.328</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Perceived LocationF</td><td align=\"left\">0.096</td><td align=\"left\">0.001</td><td align=\"left\">0.231</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual Distance_categorical100</td><td align=\"left\">0.031</td><td align=\"left\">0.000</td><td align=\"left\">0.135</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Actual Distance_categorical100: Perceived LocationF</td><td align=\"left\">0.006</td><td align=\"left\">0.000</td><td align=\"left\">0.079</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab10\"><label>Table 10</label><caption><p>Analysis of deviance table (Type III Wald Chi-squared tests) for peak latency</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Response: peak latency</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">109.9892</td><td align=\"left\">1</td><td align=\"left\"><bold>0.0001</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical</td><td align=\"left\">2.1490</td><td align=\"left\">1</td><td align=\"left\">0.1427</td></tr><tr><td align=\"left\"/><td align=\"left\">Perceived location</td><td align=\"left\">0.0257</td><td align=\"left\">1</td><td align=\"left\">0.8726</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical: perceived location</td><td align=\"left\">0.7816</td><td align=\"left\">1</td><td align=\"left\">0.3767</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\">R²</th><th align=\"left\" colspan=\"2\">95% Conf. Interval</th></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Effect</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.275</td><td align=\"left\">0.152</td><td align=\"left\">0.435</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Actual Distance_categorical100</td><td align=\"left\">0.230</td><td align=\"left\">0.101</td><td align=\"left\">0.381</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual Distance_categorical100: Perceived LocationF</td><td align=\"left\">0.060</td><td align=\"left\">0.002</td><td align=\"left\">0.182</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Perceived LocationF</td><td align=\"left\">0.002</td><td align=\"left\">0.000</td><td align=\"left\">0.062</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab11\"><label>Table 11</label><caption><p>Analysis of deviance table (Type III Wald Chi-squared tests) for onset latency</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\">χ²</th><th align=\"left\">df</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Response: onset latency</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\"/><td align=\"left\">(Intercept)</td><td align=\"left\">121.0793</td><td align=\"left\">1</td><td align=\"left\"><bold>0.0001</bold></td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical</td><td align=\"left\">1.3645</td><td align=\"left\">1</td><td align=\"left\">0.2425</td></tr><tr><td align=\"left\"/><td align=\"left\">Perceived location</td><td align=\"left\">3.5201</td><td align=\"left\">1</td><td align=\"left\">0.0606</td></tr><tr><td align=\"left\"/><td align=\"left\">Actual distance_categorical: perceived location</td><td align=\"left\">0.1728</td><td align=\"left\">1</td><td align=\"left\">0.6777</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\"/><th align=\"left\" rowspan=\"2\">R²</th><th align=\"left\" colspan=\"2\">95% Conf. Interval</th></tr><tr><th align=\"left\">Lower</th><th align=\"left\">Upper</th></tr></thead><tbody><tr><td align=\"left\"/><td align=\"left\"><italic>Effect</italic></td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">1</td><td align=\"left\">Model</td><td align=\"left\">0.119</td><td align=\"left\">0.039</td><td align=\"left\">0.277</td></tr><tr><td align=\"left\">4</td><td align=\"left\">Perceived LocationF</td><td align=\"left\">0.044</td><td align=\"left\">0.001</td><td align=\"left\">0.158</td></tr><tr><td align=\"left\">2</td><td align=\"left\">Actual Distance_categorical100</td><td align=\"left\">0.032</td><td align=\"left\">0.000</td><td align=\"left\">0.137</td></tr><tr><td align=\"left\">3</td><td align=\"left\">Actual Distance_categorical100: Perceived LocationF</td><td align=\"left\">0.002</td><td align=\"left\">0.000</td><td align=\"left\">0.062</td></tr></tbody></table></table-wrap>" ]

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[ "<table-wrap-foot><p>Correct responses are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant effects are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant results are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant results are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant results are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant results are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant results are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant results are highlighted in bold</p></table-wrap-foot>", "<table-wrap-foot><p>Significant results are highlighted in bold</p></table-wrap-foot>", "<fn-group><fn id=\"Fn1\"><label>1</label><p id=\"Par19\">To not draw attention to the question about claustrophobia, which may have provided clues on the possible stimuli distances, this information was requested as part of a list of standard questions about general health and possible allergies to material used to record the EMG signal.</p></fn><fn id=\"Fn2\"><label>2</label><p id=\"Par190\">An a-priori exclusion of outliers was decided to rather narrow the generalisability of findings than increasing the risk of false-negative results. On a single t test analysis (Crawford and Garthwaite ##REF##18416496##2007##), both outliers’ distance estimations significantly (<italic>p</italic> &lt; .05) differed from the group mean.</p></fn><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"221_2023_6740_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"221_2023_6740_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"221_2023_6740_Fig3_HTML\" id=\"MO3\"/>", "<graphic xlink:href=\"221_2023_6740_Fig4_HTML\" id=\"MO4\"/>", "<graphic xlink:href=\"221_2023_6740_Fig5_HTML\" id=\"MO5\"/>", "<graphic xlink:href=\"221_2023_6740_Fig6_HTML\" id=\"MO6\"/>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par5\">One of the first symptoms presented by patients with glottic organic lesions is dysphonia. Such complaints require a diagnostic process that includes visualization of the larynx, including assessment of the lesion’s morphology, by means of videoendoscopy (Dejonckere et al. ##REF##11307610##2001##; Hald et al. ##REF##37381839##2023##). An adjunct to this method, enabling functional assessment, are advanced diagnostic techniques, utilizing improved image capture and lighting such as laryngovideostroboscopy (LVS), narrow band imaging (NBI), and recently high-speed videoendoscopy (HSV) (Schade and Müller ##UREF##13##2005##; Svec et al. ##REF##17419520##2007##; Woo ##REF##24094798##2014##). Those techniques enable precise visualization of laryngeal structure and function allowing the diagnosis of both functional and organic dysphonia (Bohr et al. ##REF##23649746##2013##, ##REF##24686496##2014##).</p>", "<p id=\"Par6\">However after detection of organic lesions of the glottis, the most important is the differential diagnosis between benign and malignant lesions (Sigston et al. ##REF##16490871##2006##; Gandhi et al. ##UREF##4##2021##). The golden standard remains clinical assessment with the establishment of the initial diagnosis, followed by a surgical approach—either biopsy or complete removal of the lesion with subsequent determination of the final diagnosis based on postoperative histopathology. However, there exist several tools able to assist the physician in the decision-making process—especially in the initial assessment and deciding to perform either a biopsy or total surgical removal of the lesion. Those devices (among others) are NBI, LVS, and HSV. Researchers leading their constant development are attempting to use HSV in the visualization of vocal fold oscillations in organic lesions (Yamauchi et al. ##UREF##17##2021##; Kaluza et al. ##REF##36230618##2022##).</p>", "<p id=\"Par7\">In NBI technique, the light source emits narrow bands of light, corresponding to the absorption of hemoglobin, providing enhanced imaging of mucosal capillaries, allowing more precise assessment of its structure. As cancerous growth promotes blood vessels proliferation, there exist characteristic patterns, observed in malignant lesions, classified by (Ni et al. ##REF##21054921##2011##; Sun et al. ##UREF##14##2017##).</p>", "<p id=\"Par8\">The use of LVS for organic lesions has been established by previous research in this area (El-Demerdash et al. ##REF##25649284##2015##; Rzepakowska et al. ##UREF##11##2017##; Itigi et al. ##UREF##5##2022##). Unfortunately, this technique is susceptible to failure in some of the vocal fold organic masses, as it requires synchronization of strobe light with the fundamental frequency of the patient’s voice. Achieving this synchronization is difficult in short and asynchronous phonations, commonly found in patients with organic lesions. HSV, on the other hand, was until recently used mainly for research purposes and for diagnosing functional disorders of the larynx (assessment of kymographic sections was mostly qualitative, subjective analysis by experienced clinicians) (Tsutsumi et al. ##UREF##15##2017##; Woo ##REF##33166979##2020##; Kosztyła-Hojna et al. ##UREF##7##2021##; Schlegel et al. ##REF##33529244##2021##). Development of the HSV technique allowed to overcome those difficulties: eliminated most technical problems with the recording process and provided advanced methods of data analysis—including objective, quantitative assessment of vocal fold movement (Woo ##REF##24094798##2014##; Zacharias et al. ##REF##28596101##2018##; Kist et al. ##REF##34215788##2021a##; Malinowski et al. ##UREF##8##2021##). Thus, more researchers tend to utilize HSV kymographic analysis in organic lesions of the glottis, yielding promising results (Powell et al. ##REF##27716854##2016##, ##UREF##10##2020##; Gandhi et al. ##UREF##4##2021##). Despite the evolution of HSV, not all of the existing problems have been solved, especially involving the choice of parameters evaluating phonatory oscillations (Fehling et al. ##REF##32040514##2020##; Mohd Khairuddin et al. ##REF##31864891##2021##).</p>", "<p id=\"Par9\">Quantitative analysis of kymographic cross-sections allows the calculation of four main groups of parameters assessing vocal fold oscillations—amplitude measures, glottal dynamic characteristics, symmetry measures, and perturbation measures (Sielska-Badurek et al. ##REF##30353981##2019##; Krasnodębska et al. ##REF##29318925##2019##; Schlegel et al. ##REF##33529244##2021##). The first three groups describe features of vocal fold movement in the geometrical area of the glottis (spatial analysis), mainly: amplitude, open quotient, asymmetry, and phase difference. Obtained values describe properties common for all vocal cycles in analyzed phonation, focusing on the course of individual vocal cycles. As parameters included among those groups describe similar features of glottal oscillations, we decided to further describe those three groups together as so-called short-term variability (STV) parameters. STV parameters describe features common for all analyzed glottal cycles, focusing on individual cycle. Those values are not exclusive to HSV analysis, they could be previously obtained also from kymographic cross-sections derived from LVS. The fourth group—perturbation measures—are parameters describing the regularity of vocal fold oscillation (both frequency and amplitude) in time, focusing more on the temporal aspect of glottal vibrations. In comparison to STV parameters, perturbation measures (so-called long-term variability parameters) describe differences between consecutive glottal cycles. For this reason, their assessment requires analyzing more frames than in STV parameters. Those perturbation measurements could be previously obtained by means of acoustic voice analysis and recently also by assessment of HSV recordings. Values of perturbation measures are used to analyze differences between consecutive vocal cycles, describing the stability of phonation (Schlegel et al. ##REF##31009488##2019##; Malinowski et al. ##REF##37509377##2023##). LVS recordings contain far too few vocal cycles to assess this group of parameters. Furthermore, instead of recording the full glottal cycle, the LVS technique samples points along different vocal oscillations, to recreate its image.</p>", "<p id=\"Par10\">A multitude of parameters and methods of calculation causes problems in selecting the right set of them to apply to clinical purposes. Thus, currently most research effort concentrates on developing a standardized HSV investigation protocol and data analysis tools, facilitating preliminary, non-invasive detection of malignancy among organic lesions of the glottis (Turkmen and Karsligil ##REF##31493281##2019##; Kist et al. ##REF##34000199##2021b##).</p>", "<p id=\"Par11\">The aim of the study was to assess the relevance of objective vibratory parameters derived from HSV kymography (quantified amplitude, symmetry and glottal dynamic characteristics) as a support to videoendoscopy, which assists clinicians in establishing an initial diagnosis of benign and malignant glottal organic lesions before histopathologic examination.</p>" ]

[ "<title>Materials and methods</title>", "<title>Participants</title>", "<p id=\"Par12\">The study included 175 patients hospitalized in the Department of Otolaryngology, Head and Neck Oncology of the Medical University of Lodz from 09.2020 to 12.2022. The control group consisted of 50 patients: 33 women and 17 men. The inclusion criteria for this group were: &gt; 18 years of age, no dysphonia symptoms at the time of the examination, no history of dysphonia, and no structural or functional abnormalities found in endoscopic examination. Subjects in this group were between 19 and 83 years old, with an average age of 41.52 ± 17.44 years.</p>", "<p id=\"Par13\">The study group consisted of 125 patients. Inclusion criteria for the study group were: &gt; 18 years of age; current dysphonia, presence of unilateral organic lesion in the glottis. Subjects with dysphonia were later divided into two groups. The benign lesions group included 85 participants diagnosed with benign vocal lesions (including polyps, cysts, nodules, and unilateral Reinke’s edema). This group consisted of 58 women and 27 men, aged from 22 to 87 years, with the mean age of 53.28 ± 13.3 years. The second group included 40 patients (30 men and 10 women) diagnosed with early glottic cancer. Participants in this group were aged from 42 to 85 years, with an average age of 67.45 ± 7.01 years. All patients with organic lesions underwent transoral laser microsurgery (TOLMS), resulting in histopathologic confirmation of the initial diagnosis. All the malignant lesions were squamous cell carcinoma G1 or G2, classified clinically as T1 involving one vocal fold.</p>", "<p id=\"Par14\">The exclusion criteria for both groups were inability to obtain recordings with sufficient visualization quality for analysis, and organic lesions involving both sides of the larynx.</p>", "<p id=\"Par15\">Approval for this study was granted by the Ethical Committee of the Medical University of Lodz (no. RNN/96/20/KE 08/04/2020), and all patients gave written informed consent to participate in the research.</p>", "<title>Examination</title>", "<p id=\"Par16\">First, the patients were assessed by an ENT physician who made the initial diagnosis. After that, every patient was subjected to examination by means of a rigid endoscope paired with HSV camera and laser illumination. The examination equipment was supported by a computer with dedicated software allowing for the recording of video signal and storing it for further analysis. Initially, the camera was set at a recording speed of 24 frames per second (fps) to center the video sensor on the glottis and perform a primary assessment of the larynx. Next, the camera was set into high-speed recording mode, and multiple HSV sequences were captured. For this study recording speed was 3200 fps. Each sequence contained 2000 fps, with the full-time length of a single sequence of 625 ms (Malinowski et al. ##UREF##8##2021##). More details on the technical aspects of HSV recording can be found in our previous publication. Later, quality of the recordings was assessed, and the best and most representative films were selected for each patient for further assessment.</p>", "<title>Analysis</title>", "<p id=\"Par17\">Detailed kymographic analysis was performed to quantitatively assess vocal fold vibrations. As described by Yamauchi et al. sets of data from HSV kymography can be classified as three dimensions of HSV—mediolateral (x), longitudinal (y), and temporal (t), as shown in Fig. ##FIG##0##1## (Yamauchi et al. ##UREF##17##2021##). The first two—the x- and y-axis—describe spatial properties of glottal oscillations and can be assessed subjectively (visual-perceptual rating), by laryngotopography and by means of HSV (Sakakibara et al. ##UREF##12##2010##; Tsuji et al. ##REF##25992109##2014##; Yamauchi et al. ##UREF##16##2015##). The temporal aspect can be evaluated either on its own (by analysis of glottal area and width waveform) or along with mediolateral dimension—using digital kymography (Schlegel et al. ##REF##32601277##2020##; Kist et al. ##REF##34215788##2021a##; Yousef et al. ##UREF##18##2023##). In this study, to compare involved and healthy vocal folds, we focused on the spatial aspect of HSV analysis (x- and y-axis), resulting in the calculation of STV parameters including amplitude measures, glottal dynamic characteristics, and symmetry measures. Those parameters describe the movement of vocal folds along and perpendicularly to the glottal axis.</p>", "<p id=\"Par18\">First, the software automatically selected a part of the recording for further analysis. Contrary to LVS, in the case of HSV recordings, manual stabilization and centering of the image for each frame was not required, because, in such a short recording time (625 ms), the movement of the endoscope tip is negligible. Later the vocal folds edges were identified semi-automatically—the examiner marked them in five points on a single representative frame, and based on those points, the software indicated them on all frames and along the whole length of the glottis. The examiner was then able to verify and adjust the automated detection in case of any discrepancy. In the final step, the software calculated a set of STV parameters describing characteristics of the movement of vocal folds during the glottal cycle, specifically: amplitude measures, glottal dynamic characteristics, and symmetry measures. Amplitude measures include four parameters: average amplitude (AmpAvg), the average amplitude of the middle third of the glottis (AmpAvg_2/3), the average amplitude of the involved vocal fold (AmpInvolvedAvg), and the average amplitude of the healthy vocal fold (AmpHealthyAvg)—their values indicate the average resultant amplitude of vocal fold movement for the whole glottal gap, its middle third part, involved, and healthy vocal fold, respectively. This parameter is calculated as an averaged value for all points along the length of respective vocal fold. Whenever a parameter below has a suffix “_2/3”, it relates to the middle third part of the glottal length. We decided to include those parameters as the middle part of the glottis which is known to be the location of the maximum amplitude of oscillations, and disruptions in this area tend to have a larger impact on phonation. In our study, organic lesions were always unilateral, so based on the location of the lesion, we compared both folds in a series of analyses. For this purpose, we used AmpInvolvedAvg and AmpHealthyAvg to compare vibrations of healthy and involved vocal folds. An exception was made in the statistical analysis with regard to these parameters—comparison was performed only in benign and malignant lesion groups. Among glottal dynamic characteristics, four parameters are calculated: average open quotient (OQAvg), OQAvg_2/3, relative glottal gap area (RGGA), and non-opening. OQAvg and OQAvg_2/3 describe the average open quotient for the whole glottal gap and its middle third part, respectively, indicating the ratio of the glottal opening phase to the whole length of the vocal cycle. RGGA defines the ratio of minimal to maximal area of the glottis during the cycle, while non-opening indicates part of the glottis without opening during the cycle. Symmetry measures include five parameters: average amplitude asymmetry (AmplAsymAvg), AmplAsymAvg_2/3, average phase asymmetry (PhaseAsymAvg), PhaseAsymAvg_2/3, and absolute average phase difference (AbsPhaseDiffAvg). AmplAsymAvg and AmplAsymAvg_2/3 are coefficients comparing individual amplitudes of both vocal folds movement in relation to each other for the whole glottal gap and its middle third part, respectively. PhaseAsymAvg and PhaseAsymAvg_2/3 are coefficients comparing the sum of individual amplitudes of vocal fold motion to the amplitude of their resultant movement. Finally, AbsPhaseDiffAvg describes the absolute mean value of phase difference for whole vocal folds. The parameters are precisely described in Supplementary Table 1 and were calculated as described by Sielska-Badurek et al. and Just—inventor of the software (Just et al. ##UREF##6##2016##; Sielska-Badurek et al. ##REF##30353981##2019##).</p>", "<title>Statistical analysis</title>", "<p id=\"Par19\">First, we used the Shapiro–Wilk test to check assumptions regarding the distribution of analyzed variables. Depending on fulfilled assumptions, for two groups of patients (benign–malignant and involved–healthy), either non-parametric <italic>U</italic> Mann–Whitney test or parametric <italic>T</italic> test was performed.</p>", "<p id=\"Par20\">For three groups (norm–benign–malignant), we used a one-way ANOVA test. Depending on fulfilled suppositions, we chose either parametric test to analyze variance or non-parametric Kruskal–Wallis test. If the results of the test showed significant differences between mean values or distribution functions, we performed appropriate post hoc tests: non-parametric multiple comparison test or least significant differences (LSD) test.</p>", "<p id=\"Par21\">Next, we performed a ROC analysis in two variants to check which of the parameters would be a good classifier. To do that, patients were split into two, creating a two-state variable. For the first variant, patients were split into norm and benign + malignant clusters, and for the second variant into benign and malignant clusters. The ROC curve was plotted for each of the parameters and the AUC area was calculated. Results showed which parameters are significant as classifiers. Next, we used Youden index, to determine a cut-off point for each of the parameters. Youden Index is a value giving information on the maximum distance of the points on the ROC curve from the diagonal of the square with sides equal to 1 (red line on the ROC diagrams). For this point, we presented the values of sensitivity and specificity. The parameters’ values were later correlated with the presence and type of lesion, dividing them into either boosters or inhibitors. Values of boosters were increasing along with the risk of disease (either any lesion or malignancy, depending on the variant of ROC analysis as described above), and values of inhibitors were decreasing conversely to the growing risk of disease.</p>", "<p id=\"Par22\">Calculations were performed using STATISTICA.PL software, version 13.3 (Statsoft, Cracov) and Microsoft Excel.</p>" ]

[ "<title>Results</title>", "<title>Qualitative assessment</title>", "<p id=\"Par23\">Aside from numerical values of parameters, also four graphs were generated—one for each parameter group and a phonovibrogram visualizing the movement of vocal fold edges in relation to the glottal axis. In Fig. ##FIG##1##2##, we present a comparison of analysis results for two patients: Subject 1—a 56-year-old male, complaining of mild to severe dysphonia. Initial examination revealed a polypoid mass on the right vocal fold. Subjective kymographic assessment showed a moderate decrease in amplitude of the involved vocal fold, without significant asymmetry or phase difference. As shown on the phonovibrogram, there was a non-opening area of the glottis encompassing the lesion. The average amplitude of the involved vocal fold reached 2.7%FL and the resultant amplitude was 6.5%FL. Values of average amplitude are expressed in the percentage of the total length of the respective vocal fold (percent of fold length–%FL). Surgical removal of the mass was performed, and the patient achieved satisfying postoperative vocal results. In this case, histopathology confirmed the initial diagnosis. Subject 2—a 69-year-old male, complaining of severe dysphonia, initial examination revealed a large polypoid mass on the right vocal fold. Subjective analysis revealed a significant decrease in the amplitude of the involved vocal fold—especially visible on the phonovibrogram as the dark red color of the lower part of the diagram. On phonovibrograms, brightness increases along with the amplitude of oscillations. There was no significant elevation of asymmetry or phase difference. As noticed in the preoperative HSV examination, in this patient, the average amplitude of the involved vocal fold reached 1.0%FL, and the resultant amplitude was 2.5%FL. Decreased (in comparison to Subject 1) values of amplitude indicated a risk of deep tissue infiltration. A surgical approach (TOLMS) was implemented with the removal of the mass along with its pedicle—postoperative histopathology revealed squamous cell carcinoma with no malignant infiltration of the pedicle and free vocal fold edge. This comparison is an accurate example of how advanced visualization techniques with objective analysis can assist clinicians in establishing initial diagnosis. A detailed description of STV analysis for the two subjects is provided in Fig. ##FIG##1##2##. </p>", "<title>Objective analysis—parameters</title>", "<p id=\"Par24\">All the parameters were compared in three groups—healthy participants, benign lesion subjects, and malignant lesion subjects. One-way ANOVA test was performed to determine if the distribution of the parameters differs between all three groups altogether. Depending on fulfilled suppositions, we chose either parametric test to analyze variance or non-parametric Kruskal–Wallis test (one-way ANOVA on ranks). Fundamental frequency did not differ between the groups. Among STV parameters, significant diversities between the groups were found for 10 out of 14. Detailed results are shown in Table ##TAB##0##1##.</p>", "<p id=\"Par25\">Next, we performed a bilateral multiple comparison test to find out if the parameters are able to assess subjects between norm, benign, and malignant lesion groups, giving hope to use them as a predictive parameter. In our previous studies (Malinowski et al. ##REF##37509377##2023##), we found out that there are more parameters able to facilitate the detection of the presence of any organic lesion (both benign and malignant), than to facilitate the prediction of malignancy—demonstrating statistically significant differences between benign and malignant organic lesion. Out of the ten STV parameters demonstrating significant differences between all the groups, we determined that four of them also show differences between benign and malignant lesion groups. Those parameters were: AmpAvg, AmpInvolvedAvg, AmpAsymAvg, and AbsPhaseDiffAvg. The values of amplitude were decreasing from benign to malignant lesions, on the other hand, asymmetry and phase difference were increasing with the appearance of malignancy. Results for those parameters are shown in Fig. ##FIG##2##3##. The remaining six parameters: (AmpAvg_2/3, non-opening, OQAvg_2/3, AmpAsymAvg_2/3, PhaseAsymAvg, PhaseAsymAvg_2/3) presented similar mathematical trends—decreasing values of amplitude and open quotient and increasing values of asymmetry along with the risk of malignancy, however without reaching statistical significance between benign and malignant lesion groups. Significant differences were found only between healthy subjects and whole organic lesion groups (both benign and malignant altogether).</p>", "<p id=\"Par26\">The parameters comparing involved and healthy vocal fold were subjected to another analysis, comparing values of parameters between involved and healthy vocal folds individually among benign and malignant lesions. We found that the amplitude of healthy vocal folds displayed a higher resultant amplitude than folds involved with organic lesions. This difference was significant for both benign and malignant lesions (Fig. ##FIG##3##4##).</p>", "<p id=\"Par27\">In the next step, we performed AUC ROC analysis in two variants. In the first variant, we assessed the performance of the parameters in detecting the presence of organic lesions. The best performance was observed for AmplAsymAvg, reaching an AUC of 0.822 with 60% sensitivity and 90% specificity (<italic>p</italic> &lt; 0.0001). Altogether six parameters reached AUC values above 0.7, with varying sensitivity and specificity as shown in Table ##TAB##1##2##. The highest sensitivity was reached by PhaseAsymAvg with an AUC of 0.721, sensitivity of 88%, and specificity of 54%, <italic>p</italic> &lt; 0.0001. On the other hand, the highest specificity was reached by OQAvg_2/3 with an AUC of 0.647, sensitivity of 42%, and specificity of 92%. Detailed results are shown in Table ##TAB##1##2## and ROC curves are shown in Fig. ##FIG##4##5##. The parameters can also be assessed as either boosters or inhibitors. Values of boosters were increasing along with the risk of organic lesion and values of inhibitors were decreasing conversely to the growing risk of lesion. The study showed that inhibitors were amplitude and open-quotient-related parameters, meaning that both the amplitude and opening of vocal folds were decreased in malignant lesions. Boosters were asymmetry and phase difference parameters—those properties of the glottal movement were increased in case of malignancy. For each parameter, by means of the Youden Index, a cutting point was calculated. It was a proposed value for the detection of the presence of any organic lesion. Depending on booster or inhibitor properties of the parameter, its values above (for booster) or below (for inhibitor) the cutting point suggest the presence of an organic lesion; on the other hand, values below (for booster) or above (for inhibitor) indicate normophonic patient, respectively. The sensitivity and specificity of the stated cutting point are also shown in the table.</p>", "<p id=\"Par28\">In the second variant of ROC analysis, we compared the performance of the parameters in the preliminary detection of malignancy among organic lesions. AUC values in this variant were generally lower. The four parameters with the largest values were: AmpInvolvedAvg, AbsPhaseDiffAvg, AmplAsymAvg, and AmplAsymAvg_2/3. The greatest value of AUC was reached by AmplAsymAvg: 0.719 with a sensitivity of 65% and specificity of 76.5% (<italic>p</italic> &lt; 0.0001). The highest sensitivity was achieved by AmpInvolvedAvg with an AUC of 0.7, sensitivity of 72.5%, and specificity of 65.9% (<italic>p</italic> = 0.0002). On the other hand, the highest specificity was reached by AbsPhaseDiffAvg with an AUC of 0.676, sensitivity of 57.5%, and specificity of 78.8% (<italic>p</italic> = 0.0009). Detailed results are shown in Table ##TAB##2##3## and Fig. ##FIG##5##6##. As mentioned above, the parameters displayed properties of either boosters or inhibitors with the same types of parameters belonging to each cluster as in the first variant of ROC analysis. Cutting point was calculated for each parameter as described above.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par29\">High-speed videoendoscopy is an innovative, promising technique for vocal fold vibratory assessment, giving hope to surpass LVS, especially in the assessment of organic lesions, the latter being inapplicable to non-sustained phonations or moderate to severe dysphonia. The evaluation of vocal fold vibrations plays a pivotal role in the detection and diagnosis of glottal organic lesions, being able to assist the clinician in the decision-making process, possibly paving the way for the so-called “optical biopsy” (Volgger et al. ##REF##28231400##2017##; Mehlum et al. ##UREF##9##2020##). This study aimed to assess the relevance of vibratory parameters (of vocal fold vibrations) quantified amplitude, symmetry, and glottal dynamic characteristics derived from HSV kymography in benign and malignant vocal fold lesions as a preliminary prediction before receiving histopathology results.</p>", "<p id=\"Par30\">We compared parameters evaluating vocal fold vibrations in patients divided into three groups depending on the diagnosis: normophonic group, benign lesion group, and malignant lesion group, with unilateral organic lesions of the glottis. First, we compared the study group of 125 subjects diagnosed with unilateral organic lesions of vocal folds to the control group of 50 normophonic subjects. In the next step, we compared 40 subjects diagnosed with malignant and 85 subjects with benign vocal lesions. Diagnosis of all the organic lesions was confirmed histopathologically. In the study, we aimed to compare vibratory characteristics of healthy and involved vocal fold; therefore, we decided to include only unilateral masses of glottis. We observed in HSV imaging that benign lesions were usually soft, resulting in slight altering of the involved vocal fold’s elasticity and pliability. In cancerous lesions, on the other hand, the infiltration leads to an increase in stiffness of the vocal fold, leading to a greater decrease in amplitude of oscillations (or even absence of phonatory movement) in comparison with benign masses. This decrease in amplitude was shown on the phonovibrogram as the dark red color of the lower part of the diagram—describing the involved vocal fold.</p>", "<p id=\"Par31\">The kymographic analysis of HSV recordings enables an objective assessment of vocal fold oscillations. Sets of data from HSV kymography, as mentioned above and described by Yamauchi et al. can be classified as three dimensions of HSV—mediolateral (x), longitudinal (y), and temporal (t) (Yamauchi et al. ##UREF##17##2021##). In our previous work, we focused mostly on perturbation measures; however, no parameter was able to singly differentiate benign and malignant glottal lesions—only multivariable analysis allowed selection of statically significant parameters, yielding promising results (Malinowski et al. ##REF##37509377##2023##). In this study, we decided to focus on the STV parameters (x and y dimensions) and evaluate their proficiency in the prediction of both benign and malignant organic glottal lesions.</p>", "<p id=\"Par32\">Our study determined that the parameters able to differentiate normophonic and dysphonic patients (detecting presence of organic glottal lesions) in our study were: AmpAvg, AmpInvAvg, AmpAvg_2/3, Non-opening, OQAvg_2/3, AmpAsymAvg_2/3, AmpAsymAvg, PhaseAsymAvg, PhaseAsymAvg_2/3, AbsPhaseDiffAvg. The presence of an organic lesion causes disruptions of vocal oscillation, reflected in the parameter values. Specifically, the presence of a lesion caused a decrease in average amplitude and open quotient. On the other hand, asymmetry, phase difference, and non-opening parameters were increased. Involved vocal fold due to the effect of the lesion’s mass and infiltration tends to become less elastic and its vibrations are decreased—the effect increases from soft benign lesions to stiff and infiltrative cancerous masses. It can be especially noticed in values of AmpInvolvedAvg—parameter describing specifically the amplitude of vocal fold involved with the lesion, taking into account asymmetry of the material property between involved and non-involved vocal fold (tissue stiffness) (Colden et al. ##REF##11307902##2001##; Gugatschka et al. ##REF##18057948##2008##).</p>", "<p id=\"Par33\">Among glottal dynamic characteristics. Open quotient for the middle part of the glottis and non-opening percentage showed significant differences between normophonic subjects and patients with any organic lesion, while no significant difference was found between malignant and benign masses. A possible interpretation is that the glottal insufficiency caused by the presence of any hypertrophic pathology is similar between both groups and may have resulted from entrapment of a polypoid mass between the free edges of the vocal fold (which could also explain the non-opening percentage). The reason the open quotient was significant only for the middle part of the glottis can be explained by the location of lesions in studied patients: most of the lesions were located near the middle of vocal fold length.</p>", "<p id=\"Par34\">In the available literature, there are limited studies making an attempt at differentiation of benign and malignant lesions based on HSV-derived parameters. However, (Patel et al. ##REF##18646437##2008##) reported rates of successful vibratory assessment in subjects with G1, G2, and G3 voices of 100, 36, and 0% by LVS, compared to 100% using HSV via perceptual assessment. Our observations were similar; furthermore, we determined that some of the STV parameters are able to facilitate preliminary detection of cancer among organic lesions. While analyzing the STV parameters, we determined that the following can be used for this task: AmpAvg (<italic>p</italic> = 0.006), AmpAsymAvg (<italic>p</italic> &lt; 0.001), AbsPhaseDiffAvg (<italic>p</italic> &lt; 0.001), and AmpInvolvedAvg (<italic>p</italic> &lt; 0.001). Their discriminative strength was acceptable as shown by the AUC ROC analysis—the highest value of 0.719 achieved by AmplAsymAvg.</p>", "<p id=\"Par35\">Yamauchi et al. (##UREF##17##2021##) underlined that non-vibrating areas were primarily important in the detection of glottic cancers. Similar findings were described by other authors (Zhao et al. ##REF##1910717##1991##; Djukic et al. ##UREF##2##2014##). Both amplitude asymmetry and decrease of average amplitude value reflect partial phonatory silence—the absence of vibration in parts of the vocal fold with the presence of malignant infiltration (Bigenzahn et al. ##UREF##1##1998##; Heyduck et al. ##REF##34148426##2022##). However, the presence of a non-vibrating area, in the mentioned study, was assessed subjectively, resulting in certain problems, e.g., interrater agreement. In our study, we made an attempt to use objective parameters. Chosen parameters reflect differences in the tissue of both involved and healthy vocal folds and the effect of tissue changes on their vibrations, giving important clinical information. The amplitude of vocal fold vibrations determines the maximum distance from the center of the glottal gap that each vocal fold reaches during oscillation. In the case of infiltration of the vocal fold’s layers, it becomes stiffer, and unable to vibrate; thus, the amplitude is usually decreased in cases of deep infiltration (Svec et al. ##REF##17419520##2007##; Yamauchi et al. ##UREF##17##2021##). As such, characterizing the vibration of each vocal fold with the application of quantitative analysis of HSV, using STV, parameters can provide valuable information about the texture of the tissue of the vocal fold, which can be important in the diagnosis of early glottic cancer. In our study, we determined a significant decrease in the average amplitude of the involved vocal fold in glottal cancer cases, compared to benign organic lesions (AmpInvolvedAvg, <italic>p</italic> &lt; 0.001). However, other causes of decreased amplitude must also be taken into account. For example, the presence of scar tissue can result in similar non-vibrating areas as in organic tumors of the glottis (Benninger et al. ##UREF##0##1996##; Friedrich et al. ##UREF##3##2013##). That is why differentiation must be primarily based on subjective assessment of laryngeal image by experienced physician and the objective analysis can fulfill a supporting role.</p>", "<p id=\"Par36\">Limitations of the study: research on a larger population would minimize any bias resulting from the insufficient number of participants. The study included patients with unilateral vocal fold lesions. During further studies, we plan to include patients with lesions, especially malignant, infiltrating anterior commissure with involvement of contralateral vocal fold and impairment of its function.</p>", "<p id=\"Par37\">The study indicates that the asymmetry of the amplitude coefficient could be another parameter for detecting malignancy. It can be directly related to calculations of average amplitude as the presence of decreased vibration potential in one of the folds causes heightened asymmetry of the vocal fold oscillation amplitude. Finally, we noticed elevated phase difference between affected and non-affected vocal folds in early glottal cancers. It can be explained by the effect both mass and infiltration have on the fold—increased inertia of the involved fold, creates a delay in the phase of movement, compared to the healthy one. It can be noticed that both qualitative and quantitative analysis of HSV images deliver important data, supporting the differentiation of benign and malignant lesions of the glottis, based on functional assessment of the larynx. It can provide useful supporting tool in addition to NBI—commonly used for identification of cancerous lesions basing on their structure. Thus, disease-specific analysis seems to be a reasonable approach to the applicability of HSV in clinical practice.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par38\">In conclusion, our study presents the perspectives of the application of quantified vibratory parameters (amplitude measures, glottal dynamic characteristics, and symmetry measures) derived from high-speed videolaryngoscopy as a supporting tool in the diagnosis of glottal organic lesions. We made an attempt at objectification of HSV analysis, still mostly based on subjective assessment. The comparison of phonatory movements between the healthy and involved vocal folds indicated that measurements of amplitude, asymmetry, and phase of vibrations in malignant vocal fold masses deteriorate to a significantly higher degree than in benign vocal lesions. Our results indicated that the average resultant amplitude of the involved vocal fold (AmpInvolvedAvg), average amplitude asymmetry for the whole glottis and its middle third part (AmplAsymAvg; AmplAsymAvg_2/3), and absolute average phase difference (AbsPhaseDiffAvg) can preliminarily distinguish subjects with benign from malignant vocal fold lesions. This fact reflected a perceptually observed lack or reduction in the vibratory function in the stiffer (affected by malignant lesion) vocal fold in comparison to the more pliable (healthy or affected by benign lesion) vocal fold. Thus, this method could aid preliminary differentiation between early glottic cancer and benign vocal fold masses before histopathological examination. But the golden standard remains clinical examination with videolaryngoscopy by an ENT specialist, with confirmation by histopathological examination.</p>" ]

[ "<title>Purpose</title>", "<p id=\"Par1\">The study aimed to assess the relevance of objective vibratory parameters derived from high-speed videolaryngoscopy (HSV) as a supporting tool, to assist clinicians in establishing the initial diagnosis of benign and malignant glottal organic lesions.</p>", "<title>Methods</title>", "<p id=\"Par2\">The HSV examinations were conducted in 175 subjects: 50 normophonic, 85 subjects with benign vocal fold lesions, and 40 with early glottic cancer; organic lesions were confirmed by histopathologic examination. The parameters, derived from HSV kymography: amplitude, symmetry, and glottal dynamic characteristics, were compared statistically between the groups with the following ROC analysis.</p>", "<title>Results</title>", "<p id=\"Par3\">Among 14 calculated parameters, 10 differed significantly between the groups. Four of them, the average resultant amplitude of the involved vocal fold (AmpInvolvedAvg), average amplitude asymmetry for the whole glottis and its middle third part (AmplAsymAvg; AmplAsymAvg_2/3), and absolute average phase difference (AbsPhaseDiffAvg), showed significant differences between benign and malignant lesions. Amplitude values were decreasing, while asymmetry and phase difference values were increasing with the risk of malignancy. In ROC analysis, the highest AUC was observed for AmpAsymAvg (0.719; <italic>p</italic> &lt; 0.0001), and next in order was AmpInvolvedAvg (0.70; <italic>p</italic> = 0.0002).</p>", "<title>Conclusion</title>", "<p id=\"Par4\">The golden standard in the diagnosis of organic lesions of glottis remains clinical examination with videolaryngoscopy, confirmed by histopathological examination. Our results showed that measurements of amplitude, asymmetry, and phase of vibrations in malignant vocal fold masses deteriorate significantly in comparison to benign vocal lesions. High-speed videolaryngoscopy could aid their preliminary differentiation noninvasively before histopathological examination; however, further research on larger groups is needed.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00432-023-05543-y.</p>", "<title>Keywords</title>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Author contributions</title>", "<p>Study conception and methodology were established by WP and EN-B. All authors contributed to the investigation. JM, MK, and EN-B performed the formal analysis and data curation. The first draft of the manuscript was written by JM and EN-B. Figures were drawn by JM and MK. All authors contributed to the review and editing of the initial draft. WP supervised and administered the project. All authors read and approved the final manuscript.</p>", "<title>Funding</title>", "<p>This work was supported by internal grants from Medical University of Lodz, Lodz, Poland.</p>", "<title>Data availability</title>", "<p>The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par39\">The authors have no relevant financial or non-financial interests to disclose.</p>", "<title>Ethical approval and consent to participate</title>", "<p id=\"Par40\">Approval for this study was granted by the Ethical Committee of the Medical University of Lodz (no. RNN/96/20/KE 08/04/2020), and all patients gave written informed consent to participate in the research.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Aspects of HSV analysis: <bold>A</bold> Three axes describing properties of vocal oscillations that can be assessed using different types of HSV analysis. x–mediolateral, y–longitudinal, and t–temporal data. STV analysis focuses on the evaluation of the x- and y-axis—describing geometric aspects of vocal folds oscillation both along and perpendicular to the glottal center in a few cycles, both comparing left and right vocal folds and analyzing resultant features of their vibration. Temporal (perturbation) analysis focuses more on the stability of phonation, analyzing the regularity of both amplitude and frequency in longer periods (y-axis). <bold>B</bold> Phonovibrogram—a diagram presenting the movement of the vocal folds in time in relation to the center of the glottis—the center of the diagram indicates the anterior part of the glottis; the upper part describes the movement of the left vocal fold while lower part describes the movement of the right vocal fold. <bold>C</bold> Values of STV analysis presented in the form of diagrams. From left to right: amplitude measures, glottal dynamic characteristics (open quotient), and two diagrams presenting symmetry measures (first: amplitude and phase asymmetry; second: phase difference)</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Presentation of HSV STV analysis for the two subjects described in the text. For each subject, the analysis includes <bold>1</bold> the image of the glottis (<bold>1A</bold>) with grey lines presenting three representative kymographic cross-sections for three functional parts of the glottis (from left to right) consecutively posterior (<bold>1B</bold>), middle (<bold>1C</bold>) and anterior (<bold>1D</bold>) part. <bold>2</bold> Values of STV analysis presented in the form of diagrams, along the glottal axis (y-axis on each diagram), from left to right: amplitude measures, glottal dynamic characteristics (open quotient), and two diagrams presenting symmetry measures (first: amplitude and phase asymmetry; second: phase difference). <bold>3</bold> Phonovibrogram—a diagram presenting the movement of the vocal folds in time in relation to the center of the glotti—the center of the diagram indicates the anterior part of the glottis; upper part describes the movement of the left vocal fold while lower part describes the movement of right vocal fold—darker color indicates decreased amplitude (as described in the text)</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Diagrams presenting median values of individual vibratory parameters in groups divided by diagnosis, specifically: norm, benign, and malignant. Colored arrows present <italic>p</italic> values in bilateral comparisons between the groups: green–norm vs malignant, blue–norm vs benign, and red–benign vs malignant. The parameters presented in this figure differ in a significant way not only between normophonic patients and any organic lesion but also between benign and malignant glottal lesions</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Diagrams presenting median values of average Aaplitude parameter for the healthy and involved fold, respectively. Diagrams are divided by diagnosis, specifically: benign (<bold>A</bold>) and malignant (<bold>B</bold>). Red arrows present the <italic>p</italic> value in comparison between the groups: benign vs malignant. Table <bold>C</bold> presents the results of statistical analysis for those parameters</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>ROC curves for the six best-performing vibratory parameters differentiating normophonic subjects from patients with any organic lesion of the glottis (both benign and malignant) (blue line, <bold>A</bold>–<bold>F</bold>). X- and y-axis present sensitivity and 1-specificity of points on the curve. The red line presents an AUC value of 0.5; the green line presents the value of the Youden index ending in the black square on the curve—the proposed cutting point as described in the text and Table ##TAB##1##2##</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p> ROC curves for the four vibratory parameters differentiating benign from malignant lesions of the glottis (blue line). X- and y-axis present sensitivity and 1-specificity of points on the curve. The red line presents an AUC value of 0.5; the green line presents the value of the Youden index ending in the black square on the curve—the proposed cutting point as described in the text and Table ##TAB##2##3##</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Results of Kruskal–Wallis test for individual vibratory parameters, with exclusion of OQAvg (marked with*)—this measurement’s values had normal distribution and were analyzed with the use of parametric test</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Parameter</th><th align=\"left\">Diagnosis</th><th align=\"left\"><italic>n</italic></th><th align=\"left\">Mean</th><th align=\"left\">Median</th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"3\">AmpAvg</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">10.43400</td><td char=\".\" align=\"char\">8.25000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0000</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">7.1824</td><td char=\".\" align=\"char\">6.2000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">5.62250</td><td char=\".\" align=\"char\">4.85000</td></tr><tr><td align=\"left\" rowspan=\"3\">AmpAvg_2/3</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">12.18600</td><td char=\".\" align=\"char\">10.30000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0000</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">7.8494</td><td char=\".\" align=\"char\">6.7000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">6.07750</td><td char=\".\" align=\"char\">5.25000</td></tr><tr><td align=\"left\" rowspan=\"2\">AmpInvolvedAvg</td><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">3.92941</td><td char=\".\" align=\"char\">3.40000</td><td char=\".\" align=\"char\" rowspan=\"2\">0.0003</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">2.62750</td><td char=\".\" align=\"char\">2.20000</td></tr><tr><td align=\"left\" rowspan=\"2\">AmpHealthyAvg</td><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">4.84000</td><td char=\".\" align=\"char\">4.20000</td><td char=\".\" align=\"char\" rowspan=\"2\">0.0775</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">4.32000</td><td char=\".\" align=\"char\">3.65000</td></tr><tr><td align=\"left\" rowspan=\"3\">Non-closing</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">16.71400</td><td char=\".\" align=\"char\">7.70000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.9759</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">16.9318</td><td char=\".\" align=\"char\">7.6000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">15.66500</td><td char=\".\" align=\"char\">13.75000</td></tr><tr><td align=\"left\" rowspan=\"3\">Non-opening</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">3.39600</td><td char=\".\" align=\"char\">0.30000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0024</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">10.3624</td><td char=\".\" align=\"char\">2.9000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">12.49500</td><td char=\".\" align=\"char\">5.85000</td></tr><tr><td align=\"left\" rowspan=\"3\">RGGA</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">7.72200</td><td char=\".\" align=\"char\">3.25000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.1128</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">14.0341</td><td char=\".\" align=\"char\">4.1000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">15.20500</td><td char=\".\" align=\"char\">9.75000</td></tr><tr><td align=\"left\" rowspan=\"3\">OQAvg</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">62.48400</td><td char=\".\" align=\"char\">59.95000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0793*</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">56.0271</td><td char=\".\" align=\"char\">57.6000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">53.45500</td><td char=\".\" align=\"char\">50.85000</td></tr><tr><td align=\"left\" rowspan=\"3\">OQAvg_2/3</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">66.33400</td><td char=\".\" align=\"char\">63.50000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0092</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">54.1047</td><td char=\".\" align=\"char\">53.8000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">51.98500</td><td char=\".\" align=\"char\">47.60000</td></tr><tr><td align=\"left\" rowspan=\"3\">AmplAsymAvg</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">11.48600</td><td char=\".\" align=\"char\">10.55000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0000</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">21.5353</td><td char=\".\" align=\"char\">18.6000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">32.23500</td><td char=\".\" align=\"char\">32.30000</td></tr><tr><td align=\"left\" rowspan=\"3\">AmplAsymAvg_2/3</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">9.60800</td><td char=\".\" align=\"char\">8.50000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0000</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">20.4647</td><td char=\".\" align=\"char\">18.0000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">31.05250</td><td char=\".\" align=\"char\">32.00000</td></tr><tr><td align=\"left\" rowspan=\"3\">PhaseAsymAvg</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">12.21400</td><td char=\".\" align=\"char\">6.40000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0000</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">18.1341</td><td char=\".\" align=\"char\">14.0000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">18.31000</td><td char=\".\" align=\"char\">17.50000</td></tr><tr><td align=\"left\" rowspan=\"3\">PhaseAsymAvg_2/3</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">12.07600</td><td char=\".\" align=\"char\">6.05000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0033</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">18.3306</td><td char=\".\" align=\"char\">12.3000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">17.83750</td><td char=\".\" align=\"char\">14.90000</td></tr><tr><td align=\"left\" rowspan=\"3\">AbsPhaseDiffAvg</td><td align=\"left\">Norm</td><td align=\"left\">50</td><td char=\".\" align=\"char\">37.72200</td><td char=\".\" align=\"char\">31.90000</td><td char=\".\" align=\"char\" rowspan=\"3\">0.0000</td></tr><tr><td align=\"left\">Benign</td><td align=\"left\">85</td><td char=\".\" align=\"char\">54.5729</td><td char=\".\" align=\"char\">48.2000</td></tr><tr><td align=\"left\">Malignant</td><td align=\"left\">40</td><td char=\".\" align=\"char\">70.67750</td><td char=\".\" align=\"char\">72.60000</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Comparison of vibratory parameters (achieving AUC of more than 0.7) in differentiation of normophonic subjects from patients with any organic lesion of the glottis—results of AUC ROC analysis</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Parameter</th><th align=\"left\">Booster/inhibitor</th><th align=\"left\">AUC</th><th align=\"left\">AUC lower 95%</th><th align=\"left\">AUC upper 95%</th><th align=\"left\"><italic>p</italic> value</th><th align=\"left\">Youden index</th><th align=\"left\">Cutting point</th><th align=\"left\">Sensitivity</th><th align=\"left\">Specificity</th></tr></thead><tbody><tr><td align=\"left\">AmplAsymAvg</td><td align=\"left\">Booster</td><td char=\".\" align=\"char\">0.822</td><td char=\".\" align=\"char\">0.76</td><td char=\".\" align=\"char\">0.884</td><td char=\".\" align=\"char\">0.0000</td><td char=\".\" align=\"char\">0.50</td><td align=\"left\">18.3</td><td char=\".\" align=\"char\">0.6</td><td char=\".\" align=\"char\">0.9</td></tr><tr><td align=\"left\">AmplAsymAvg_2/3</td><td align=\"left\">Booster</td><td char=\".\" align=\"char\">0.772</td><td char=\".\" align=\"char\">0.704</td><td char=\".\" align=\"char\">0.841</td><td char=\".\" align=\"char\">0.0000</td><td char=\".\" align=\"char\">0.51</td><td align=\"left\">13.8</td><td char=\".\" align=\"char\">0.67</td><td char=\".\" align=\"char\">0.84</td></tr><tr><td align=\"left\">AbsPhaseDiffAvg</td><td align=\"left\">Booster</td><td char=\".\" align=\"char\">0.754</td><td char=\".\" align=\"char\">0.671</td><td char=\".\" align=\"char\">0.837</td><td char=\".\" align=\"char\">0.0000</td><td char=\".\" align=\"char\">0.50</td><td align=\"left\">43.5</td><td char=\".\" align=\"char\">0.68</td><td char=\".\" align=\"char\">0.82</td></tr><tr><td align=\"left\">AmpAvg_2/3</td><td align=\"left\">Inhibitor</td><td char=\".\" align=\"char\">0.743</td><td char=\".\" align=\"char\">0.662</td><td char=\".\" align=\"char\">0.824</td><td char=\".\" align=\"char\">0.0000</td><td char=\".\" align=\"char\">0.42</td><td align=\"left\">7.9</td><td char=\".\" align=\"char\">0.68</td><td char=\".\" align=\"char\">0.74</td></tr><tr><td align=\"left\">PhaseAsymAvg</td><td align=\"left\">Booster</td><td char=\".\" align=\"char\">0.721</td><td char=\".\" align=\"char\">0.629</td><td char=\".\" align=\"char\">0.814</td><td char=\".\" align=\"char\">0.0000</td><td char=\".\" align=\"char\">0.42</td><td align=\"left\">7</td><td char=\".\" align=\"char\">0.88</td><td char=\".\" align=\"char\">0.54</td></tr><tr><td align=\"left\">AmpAvg</td><td align=\"left\">Inhibitor</td><td char=\".\" align=\"char\">0.71</td><td char=\".\" align=\"char\">0.624</td><td char=\".\" align=\"char\">0.796</td><td char=\".\" align=\"char\">0.0000</td><td char=\".\" align=\"char\">0.34</td><td align=\"left\">6.3</td><td char=\".\" align=\"char\">0.6</td><td char=\".\" align=\"char\">0.74</td></tr><tr><td align=\"left\">OQAvg_2/3</td><td align=\"left\">Inhibitor</td><td char=\".\" align=\"char\">0.647</td><td char=\".\" align=\"char\">0.566</td><td char=\".\" align=\"char\">0.727</td><td char=\".\" align=\"char\">0.0004</td><td char=\".\" align=\"char\">0.34</td><td align=\"left\">45.2</td><td char=\".\" align=\"char\">0.42</td><td char=\".\" align=\"char\">0.92</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Comparison of vibratory parameters in differentiating benign from malignant lesions of the glottis—results of AUC ROC analysis for chosen parameters (achieving AUC of more than 0.65)</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Parameter</th><th align=\"left\">Booster/inhibitor</th><th align=\"left\">AUC</th><th align=\"left\">AUC lower 95%</th><th align=\"left\">AUC upper 95%</th><th align=\"left\"><italic>p</italic></th><th align=\"left\">Youden index</th><th align=\"left\">Cutting point</th><th align=\"left\">Sensitivity</th><th align=\"left\">Specificity</th></tr></thead><tbody><tr><td align=\"left\">AmplAsymAvg</td><td align=\"left\">Booster</td><td char=\".\" align=\"char\">0.719</td><td char=\".\" align=\"char\">0.619</td><td char=\".\" align=\"char\">0.818</td><td char=\".\" align=\"char\">0.0000</td><td char=\".\" align=\"char\">0.41</td><td char=\".\" align=\"char\">29.6</td><td char=\".\" align=\"char\">0.650</td><td char=\".\" align=\"char\">0.765</td></tr><tr><td align=\"left\">AmpInvolvedAvg</td><td align=\"left\">Inhibitor</td><td char=\".\" align=\"char\">0.70</td><td char=\".\" align=\"char\">0.59</td><td char=\".\" align=\"char\">0.80</td><td char=\".\" align=\"char\">0.0002</td><td char=\".\" align=\"char\">0.38</td><td char=\".\" align=\"char\">2.8</td><td char=\".\" align=\"char\">0.725</td><td char=\".\" align=\"char\">0.659</td></tr><tr><td align=\"left\">AbsPhaseDiffAvg</td><td align=\"left\">Booster</td><td char=\".\" align=\"char\">0.676</td><td char=\".\" align=\"char\">0.572</td><td char=\".\" align=\"char\">0.780</td><td char=\".\" align=\"char\">0.0009</td><td char=\".\" align=\"char\">0.36</td><td char=\".\" align=\"char\">68.1</td><td char=\".\" align=\"char\">0.575</td><td char=\".\" align=\"char\">0.788</td></tr><tr><td align=\"left\">AmplAsymAvg_2/3</td><td align=\"left\">Booster</td><td char=\".\" align=\"char\">0.655</td><td char=\".\" align=\"char\">0.543</td><td char=\".\" align=\"char\">0.767</td><td char=\".\" align=\"char\">0.0067</td><td char=\".\" align=\"char\">0.33</td><td char=\".\" align=\"char\">38.3</td><td char=\".\" align=\"char\">0.450</td><td char=\".\" align=\"char\">0.882</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p>The table presents mean and median values in each diagnosis group (norm, benign, and malignant). N means the number of cases in each group</p></table-wrap-foot>", "<table-wrap-foot><p>Exclusion is OQAvg_2/3 (in green), this parameter achieved the highest specificity. Parameters are divided into boosters and inhibitors as explained in the text. Cutting point—calculated with the use of the Youden index, a proposed value for the detection of organic lesions. For boosters values, above the cutting point suggest the presence of organic lesions; on the other hand, values below indicate normophonic patient. The opposite behavior is observed for inhibitors</p></table-wrap-foot>", "<table-wrap-foot><p>Parameters are divided into boosters and inhibitors as explained in the text. Cutting point–calculated with the use of the Youden index, a proposed value for the detection of organic lesions. For boosters values, above the cutting point suggest the presence of a malignant lesion; on the other hand, values below indicate the presence of a benign lesion. The opposite behavior is observed for inhibitors</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<media xlink:href=\"432_2023_5543_MOESM1_ESM.docx\"><caption><p>Supplementary file1 (DOCX 14 kb)</p></caption></media>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Perioperative neurocognitive disorder (PND), which involves cognitive functional decline to varying degrees, is a common complication after anesthesia and surgery, especially in elderly patients (Evered et al. ##REF##30336844##2018##; Rundshagen ##REF##24622758##2014##). PND affects postoperative recovery and increases the incidence of complications and mortality (Steinmetz et al. ##REF##19225398##2009##). Therefore, elucidating the pathogenesis of PND and identifying treatment strategies will be beneficial for clinical practice (Rengel et al. ##REF##31337482##2019##).</p>", "<p id=\"Par3\">Multiple factors contribute to the development of PND, such as anesthetic drugs, surgical trauma, postoperative pain, and previous cerebrovascular diseases (Rengel et al. ##REF##31337482##2019##). However, the exact mechanisms underlying PND remain unclear, and effective therapeutic strategies are lacking. Neuroinflammation in the hippocampus is responsible for surgery-induced cognitive deficits in aged mice (Cao et al. ##REF##20691747##2010##; Hovens et al. ##REF##24517920##2014##), and microglial activation is a well-known feature of hippocampal neuroinflammation (Feng et al. ##REF##28405620##2017##). Microglia, the resident immune cells in the brain, participate in both the initiation of protective immune responses and the development of invasive inflammation during various CNS disorders (Ransohoff and El Khoury ##REF##26354893##2015##). Upon abnormal stimulation, microglia are gradually activated and secrete numerous inflammatory mediators (IL-1β, TNF-α, Cox-2, etc.), mediating the survival of surrounding cells such as neurons and astroglia, which further exaggerates the inflammatory response, leading to subsequent neuronal apoptosis and irreversible impairment of nervous system function (Block and Hong ##REF##16081203##2005##; Cao et al. ##REF##20691747##2010##). Hence, inhibiting the neuroinflammatory response mediated by activated microglia may alleviate surgery-induced neuronal apoptosis and cognitive dysfunction.</p>", "<p id=\"Par4\">P38 MAPK is a stress-induced kinase and is involved in a wide variety of cellular signal transduction pathways and the phosphorylation of transcription factors and cytosolic proteins, which regulate processes such as cell inflammation and apoptosis (Sui et al. ##REF##24333738##2014##; Wang et al. ##REF##25466482##2015##). Moreover, activated P38 further activates the downstream molecular transcription factor ATF2, which can regulate the expression of target genes and inflammation-related proteins such as TNF-α (Yu et al. ##REF##24660030##2014a##, ##REF##25614714##b##). SB239063, a potent inhibitor of the P38 MAPK pathway, ameliorates brain injury and neurological deficits in a rat model of cerebral focal ischemia (Barone et al. ##REF##11160612##2001##; Li et al. ##REF##26282496##2015##). Whether the P38MAPK/ATF2 signaling pathway is involved in hippocampal neuroinflammation mediated by microglia in the context of PND has yet to be elucidated.</p>", "<p id=\"Par5\">Therefore, our current study aimed to prove that activation of the P38MAPK/ATF2 pathway is involved in surgery-induced cognitive impairment in aged mice and that inhibition of the P38MAPK/ATF2 pathway attenuates cognitive disorders by reducing microglia-mediated neuroinflammation and neuronal apoptosis.</p>" ]

[ "<title>Materials and methods</title>", "<title>Animal protocol</title>", "<p id=\"Par6\">Female C57BL/6 J mice (16 months old, female) weighing approximately 30 g were obtained from the Laboratory Animal Centre of Tongji Medical College, Huazhong University of Science and Technology (Wuhan, China). All mice were acclimated to a new environment for 7 days on a 12:12 h light/dark cycle. The experimental protocols were performed in accordance with the National Institutes of Health (NIH) guidelines for animal care and approved by the Experimental Animal Committee of Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology.</p>", "<p id=\"Par7\">Ninety mice were randomly divided into three groups: the control (Con) group, surgery (Sur) group and surgery + SB239063 (Sur + SB) group. Mice in the Con group did not receive any special intervention. Mice in the Sur and Sur + SB groups received tibial fracture surgery. Furthermore, mice in the Sur + SB group were administered SB239063 (10 mg/kg, MedChemExpress, USA) orally 60 min before and 6 h after tibial fracture surgery. Mice in all groups were sacrificed on days 1, 3, and 7 after surgery.</p>", "<title>Surgery and anesthesia</title>", "<p id=\"Par8\">After the mice in the Sur and Sur + SB groups were anesthetized with 1.4% isoflurane and 100% oxygen, open tibial fracture surgery with intramedullary fixation was performed. In brief, the right hind limb of mice was shaved and disinfected, and then a midline incision was made on the right hind limb under aseptic conditions. A 0.38 mm pin was inserted into the tibial intramedullary canal, thus achieving intramedullary fixation. The periosteum was then stripped, and the bone was fractured at the midpoint. After surgery, the wound was irrigated, and the skin was sutured with 5–0 Vicryl sutures (Ethicon). To relieve the pain from skin incision, compound lidocaine cream was applied locally to the wound. The mice were then placed in a chamber filled with 1.4% isoflurane and 100% oxygen. The mice were anesthetized for up to 2 h total. Finally, the animals were allowed to recover spontaneously from anesthesia and returned to their own cages, where they were provided ad libitum access to food and water. During the procedure, the body temperature of the mice was maintained at 37 ± 0.5 °C with a heating pad.</p>", "<title>Open field test</title>", "<p id=\"Par9\">Locomotor activity was evaluated by the open field test. A square wooden open field (50 cm × 50 cm × 50 cm) was subdivided into 9 even squares with a white floor. The mice were individually placed in the central zone and allowed to explore for 5 min. The total distance traveled and the number of rearings in the box were recorded with a video tracking system. At the end of each trial, the floor of the chamber was cleaned with 75% ethanol to remove olfactory cues. The open field test was performed one day before the surgery and on days 1, 3, and 7 after surgery.</p>", "<title>Morris water maze test</title>", "<p id=\"Par10\">The MWM was used to evaluate spatial learning and memory in mice. The apparatus consisted of a round pool (120 cm in diameter and 50 cm in height) filled with water that was divided into four quadrants. There was an escape platform in the center of the target quadrant 1 cm beneath the water surface. During the positioning navigation test, the mice were placed in different quadrants of the pool with their heads facing the wall. Each mouse was allowed to search for the platform for 60 s and stay on the platform for 15 s. The time spent searching and mounting the platform was defined as the escape latency, which was used to assess the spatial learning ability of the mice. The mice that failed to find the platform within 60 s were guided manually to the platform and left on the platform for 15 s, and the escape latency was recorded as 60 s. The training was performed four times a day for five successive days before the operation, and the platform was kept in the same location throughout the training process. In the spatial exploration test, we removed the platform, the mice were placed in the quadrant opposite the target quadrant facing the pool wall, and they were allowed to swim freely for 60 s. The time spent searching for the target quadrant (the quadrant where the platform was previously located) and the number of times the mice crossed the original platform position (number of platform crossings) were recorded to assess memory. This test was performed on days 1, 3, and 7. The water in the pool was changed every day and made opaque by nontoxic white paint, and the temperature was maintained at 23–25 °C. The paths of the mice were recorded and analyzed with a computerized video tracking system.</p>", "<title>Fear conditioning test</title>", "<p id=\"Par11\">Fear conditioning was performed to evaluate the hippocampus-dependent learning and memory of the mice. In the training phase, the mice were placed in a conditioning chamber with a stainless steel shock grid floor in the absence of any stimuli for 3 min for adaptation. Then, three pairs of conditioned-unconditioned stimuli were delivered at an interval of 30 s. Each pair of conditioned-unconditioned stimuli consisted of a 30 s, 80 dB tone (conditioned stimulus) and then a 2 s, 0.75 mA electrical foot shock (unconditioned stimulus). In the testing phase, the mice were placed in the original chamber in the absence of stimulation for 5 min. The freezing time of the animals, i.e., the duration for which the animals showed no movement except for respiration, was recorded to assess contextual memory. Cued fear memory was tested by delivering a continuous 3 min tone in the same chamber and recording the freezing time with tracking system software.</p>", "<title>Western blotting</title>", "<p id=\"Par12\">Hippocampal tissues from the mice were homogenized in a mixture of RIPA lysis buffer, PMSF, and phosphatase and protease inhibitors and incubated for 30 min on ice. Then, the lysates were centrifuged at 12,000 rpm for 15 min at 4 °C to remove the sediment. The total protein concentration was determined by a BCA protein assay kit (Boster, Wuhan, China). Subsequently, the samples were mixed with 5 × loading buffer. After denaturation for 10 min at 100 °C, equal amounts of protein (50 μg/lane) from each sample were separated by SDS–PAGE and transferred to PVDF membranes (Millipore, Bedford, MA, USA). The membranes were then blocked with 5% skim milk in TBST for 2 h at room temperature. The blots were incubated overnight at 4 °C with the following primary antibodies: anti-P38 (1:1000, #8690, Cell Signaling Technology, USA), anti-p-P38 (1:1000, #4511, Cell Signaling Technology, USA), anti-ATF2 (1:1000, #35031, Cell Signaling Technology, USA), anti-IL-1β (1:500, #ab200478, Abcam, Cambridge, UK), anti-TNF-α (1:1000, #17590-1-AP, Proteintech, Wuhan, China), anti-caspase 3 (1:1000, #ab44976, Abcam, Cambridge, UK), anti-bax (1:1000, #50599-2-lg, Proteintech, Wuhan, China), anti-bcl-2 (1:1000, #12789-1-AP, Proteintech, Wuhan, China), anti-GAPDH (1:1000, #ab37168, Abcam, Cambridge, UK), and anti-β-actin (1:1000, #A01010, Abbkine). The next day, the membranes were washed 3 times for 10 min each time with TBST and then incubated for 2 h at RT with HRP-conjugated goat anti-rabbit (1:5000, A21020, Abbkine, Carlsbad, CA) or goat anti-mouse (1:5000, A21010, Abbkine, Carlsbad, CA) secondary antibodies. Finally, the blots were detected with a SuperLumia ECL Plus HRP Substrate Kit (K22030; Abbkine, Carlsbad, CA) and photographed by Image Lab software (Bio-Rad, USA).</p>", "<title>Real-time PCR</title>", "<p id=\"Par13\">Total RNA from the hippocampi of mice was extracted. A standard cDNA Synthesis kit (Takara Bio Inc., Japan) was used for real-time PCR. In the 20-μl reaction, 1 μg of total RNA was added. Supplementary Table ##SUPPL##0##S1## shows the primer sequences.</p>", "<p id=\"Par14\">The thermal cycling conditions for each real-time PCR included a holding stage at 95 °C for 30 s; 40 cycles of amplification at 95 °C for 5 s and 60 °C for 30 s; and a melting curve stage at 95 °C for 15 s, 60 °C for 1 min, and 95 °C for 15 s. Gene expression was analyzed by 2^−ΔΔct.</p>", "<title>Immunofluorescence staining</title>", "<p id=\"Par15\">After the behavioral tests, the animals were anesthetized with isoflurane and transcardially perfused with PBS followed by 4% paraformaldehyde (PFA). The brains were rapidly harvested, postfixed in 4% PFA overnight, and then placed in 20% and 30% sucrose at 4 °C until they sank. After being embedded in optimal cutting temperature (20 °C), the brains were cut into 10 µm thick sections by a cryostat microtome and mounted on glass slides. The sections were blocked with 10% donkey serum albumin for 45 min at RT before being incubated with a rabbit anti-Iba-1 antibody (1:200, #ab5076, Abcam, Cambridge, UK) or mouse anti-NeuN antibody (1:100; #ab104224, Abcam, Cambridge, UK) overnight at 4 °C. On the following day, the sections were washed four times for 10 min each time using PBST and then incubated with donkey anti-goat secondary antibody (Abbkine, Carlsbad, CA) for 2 h at room temperature in the dark. Finally, tissue sections were exposed to DAPI for 5 min, and the immunostained sections were visualized with a fluorescence microscope (DM2500, Leica, Germany) equipped with an imaging system.</p>", "<title>Nissl staining</title>", "<p id=\"Par16\">After being anesthetized with 10% chloral hydrate (0.3 ml/100 g) by intraperitoneal injection, the mice were perfused with PBS followed by 4% paraformaldehyde (PFA) via the left ventricle. The brains were removed and kept in PFA at 4 °C. The next day, the brains were embedded in optimal cutting temperature (20 °C) and cut into 8 μm thick sections. The slices were dehydrated in gradient alcohol solutions and then treated with Nissl staining solution for 10 min. The number of Nissl bodies in the hippocampal CA1 region was determined with IPP version 6.0 software to assess neuronal loss.</p>", "<title>Statistical analysis</title>", "<p id=\"Par17\">SPSS version 19.0 was used. All data are expressed as the mean ± SEM. We applied one-way ANOVA followed by post hoc tests to evaluate multiple comparisons. When the data follows a normal distribution, we employ the statistical method of Fisher’s Least Significant Difference (LSD); when the data does not follow a normal distribution, we use Dunnett’s Test. <italic>P</italic> &lt; 0.05 was considered to indicate a statistically significant difference.</p>" ]

[ "<title>Results</title>", "<title>Hippocampus-dependent memory was impaired in aged mice after anesthesia and surgery</title>", "<p id=\"Par18\">Locomotor activity was assessed by the total distance traveled in the open field chamber. There were no significant differences among the groups (Fig. ##FIG##0##1##A), indicating that locomotor activity was not affected by surgery or treatment.</p>", "<p id=\"Par19\">We assessed the cognitive functions of mice by the MWM and FCT. In the MWM test, compared with the Con group, the mice with PND in the Sur group had a significantly longer escape latency and made fewer platform crossings on days 1, 3 and 7 (Fig. ##FIG##0##1##F). However, the mice in the Sur + SB group had a significantly shorter escape latency and made more platform crossings than those in the Sur group (Fig. ##FIG##0##1##F). In swimming speed, there was no difference among the groups at any time point (Fig. ##FIG##0##1##D). In the FCT, surgery and anesthesia decreased the freezing time of the mice in the Sur group on days 1, 3 and 7 in the contextual memory test. The freezing time in the contextual memory test was increased in the Sur + SB group compared with the Sur group on days 1 and 3 (<italic>P</italic> &lt; 0.05, Fig. ##FIG##0##1##B). No significant difference in freezing time in the tone test was observed among the groups (Fig. ##FIG##0##1##C). These results indicated that anesthesia and surgery can impair the cognitive functions of aged mice.</p>", "<title>The P38MAPK/ATF2 signaling pathway was activated in the hippocampus of aged mice with PND</title>", "<p id=\"Par20\">The protein expression of P38, p-P38, ATF2, and p-ATF2 was evaluated by Western blotting (Fig. ##FIG##1##2##A–C). Rapid phosphorylation of P38 and a decrease in the expression of the downstream factor ATF2 in the hippocampus were observed in mice with PND in the Sur group, but similar alterations were not observed in the Con group (Fig. ##FIG##1##2##D, E). SB239063, a specific P38 inhibitor, prevented the activation of P38 and restored ATF2 expression (Fig. ##FIG##1##2##D, E).</p>", "<p id=\"Par21\">The above results showed that activation of the P38MAPK/ATF2 signaling pathway was involved in PND and that SB239063 alleviated cognitive impairment in aged mice by inhibiting the P38MAPK/ATF2 signaling pathway.</p>", "<title>SB239063 reduced the expression of TNF-α and IL-1β in the hippocampus by inhibiting the P38MAPK signaling pathway</title>", "<p id=\"Par22\">We assessed the effects of surgery and SB239063 on the expression levels of the proinflammatory factors TNF-α and IL-1β in the hippocampus by RT–PCR and Western blotting.</p>", "<p id=\"Par23\">Compared with those in the Con group, the TNF-α and IL-1β levels in the hippocampi of the mice in the Sur group were markedly increased on days 1, 3 and 7 (<italic>P</italic> &lt; 0.05, Fig. ##FIG##2##3##). Mice that received SB239063 treatment exhibited decreased hippocampal protein expression of TNF-α and IL-1β on days 1 and 3 (Fig. ##FIG##2##3##D, E) and decreased hippocampal gene expression levels of TNF-α and IL-1β on days 1, 3 and 7 (Fig. ##FIG##2##3##F, G), suggesting that SB239063 could inhibit the production of proinflammatory factors such as TNFα and IL-1β in the hippocampus of mice with PND and that the P38MAPK signaling pathway was involved in this process.</p>", "<title>SB239063 inhibited microglial activation in the CA1 region of the hippocampus</title>", "<p id=\"Par24\">Activated microglia can secrete excessive proinflammatory mediators, which contribute to the development of neuroinflammation. To explore the effect of SB239063 on microglial activation, we used immunostaining to detect the microglial marker Iba-1. Microglial activation in the CA1 region of the hippocampus was markedly increased in the Sur group compared with the Con group on days 1, 3, and 7, as indicated by many Iba1 cells. Activated microglia had larger cell bodies, were poorly ramified, and had short and thick processes (Fig. ##FIG##3##4##). Nevertheless, these changes were attenuated by SB239063 treatment through suppression of the P38MAPK/ATF2 pathway.</p>", "<title>SB239063 decreased neuronal apoptosis following surgery</title>", "<p id=\"Par25\">To further confirm the mechanisms by which the P38MAPK/ATF2 pathway contributes to cognitive dysfunction, we assessed neuronal apoptosis by performing immunofluorescence for the neuronal marker NeuN and measuring the expression levels of caspase-3 and Bax/Bcl-2 in the hippocampus. Surgery induced a dramatic increase in caspase-3 and Bax/Bcl-2 expression in the hippocampus and a significant reduction in NeuN expression in the CA1 area of the hippocampus on days 1, 3 and 7. However, compared to the Sur group, the mice in the Sur + SB group exhibited an obvious decrease in caspase-3 and Bax/Bcl-2 expression and an increase in NeuN expression. As shown in Fig. ##FIG##4##5## and Fig. ##FIG##5##6##, treatment with SB239063 significantly inhibited neuronal apoptosis and improved neurogenesis on days 1 and 3. These results suggested that SB239063 may help prevent neuronal injury in the hippocampus induced by surgery.</p>", "<title>SB239063 inhibited neuronal loss induced by hippocampal apoptosis</title>", "<p id=\"Par26\">Nissl staining was conducted to evaluate the number of neurons in the CA1 region of the hippocampus. As shown in Fig. ##FIG##6##7##, neurons were diffusely deteriorated, and many Nissl bodies were lost in the Sur group compared to the Con group. However, SB239063 increased the number of surviving neurons on days 1 and 3 (<italic>P</italic> &lt; 0.05), but no difference was observed in the number of neurons between the Sur and Sur + SB groups on day 7 (<italic>P</italic> &gt; 0.05). Thus, neuronal loss in the CA1 region was reduced by SB239063.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par27\">In the current work, we aimed to study whether the P38MAPK/ATF2 signaling pathway is involved in neuroinflammation, neuronal apoptosis and cognitive impairment in aged mice subjected to orthopedic surgery under isoflurane anesthesia and to explore the neuroprotective mechanisms of SB239063 against PND. Our data suggested that activation of the P38 MAPK/ATF2 signaling pathway in response to surgical trauma plays a critical role in neuroinflammation and cognitive dysfunction. Treatment with SB239063, a P38 inhibitor, prevents PND by ameliorating inflammation and neuronal apoptosis in the hippocampus.</p>", "<p id=\"Par28\">Early clinical studies on PND focused on cardiac surgery, and noncardiac surgery was later found to have similar neurological effects as cardiac surgery (Evered et al. ##REF##21474666##2011##), with the incidence of these effects being higher in elderly patients. According to reports, the incidence of postoperative cognitive impairment in patients over 65 years old was 26% and 10% within weeks and at 3 months after surgery, respectively (van Harten et al. ##REF##22321085##2012##). Twenty-five percent of elderly patients developed PND 7 days after hip replacement (Ji et al. ##REF##23085747##2013##). We used a mouse model of tibial fracture originally described by Harry et al. (Harry et al. ##REF##18404722##2008##) to determine the impact of peripheral trauma on postoperative cognitive function (Xiong et al. ##REF##30507912##2018##). After this surgery, the levels of peripheral and central inflammatory markers in the mice changed significantly, and hippocampal microglia were activated in large numbers. These changes are related to defects in hippocampal neuroplasticity and cognitive function after surgery (Cibelli et al. ##REF##20818791##2010##; Terrando et al. ##REF##21041647##2010##). Clinically, similar changes are observed in elderly people with PND after orthopedic surgery (Hirsch et al. ##REF##27577265##2016##; Neerland et al. ##REF##27341529##2016##). In this study, the Morris water maze and fear conditioning test were used to assess learning and memory, which are important aspects of cognitive function in aged mice. Our results showed that mice with impaired hippocampus-dependent learning and memory exhibited a longer escape latency to reach the platform and fewer original platform crossings in the Morris water maze test and increased freezing time in the contextual fear memory test on Day 1 and Day 3 after surgery.</p>", "<p id=\"Par29\">The hippocampus is an important functional brain area for learning and memory formation. Neuroinflammation of the hippocampus plays a vital role in the progression of cognitive impairment and is probably the critical mechanism underlying PND (Cao et al. ##REF##20691747##2010##; Vacas et al. ##REF##23558082##2013##). Surgical trauma can induce inflammation in the peripheral immune system, causing endothelial cells and phagocytes to secrete and release many inflammatory mediators, such as TNF-α, IL-1β, IL-6, and COX-2 (Cibelli et al. ##REF##20818791##2010##; Terrando et al. ##REF##21041647##2010##). These mediators are not only directly involved in the inflammatory response but also disrupt the permeability of the blood–brain barrier through passive diffusion energy-dependent carriers and other pathways, which can further activate microglia in the nervous system, causing brain injury and cognitive impairment (Wardill et al. ##REF##27367824##2016##; Yu et al. ##REF##24660030##2014a##, ##REF##25614714##b##). Furthermore, neuroinflammation may influence neuronal functions either directly or through regulation of intraneuronal pathways, eventually causing neuronal apoptosis, which is another important contributor to the development of PND (Hovens et al. ##REF##24517920##2014##; Li et al. ##REF##28414034##2017##). Excessive neuronal apoptosis can impair the function of the central nervous system and lead to cognitive impairment (Jiang et al. ##REF##29534734##2018##; Peng et al. ##REF##29181847##2018##). Attenuation of the neuroinflammatory response mediated by microglia in the hippocampus of mice can reduce neuronal apoptosis and alleviate cognitive dysfunction (Liu et al. ##REF##31102026##2019##; Zhang et al. ##REF##33385375##2020##). This suggests that hippocampal neuroinflammation and neuronal apoptosis are involved in the occurrence and development of perioperative neurocognitive impairment. In our study, Western blotting and PCR were applied to measure the expression levels of inflammatory and apoptosis-related factors in the hippocampi of aged mice after surgery. Our results showed that the expression levels of proinflammatory and proapoptotic factors were significantly increased, while the expression of antiapoptotic factors was decreased; these changes were associated with impairment of learning and memory in the mice after surgery.</p>", "<p id=\"Par30\">Activated microglia have been shown to be markers of inflammation in the central nervous system and can mediate subsequent neuronal apoptosis. Increasing evidence suggests that activation of microglia is responsible for hippocampal neuroinflammation after surgery and anesthesia (Csuka et al. ##REF##10943727##2000##; Simon et al. ##REF##29427657##2019##). Microglia, which are normally in a resting state, are critical for maintaining homeostasis in the CNS (Ousman and Kubes ##REF##22837040##2012##). Once activated by various stresses, microglia not only secrete much reactive oxygen species and proinflammatory factors to regulate the survival of surrounding cells but also respond to different proinflammatory signals from other cells, leading to a vicious cycle (Lannes et al. ##REF##29371994##2017##; Okuno et al. ##REF##15356200##2004##). Activation of microglia has been proven to be an early sign of neuroinflammation and neuronal apoptosis in neurodegenerative diseases (Lloyd-Burton et al. ##REF##23467362##2013##; Maqbool et al. ##REF##24119288##2013##). Hovens found that activation of hippocampal microglia is closely related to spatial memory disorders (Hovens et al. ##REF##25460037##2015##). In animal models of tibial fractures, activated mast cells in the central nervous system can directly cause hippocampal neuron damage and apoptosis by activating microglia, leading to postoperative cognitive dysfunction (Zhang et al. ##REF##27245661##2016##). Similar to the results presented in our study, surgery led to significant activation of microglia, as indicated by Iba-1 immunoreactivity for up to 7 days. Neuronal apoptosis was observed simultaneously in the CA1 area of the hippocampus. Microglial activation was effectively decreased in the SB group compared with the Sur group, and postoperative neurocognitive disorder was alleviated. Likewise, PCR and Western blotting showed that inhibiting microglial activation prevented the release of proinflammatory cytokines and impaired neuronal function after surgery.</p>", "<p id=\"Par31\">As a mitogen-activated protein kinase (MAPK) family member, p38 MAPK, a point of convergence for different signaling processes involved in inflammation, apoptosis and autophagy, can be preferentially activated by various stresses, such as trauma, proinflammatory cytokines and DNA damage (Duch et al. ##REF##22820251##2012##; Takeda and Ichijo ##REF##12390245##2002##). The potential roles of p38 MAPK signaling pathways in neuroinflammation and neuronal apoptosis have attracted a great deal of attention (Munoz et al. ##REF##17784957##2007##; Roy et al. ##REF##25676389##2015##). BFNM can inhibit LPS-induced inflammatory responses through the P38MAPK/ATF2 signaling pathway and exert an anti-inflammatory effect. Blocking the middle cerebral artery significantly increases the activity of P38MAPK and neuronal apoptosis. Inhibition of p38 MAPK and reduction of p-p38 protein expression can effectively decrease neuronal apoptosis and ameliorate cerebral ischemia–reperfusion injury (Li et al. ##REF##26282496##2015##). SB203580, another p38 MAPK inhibitor, inhibited isoflurane-induced inflammation, oxidative stress, and apoptosis (Liu et al. ##REF##33519423##2020##). In addition, activated p38 MAPK can participate in the cellular apoptosis process by regulating the expression of mitochondrial proapoptotic proteins, such as Bcl-2 family members (Guan et al. ##REF##16243436##2006##; Okuno et al. ##REF##15356200##2004##). Caspase 3 is the executor of cell apoptosis. The regulatory effect between p38 MAPK and caspases is bidirectional, which means that p38 activates caspases to mediate apoptosis, and activated caspases in turn lead to p38 phosphorylation (Moosavi et al. ##REF##17543571##2007##; Song et al. ##REF##21996423##2011##). We detected a significantly higher rate of p38 phosphorylation in the hippocampi of mice with PND, while SB239063 treatment greatly reduced the ratio of p-p38. SB239063 reduced the production of TNF-α, IL-1β, bax/bcl-2, and caspase-3 and the expression level of Iba1 in the hippocampus by inhibiting the p38 MAPK/ATF2 pathway.</p>", "<p id=\"Par32\">The p38 MAPK pathway exerts a wide variety of cellular functions, mostly by regulating multiple downstream molecules. One of the downstream targets of p38 MAPK, ATF2, is expressed ubiquitously, with the highest expression level being found in the brain (Gozdecka and Breitwieser ##REF##22260696##2012##; Hu et al. ##REF##10077326##1999##). This transcription factor is reported to be a component of the basic cell machinery required for neuronal physiology, which may contribute to the complexity of the effects of the p38 MAPK/ATF2 signaling pathway on neuronal inflammation and apoptosis (Pearson et al. ##REF##15878807##2005##; Yu et al. ##REF##24660030##2014a##, ##REF##25614714##b##). Once activated, ATF2 transcriptionally regulates various gene targets that control cellular responses, ranging from the transcription factors Jun and Fos to extracellular cytokines and intracellular signaling pathways (Morton et al. ##REF##15304344##2004##). ATF2 knockout mice exhibited impaired migration of some neuronal populations and impaired neurological development (Yu et al. ##REF##24660030##2014a##, ##REF##25614714##b##). In Alzheimer’s and Parkinson’s disease, ATF2 expression is downregulated in the hippocampus and caudate nucleus (Pearson et al. ##REF##15878807##2005##), indicating that ATF2 is essential for neuronal viability and normal neurological functions. Rapid and long-lasting suppression of ATF2 expression has been regarded as a common response to neuronal damage in the CNS (Martin-Villalba et al. ##REF##9813301##1998##). Considering that ATF2 is critical for hippocampal neurogenesis and memory processing, we speculated that the expression of ATF2 is responsible for inflammation and neuronal apoptosis in the hippocampus associated with cognitive impairment. Furthermore, our findings confirmed that the upregulation of p-P38 expression and reduction in ATF2 expression were consistent with indicators of inflammation and apoptosis in the hippocampus of aged mice with PND. However, after SB239063 treatment, the expression levels of p-p38 and ATF2 were restored to normal levels, the expression of inflammatory factors was reduced, and excessive activation of microglia and apoptosis of neurons were inhibited, affecting the development of postoperative cognitive dysfunction.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par33\">In summary, our research revealed that activation of the p38MAPK-ATF2 pathway is involved in the development of PND in aged mice. Inhibiting the p38MAPK-ATF2 pathway may be a neuroprotective strategy for cognitive dysfunction induced by surgery through attenuation of microglia-mediated neuroinflammation and inhibition of neuronal apoptosis in the hippocampus.</p>" ]

[ "<p>Communicated by Sreedharan Sajikumar.</p>", "<p id=\"Par1\">Accumulating evidence indicates that microglia-mediated neuroinflammation in the hippocampus contributes to the development of perioperative neurocognitive disorder (PND). P38MAPK, a point of convergence for different signaling processes involved in inflammation, can be activated by various stresses. This study aims to investigate the role of the P38MAPK/ATF2 signaling pathway in the development of PND in mice. Aged C57BL/6 mice were subjected to tibial fracture surgery under isoflurane anesthesia to establish a PND animal model. The open field test was used to evaluate the locomotor activity of the mice. Neurocognitive function was assessed with the Morris water maze (MWM) and fear conditioning test (FCT) on postoperative days 1, 3 and 7. The mice exhibited cognitive impairment accompanied by increased expression of proinflammatory factors (IL-1β, TNF-α), proapoptotic molecules (caspase-3, bax) and microglial activation in the hippocampus 1, 3 and 7 days after surgery. Treatment with SB239063 (a P38MAPK inhibitor) decreased the expression of proinflammatory factors, proapoptotic molecules and Iba-1 in the CA1 region of the hippocampus. The number of surviving neurons was significantly increased. Inhibition of the P38MAPK/ATF2 signaling pathway attenuates hippocampal neuroinflammation and neuronal apoptosis in aged mice with PND, thus improving the perioperative cognitive function of the mice.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00221-023-06730-6.</p>", "<title>Keywords</title>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Author contributions</title>", "<p>MZ wrote the main manuscript text. MZ, SL and YT conducted the experiments. WC prepared all the figures. XW and WC revised the manuscript. ZZ and ZZ provided the ideas of the research.</p>", "<title>Funding</title>", "<p>This research was funded by National Natural Science Foundation of China, grant number 81371251 and National Natural Science Foundation of China, grant number 82004164.</p>", "<title>Data availability</title>", "<p>The data presented in this study are available on request from the first author.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par34\">The authors declare that there is no conflict of interest.</p>", "<title>Institutional review board statement</title>", "<p id=\"Par35\">The animal study protocol was approved by the Experimental Animal Committee of Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology.</p>", "<title>Informed consent</title>", "<p id=\"Par36\">Not applicable.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Behavioral tests in aged mice. The open-field test was performed to assess the locomotor activity of the mice by total distance traveled (<bold>A</bold>). The percent freezing time in the context test (<bold>B</bold>) and tone test (<bold>C</bold>). Swimming speed in the MWM on postoperative days 1, 3, and 7 (<bold>D</bold>). The escape latency and swimming speed during training in the MWM before surgery are shown (<bold>E</bold>). Effects of surgery and SB239063 on the escape latency and platform crossings of mice in the MWM (<bold>F</bold>). The data are plotted as the mean ± SEM (<italic>n</italic> = 10). <italic>*P</italic> &lt; 0.05, <italic>**P</italic> &lt; 0.01, <italic>***P</italic> &lt; 0.001 versus the Con group, <italic>#P</italic> &lt; 0.05, <italic>##P</italic> &lt; 0.01 versus the Sur group</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Effects of surgery and SB239063 on the P38MAPK/ATF2 signaling pathway in aged mice on postoperative days 1, 3 and 7. Western blotting showed the expression of P-38, p-P38 and ATF2 in the hippocampus (<bold>A</bold>–<bold>C</bold>). The expression of P-38, p-P38 and ATF2 was normalized to that of GAPDH as an internal control (<bold>D</bold>, <bold>E</bold>). The data are plotted as the mean ± SEM (<italic>n</italic> = 5). <italic>**P</italic> &lt; 0.01, <italic>***P</italic> &lt; 0.001 versus the Con group, <italic>#P</italic> &lt; 0.05, <italic>##P</italic> &lt; 0.01 versus the Sur group</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Effects of surgery and SB239063 on proinflammatory factors in the hippocampus on postoperative days 1, 3 and 7. Western blotting showed the protein expression levels of IL-1β and TNF-α in the hippocampus (<bold>A</bold>–<bold>C</bold>). The expression of IL-1β and TNF-α was normalized to that of GAPDH as an internal control (<bold>D</bold>, <bold>E</bold>). Real-time PCR was performed to analyze the relative mRNA expression levels of IL-1β and TNF-α in the hippocampus (<bold>F</bold>, <bold>G</bold>). The data are plotted as the mean ± SEM (<italic>n</italic> = 5). <italic>*P</italic> &lt; 0.05, <italic>**P</italic> &lt; 0.01, <italic>***P</italic> &lt; 0.001, <italic>****P</italic> &lt; 0.0001 versus the Con group, <italic>#P</italic> &lt; 0.05, <italic>##P</italic> &lt; 0.01, <italic>###P</italic> &lt; 0.001 versus the Sur group</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Effect of surgery and SB239063 on microglia in the hippocampal CA1 area of the mice on days 1, 3 and 7. Immunofluorescence images show the number and morphology of Iba-1 (red pixels) in the hippocampus (<bold>A</bold>). Quantitative analyses of Iba-1 (<bold>B</bold>). The data are plotted as the mean ± SEM (<italic>n</italic> = 3). <italic>**P</italic> &lt; 0.01, <italic>***P</italic> &lt; 0.001 versus the Con group, <italic>###P</italic> &lt; 0.001 versus the Sur group. Magnification: 100 × or 400 × . Scale bar = 100 μm</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Effects of SB239063 on apoptosis-related proteins in the hippocampus on days 1, 3 and 7. Western blotting showed the expression of bax, bcl-2, and caspase-3 in the hippocampus (<bold>A</bold>–<bold>C</bold>). The expression of bax, bcl-2 and caspase-3 was normalized to that of GAPDH as an internal control (<bold>D</bold>–<bold>F</bold>). Real-time PCR was performed to analyze the relative mRNA expression levels of bax, bcl-2, and caspase-3 in the hippocampus (<bold>G</bold>–<bold>I</bold>). The data are plotted as the mean ± SEM (<italic>n</italic> = 4). <italic>*P</italic> &lt; 0.05, <italic>**P</italic> &lt; 0.01, <italic>***P</italic> &lt; 0.001 versus the Con group, <italic>#P</italic> &lt; 0.05, <italic>##P</italic> &lt; 0.01 versus the Sur group</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Effect of SB239063 on neurons in the hippocampal CA1 area of mice. Immunofluorescence images show the number of NeuN (green pixels) in the hippocampus (<bold>A</bold>). Quantitative analyses of NeuN (<bold>B</bold>). The data are plotted as the mean ± SEM (<italic>n</italic> = 5). <italic>**P</italic> &lt; 0.01, <italic>***P</italic> &lt; 0.001, <italic>****P</italic> &lt; 0.0001 versus the Con group, <italic>##P</italic> &lt; 0.01, <italic>###P</italic> &lt; 0.001 versus the Sur group. Magnification: 100 × . Scale bar = 100 μm</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><p>Effect of SB239063 on neuronal loss in the hippocampal CA1 area of mice. Nissl staining reflected the density of surviving neurons in the CA1 of the hippocampus (<bold>A</bold>). Quantitative analyses of Nissl bodies (<bold>B</bold>). The data are plotted as the mean ± SEM (<italic>n</italic> = 5). <italic>**P</italic> &lt; 0.01, <italic>***P</italic> &lt; 0.001 versus the Con group, <italic>##P</italic> &lt; 0.01 versus the Sur group, ^{<italic>&amp;</italic>}<italic>P</italic> &lt; 0.05 versus the Sur + SB group. Magnification: 100 × . Scale bar = 100 μm</p></caption></fig>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">The basic morphology of the endoplasmic reticulum (ER) in muscle has been known since the initial electron microscopic studies in the 1950’s by Bennett and Porter [##REF##13080198##1##] and Palade and Porter [##REF##13438910##2##], when it was termed the sarcoplasmic reticulum (SR)¹, given its unique structure that repeats across all sarcomeres in the myocyte. Studies over many decades have focused on its Ca²⁺ handling properties, beginning with extensive characterization of the important Ca²⁺ translocating ATPase activity, now termed SERCA, for SR, ER- Ca²⁺-ATPase [##REF##5229806##3##, ##REF##14169170##4##]. Much later, a ryanodine-sensitive Ca²⁺-releasing activity was identified [##REF##6271762##5##–##REF##3680217##7##]. Extensive analyses of Ca²⁺ transport in membrane preparations from skeletal muscle also led to established membrane subfractionation protocols, and isolation of membranes of distinct densities that contained different protein composition. Meissner [##REF##124589##8##] reported the first fractionation of skeletal muscle membranes by isolating a fraction of heavy vesicles that contained the electron-opaque protein polymer calsequestrin [##REF##6448074##9##], and later shown to contain foot processes consistent with morphological depictions of junctional SR [##REF##2849609##10##]. The lighter membranes showed less of the dense luminal protein content, and was concluded to contain free (non-junctional) SR vesicles [##REF##124589##8##, ##REF##6448074##9##].</p>", "<p id=\"Par3\">A technique for subfractionation of microsomes from heart tissue was later developed that took advantage of the ability of cardiac SR microsomes to concentrate Ca oxalate within their lumens [##REF##4182374##11##–##REF##216677##13##]. While these studies were originally developed to biochemically separate sarcolemma and SR, subsequent work [##REF##6271762##5##] showed that the Ca oxalate loading had actually produced two distinct types of SR membranes, with roughly half of membrane protein in the densest membrane fraction. And though it was known by then that the drug ryanodine could stimulate Ca²⁺ accumulation into SR membrane vesicles at high concentrations, these dense membranes were ryanodine insensitive [##REF##6271762##5##].</p>", "<p id=\"Par4\">In contrast, a second membrane fraction of lower density (unable to traverse a 1.5 M sucrose cushion) was highly sensitive to ryanodine [##REF##6271762##5##]. Indeed, by inhibiting Ca²⁺ leak, 0.3 mM ryanodine added during membrane isolation converted SR membranes of lower density into high density (high Ca oxalate) vesicles [##REF##8119936##14##]. The densities of SR membrane vesicles, as well as the distribution of SR proteins between the two subfractions, are regulated by the relative levels of SERCA and ryanodine receptor (RyR) contained in the fragmented SR patches.</p>", "<p id=\"Par5\">Several studies have used SERCA-positive membrane subpopulations to either validate the identity of a putative junctional SR protein [##REF##6271762##5##, ##REF##6203912##15##–##REF##10497235##17##], or non-junctional SR protein [##REF##8119936##14##, ##REF##2103513##18##–##REF##6853518##21##]. We hypothesized that Ca²⁺ accumulation and release from cardiac SR was not only a property of specialized subdomains in cardiomyocytes, but was elevated throughout the entire ER/SR organelle in the heart. As such, Ca oxalate loading of membrane vesicles would permit the enrichment of additional cardiac ER/SR subdomains. We hypothesized that, like the known distinct enrichments of junctional and free SR membranes, evaluation of the SR proteome during membrane enrichment steps would generate enrichment data for every protein in cardiac ER/SR, reflective of its sites and attachments within the sarcomeres of cardiomyocytes.</p>", "<p id=\"Par6\">We have determined the complete protein compositions of membrane vesicles generated by SERCA-dependent Ca oxalate loading, finding 354 proteins that are enriched as a result of SERCA activation. In addition, we report that a co-enrichment of functionally related proteins results from their similar distribution among membrane patches, reflecting the enrichment of ER/SR subdomains in close proximity to SERCA2 and RyR2 activities in intact cardiomyocytes.</p>" ]

[ "<title>Methods</title>", "<title>Preparation of crude cardiac sarcoplasmic reticulum vesicles</title>", "<p id=\"Par7\">Cardiac microsomes were isolated from female mongrel dog left ventricular tissue, and loaded with Ca oxalate as previously described, with minor modifications [##REF##6271762##5##]. Briefly, heart tissue was homogenized in 10 mM NaCO₃ at 1:20 dilution (buffer volume/tissue wet weight). Cardiac microsomes were isolated by differential centrifugation, isolating microsomes between 10,000 and 75,000 × g_max. In contrast to the previously published method, a final wash of the pellet in 0.6 M KC1, 30 mM histidine, pH 7.0, was not carried out. The investigation conforms to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No. 85-23, revised 1996). Animal research was approved by the Wayne State University Animal Investigation Committee (protocol #A 04-02-13).</p>", "<title>Ca oxalate loading of SR</title>", "<p id=\"Par8\">Loading of crude cardiac microsomes, 75 mg of protein were resuspended in 40 ml of an ice-cold medium containing 50 mM histidine, 100 mM KCI, 65 mM MgCl₂, 60 mM Na₂ATP, 25 mM Tris/EGTA, 20 mM CaCl₂, and 5 mM Tris oxalate (pH 7.1). The suspension was rapidly warmed to 37 °C to initiate active and rapid Ca²⁺ uptake, and the incubation was conducted for 10 min with 5 mM additional Tris/oxalate added after the first 5 min of incubation. The suspension was then immediately centrifuged at 4 ℃ for 30 min at 100,000 × g_max. The resulting brownish membrane pellet included a central white region, indicative of the Ca oxalate precipitate inside the highest density membranes. The whitish center was not present if ATP was not included in the Ca oxalate loading step (Fig. ##FIG##0##1##A).</p>", "<title>Isolation of medium and high density membrane vesicles after Ca oxalate loading</title>", "<p id=\"Par9\">Subfractionation of Ca oxalate loaded membranes was carried out essentially as previously described [##REF##6271762##5##]. Briefly, membrane pellets were resuspended in 0.25 M sucrose containing 300 mM KC1, 50 mM sodium pyrophosphate, and 100 mM Tris (pH 7.2). This material was layered over a discontinuous sucrose gradient of 0.6 M, 0.8 M, 1.0 M, and 1.5 M sucrose dissolved in the same buffer. After centrifugation at 125,000 × g_max for 2 h, membranes were collected from both the 1.5 M sucrose cushion (MedSR) or as the white pellet at the bottom of the gradient (HighSR). These two subfractions were not present in membranes not Ca oxalate loaded (Fig. ##FIG##0##1##B). MedSR was diluted with 4 volumes of ice-cold H₂O, and then sedimented at 105,000 × g_max for 60 min. MedSR and HighSR were resuspended in 0.25 M sucrose, 10 mM histidine, and stored frozen at − 20 °C. Protein was determined by the method of Lowry et al. (17).</p>", "<title>Preparation of protein samples for mass spectrometric analysis</title>", "<p id=\"Par10\">To evaluate the protein composition of the two SERCA-positive membrane fractions, relative to the crude cardiac membranes, we analyzed exactly 20 μg each of MVs, MedSR, and HighSR membranes by SDS-PAGE. The wet gel was stained with SPYRO Ruby red to visualize the protein separations qualitatively (Fig. ##FIG##0##1##C).</p>", "<title>Tryptic digestion of SR samples</title>", "<p id=\"Par11\">For in-gel digestion (GeLC-MS/MS), each lane (crude cardiac microsomes (MV), MedSR, or HighSR membranes) was cut into 20 slices for improved sampling (Fig. ##FIG##0##1##C). Gel slices were equilibrated in H₂O, dried, and digested with trypsin added in dilute solution (1:10 w/w) and digested overnight at 37 °C.</p>", "<title>LC–MS/MS analysis and database search</title>", "<p id=\"Par12\">Tryptic peptides were separated by reverse phase chromatography (Magic C18 column, Michrom), followed by ionization with the ADVANCE ion source (Michrom), and then analyzed in an LTQ-XL mass spectrometer (Thermo Fisher Scientific). For each MS scan, up to seven MS/MS scans were obtained using collision-induced dissociation. Data analysis was performed using Proteome Discoverer 1.1 (Thermo) that incorporated the Mascot algorithm (Matrix Science). The NCBI database was used against mammalian protein sequences and a reverse decoy protein database was run simultaneously for false discovery rate (FDR) determination. Secondary analysis was performed using Scaffold (Proteome Software). A fixed modification of + 57 on cysteine (carbamidomethylation) and variable modifications of + 16 on methionine (oxidation) and + 42 on protein <italic>N</italic>-terminus (acetylation) were included in the database search. Minimum protein identification probability was set at ≥ 95%, with 1 unique peptide at ≥ 95% minimum peptide identification probability. From 62,000 individual peptide spectra obtained, we identified 1105 different proteins, along with their relative levels within each of the three different membrane fractions, when levels were sufficient. Raw data and search results have been submitted to the ProteomeXchange via PRIDE with accession PXD022455 (Username: [email protected], Password: G1wlk66N).</p>", "<title>Semi-quantitative assessments of protein abundance</title>", "<p id=\"Par13\">An abundance <italic>index</italic> (<italic>A</italic>_SR) was calculated for each protein, calculated as the number of its peptide spectra, divided by protein molecular weight as a rough correction for available target peptides, then normalized to the spectral level for SERCA2, which we defined as <italic>A</italic>_SR = 100.0 (Table ##TAB##0##1##). <italic>A</italic>_SR values are a crude surrogate for protein abundance, since factors unrelated to protein abundance will affect the quantifcation of tryptic peptides. Nonetheless, <italic>A</italic>_SR values across sets of functionally related proteins can provide useful comparisons. </p>" ]

[ "<title>Results and discussion</title>", "<title>Protein composition of crude cardiac microsomes</title>", "<p id=\"Par14\">In a preparation of cardiac microsomes (MVs), we found 1102 proteins (see Online Resource 1). The most abundant peptides from crude cardiac MV membranes were from known mitochondrial proteins. The three proteins with the highest <italic>A</italic>_SR values in cardiac microsomes were ATP/ADP translocase and ATP synthase, <italic>α</italic> and <italic>β</italic> subunits, with known mitochondrial proteins accounted for 7 of the top 10 proteins. The other three major proteins among the top ten highest <italic>A</italic>_SR values were SERCA2, a keratin 1 isoform, and cardiac <italic>α</italic>1 actin. The focus of our experiments, however, was not directed at crude cardiac microsomal proteins, but instead, at proteins that are enriched in cardiac SR. Of the top 10 microsomal proteins detected, only SERCA2 was enriched in the denser membrane vesicles that result when Ca²⁺ transport is activated by addition of ATP.</p>", "<title>Enrichment of membrane vesicles by SERCA activation</title>", "<p id=\"Par15\">The two enriched SR subfractions analyzed in this study have previously been described as <italic>junctional SR</italic> and <italic>free SR</italic> vesicles; however, with the much greater number of proteins identified through the use of our GeLC-MS/MS analysis, we have substituted the terms “medium-density SR membranes” (MedSR) and “high-density SR membranes” (HighSR), for these two membrane subpopulations (Table ##TAB##0##1##). This terminology allows us to discuss the larger collection of proteins, whether or not they participate directly in Ca²⁺ handling functions.</p>", "<p id=\"Par16\">Comparing the abundance of each protein (<italic>A</italic>_SR) in MedSR and HighSR membranes with its abundance in MVs, we determined protein enrichments in SR (<italic>E</italic>_SR) (Table ##TAB##0##1##). Calculated from ratios of <italic>A</italic>_SR values, the enrichment values were relatively unaffected by the sampling issues for any given protein. We used the value of E_SR to define <italic>SERCA-positive SR</italic> proteins as those proteins that were enriched by SERCA activation at least 2.0-fold (<italic>E</italic>_SR ≥ 2.0). For 354 SERCA-positive SR proteins, the enrichments varied, but the average enrichment was 8.0-fold (avg <italic>E</italic>_SR = 8.0).</p>", "<p id=\"Par17\">In contrast to enrichment of SR proteins in total SR (HighSR <italic>plus</italic> MedSR), enrichments in HighSR <italic>versus</italic> MedSR membranes (<italic>E</italic>_sub), reflect differences in the way small membrane patches are pulled apart, yielding small vesicles with varying levels of Ca²⁺ release activity (RyR) on top of their very active Ca²⁺ accumulation. Thus, individual proteins that segregate with <italic>MedSR</italic> were more likely to contain membrane patches that contain RyR; that is, closer to junctional SR sites in vivo. To evaluate this distribution as a single number, we defined <italic>E</italic>_sub as the difference between levels in the two SR fractions divided by the total (Table ##TAB##0##1##). Proteins more enriched in High SR yielded a positive number with a theoretical maximal value of 1.0, and proteins enriched in MedSR yielded a negative number with a theoretical maximal value of − 1.0. Values actually ranged from + 0.90 to − 0.90.</p>", "<title>Characterization of SR proteins based upon enrichments among membrane subpopulations</title>", "<p id=\"Par18\">Of the top 10 microsomal proteins detected in our ventricular muscle sample, only one (SERCA2) was enriched by SERCA activation (<italic>E</italic>_SR = 3.4). Among 200 microsomal proteins with the highest <italic>A</italic>_SR values (Fig. ##FIG##1##2##A, <italic>blue bars</italic>), only 40 proteins were enriched at least 2.0-fold by SERCA activation (<italic>red bars</italic>). All SR proteins previously identified as resident to cardiac SR using immunological methods were among the proteins enriched by SERCA activation in our study.</p>", "<p id=\"Par19\">For 14 of the best characterized SR proteins (Fig. ##FIG##1##2##B, <italic>green bars</italic>), the average fold enrichment in SR over crude cardiac microsomes (<italic>E</italic>_SR) was 5.0 ± 1.6 (mean ± S.D.). When sorted based on their relative distribution between SR subcompartments (<italic>E</italic>_sub), all of the known junctional SR proteins were more enriched in MedSR (Fig. ##FIG##2##3##A), consistent with the idea that MedSR membrane patches probably contain more RyR molecules, possibly combined with less SERCA. Luminal ER/SR proteins, on the other hand, were highly enriched in HighSR (except for calsequestrin-2). SERCA2, SERCA1, and phospholamban were more equally distributed among the membrane vesicles, consistent with a more equal activation of Ca²⁺ loading in both SR populations. Despite the similar enrichments of known SR proteins, their relative abundances (<italic>A</italic>_SR, Fig. ##FIG##2##3##B) varied greatly, consistent with data widely known from protein staining of SDS-gels [##REF##6203912##15##, ##REF##2103513##18##].</p>", "<p id=\"Par20\">For the entire set of 354 proteins in SERCA-positive membranes, <italic>E</italic>_sub spanned a continuous range of values from + 0.90 to − 0.90, corresponding to proteins at a 90% greater level in HighSR, or in MedSR, respectively (Fig. ##FIG##3##4##). Interestingly, for sets of proteins with related function, <italic>E</italic>_sub values were clustered together, in support of the idea that membrane fragments are generated from ER/SR membrane patches that contain characteristic ratios of SERCA and RyR levels.</p>", "<title>High abundance proteins illustrate wider functions in cardiac SR than only Ca²⁺ handling</title>", "<p id=\"Par22\">A_SR values are based upon the number of peptide spectra attributed to a particular protein, but are only semi-quantitative, as they assume similar coverage of every protein sequence by LC–MS/MS, which does not occur [##REF##14608001##22##]. Yet, it was very interesting to look at the proteins with the highest A_SR values, as it illustrates the scope of protein functions in cardiac SR. The 5 most abundant proteins in our SERCA-positive SR sample were SERCA2, desmin, sarcalumenin, phospholamban, and calsequestrin-2 (CSQ2), accounting for about a quarter of SR protein mass (percent of total spectra) (Fig. ##FIG##4##5##). SERCA2a and phospholamban are well known major constituents of cardiac SR [##REF##6271762##5##, ##REF##216677##13##], and, as expected, their very high <italic>A</italic>_SR values were a predictable consequence of their activity in Ca oxalate loading of SR vesicles.</p>", "<p id=\"Par23\">Sarcalumenin is a known luminal constituent of cardiac SR membranes [##REF##2103513##18##, ##REF##2762314##23##], but of uncertain function. It is comprised of two well known splice variants: one generally defined by its roughly 150-kDa apparent molecular weight on standard SDS-gels, and one defined by a roughly 53-kDa [##REF##2521635##24##]. Sarcalumenin was previously reported to be a major luminal SR protein in rabbit skeletal muscle SR, using similar proteomic methods [##REF##23713034##25##]. Desmin, a muscle-specific intermediate filament protein of striated muscle [##REF##1069986##26##], was found at <italic>A</italic>_SR levels comparable to that of SERCA2 (Fig. ##FIG##4##5##). Desmin is a muscle-specific intermediate filament protein that was recovered at high levels because its strong attachment to SERCA-positive membranes was maintained even under the high ionic strength isolation buffer used here [##REF##1069986##26##]. Whereas it was found at <italic>A</italic>_SR levels nearly equal to that of SERCA2 (<italic>A</italic>_SR = 0.96) in our heart sample, in skeletal muscle SR it was reported to be present only at 0.8% of SERCA1 levels in skeletal muscle microsomes [##REF##23713034##25##].</p>", "<p id=\"Par24\">Surprisingly high <italic>A</italic>_SR values were also found for many proteins barely discussed in the cardiac research literature. For example, NADH-cytochrome b5 reductase gave the highest <italic>A</italic>_SR value of a non-traditional cardiac SR protein (<italic>A</italic>_{<italic>SR</italic>} = 30.0; 6th highest). Salviati et al. [##REF##7034720##27##] in 1981 reported very high levels of this redox enzyme, as well as cytochrome b5 itself (<italic>A</italic>_{<italic>SR</italic>} = 5.1; 69th highest), in the SR of slow skeletal muscle. They identified it as a prominent protein band visible by protein staining of SDS-gels, and showed it to be similar to the ER-bound enzyme in liver microsomes where it exists at very high levels. More recently, NADH-cytochrome b5 reductase transcript was also reported to be high in heart, among human tissues examined [##REF##24309898##28##].</p>", "<p id=\"Par25\">A prominent escort protein for rab proteins, PRA1 (prenylated rab acceptor 1), was prominently detected (<italic>A</italic>_{<italic>SR</italic>}<italic> = </italic>25.0, 7th highest). The presence of abundant histone H4 (<italic>A</italic>_{<italic>SR</italic>} = 21.0, 8th highest), and other less abundant histones (Table ##TAB##0##1##, Appendix) may suggest a role as a secreted antimicrobial protein [##REF##19536143##29##, ##REF##23150794##30##] or copper reductase enzyme [##REF##32631887##31##].</p>", "<p id=\"Par26\">The high level of CDP-diacylglycerol-inositol 3-phosphatidyltransferase, isoform 1 <italic>(CDITP, A</italic>_{<italic>SR</italic>} = 20.7, 9th highest<italic>),</italic> was consistent with early studies by Kasinathan and Kirchberger [##REF##2840949##32##] showing that cardiac SR contained CDITP enzyme activity, and postulated its involvement in phospholamban phosphorylation through the Ca²⁺, calmodulin-dependent protein kinase. No additional studies have been carried out in SR to our knowledge. Interestingly, the SR protein with the next highest <italic>A</italic>_SR (VAP-B) is a prominent intra-organellar tethering protein that also plays a putative role in the transfer of synthesized PI to the plasma membrane. Both VAP-B and VAP-A <italic>(A</italic>_{<italic>SR</italic>} = 18.5 and 11,3, 10th and 24th highest, resp<italic>.)</italic> were among multiple ER tethering proteins present [##REF##20192774##33##–##UREF##0##41##] (Table ##TAB##1##2##). The combined actions of these abundant ER/SR proteins may promote new plasma membrane sites for PI signaling activity in heart [##REF##10949023##42##–##REF##24001019##45##]. Extended synaptotagmins, detected at low <italic>A</italic>_SR levels, can also transport glycerolipids between the ER and plasma membrane bilayers via a unique lipid-harboring domain [##REF##28363589##46##].</p>", "<p id=\"Par28\">Also yielding a high A_SR value was fat storage-inducing transmembrane protein 2 (FIT2) (<italic>A</italic>_{<italic>SR</italic>} = 18.5, 11th highest), which plays an important role in the formation of lipid droplets and the distribution of lipids between the ER membrane and lipid droplets [##REF##22106267##47##–##REF##30923760##49##]. Alpha crystalline B (<italic>A</italic>_{<italic>SR</italic>} = <italic>18.3, 12th highest</italic>) occurs in situ as globular polymers [##REF##1628387##50##]. In total, five prominent filamentous proteins co-enriched with SERCA-positive membrane: desmin and crystalline <italic>α</italic>B, vimentin 12, keratin II 6B, and beta-tubulin 2C (Table ##TAB##1##2##, Appendix).</p>", "<title>Functional sets of proteins in cardiac ER/SR</title>", "<p id=\"Par29\">The identification of sets of proteins related to known SR and ER functions added consistency and context to the 354 proteins found in our analysis. Proteins involved in related ER/SR functions were present as complete sets in SERCA-positive membranes. And, while these ER/SR subdomains were present in widely varying abundances (<italic>A</italic>_SR values), their enrichment factors (<italic>E</italic>_SR and <italic>E</italic>_sub) were remarkably similar, consistent with their distribution together in membrane patches (vesicles after homogenization). The vast majority of these 354 proteins have not been previously identified in cardiac SR. We briefly summarize the major functional sets of proteins found, and compare their constituent protein enrichments and relative abundances.</p>", "<title>SR Ca^2 + pumping</title>", "<p id=\"Par30\">The most abundant peptide spectra, not surprisingly, were from SERCA2. Peptides from phospholamban, a subunit of SERCA2a that dissociates with PKA-dependent phosphorylation were detected at roughly 50% of SERCA2. The need for inclusion of the MW factor to the calculation of <italic>A</italic>_SR values can be easily appreciated in this case, with the 20-fold difference in mass between SERCA and phospholamban molecules. While the relative levels of SERCA2 and phospholamban from this single mongrel canine heart sample will be subject to error and biological variability, the set of three proteins that function in Ca²⁺ pumping (SERCA2, phospholamban, and SERCA1) were the 1st, 4th, and 15th highest <italic>A</italic>_SR values, accounting for roughly 11% of spectra, supporting the view that Ca²⁺ accumulation is a primary function of the cardiac ER/SR. Their enrichments in SR (<italic>E</italic>_SR), and distribution between MedSR and HighSR membrane subcompartments (<italic>E</italic>_sub) were also highly similar (Fig. ##FIG##4##5## and Online Resource S1).</p>", "<title>Intraluminal ER/SR proteins</title>", "<p id=\"Par31\">Intraluminal proteins represented an abundant set of proteins based on their number and high <italic>A</italic>_SR values, constituting about 12% of total SR protein, with about half of the mass due to sarcalumenin and calsequestrin (Table ##TAB##2##3##). Many luminal SR proteins are those carrying a <italic>C</italic>-terminal sequence Lys-Asp-Glu-Leu (KDEL), which interacts with KDEL receptors to retrieve these proteins from the Golgi back to ER compartments [##REF##3545499##51##–##REF##33037041##54##]. Protein disulfide isomerase (PDI) isoforms, although not previously identified in heart tissue, were among the proteins most enriched in SR (Table ##TAB##2##3##); also, more highly enriched in HighSR than MedSR (Fig. ##FIG##2##3##A) consistent with the common notion that free SR is essentially cardiac smooth ER, and that it contains less RyR [##REF##32353354##55##].</p>", "<title>Junctional SR proteins</title>", "<p id=\"Par32\">The Ca oxalate loading method was previously used to identify several major junctional SR proteins, including calsequestrin-2, cardiac triadin, junctin, and RyR2 [##REF##6203912##15##, ##REF##8530521##16##, ##REF##6619149##56##, ##REF##8550602##57##]. These 4 major junctional SR proteins, along with junctophilin-2, all presented here with relatively high levels of A_SR, accounting for roughly 5% of total SR peptide spectra.</p>", "<p id=\"Par33\">Levels of couplon proteins reported in rabbit fast-twitch skeletal muscle SR [##REF##23713034##25##] show interesting parallels with our data from canine heart (Fig. ##FIG##5##6##). While the SR samples were prepared quite differently, the two tissue samples were each analyzed using standard LC–MS/MS analyses of tryptic digests. The resulting patterns of relative abundance were qualitatively, if not semi-quantitatively, similar among junctional SR proteins in the two membranes (Fig. ##FIG##5##6##). Moreover, together, the two studies validate past reports of isoform specificities previously based on SDS-PAGE and immunoblot analyses. Junctin, a splice variant of junctate and aspartyl <italic>β</italic>-hydroxylase [##REF##17706594##58##], could not be distinguished based on the peptides sequenced. Treves et al. [##REF##11007777##59##] previously reported that no gross differences occurred immunologically between junctin and junctate levels in heart homogenates, suggesting that junctin may be roughly half of the A_SR level reported here. Co-enrichment of L-type Ca²⁺ channel with junctional SR markers was further evidence of a stable protein complex of couplon proteins with the sarcolemmal T-tubule membrane [##REF##6853518##21##].</p>", "<title>Peroxisomal proteins and rab proteins in MedSR</title>", "<p id=\"Par36\">In addition to the enrichment of junctional SR proteins, MedSR membranes were also enriched in peroxisomal proteins, rab proteins, and caveolar proteins (Fig. ##FIG##6##7##), but the three types of protein-containing vesicles varied in their membrane enrichments. Peroxisomal proteins were very uniquely enriched in SERCA-positive membranes, and their enrichment was highly variable (E_SR = 26.7 ± 22.3) (Fig. ##FIG##7##8##A). In addition, peroxisomal proteins were extraordinarily enriched in MedSR compared to HighSR membranes (avg E_sub = − 0.50 ± 0.09). By comparison, junctional SR proteins were much less enriched in MedSR compared to HighSR (avg E_sub = − 0.24 ± 0.10, for 4 couplon proteins). The reason for this unusual enrichment of peroxisomal proteins in SERCA-positive membranes is unknown, and much remains to be learned about this peculiar ER subdomain [##REF##25608554##61##–##REF##28146471##63##].</p>", "<p id=\"Par37\">When <italic>E</italic>_sub values were averaged for several sets of functionally related proteins, average <italic>E</italic>_sub values covered a range of distribution between the two SR subpopulations (Fig. ##FIG##7##8##A), suggesting that individual membrane patches are enriched in separate functional subdomains, with each subdomain exhibiting particular Ca²⁺ transport properties that reflect its inclusion of SERCA and RyR protein.</p>", "<p id=\"Par39\">Rabs and other small GTPases were also highly enriched in MedSR, exhibiting <italic>E</italic>_sub values similar to those of known junctional SR proteins (Fig. ##FIG##7##8##A, B). Rab proteins are fundamental regulators of organelle biogenesis and vesicle transport, and constitute the largest subset of the ras superfamily of small GTPases [##REF##10966806##64##]. In addition to abundant rabs, the rab associated protein PRA-1 <italic>(A</italic>_{<italic>SR</italic>} = <italic>25.0, 7</italic>th <italic>highest</italic>), and hedgehog acyltransferase-like protein (aka mitsugamin-56 [##REF##25841338##65##]) were also enriched in SR (Online Resource 1). The possible close physical proximity of rabs to junctional SR sites is consistent with evidence of protein secretion in cultured cardiomyocytes emanating from sites close to junctional SR [##REF##30919218##66##].</p>", "<title>Rough ER proteins</title>", "<p id=\"Par40\">Cardiac rough ER is a critical subdomain of ER, and in cardiomyocytes has a predominantly perinuclear morphology that is distinct from the repeating SR sarcomeres that control contraction [##REF##30919218##66##, ##UREF##1##67##]. Yet, SERCA-positive SR membrane vesicles also contained a complete collection of known rough ER proteins involved in translation, translocation, and N-linked glycosylation (Table ##TAB##2##3##, Appendix). Rough ER proteins were of relatively low abundance (A_SR = 4.0 ± 1.7), but very highly enriched over crude MVs (E_SR = 6.0 ± 2.5) (Fig. ##FIG##7##8##A).</p>", "<title>Lipid metabolism and lipid modifications of proteins</title>", "<p id=\"Par41\">Numerous enzymes involved in lipid metabolism were enriched in SERCA-positive membranes. The highest A_SR value (= 20.7) resulted from CDITP, which appends inositol-3-phosphate to diacylglycerol, with numerous lipid metabolizing proteins present at lower A_SR levels (Fig. 1, Appendix).</p>", "<title>Proteins involved in ER membrane structure and dynamics</title>", "<p id=\"Par42\">Many cardiac ER/SR proteins are those thought to play roles in distributing and trafficking proteins across the biosynthetic pathway. Several act by guiding membrane patches along transport filaments; these include Ca²⁺-binding protein p22, vesicle-trafficking protein Sec22b, vesicle-associated membrane protein 2 (VAMP-2), and vesicle transport protein Sec20 [##REF##8626580##68##–##REF##24705552##71##]. The mammalian proteins of the p24 family (TMED 10, 9, 2, 1) are involved in selective loading of cargo in transport vesicle between membrane compartments, and their subunit co-enrichment is consistent with previous reports in nonmuscle cell types [##REF##7729411##72##, ##REF##19566487##73##]. Finally, other ER proteins may function in the maintaining the structure of ER subcompartments, such as reticulons − 2 and − 4 [##REF##16469703##74##], lunapark-3 [##REF##23478217##75##], and climp-63 [##REF##17567679##76##]. Proteins involved in ER/SR dynamics are tabulated, along with enrichment values, in Table 4, Appendix.</p>", "<title>Relative abundances within functional sets of cardiac ER/SR proteins</title>", "<p id=\"Par43\">In spite of these substantial variations in A_SR among functional sets of proteins, the enrichment properties <italic>E</italic>_sub and <italic>E</italic>_SR among the same sets were remarkably consistent; both because of their physical segregation in membrane vesicles, but also because enrichment values are derived from <italic>ratios</italic> of <italic>A</italic>_SR values in two preparations. For example, a large number of known KDEL proteins were found in SR, exhibiting a wide range of <italic>A</italic>_SR values (6.3 ± 9.0, N = 7 proteins). For the same 7 KDEL proteins, however, <italic>E</italic>_sub values were 0.47 ± 0.08, and <italic>E</italic>_SR values were 7.1 ± 3.7. Plotting <italic>A</italic>_SR values for the top 2–4 proteins of different groups of proteins (Fig. ##FIG##8##9##), provided some semi-quantitative insight into how different ER/SR subdomains may contribute to overall SR function. </p>" ]

[ "<title>Results and discussion</title>", "<title>Protein composition of crude cardiac microsomes</title>", "<p id=\"Par14\">In a preparation of cardiac microsomes (MVs), we found 1102 proteins (see Online Resource 1). The most abundant peptides from crude cardiac MV membranes were from known mitochondrial proteins. The three proteins with the highest <italic>A</italic>_SR values in cardiac microsomes were ATP/ADP translocase and ATP synthase, <italic>α</italic> and <italic>β</italic> subunits, with known mitochondrial proteins accounted for 7 of the top 10 proteins. The other three major proteins among the top ten highest <italic>A</italic>_SR values were SERCA2, a keratin 1 isoform, and cardiac <italic>α</italic>1 actin. The focus of our experiments, however, was not directed at crude cardiac microsomal proteins, but instead, at proteins that are enriched in cardiac SR. Of the top 10 microsomal proteins detected, only SERCA2 was enriched in the denser membrane vesicles that result when Ca²⁺ transport is activated by addition of ATP.</p>", "<title>Enrichment of membrane vesicles by SERCA activation</title>", "<p id=\"Par15\">The two enriched SR subfractions analyzed in this study have previously been described as <italic>junctional SR</italic> and <italic>free SR</italic> vesicles; however, with the much greater number of proteins identified through the use of our GeLC-MS/MS analysis, we have substituted the terms “medium-density SR membranes” (MedSR) and “high-density SR membranes” (HighSR), for these two membrane subpopulations (Table ##TAB##0##1##). This terminology allows us to discuss the larger collection of proteins, whether or not they participate directly in Ca²⁺ handling functions.</p>", "<p id=\"Par16\">Comparing the abundance of each protein (<italic>A</italic>_SR) in MedSR and HighSR membranes with its abundance in MVs, we determined protein enrichments in SR (<italic>E</italic>_SR) (Table ##TAB##0##1##). Calculated from ratios of <italic>A</italic>_SR values, the enrichment values were relatively unaffected by the sampling issues for any given protein. We used the value of E_SR to define <italic>SERCA-positive SR</italic> proteins as those proteins that were enriched by SERCA activation at least 2.0-fold (<italic>E</italic>_SR ≥ 2.0). For 354 SERCA-positive SR proteins, the enrichments varied, but the average enrichment was 8.0-fold (avg <italic>E</italic>_SR = 8.0).</p>", "<p id=\"Par17\">In contrast to enrichment of SR proteins in total SR (HighSR <italic>plus</italic> MedSR), enrichments in HighSR <italic>versus</italic> MedSR membranes (<italic>E</italic>_sub), reflect differences in the way small membrane patches are pulled apart, yielding small vesicles with varying levels of Ca²⁺ release activity (RyR) on top of their very active Ca²⁺ accumulation. Thus, individual proteins that segregate with <italic>MedSR</italic> were more likely to contain membrane patches that contain RyR; that is, closer to junctional SR sites in vivo. To evaluate this distribution as a single number, we defined <italic>E</italic>_sub as the difference between levels in the two SR fractions divided by the total (Table ##TAB##0##1##). Proteins more enriched in High SR yielded a positive number with a theoretical maximal value of 1.0, and proteins enriched in MedSR yielded a negative number with a theoretical maximal value of − 1.0. Values actually ranged from + 0.90 to − 0.90.</p>", "<title>Characterization of SR proteins based upon enrichments among membrane subpopulations</title>", "<p id=\"Par18\">Of the top 10 microsomal proteins detected in our ventricular muscle sample, only one (SERCA2) was enriched by SERCA activation (<italic>E</italic>_SR = 3.4). Among 200 microsomal proteins with the highest <italic>A</italic>_SR values (Fig. ##FIG##1##2##A, <italic>blue bars</italic>), only 40 proteins were enriched at least 2.0-fold by SERCA activation (<italic>red bars</italic>). All SR proteins previously identified as resident to cardiac SR using immunological methods were among the proteins enriched by SERCA activation in our study.</p>", "<p id=\"Par19\">For 14 of the best characterized SR proteins (Fig. ##FIG##1##2##B, <italic>green bars</italic>), the average fold enrichment in SR over crude cardiac microsomes (<italic>E</italic>_SR) was 5.0 ± 1.6 (mean ± S.D.). When sorted based on their relative distribution between SR subcompartments (<italic>E</italic>_sub), all of the known junctional SR proteins were more enriched in MedSR (Fig. ##FIG##2##3##A), consistent with the idea that MedSR membrane patches probably contain more RyR molecules, possibly combined with less SERCA. Luminal ER/SR proteins, on the other hand, were highly enriched in HighSR (except for calsequestrin-2). SERCA2, SERCA1, and phospholamban were more equally distributed among the membrane vesicles, consistent with a more equal activation of Ca²⁺ loading in both SR populations. Despite the similar enrichments of known SR proteins, their relative abundances (<italic>A</italic>_SR, Fig. ##FIG##2##3##B) varied greatly, consistent with data widely known from protein staining of SDS-gels [##REF##6203912##15##, ##REF##2103513##18##].</p>", "<p id=\"Par20\">For the entire set of 354 proteins in SERCA-positive membranes, <italic>E</italic>_sub spanned a continuous range of values from + 0.90 to − 0.90, corresponding to proteins at a 90% greater level in HighSR, or in MedSR, respectively (Fig. ##FIG##3##4##). Interestingly, for sets of proteins with related function, <italic>E</italic>_sub values were clustered together, in support of the idea that membrane fragments are generated from ER/SR membrane patches that contain characteristic ratios of SERCA and RyR levels.</p>", "<title>High abundance proteins illustrate wider functions in cardiac SR than only Ca²⁺ handling</title>", "<p id=\"Par22\">A_SR values are based upon the number of peptide spectra attributed to a particular protein, but are only semi-quantitative, as they assume similar coverage of every protein sequence by LC–MS/MS, which does not occur [##REF##14608001##22##]. Yet, it was very interesting to look at the proteins with the highest A_SR values, as it illustrates the scope of protein functions in cardiac SR. The 5 most abundant proteins in our SERCA-positive SR sample were SERCA2, desmin, sarcalumenin, phospholamban, and calsequestrin-2 (CSQ2), accounting for about a quarter of SR protein mass (percent of total spectra) (Fig. ##FIG##4##5##). SERCA2a and phospholamban are well known major constituents of cardiac SR [##REF##6271762##5##, ##REF##216677##13##], and, as expected, their very high <italic>A</italic>_SR values were a predictable consequence of their activity in Ca oxalate loading of SR vesicles.</p>", "<p id=\"Par23\">Sarcalumenin is a known luminal constituent of cardiac SR membranes [##REF##2103513##18##, ##REF##2762314##23##], but of uncertain function. It is comprised of two well known splice variants: one generally defined by its roughly 150-kDa apparent molecular weight on standard SDS-gels, and one defined by a roughly 53-kDa [##REF##2521635##24##]. Sarcalumenin was previously reported to be a major luminal SR protein in rabbit skeletal muscle SR, using similar proteomic methods [##REF##23713034##25##]. Desmin, a muscle-specific intermediate filament protein of striated muscle [##REF##1069986##26##], was found at <italic>A</italic>_SR levels comparable to that of SERCA2 (Fig. ##FIG##4##5##). Desmin is a muscle-specific intermediate filament protein that was recovered at high levels because its strong attachment to SERCA-positive membranes was maintained even under the high ionic strength isolation buffer used here [##REF##1069986##26##]. Whereas it was found at <italic>A</italic>_SR levels nearly equal to that of SERCA2 (<italic>A</italic>_SR = 0.96) in our heart sample, in skeletal muscle SR it was reported to be present only at 0.8% of SERCA1 levels in skeletal muscle microsomes [##REF##23713034##25##].</p>", "<p id=\"Par24\">Surprisingly high <italic>A</italic>_SR values were also found for many proteins barely discussed in the cardiac research literature. For example, NADH-cytochrome b5 reductase gave the highest <italic>A</italic>_SR value of a non-traditional cardiac SR protein (<italic>A</italic>_{<italic>SR</italic>} = 30.0; 6th highest). Salviati et al. [##REF##7034720##27##] in 1981 reported very high levels of this redox enzyme, as well as cytochrome b5 itself (<italic>A</italic>_{<italic>SR</italic>} = 5.1; 69th highest), in the SR of slow skeletal muscle. They identified it as a prominent protein band visible by protein staining of SDS-gels, and showed it to be similar to the ER-bound enzyme in liver microsomes where it exists at very high levels. More recently, NADH-cytochrome b5 reductase transcript was also reported to be high in heart, among human tissues examined [##REF##24309898##28##].</p>", "<p id=\"Par25\">A prominent escort protein for rab proteins, PRA1 (prenylated rab acceptor 1), was prominently detected (<italic>A</italic>_{<italic>SR</italic>}<italic> = </italic>25.0, 7th highest). The presence of abundant histone H4 (<italic>A</italic>_{<italic>SR</italic>} = 21.0, 8th highest), and other less abundant histones (Table ##TAB##0##1##, Appendix) may suggest a role as a secreted antimicrobial protein [##REF##19536143##29##, ##REF##23150794##30##] or copper reductase enzyme [##REF##32631887##31##].</p>", "<p id=\"Par26\">The high level of CDP-diacylglycerol-inositol 3-phosphatidyltransferase, isoform 1 <italic>(CDITP, A</italic>_{<italic>SR</italic>} = 20.7, 9th highest<italic>),</italic> was consistent with early studies by Kasinathan and Kirchberger [##REF##2840949##32##] showing that cardiac SR contained CDITP enzyme activity, and postulated its involvement in phospholamban phosphorylation through the Ca²⁺, calmodulin-dependent protein kinase. No additional studies have been carried out in SR to our knowledge. Interestingly, the SR protein with the next highest <italic>A</italic>_SR (VAP-B) is a prominent intra-organellar tethering protein that also plays a putative role in the transfer of synthesized PI to the plasma membrane. Both VAP-B and VAP-A <italic>(A</italic>_{<italic>SR</italic>} = 18.5 and 11,3, 10th and 24th highest, resp<italic>.)</italic> were among multiple ER tethering proteins present [##REF##20192774##33##–##UREF##0##41##] (Table ##TAB##1##2##). The combined actions of these abundant ER/SR proteins may promote new plasma membrane sites for PI signaling activity in heart [##REF##10949023##42##–##REF##24001019##45##]. Extended synaptotagmins, detected at low <italic>A</italic>_SR levels, can also transport glycerolipids between the ER and plasma membrane bilayers via a unique lipid-harboring domain [##REF##28363589##46##].</p>", "<p id=\"Par28\">Also yielding a high A_SR value was fat storage-inducing transmembrane protein 2 (FIT2) (<italic>A</italic>_{<italic>SR</italic>} = 18.5, 11th highest), which plays an important role in the formation of lipid droplets and the distribution of lipids between the ER membrane and lipid droplets [##REF##22106267##47##–##REF##30923760##49##]. Alpha crystalline B (<italic>A</italic>_{<italic>SR</italic>} = <italic>18.3, 12th highest</italic>) occurs in situ as globular polymers [##REF##1628387##50##]. In total, five prominent filamentous proteins co-enriched with SERCA-positive membrane: desmin and crystalline <italic>α</italic>B, vimentin 12, keratin II 6B, and beta-tubulin 2C (Table ##TAB##1##2##, Appendix).</p>", "<title>Functional sets of proteins in cardiac ER/SR</title>", "<p id=\"Par29\">The identification of sets of proteins related to known SR and ER functions added consistency and context to the 354 proteins found in our analysis. Proteins involved in related ER/SR functions were present as complete sets in SERCA-positive membranes. And, while these ER/SR subdomains were present in widely varying abundances (<italic>A</italic>_SR values), their enrichment factors (<italic>E</italic>_SR and <italic>E</italic>_sub) were remarkably similar, consistent with their distribution together in membrane patches (vesicles after homogenization). The vast majority of these 354 proteins have not been previously identified in cardiac SR. We briefly summarize the major functional sets of proteins found, and compare their constituent protein enrichments and relative abundances.</p>", "<title>SR Ca^2 + pumping</title>", "<p id=\"Par30\">The most abundant peptide spectra, not surprisingly, were from SERCA2. Peptides from phospholamban, a subunit of SERCA2a that dissociates with PKA-dependent phosphorylation were detected at roughly 50% of SERCA2. The need for inclusion of the MW factor to the calculation of <italic>A</italic>_SR values can be easily appreciated in this case, with the 20-fold difference in mass between SERCA and phospholamban molecules. While the relative levels of SERCA2 and phospholamban from this single mongrel canine heart sample will be subject to error and biological variability, the set of three proteins that function in Ca²⁺ pumping (SERCA2, phospholamban, and SERCA1) were the 1st, 4th, and 15th highest <italic>A</italic>_SR values, accounting for roughly 11% of spectra, supporting the view that Ca²⁺ accumulation is a primary function of the cardiac ER/SR. Their enrichments in SR (<italic>E</italic>_SR), and distribution between MedSR and HighSR membrane subcompartments (<italic>E</italic>_sub) were also highly similar (Fig. ##FIG##4##5## and Online Resource S1).</p>", "<title>Intraluminal ER/SR proteins</title>", "<p id=\"Par31\">Intraluminal proteins represented an abundant set of proteins based on their number and high <italic>A</italic>_SR values, constituting about 12% of total SR protein, with about half of the mass due to sarcalumenin and calsequestrin (Table ##TAB##2##3##). Many luminal SR proteins are those carrying a <italic>C</italic>-terminal sequence Lys-Asp-Glu-Leu (KDEL), which interacts with KDEL receptors to retrieve these proteins from the Golgi back to ER compartments [##REF##3545499##51##–##REF##33037041##54##]. Protein disulfide isomerase (PDI) isoforms, although not previously identified in heart tissue, were among the proteins most enriched in SR (Table ##TAB##2##3##); also, more highly enriched in HighSR than MedSR (Fig. ##FIG##2##3##A) consistent with the common notion that free SR is essentially cardiac smooth ER, and that it contains less RyR [##REF##32353354##55##].</p>", "<title>Junctional SR proteins</title>", "<p id=\"Par32\">The Ca oxalate loading method was previously used to identify several major junctional SR proteins, including calsequestrin-2, cardiac triadin, junctin, and RyR2 [##REF##6203912##15##, ##REF##8530521##16##, ##REF##6619149##56##, ##REF##8550602##57##]. These 4 major junctional SR proteins, along with junctophilin-2, all presented here with relatively high levels of A_SR, accounting for roughly 5% of total SR peptide spectra.</p>", "<p id=\"Par33\">Levels of couplon proteins reported in rabbit fast-twitch skeletal muscle SR [##REF##23713034##25##] show interesting parallels with our data from canine heart (Fig. ##FIG##5##6##). While the SR samples were prepared quite differently, the two tissue samples were each analyzed using standard LC–MS/MS analyses of tryptic digests. The resulting patterns of relative abundance were qualitatively, if not semi-quantitatively, similar among junctional SR proteins in the two membranes (Fig. ##FIG##5##6##). Moreover, together, the two studies validate past reports of isoform specificities previously based on SDS-PAGE and immunoblot analyses. Junctin, a splice variant of junctate and aspartyl <italic>β</italic>-hydroxylase [##REF##17706594##58##], could not be distinguished based on the peptides sequenced. Treves et al. [##REF##11007777##59##] previously reported that no gross differences occurred immunologically between junctin and junctate levels in heart homogenates, suggesting that junctin may be roughly half of the A_SR level reported here. Co-enrichment of L-type Ca²⁺ channel with junctional SR markers was further evidence of a stable protein complex of couplon proteins with the sarcolemmal T-tubule membrane [##REF##6853518##21##].</p>", "<title>Peroxisomal proteins and rab proteins in MedSR</title>", "<p id=\"Par36\">In addition to the enrichment of junctional SR proteins, MedSR membranes were also enriched in peroxisomal proteins, rab proteins, and caveolar proteins (Fig. ##FIG##6##7##), but the three types of protein-containing vesicles varied in their membrane enrichments. Peroxisomal proteins were very uniquely enriched in SERCA-positive membranes, and their enrichment was highly variable (E_SR = 26.7 ± 22.3) (Fig. ##FIG##7##8##A). In addition, peroxisomal proteins were extraordinarily enriched in MedSR compared to HighSR membranes (avg E_sub = − 0.50 ± 0.09). By comparison, junctional SR proteins were much less enriched in MedSR compared to HighSR (avg E_sub = − 0.24 ± 0.10, for 4 couplon proteins). The reason for this unusual enrichment of peroxisomal proteins in SERCA-positive membranes is unknown, and much remains to be learned about this peculiar ER subdomain [##REF##25608554##61##–##REF##28146471##63##].</p>", "<p id=\"Par37\">When <italic>E</italic>_sub values were averaged for several sets of functionally related proteins, average <italic>E</italic>_sub values covered a range of distribution between the two SR subpopulations (Fig. ##FIG##7##8##A), suggesting that individual membrane patches are enriched in separate functional subdomains, with each subdomain exhibiting particular Ca²⁺ transport properties that reflect its inclusion of SERCA and RyR protein.</p>", "<p id=\"Par39\">Rabs and other small GTPases were also highly enriched in MedSR, exhibiting <italic>E</italic>_sub values similar to those of known junctional SR proteins (Fig. ##FIG##7##8##A, B). Rab proteins are fundamental regulators of organelle biogenesis and vesicle transport, and constitute the largest subset of the ras superfamily of small GTPases [##REF##10966806##64##]. In addition to abundant rabs, the rab associated protein PRA-1 <italic>(A</italic>_{<italic>SR</italic>} = <italic>25.0, 7</italic>th <italic>highest</italic>), and hedgehog acyltransferase-like protein (aka mitsugamin-56 [##REF##25841338##65##]) were also enriched in SR (Online Resource 1). The possible close physical proximity of rabs to junctional SR sites is consistent with evidence of protein secretion in cultured cardiomyocytes emanating from sites close to junctional SR [##REF##30919218##66##].</p>", "<title>Rough ER proteins</title>", "<p id=\"Par40\">Cardiac rough ER is a critical subdomain of ER, and in cardiomyocytes has a predominantly perinuclear morphology that is distinct from the repeating SR sarcomeres that control contraction [##REF##30919218##66##, ##UREF##1##67##]. Yet, SERCA-positive SR membrane vesicles also contained a complete collection of known rough ER proteins involved in translation, translocation, and N-linked glycosylation (Table ##TAB##2##3##, Appendix). Rough ER proteins were of relatively low abundance (A_SR = 4.0 ± 1.7), but very highly enriched over crude MVs (E_SR = 6.0 ± 2.5) (Fig. ##FIG##7##8##A).</p>", "<title>Lipid metabolism and lipid modifications of proteins</title>", "<p id=\"Par41\">Numerous enzymes involved in lipid metabolism were enriched in SERCA-positive membranes. The highest A_SR value (= 20.7) resulted from CDITP, which appends inositol-3-phosphate to diacylglycerol, with numerous lipid metabolizing proteins present at lower A_SR levels (Fig. 1, Appendix).</p>", "<title>Proteins involved in ER membrane structure and dynamics</title>", "<p id=\"Par42\">Many cardiac ER/SR proteins are those thought to play roles in distributing and trafficking proteins across the biosynthetic pathway. Several act by guiding membrane patches along transport filaments; these include Ca²⁺-binding protein p22, vesicle-trafficking protein Sec22b, vesicle-associated membrane protein 2 (VAMP-2), and vesicle transport protein Sec20 [##REF##8626580##68##–##REF##24705552##71##]. The mammalian proteins of the p24 family (TMED 10, 9, 2, 1) are involved in selective loading of cargo in transport vesicle between membrane compartments, and their subunit co-enrichment is consistent with previous reports in nonmuscle cell types [##REF##7729411##72##, ##REF##19566487##73##]. Finally, other ER proteins may function in the maintaining the structure of ER subcompartments, such as reticulons − 2 and − 4 [##REF##16469703##74##], lunapark-3 [##REF##23478217##75##], and climp-63 [##REF##17567679##76##]. Proteins involved in ER/SR dynamics are tabulated, along with enrichment values, in Table 4, Appendix.</p>", "<title>Relative abundances within functional sets of cardiac ER/SR proteins</title>", "<p id=\"Par43\">In spite of these substantial variations in A_SR among functional sets of proteins, the enrichment properties <italic>E</italic>_sub and <italic>E</italic>_SR among the same sets were remarkably consistent; both because of their physical segregation in membrane vesicles, but also because enrichment values are derived from <italic>ratios</italic> of <italic>A</italic>_SR values in two preparations. For example, a large number of known KDEL proteins were found in SR, exhibiting a wide range of <italic>A</italic>_SR values (6.3 ± 9.0, N = 7 proteins). For the same 7 KDEL proteins, however, <italic>E</italic>_sub values were 0.47 ± 0.08, and <italic>E</italic>_SR values were 7.1 ± 3.7. Plotting <italic>A</italic>_SR values for the top 2–4 proteins of different groups of proteins (Fig. ##FIG##8##9##), provided some semi-quantitative insight into how different ER/SR subdomains may contribute to overall SR function. </p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par45\">In this study, we used the technique of Ca oxalate loading of cardiac SR membrane vesicles to produce two SR membrane subpopulations (MedSR and HighSR), thereby enriching patches of cardiac ER/SR membrane that contain combinations of SERCA <italic>and</italic> RyR levels. Roughly one third of microsomal proteins were enriched in SERCA-positive membranes, and about a third of those were more enriched in the MedSR membranes, indicating the presence of enriched RyR in the same SR patch, and suggesting a relative proximity to junctional SR, or at least a biochemically distinct membrane subdomain. The activation of SERCA activity in our current study, an historical measure of SR function, led to the enrichment of proteins from every ER subcompartment, supporting a view that cardiac ER and SR should cannot be demarcated based only upon their ability to function in Ca²⁺ handling.</p>", "<p id=\"Par46\">Proteins enriched in SERCA-positive SR vesicles were defined as any protein that was enriched ≥ 2.0-fold over its level in crude heart microsomes. This single enrichment criterion selected 354 proteins of 1102 total proteins in crude microsomes, while excluding all mitochondrial, contractile protein, and other known organellar contaminants. Even major mitochondrial and contractile protein contaminants were eliminated by this simple measure of enrichment. SERCA-positive SR proteins encompassed proteins from all known functional ER and SR subdomains, leading us to conclude that SERCA-positive membranes represent cardiac ER and SR.</p>", "<p id=\"Par47\">The enrichment of junctional SR proteins in MedSR membranes was previously demonstrated by immunoblot analyses to be a feature of this SR preparation [##REF##6271762##5##, ##REF##6203912##15##, ##REF##2103513##18##, ##REF##6853518##21##, ##REF##9287354##77##]. In the present study, we found that the values of E_sub for 354 proteins formed a continuous range from − 0.9 (largely detected only in MedSR) to + 0.9 (largely detected only in HighSR membranes) (Fig. ##FIG##3##4##). Other functional protein groups exhibited similarly segregated values (Figs. ##FIG##2##3##, ##FIG##3##4##, ##FIG##7##8##), suggesting that they too were physically distributed into at least two divergent subcellular sites: those closer to junctional SR and those further removed from such sites. The segregation of protein functional groups in terms of E_SR and E_sub shows that vesicles are derived from small enough membrane surfaces to fractionate with different enrichment patterns, and do not simply represent huge sections of membrane surface.</p>", "<p id=\"Par48\">In summary, enrichment of cardiac membranes by Ca oxalate loading leads to the enrichment of ER/SR proteins, distributed between membrane fractions that differ in Ca²⁺ leak through RyR. The distribution of individual proteins between the two fractions (Esub), and the consistent enrichments found among different functional sets of proteins, reflects the connections between ER/SR subdomains and the well-studied spatial relationships between junctional and free SR. Our data present for the first time a reliable estimation of cardiac ER/SR protein content, along with a semi-quantitative assessment of prominent sets of functional ER/SR subdomains present in a microsomal preparation of canine ventricular tissue.</p>" ]

[ "<p id=\"Par1\">The importance of sarcoplasmic reticulum (SR) Ca²⁺-handling in heart has led to detailed understanding of Ca²⁺-release and re-uptake protein complexes, while less is known about other endoplasmic reticulum (ER) functions in the heart. To more fully understand cardiac SR and ER functions, we analyzed cardiac microsomes based on their increased density through the actions of the SR Ca²⁺-ATPase (SERCA) and the ryanodine receptor that are highly active in cardiomyocytes. Crude cardiac microsomal vesicles loaded with Ca oxalate produced two higher density subfractions, MedSR and HighSR. Proteins from 20.0 μg of MV, MedSR, and HighSR protein were fractionated using SDS-PAGE, then trypsinized from 20 separate gel pieces, and analyzed by LC–MS/MS to determine protein content. From 62,000 individual peptide spectra obtained, we identified 1105 different proteins, of which 354 were enriched ≥ 2.0-fold in SR fractions compared to the crude membrane preparation. Previously studied SR proteins were all enriched, as were proteins associated with canonical ER functions. Contractile, mitochondrial, and sarcolemmal proteins were not enriched. Comparing the levels of SERCA-positive SR proteins in MedSR versus HighSR vesicles produced a range of SR subfraction enrichments signifying differing levels of Ca²⁺ leak co-localized in the same membrane patch. All known junctional SR proteins were more enriched in MedSR, while canonical ER proteins were more enriched in HighSR membrane. Proteins constituting other putative ER/SR subdomains also exhibited average <italic>E</italic>_sub enrichment values (mean ± S.D.) that spanned the range of possible <italic>E</italic>_sub values, suggesting that functional sets of proteins are localized to the same areas of the ER/SR membrane. We conclude that active Ca²⁺ loading of cardiac microsomes, reflecting the combined activities of Ca²⁺ uptake by SERCA, and Ca²⁺ leak by RyR, permits evaluation of multiple functional ER/SR subdomains. Sets of proteins from these subdomains exhibited similar enrichment patterns across membrane subfractions, reflecting the relative levels of SERCA and RyR present within individual patches of cardiac ER and SR.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s11010-023-04708-0.</p>", "<title>Keywords</title>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Acknowledgements</title>", "<p>We thank Joseph Caruso, Ph.D. for expert assistance with analyses of mass spectrometry data, Timothy McFarland, Ph.D. for careful analysis of membrane protein concentrations and SDS-PAGE; Stephanie Kokoszka, Ph.D. for helpful discussions regarding protein sorting strategies, and Ashley Morgan, B.S. for expert technical assistance.</p>", "<title>Author contributions</title>", "<p>SEC: conceptualization, methodology, writing. NJC: data curation, software. PMS: Supervision, investigation, methodology. ZC: validation, investigation. XC: resources, conceptualization.</p>", "<title>Funding</title>", "<p>We acknowledge the support of a grant from the Office of the Vice President for Research at Wayne State University (S.C.). Assistance of the Wayne State University Proteomics Core was supported through NIH (Grant Nos. P30 ES020957, P30 CA 022453 and S10 OD010700). This work was also supported by the National Institutes of Health [Grant No. 1R01DK110314 (X. C.)], and the American Heart Association. [Grant No. 18TPA34170284 /ZC/2018].</p>", "<title>Data availability</title>", "<p>The datasets generated during and/or analyzed during the current study are available at Figshare.com; Filename: CardiacSRproteome; <ext-link ext-link-type=\"uri\" xlink:href=\"https://doi.org/10.6084/m9.figshare.19953701\">https://doi.org/10.6084/m9.figshare.19953701</ext-link>. Raw data and search results have been submitted to the ProteomeXchange via PRIDE with accession PXD022455 (Username: [email protected], Password: G1wlk66N).</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par50\">The authors have no relevant financial or non-financial interests to disclose.</p>", "<title>Ethical approval</title>", "<p id=\"Par51\">The investigation conforms to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No. 85-23, revised 1996). Animal research was approved by the Wayne State University Animal Investigation Committee (protocol #A 04-02-13).</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Purification of SR membranes from heart tissue using Ca oxalate loading. <bold>A</bold> Crude microsomal vesicles (MV) were isolated by differential sedimentation, then incubated under Ca²⁺ loading conditions without ATP (− ATP) or + ATP. <bold>A</bold> Ca oxalate precipitate inside SR vesicles appears as a whitish pellet, following activation of SERCA2a (<italic>arrow)</italic>. <bold>B</bold> Separation of MVs on a discontinuous sucrose gradient showed banding of MedSR membrane vesicles afloat on a sucrose concentration (suc conc) of 1.5 M (density <italic>ρ</italic> ~ 1.2), and pelleting of more heavily Ca oxalate- oaded HighSR membrane vesicles through 1.5 M sucrose (HighSR pellet not visible in figure). <bold>C</bold> 20.0 μg of MV, MedSR, and HighSR protein were fractionated using SDS-PAGE, then trypsinized from 20 separate gel pieces (schematically shown by lines) and analyzed by LC–MS/MS. Even when visualized by protein stain, one sees proteins more enriched in MedSR and HighSR (<italic>arrowhead</italic>) or less enriched (<italic>double arrowheads</italic>)</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Protein enrichments resulting from Ca oxalate loading of SR vesicles<bold>. A</bold> sorting of proteins identified in crude cardiac microsomal vesicles (MV) in order of decreasing peptide abundance, with only the first 200 proteins shown here (<italic>blue bars</italic>)<italic>.</italic> Superimposed is a plot of their fold enrichment in SR fractions (<italic>red bars</italic>). Only about 40 of the 200 were enriched by SERCA activation (E_SR = 2.0, <italic>pale gray line</italic>), defining a set of SR proteins, as discussed in this study. The most abundant SR-enriched protein was SERCA2. <bold>B</bold> sorting of all 354 SR-enriched proteins by E_SR values (which includes the 40 red values in panel A). Shown in green are the E_SR values of 14 known cardiac SR proteins, enriched in SERCA-positive membranes on an average of 5.0 ± 1.6 (SD) over crude membrane vesicles; 2.0-fold enrichment in SR is marked (<italic>arrowhead</italic>). CXN, <italic>calnexin</italic>; JCT, <italic>junctin plus junctate</italic>; PLB, <italic>phospholamban</italic>; CSQ2, <italic>calsequestrin-2</italic>; TRD, <italic>triadin</italic>; HRC, <italic>histidine-rich Ca</italic>^{<italic>2</italic>+}<italic>-binding protein</italic>; SCL, <italic>sarcalumenin</italic>; JP2, <italic>junctophilin-2</italic>; glucose regulated protein of M_r = 94,000, GRP94</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Known cardiac SR proteins distribute between HighSR and MedSR consistent with previous immunological studies. A Well-studied SR proteins exhibit E_sub values from + 0.60 to − 0.45 (<italic>left hand y-axis</italic>), which corresponds to a roughly fourfold greater level in HighSR membranes to threefold greater in MedSR, respectively (<italic>right hand y-axis</italic>). Negative values of E_sub based on mass spectrometry data predict the same SR subdomain distribution described in the literature for 15 non-junctional SR (<italic>blue bars</italic>) and 7 junctional SR (<italic>red bars</italic>) proteins, based on immunological studies. Three SR proteins involved in Ca²⁺ uptake (<italic>white bars</italic>) were more evenly distributed between SR subfractions. <bold>B</bold> Relative abundances for the same 22 proteins show far greater variability. The A_SR value for junctin/junctate (JCT/JCTA) is shaded in two halves (<italic>asterisk</italic>, *) to approximate the portion that corresponds only to junctin. PDI, <italic>protein disulfide isomerase</italic>; Calret, <italic>calreticulin;</italic> GRP94, <italic>glucose-regulated protein of M</italic>_{<italic>r</italic>} = <italic>94,000</italic>; SCL, <italic>sarcalumenin</italic>; Calnex, <italic>calnexin</italic>; HRC, <italic>histidine-rich Ca</italic>^{<italic>2</italic>+}<italic>-binding protein</italic>; PLB, <italic>phospholamban</italic>; CSQ2, <italic>calsequestrin-2;</italic> JP2, <italic>junctophilin-2</italic>; TRD, <italic>triadin</italic>; LTCC<italic>, L-type Ca</italic>^{<italic>2</italic>+}\n<italic>channel α-subunit</italic></p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Distributions between HighSR and MedSR are similar for sets of proteins with similar functions. <italic>E</italic>_sub values for all 354 SERCA-positive SR proteins (<italic>shaded gray area</italic>) range from + 0.90 to − 0.90 (90% more enriched in HighSR or in MedSR, respectively). Distribution of any one protein between the two density layers reflects in part, its physical proximity to junctional SR sites. Co-enrichment of proteins with similar function within common membrane fragments therefore reflects similar relative levels of (nearby) SERCA2 and RyR</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>The 15 most abundant SR proteins based on A_SR values. A_SR values are expressed as a percentage of SERCA2 A_SR (= 100.0). An asterisk denotes the fact that junctin and junctate were not distinguishable in this study. The 15 proteins shown represented 38% of all spectra from all 354 proteins in SERCA-positive membranes</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>A_SR values for well known junctional SR proteins from a preparation of cardiac or skeletal muscle SR. Levels of individual proteins are normalized to that of either SERCA2a (= 100.0) for cardiac (Card) SR, or to the levels of SERCA1 (= 100.0) for rabbit fast-twitch muscle (Skel) SR proteins as reported in ref. [##REF##23713034##25##]. Note differences in ordinate scales for the three panels shown. Skel data were obtained from a similar proteomic analysis by Liu et al. [##REF##23713034##25##] using the classic preparation of heavy SR prepared from rabbit fast-twitch skeletal muscle that is based upon microsome sedimentation rates [##REF##124589##8##]. RyR, ryanodine receptor; CSQ, calsequestrin-2; JCT, junctin (plus junctate for Card data); TRD, triadin (cardiac isoform for Card); JP, junctophilin; LTCC, L-type Ca²⁺ channel. Text below bars designates isoforms or subunits. Double shading of Card JCT denotes the approximate half of peptide spectra that may have arisen from junctate</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><p>Junctional SR and other ER/SR subdomains enriched in MedSR membranes. SR proteins with negative <italic>E</italic>_sub values (more enriched in MedSR) were sorted by A_SR (highest to lowest). Only the 50 highest A_SR values are shown. Rab isoforms were an abundant set of enriched proteins (<italic>green bars with labeled isoform</italic>). The total peptide spectra for JCT plus junctate is shown here (JCT, <italic>asterisk</italic> *)</p></caption></fig>", "<fig id=\"Fig8\"><label>Fig. 8</label><caption><p>Sets of functionally related proteins undergo similar enrichments <bold>A</bold> Subsets of ER/SR proteins with related functions: average enrichment in SR (E_SR mean ± S.D., <italic>y-axis</italic>) and average distribution between SR subfractions (E_sub mean ± S.D.), <italic>x-axis</italic>. The numbers shown in parentheses are the number of proteins averaged from each set. <bold>B</bold> E_SR and E_sub values for individual rabs (<italic>purple rings</italic>) and other small GTPases are shown. Abundance values (A_SR) are proportional to symbol diameters. The 3 most abundant rabs are labeled (2A, 1A, and 1B)</p></caption></fig>", "<fig id=\"Fig9\"><label>Fig. 9</label><caption><p>The 2–4 most abundant ER/SR proteins in each functional subset. A_SR values sharply decline for the first 2–4 protein of each functional set. Plots are offset along the x-axis to improve visual clarity. A_SR values for junctional SR proteins only include transmembrane proteins (cf. Figure ##FIG##5##6##), excluding calsequestrin-2 which is grouped with the very abundant sarcalumenin as two very abundant luminal proteins of uncertain function. Proteins with common functions are represented in color-coded sets using similar color tags. Proteins are also color tagged in the table of all proteins (Online Resource 1)</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Key definitions and abbreviations used in this study</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"2\">Membrane preparations</th></tr></thead><tbody><tr><td align=\"left\"> MV</td><td align=\"left\"> Crude cardiac microsomal <bold>v</bold>esicles</td></tr><tr><td align=\"left\"> MedSR</td><td align=\"left\"> Medium density Ca oxalate loaded SR, enriched in every junctional SR marker</td></tr><tr><td align=\"left\"> HighSR</td><td align=\"left\"> High(est) density Ca oxalate loaded SR, enriched in free SR (non-junctional) vesicles</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"2\">Parameter determined for each protein</th><th align=\"left\">Range of values</th></tr></thead><tbody><tr><td align=\"left\"> E_SR</td><td align=\"left\"> Enrichment in SR <italic>(MedSR</italic> + <italic>HighSR)/ MV</italic></td><td align=\"left\"> ≥ 2.0 for SR (average: 8.0-fold)</td></tr><tr><td align=\"left\"> E_sub</td><td align=\"left\"><p> Enrichment in HighSR compared to MedSR</p><p> (<italic>HighSR – MedSR)/ (HighSR</italic> + <italic>MedSR)</italic></p></td><td align=\"left\"><p> = 0.90 (A_SR value 90% greater in HighSR)</p><p> =  − 0.90 (A_SR value 90% greater in MedSR)</p><p> = 0.00 (equally distributed)</p></td></tr><tr><td align=\"left\"> A_SR</td><td align=\"left\"> Spectral Abundance in SR <italic>(MedSR</italic> + <italic>HighSR)</italic>, divided by molecular weight, normalized to SERCA2<italic> (</italic>= <italic>100.0)</italic></td><td align=\"left\"><p> 0.05–100.0</p><p><italic>A</italic>_{<italic>SR</italic>}<italic> (SERCA2) ≡ </italic>100.0</p></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Membrane contact site (MCS) proteins enriched in cardiac ER/SR. MCS proteins are sorted by <italic>A</italic>_SR values, and their rank order among 354 proteins that are in SERCA-positive SR (Rank). High values of A_SR for VAP-B and VAP-A reflect the importance of cardiac ER/SR in transporting proteins and lipids to distal parts of the myocyte. Other proteins involved in ER inter-organellar contact include junctophilin-2, and extended synaptotagmins. Only junctophilin-2 showed a negative <italic>E</italic>_sub value, consistent with its reported enrichment in junctional SR (cf. Figure ##FIG##2##3##A)</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Membrane contact site protein</th><th align=\"left\">Rank</th><th align=\"left\">A_SR</th><th align=\"left\">E_SR</th><th align=\"left\">E_sub</th><th align=\"left\">Role</th></tr></thead><tbody><tr><td align=\"left\">VAP-B (vesicle-associated membrane protein (VAMP)-associated protein B)</td><td align=\"left\">10</td><td char=\".\" align=\"char\">18.5</td><td char=\".\" align=\"char\">5.6</td><td char=\".\" align=\"char\">0.40</td><td align=\"left\" rowspan=\"2\">Associated with VAMP subfamily of SNARES; involved in lipid transfer from ER on lipid transfer proteins</td></tr><tr><td align=\"left\">VAP-A</td><td align=\"left\">24</td><td char=\".\" align=\"char\">11.3</td><td char=\".\" align=\"char\">7.4</td><td char=\".\" align=\"char\">0.29</td></tr><tr><td align=\"left\">Junctophilin-2</td><td align=\"left\">55</td><td char=\".\" align=\"char\">5.9</td><td char=\".\" align=\"char\">3.1</td><td char=\".\" align=\"char\">− 0.23</td><td align=\"left\">Binds to PI enriched plasma membrane lipids (MORN sites) at junctional SR</td></tr><tr><td align=\"left\">extended synaptotagman-2</td><td align=\"left\">288</td><td char=\".\" align=\"char\">0.55</td><td char=\".\" align=\"char\">5.7</td><td char=\".\" align=\"char\">0.33</td><td align=\"left\" rowspan=\"2\">Tethers ER to the plasma membrane by C-terminal MCS, and transports glycerolipids between the two bilayers</td></tr><tr><td align=\"left\">extended synaptotagman-1</td><td align=\"left\">308</td><td char=\".\" align=\"char\">0.37</td><td char=\".\" align=\"char\">3.1</td><td char=\".\" align=\"char\">0.13</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Proteins of the ER/SR lumen. Resident luminal ER/SR proteins, listed in order of decreasing A_SR. Proteins known to be highly specific for cardiac and skeletal muscle myocytes cells are indicated (<italic>shaded rows</italic>) [##REF##2103513##18##]. All other proteins except calnexin [##REF##8102790##60##] likely act as ER protein chaperones, and are maintained in ER through a <italic>C</italic>-terminal –KDEL retrieval signal. GRP78, glucose-regulated protein, M_r = 78 kDa; PDI, protein disulfide isomerase; His-rich Ca²⁺ BP, histidine-rich Ca²⁺ binding protein. Rank identifies proteins by their order among 354 proteins in SERCA-positive SR sorted by <italic>A</italic>_SR (see Online Resource 1)</p></caption></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Small lotic waterbodies, (semi-)artificial and natural, contribute to biodiversity and ecosystem services (Biggs et al. ##UREF##8##2017##). They provide microhabitats and exhibit a variety of species (Armitage et al. ##UREF##1##2003##; Verdonschot et al. ##UREF##66##2011##), including uncommon to very rare taxa (Verdonschot ##UREF##64##2012##). Especially for species which lost their primary habitat, small lotic waterbodies become a refuge as a secondary one. The damselfly <italic>Coenagrion mercuriale</italic> (Charpentier 1840) is an example for those species, protected and covered by the Habitats Directive Annex II Council Directive 92/43/EEC (Council of the European Communities ##UREF##15##1992## [Habitats Directive]; Sternberg and Buchwald ##UREF##55##1999##), which represents the Natura 2000 network together with the Birds Directive. The primary habitat of the threatened <italic>C. mercuriale</italic> are drains of calcareous fens which occurrence declined due to the beginning of fenland exploitation around the 17th century and finally led to massive destruction of fens in the 20th century (Succow and Jeschke ##UREF##57##2022##). After all, <italic>C. mercuriale</italic> colonized a different, but equivalent habitat type: sunny, little to moderate flowing small waterbodies with winter-green submerged water-vegetation (Wildermuth and Martens ##UREF##74##2019##), which themselves also represent a protected habitat type 3260 “Water courses of plain to montane levels with the Ranunculion fluitantis and Callitricho-Batrachion vegetation” of Annex I Habitats Directive.</p>", "<p id=\"Par3\">The Habitats Directive was implemented in 1992 to reach a good nature conservation status and to maintain biodiversity, involving management plans as well for Natura 2000 sites. However, the state of nature report 2013–2018 identified that management actions exist for 60% of the habitat sites only, yet only a few are implemented since personal and financial resources are missing (European Environment Agency ##UREF##20##2020##). In this study, the habitat type 3260 and a variety of species (e.g. <italic>Natrix tesselata, Lampetra planeri, Misgurnus fossilis, C. mercuriale, Coeagrion ornatum, Unio crassus</italic>) are of interest according to the Habitats Directive (Ssymank et al. ##UREF##53##2021##). A favorable habitat conservation status includes per definition in Art. 1e of the Habitats Directive also a good status of its “typical species” (Art. 1i). However, animal species are still largely neglected in practical nature conservation and management of habitats. Many of these typical species have certain habitat requirements in common with the target species <italic>C. mercuriale</italic>, like slow currents and macrophytes. In addition, small lotic waterbodies which are part of a catchment area of &gt;10 km² are covered by the European Water Framework Directive [WFD], which aims to reach a good ecological potential for heavily modified waterbodies and a good ecological status for natural waterbodies (European Parliament and European Council ##UREF##21##2000## [EU Water Framework Directive]).</p>", "<p id=\"Par4\">The habitat type 3260 and therefore its target species <italic>C. mercuriale</italic> is mainly threatened by agricultural use, pollution, hydraulic-engineering actions and frequent water management (Ssymank et al. ##UREF##53##2021##), indicating the necessity of well-conducted management plans for this habitat. However, management of small lotic waterbodies must address specific requirements: when water management is performed too intensive, it is a threat to the biodiversity as well as when water management is not performed or too extensive, so that the habitat conditions are not maintained.</p>", "<p id=\"Par5\">Water management practices as mowing of aquatic vegetation affect invertebrates (Kaenel et al. ##UREF##31##1998##). For lotic waterbodies, Wright et al. (##UREF##75##1992##) identified a positive relation between macroinvertebrates and the presence of macrophytes. Especially for Zygoptera (Odonata), submerged macrophytes are crucial (Buchwald ##UREF##10##1989##; Painter ##UREF##42##1998##). For fish, a waterbody’s vegetation provides shelter, shade and spawning substrates (Mills ##UREF##36##1981##; Swales ##UREF##58##1982##). In case of strong hydraulic forces, reed can slow down the current in the waterbody so submerged macrophytes might also find better conditions to grow along reed (Clark and Samways ##UREF##12##1996##).</p>", "<p id=\"Par6\">Besides short-term effects, previous studies analyzed the recovery and long-term effect of aquatic vegetation mowing, ranging from 4–6 months (Kaenel et al. ##UREF##31##1998##) or even 8–11 months (Monahan and Caffrey ##UREF##38##1996##). A higher negative impact of weed cutting has been analyzed on the abundance of less mobile invertebrate species which may reduce their predator’s abundance in turn due to limited food availability (Kaenel et al. ##UREF##31##1998##). In long-term, macrophyte communities differ in species diversity and richness, indicating higher values for uncut sites (Baattrup-Pedersen et al. ##UREF##2##2002##).</p>", "<p id=\"Par7\">Even when there are expected negative effects by water management practices on biodiversity, they do support abundance and diversity of animals as well. Therefore, to maintain high biodiversity in small waterbodies, a certain water management can support (Clarke ##UREF##13##2015##). Water management prevents sediment accumulation by dredging and regulates vegetation by weeding and mowing, maintaining the hydraulic function (Needelman et al. ##UREF##40##2007##). Not overgrown and clear of reed sections are favored oviposition sites for Odonata (Buchwald ##UREF##10##1989##; Painter ##UREF##42##1998##). <italic>C. mercuriale</italic> prefers a medium vegetation cover for example, avoiding high coverage (Buchwald ##UREF##10##1989##). Sites with high frequency of emergent vegetation can exhibit a lower macroinvertebrate family richness (Wright et al. ##UREF##75##1992##). Shade cover, such as by trees, can reduce abundance of Odonata (Remsburg et al. ##UREF##46##2008##), and ecological practices are known to have a positive influence on the abundance and diversity of amphibians (Maes et al. ##UREF##34##2008##). Since water vegetation is required but without complete cover and shading of the waterbody (Rouquette and Thompson ##UREF##51##2005##), threatened species as <italic>C. mercuriale</italic> are dependent on water management concepts that are considering conservation interests. Concepts concerning water management have been developed by many countries (Finér et al. ##UREF##23##2018##; West Sussex County Council ##UREF##67##2018##). In Germany, legal requirements to water management are given through the Federal Water Act (Wasserhaushaltsgesetz ##UREF##65##2009##) and several guidelines from the German Association for Water, Wastewater and Waste [DWA] (e.g. the leaflet from the DWA ##UREF##17##2010##) and federal states (e.g. Niedersächsischer Landesbetrieb für Wasserwirtschaft, Küsten- und Naturschutz [NLWKN] ##UREF##41##2020##). Existing water management concepts include seasonality, frequency, practice and equipment. The latter has undergone vast changes, mainly in the last century from manual to motorized, intensifying agricultural practices (Baattrup-Pedersen and Riis ##UREF##4##2004##; van de Poel and Zehm ##UREF##62##2014##).</p>", "<p id=\"Par8\">Despite the multiplicity of studies concerning the ecological value and management of small lotic waterbodies, the current practice of water management needs further investigation. The major aim of our study was to investigate the current status of water management especially within the range of the highly, on small lotic waterbody dependent target species <italic>C. mercuriale</italic> to evaluate its biodiversity compatibility and its status to integrate it in the efforts of nature conservation. To gain information about the status in Germany, a questionnaire is used. The questionnaire aims to collect data on reasons, equipment, seasonality, undertaken actions, ecological considerations, and additionally socio-demographic data. The latter is included to understand if there is a correlation between the structure of the executive authority and the water management. The results are then compared with previous studies concerning water management and nature conservation to discuss whether and how the current status meets the recent research on nature conservation and water management interests and requirements. The reconciliation of those two interests aims to improve water management with regard to biodiversity conservation and the goals of the Habitats Directive.</p>" ]

[ "<title>Methods</title>", "<title>Survey and Data Collection</title>", "<p id=\"Par9\">As <italic>C. mercuriale</italic> is the target species, the study area covers the range of <italic>C. mercuriale</italic> in Germany. The current range of <italic>C. mercuriale</italic> includes 12 out of 16 German federal states. Background data about the range were retrieved from the dragonfly atlas Germany (Brockhaus et al. ##UREF##9##2015##) and the dragonfly atlases from the federal states or other sources (Baumann et al. ##UREF##5##2021##; Bayerisches Landesamt für Umwelt ##UREF##7##2016##; Hill et al. ##UREF##27##2011##; Hunger et al. ##UREF##29##2006##; Jäger ##UREF##30##2019##; Menke et al. ##UREF##35##2016##; Müller et al. ##UREF##39##2018##; Trockur et al. ##UREF##58##2010##; Zimmermann et al. ##UREF##75##2005##). In addition, the databases ArtenFinder-Portal for Rhineland-Palatinate (Stiftung Natur und Umwelt Rheinland-Pfalz ##UREF##55##2020##), ASL database Bavaria (Bayerisches Landesamt für Umwelt ##UREF##6##2020##) and SGL database for Baden-Wuerttemberg (SGL ##UREF##51##2020##) were consulted. Authorities within the range of <italic>C. mercuriale</italic> in fenlands were not addressed. We identified authorities responsible for management of small lotic waterbodies. Small lotic waterbodies are classified either as second or third order waterbodies, depending on the federal state laws. The management responsibility lies with the owner of the surface waterbodies. Usually, these owners are municipalities in the case of second/third order waterbodies. However, management responsibility can be devolved to associations and companies by the owners. Additionally, owners can be state governments or other governing authorities as well, causing difficulties in identifying responsible authorities. Therefore, the type of authorities can be municipalities, associations, companies, state governments or other governing authorities (Fig. ##FIG##0##1##).</p>", "<p id=\"Par10\">To gain data on management practices, we prepared a questionnaire. The questionnaire consisted of 21 questions of study interest and one additional for contact details (see Supplementary Information, translated questionnaire). Questions were divided into three sets of questions: (1) socio-demographic (personal) questions, (2) specific questions about water management and (3) questions on the biological background. Socio-demographic (personal) questions involved questions about structure, employees, reasons and relevance for water management, ecological examination and the customer. The reasons and their relevance to the authority included both water management and nature conservation interests. Actions at the water bed/the riparian side/the periphery, equipment, time frame, destination of accruing material due to the actions, scheme type and the working direction, against or with the current, were part of the second set of questions. The equipment question was multiple choice. For water management in bed, several equipment was suggested as e.g. “mowing bucket” and “using a spacer”, followed by an additional free text field for additional equipment. For water management at the shore/bank, equipment was suggested as e.g. “scythe” and “bar mower”, followed by an additional free text field for additional equipment. The whole list of the equipment can be found on page 6 of the questionnaire in the supplement. The shore/bank equipment was combined since according to the feedback of the water management authorities this is performed with the same equipment, i.e. the shore vegetation is managed in the same way as the bank. In addition, participants were asked when actions in water management were performed during the year, according to the seasons. They could specify which actions were performed with additional free text fields.</p>", "<p id=\"Par11\">The biological background and third set of questions involved questions about conservation sites, biological/chemical analysis as for example through fish or nitrate monitoring, knowledge about the occurrence of strongly and especially protected species, knowledge about the damselfly <italic>C. mercuriale</italic> and conservation of species in general. The difference between biological/chemical analysis and the question of the first set of questions of ecological examination is made due to the direct monitoring prior to the water management (ecological examination) which can be done by the authority itself and the scientific monitoring according to for example the WFD (biological/chemical analysis).</p>", "<p id=\"Par12\">Frequency questions were based on water management actions of the leaflet from the DWA (##UREF##17##2010##). The participants should not answer for their whole area to avoid answers concerning rotating practices at different reaches. This means, that authorities might manage every year reaches, but every year different ones with a rotating system. Therefore, the same reach might be managed only every two or three years, which is the answer that was wanted. In addition, they should differentiate their answer between waterbodies that are managed frequently/far-from-nature and waterbodies that are managed rarely/close-to-nature. According to the received answer during the pre-test (see below), this distinction is made by the authorities.</p>", "<p id=\"Par13\">Questions were designed by categorical variables, mostly allowing multiple choice answers and additional free text fields for additional information if necessary. The participants were asked to answer according to their general water management performance to avoid answers with regard to special and unique water management at reaches of waterbodies (e.g. as part of a conservation project).</p>", "<p id=\"Par14\">A pre-test was carried out by a water management association in Lower Saxony to check the questionnaire for application. After the pre-test, the questionnaire was adapted. Questionnaires were sent by e-mail to the German water management authorities with regard to surface waterbodies.</p>", "<p id=\"Par15\">Subsequently, data collection took place between August 2020 and November 2021. After contacting 181 authorities, 94 questionnaires were distributed, from which 75 (<italic>N</italic> = 181, 41%) were filled out.</p>", "<title>Data Analysis</title>", "<p id=\"Par16\">Statistical analysis was performed with Excel and R (R Core Team ##UREF##44##2022##). In R, the packages ggplot2 (Wickham ##UREF##70##2016##), readxl (Wickham and Bryan ##UREF##72##2022##), reshape2 (Wickham ##UREF##69##2007##), tidyverse (Wickham et al. ##UREF##71##2019##) and ggpubr (Kassambara ##UREF##32##2020##) were used for the diagrams. For significance test, the packages readxl (Wickham and Bryan ##UREF##72##2022##) and psych (Revelle ##UREF##48##2022##) were used.</p>", "<p id=\"Par17\">A heat map was created to plot the reasons for water management and their relevance. With the heat map, the number of given answers by the participants can be rated easily by the reader. A bar plot was created to plot the frequency of several actions taking place in the bed as well at the bank. Differently colored bars were used to indicate frequently/far-from-nature and rarely/close-to-nature water management according to the participants’ answers and the number of counts of different answers. Two bar plots were created to plot the number of counts of the used equipment. For better readability, the bar plots were created without the additional equipment answers. Correlations between the usage of equipment and the consideration of species when selecting and applying actions in water management were further analyzed using the Chi-squared test and phi-coefficient due to dichotomous variables. To plot the three parameters seasonality, actions and their count, a three-dimensional diagram was created. A logistic regression was performed to analyze if there is a correlation between the ecological examination and the water management actions in dependence of seasonality. The destinations and their counts of four material accruing due to water management were plotted with four arranged bar plots, one plot for each material (mowing, dug-out, weeding, pruning material). Bars were colored following the three categories “left at site” (red), “disposal” (black) and “utilization” (green) for rating the destinations easily. With a pie chart, the count of the answers “yes, no/not answered, other” to the question of clarifying the occurrence of strongly/especially protected species were plotted to give a clear overview of the majority’s answer. To specify the answer “yes” to the latter, a bar plot was created to demonstrate the main information source.</p>" ]

[ "<title>Results</title>", "<p id=\"Par18\">The analysis of reasons for water management by the authorities showed that a few participants did consider reasons but did not specify the relevance (Fig. ##FIG##1##2##, “relevant, without specification”). High relevance was conceded to the “preservation of the water bed as well as protection of water runoff” by the majority of the participants (<italic>n</italic> = 57, 76%). Approximately, half of the participants conceded “preservation and furthering of the ecological viability of the waterbody (…)” as well as “preservation of the waterbody in a water-management way” as highly relevant (<italic>n</italic> = 42, 56%, <italic>n</italic> = 38, 51%). “Flood control” and “preservation of the littoral side” were of high relevance for less than half of the participants. “Legal site protection” played a minor part (n(minor) = 21, 28%, n(no relevance) = 21, 28%).</p>", "<p id=\"Par19\">However, the majority (73 out of 75 participants, 97%) stated to consider species conservation interests when selecting and applying actions in water management which was asked by another question. One participant noted that they do not consider species conservation interests yet. Another one did not answer the question. In addition, 53 out of 75 participants (71%) stated to examine the waterbody ecologically before water management, with regard to flora and fauna. Eighteen participants (24%) did not examine the waterbody beforehand, four did not answer the question.</p>", "<p id=\"Par20\">The majority of the authorities distinguished between frequently/far-from-nature managed waterbodies and rarely/close-to-nature managed waterbodies. For most actions concerning bed and bank, there were differences between the medians of frequently/far-from-nature and rarely/close-to-nature management (Fig. ##FIG##2##3##). For removal of litter and refuse (bed) as well as neophytes’ control and grazing (bank), medians were the same. Cleaning of bed was not very frequently performed (median &gt;3 years for frequently/far-from-nature, median never for rarely/close-to-nature respectively). The greatest difference in frequency was present in mowing of water vegetation, followed by weeding. Frequently managed waterbodies were mostly weeded and mowed in bed annually.</p>", "<p id=\"Par21\">For the equipment in bed (Fig. ##FIG##3##4##), the mowing bucket was the mostly used equipment (<italic>n</italic> = 56, 75%), followed by manual equipment as shovel or scythe (<italic>n</italic> = 49, 65%), the ditch cleaning bucket (<italic>n</italic> = 40, 53%) and the shovel excavator (<italic>n</italic> = 34, 45%). For the equipment on shore and bank (Fig. ##FIG##3##4##), string trimmers were used by the majority of the participants (<italic>n</italic> = 64, 85%), followed by flail mower (<italic>n</italic> = 46, 61%), mowing bucket (<italic>n</italic> = 44, 59%), hand-guided (motorized) bar mower (<italic>n</italic> = 36, 48%) and bar mower (<italic>n</italic> = 33, 44%). The most abundant combination of equipment that was selected by 6 of 75 (8%) participants has been “mowing bucket – manual equipment (e.g. shovel, spade, scythe, pitchfork) – ditch cleaning bucket – shovel excavator” for water management in bed. For the shore, the most abundant two combinations of equipment that were selected by each 6 of 75 (8%) participants have been “string trimmer – mowing bucket – flail mower” and “string trimmer – flail mower”. However, there was a scattered picture of equipment combinations, which was demonstrated by the low number of the same choice. Using the trencher was significantly linked to the response that no species conservation interests were regarded to (<italic>r</italic>(1) = 0.7; <italic>p</italic> &lt; 0.001).</p>", "<p id=\"Par22\">Regarding the actions and seasonality, dredging shows small numbers, with its highest in autumn. There were emphases for specific different actions: the emphasis for pruning lied in winter, the emphasis for weeding in summer and autumn and the emphasis for mowing of the bank/buffer strip lied in summer and autumn as well (Fig. ##FIG##4##5##). The logistic regression model was statistically significant for autumn (X2 (4, <italic>N</italic> = 75) = 0.04, <italic>p</italic> = 0.0055; OR = 9.72, 97.5% [57.97]), indicating that autumn was the preferred season for water management actions when waterbodies were ecologically examined beforehand.</p>", "<p id=\"Par23\">Mowing, dug-out and weeding material was mostly left at site (Fig. ##FIG##5##6##). Mowing and weeding material was commonly composted, when its further utilization was specified (<italic>n</italic> = 12, 16%, <italic>n</italic> = 11, 15%). Dug-out material was mostly used for agricultural (<italic>n</italic> = 11, 15%), pruning material for woodchips purpose (<italic>n</italic> = 12, 16%), when its further utilization was specified. A great amount was disposed without specification, which could either mean that the material was utilized or disposed on the dump. When pruning material was left at site, it was often reinstalled into the bed or bank as structural element for example.</p>", "<p id=\"Par24\">Conservation interests were clarified by the majority of the participants (89%) in the context of clarification of the occurrence of strongly/especially protected species (Fig. ##FIG##6##7##). Three participants selected other methods, as it is once the case for the authority being an environmental agency itself, once a biological association which water management is aligned regarding two species of the Habitats Directive (<italic>C. mercuriale, U. crassus</italic>) and once another, not specified clarification. Five participants did not answer the question, which could either indicate that they do not clarify occurrences, or they did not want to answer. Four out of five participants that did not select any answer for clarification, stated additionally to not examine the waterbody ecologically before water management, with regard to flora and fauna.</p>", "<p id=\"Par25\">In the majority, information were retrieved from notifications of the lower nature conservation authority (Fig. ##FIG##7##8##, 63%). Less relevance did have commissioned ecological opinions. The remaining four clarification possibilities have been not provided by default in the questionnaire. However, fourteen participants stated to clarify occurrences by species and biotope mapping which is often part of monitoring programs of governing authorities.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par26\">The present study reveals information about the current water management of small lotic waterbodies. Within the range of the threatened, on small lotic waterbody dependent damselfly <italic>C. mercuriale</italic>, high diversity in taking actions is present. This indicates that water management is sometimes performed with regard to nature conservation interests, but still not throughout the whole studied area. Water management practices are a threat to biodiversity and especially species listed under the Habitats Directive when performed too intensive concerning frequency, equipment, seasonality and applied method which is however often the case according to the study’s results. However, water management is required to maintain the specific habitat conditions. Therefore, water management practices need to be set in context with nature conservation interests on the one hand and with water management interests on the other hand. Eventually it is challenging, but necessary, to address and reconcile both, water management and nature conservation interests to ensure biodiversity and to meet the goals of the Habitats Directive.</p>", "<title>Nature Conservations Interests</title>", "<p id=\"Par27\">The results indicated that nature conservation is of minor interest in water management compared to retaining the hydrological function for example, yet this does not have to be mutually exclusive. Nevertheless, species are impacted by several components in water management, as the seasonality, equipment and frequency. Bączyk et al. (##REF##29426140##2018##) reviewed impacts of in-channel equipment on macroinvertebrates, fish and the general ecological status, with the majority of the reviewed studies indicating negative influences of dredging, macrophyte removal and channel regulation. The reviewing authors suggest to yield precedence to less invasive actions as weed cutting than intense dredging, for instance. In our study, dredging is not frequently performed in the majority of cases. The small number of participants that are practicing dredging more frequently once a year or even more should consider less intense practices, as weeding. Annually weeding and mowing of aquatic vegetation was the median frequency, meeting research outcome. For streams with more than one weed cutting per year, Baattrup-Pedersen et al. (##UREF##3##2018##) analyzed that the ecological status was moderate to bad. Species diversity and composition decline with the named frequent practices (Baattrup-Pedersen et al. ##UREF##2##2002##). According to van Strien et al. (##UREF##63##1991##), optimum species richness of ditch bank vegetation occurs with cleaning once every 2–3 years. Therefore, annually weeding and mowing of vegetation in bed should be the bottom line in frequency, when there is no less maintenance frequency possible according to the duly runoff.</p>", "<p id=\"Par28\">Technical inventions for equipment increased to match the need for increasing yield. With the motorization of to date existing manually applied mechanical machines, greater and faster machines became popular. This circumstance resulted in increasing negative impacts on species. Aldridge (##UREF##0##2000##) analyzed that 3–23% of a mussel population was found in the spoil after dredging, whereas weed boats did damage a small number, but did not remove any mussels. In our study, dredging is performed with a ditch cleaning bucket or shovel excavator in the majority of cases, yet not frequently. For perennial ditches, dredging with the wheel trencher is forbidden according to the German Federal Nature Conservation Act since 2009, if a significant damage is expected for the ecosystem and especially the fauna (Bundesregierung 2009/18.08.2021 [BNatSchG]). Our results reflect the legal landscape: the use of the wheel trencher is significantly correlated to no consideration of conservation species’ interests. If they would be considered, damage would be expected since small lotic waterbodies exhibit a variety of (rare) species. In the case of Natura 2000 sites with the EU habitat 3260, this also reflects a lack in legal implementation and management as most of these species are part of the habitats typical species and habitat deterioration is to prevent in designated sites according to Art. 6 (2) Habitats Directive. However even official monitoring schemes under the Habitats Directive have this shortcoming as typical animal species are mostly not monitored and missing the German agreed monitoring assessment schemes (Bundesamt für Naturschutz and Bund-Länder-Arbeitskreis FFH-Monitoring &amp; Berichtspflicht ##UREF##11##2017##).</p>", "<p id=\"Par29\">The mowing bucket is the mostly used equipment in water management of the bed in the present study, followed by manual equipment as shovel or scythe. Monahan and Caffrey (##UREF##38##1996##) analyzed that the mowing bucket does have a great impact on macroinvertebrate numbers, causing the greatest reduction compared to three other weeding techniques (in their study: harvester, chemical herbicide dichlobenil, Wilder boat). Conventional restricted hydraulic possibilities of swiveling and an often-obstructed sight leads to interference with bed and soil, causing erosion and similar ecological impacts as dredging. Therefore, the mowing bucket is only recommended when applied 10 cm over the bed, e.g. by using a spacer (DVWK ##UREF##18##1992##). Equipment with a spacer is used by approximately 15% of the participants. Prospectively, there are new inventions concerning the mowing bucket, as a fully pivotable, ecologically working hydraulic small mowing bucket, mowing only a narrow channel (Tschöpe ##UREF##60##2020##).</p>", "<p id=\"Par30\">Since large numbers and biomass of invertebrates are removed with the cut weed (Dawson et al. ##UREF##16##1991##), it is recommended to leave the material at site for a short time to reduce these impacts. Fauna can then escape into adjacent biotopes and the transportation of dry matter is facilitated (DVWK ##UREF##18##1992##). A small amount of the participants additionally states to have left the material at site for short before removing it, even when this process is more time-consuming and expensive since it includes two operations.</p>", "<p id=\"Par31\">The scythe has smaller impacts on physical habitat quality than the mowing boat, whose applied method differs itself between a less intense shallow method and a deep one (Rasmussen et al. ##UREF##45##2021##). In addition, mowing boats with scythe chains or triangular scythes interfere with soil, whereas T-front mowers above the bed spare fauna and bed (DVWK ##UREF##18##1992##).</p>", "<p id=\"Par32\">Regarding equipment used for the bank and shore, various studies exist concerning the impacts of mowing on different animals (e.g. Classen et al. ##UREF##14##1996##; Grendelmeier ##UREF##25##2011##; Hemmann et al. ##UREF##26##1987##; Humbert et al. ##UREF##28##2010##). van de Poel and Zehm (##UREF##62##2014##) reviewed tendencies and effects on animal species which often are injured or killed by mowing equipment. The reviewing authors state that rotary machines do have a greater impact than cutting machines, since rotary machines work in a greater working space with a higher velocity. Consequently, the greater impact of rotary machines on the fauna is opposite to their efficiency. In our study, rotary machines are used by the majority (e.g. hand-guided string trimmer 85%, flail mower 61%). Analyzed for roadside verges, the flail mulcher has a great negative impact on arthropods, with the highest loss of 87% for Lepidoptera (Steidle et al. ##UREF##54##2022##). From an efficiency perspective, the flail mulcher can remove smaller groves, directly mulches the cut grass and leaves it at site, saving the procedure of transportation. However, the ecological impact is not neglectable as well as the availability of excess nutrients which fasten up regrowth. Less intense mowing techniques than rotary machines are yet used by several participants. Those include the hand-guided bar mower (48% of the participants), bar mower (44%) and scythe (32%). The mowing bucket (approx. 59%) works with the bar mower technique as well but can affect the soil as it is discussed before.</p>", "<p id=\"Par33\">To our knowledge, research studies advise to refrain water management practices in the water bed in spring, with regard to both flora and fauna (e.g. Kaenel et al. ##UREF##31##1998##; Westlake and Dawson ##UREF##68##1988##). In the present study, weeding and dredging practices are performed by the participants’ minority in spring, following the research recommendations. Weeding and dredging in spring and (early) summer affect fish, breeding birds and mussels (Aldridge ##UREF##0##2000##). The Roach <italic>Rutilus rutilus</italic> is spawning in spring and early summer for example, with eggs on vegetation close to the surface, leading to the threat by water management of falling water levels (Mills ##UREF##36##1981##). Disturbing water management does have a negative impact on amphibian spawn and larvae in spring and early summer, when they are present (Leiders and Röske ##UREF##33##1996##; Twisk et al. ##UREF##61##2000##). Concerning vegetation diversity, weeding in autumn leaves diaspores of annual vegetation, whereas a great amount of competitive perennial vegetation is removed (Garniel ##UREF##24##2012##). Furthermore, amphibians do hibernate in soil or under moss in winter (Holenweg and Reyer ##REF##28308742##2000##), so that water management in bed represents a threat in winter (Leiders and Röske ##UREF##33##1996##). However, dredging is still performed by approximately 15% in winter, weeding by around 11% respectively. The majority does perform weeding, dredging and mowing in summer and autumn, which mostly avoids reproduction, spawning and hibernation times. Pruning is performed by the distinct majority in winter, which matches the legally given times of pruning outside forests (exceptional is maintenance pruning) between 1st of September and 28th of February in Germany (Bundesregierung 2009/18.08.2021 [BNatSchG]). There are similar effects of bank and meadow mowing (Leiders and Röske ##UREF##33##1996##). Meadow floral species can be mown twice a year, whereas tall herbaceous vegetation and reed should be mown only once in autumn (Leiders and Röske ##UREF##33##1996##). For <italic>C. mercuriale</italic>, observations by Röske (##UREF##50##1995##) even indicate that already regrowing bank areas are more preferred than uncut ones as well as recently mown more or less bare bank areas. However, working techniques do mostly allow only one operation, both in bed and shore/bank actions, as it is more cost-efficient and requires less staff.</p>", "<p id=\"Par34\">Emphases of weeding and mowing of bank/buffer strip in summer and autumn indicate that the majority of the water management authorities is already avoiding seasonal conservation conflicts during spring and winter. Research tends to result in preferring late summer and autumn for water management actions, especially for waterbed actions. Our study indicates that authorities might prefer autumn as water management season when waterbodies are ecologically examined beforehand. However, there are a few participants practicing weeding in spring and winter, disturbing fauna during these seasons.</p>", "<title>Water Management Interests</title>", "<p id=\"Par35\">Besides nature conservation interests, water management interests must be addressed as well to extend the point of view when reconciling both interests. Increasing aquatic vegetation growth can cause failure of the waterbody’s drainage function (Aldridge ##UREF##0##2000##), which is reflected by the participants’ answers: The highest and most rated reason for water management was the preservation of the water bed as well as the protection of water runoff. Traditional reasons for water management in agricultural land, such as the mitigation of floods (Bączyk et al. ##REF##29426140##2018##), were highly relevant for 44% of the participants. The results indicate that nature conservation interests as legal site protection indeed hold a minor part for the reasons of water management, whereas water management interests as mitigation of flood are of higher relevance. However, the majority of the water management authorities might consider some sort of ecological significance since they distinguished between frequently/far-from-nature and rarely/close-to-nature managed waterbodies. Even when management actions can differ due to site-specific, hydrological properties, general tendencies demonstrated that there is a great difference in frequencies when mowing of water vegetation and weeding are performed. Cleaning of bed as dredging is not frequently performed, yet it sometimes has to be carried out when silt accumulation takes place.</p>", "<p id=\"Par36\">Challenging the failure of the waterbody’s drainage function due to aquatic vegetation, late summer is suggested due to a decelerated regrowth (Baattrup-Pedersen et al. ##UREF##3##2018##). Westlake and Dawson (##UREF##68##1988##) even analyzed that autumn is the preferable season for weeding, which reduces plant biomass in contrast to weeding in spring, keeping water levels low, preventing flooding and avoiding late summer cuts. According to our results, weeding is already performed mostly in summer and autumn.</p>", "<p id=\"Par37\">Regarding further challenges in water management, a participant stated (authors’ translation): “The use (in the worst-case disposal, in the best-case utilization) of the landscape management material is one of the greatest challenges.” This is demonstrated by our study as well. Accruing material in water management is mostly left at site or just disposed without utilization. Pruning material is used by 16% of the participants for thermic utilization. A high amount of the mowing and weeding material is left at site, leading to the reflow of nutrients of rotting vegetation into the waterbody, promoting vegetation growth as nutrient-rich fertilizer (Moeller and Zehnsdorf ##UREF##37##2017##). In addition, left at site mowing/weeding material can float, drift and cause problems in the runoff at sites further downstream as well as causing bleak areas due to inhibition of vegetation growth (1992). As a result of eutrophication induced by left at site material, changes in bank vegetation composition are expected to nutrient indicator plants as <italic>Urtica dioica</italic> (DVWK ##UREF##18##1992##). The flail mower combines cutting und mulching, so that the mowing material is left at the site.</p>", "<p id=\"Par38\">Accruing material in water management has a great potential to be used, even when the current numbers did not reflect the possibilities. Legal regulations might be complicated to understand, so that further consideration of utilization is time-consuming. In addition, transportation and disposal are expensive in regard to other water management practices. It is simple to save costs by letting the material at site. However, vegetation growth is then promoted, leading to more frequent water management – so it is questionable, if this saves costs after all.</p>", "<title>Reconciliation of Both Interests</title>", "<p id=\"Par39\">Communication is crucial to reconcile water management and conservation interests. To address ecosystem services and the loss of biodiversity (Young et al. ##UREF##74##2014##), knowledge exchange is essential for effective environmental management (Fazey et al. ##UREF##22##2013##). However, there are deficiencies in communication. Exchange often takes place within or between expert associations (Riecken et al. ##UREF##49##2020##), so that scientific transfer happens “behind closed doors” and does not reach practitioners. The dealing with the wheel trencher reflects the poor communication between science, policy and practice: The research already pointed out strong negative ecological effects of the wheel trencher for several decades (Leiders and Röske ##UREF##33##1996##). However, it was prohibited nationwide not before 2009.</p>", "<p id=\"Par40\">Since primary scientific literature is infrequently accessed due to time consuming search and reading (Pullin et al. ##UREF##43##2004##), research outcome does not always reach practice. Poor communication leads to reliance on the current status, continuing with the practice that has always been performed (Pullin et al. ##UREF##43##2004##). On top negative changes due to more intensive practices or “better” modern equipment are often completely neglected or ignored. However, interest in communication and the provision of recommendations are present. In our study, several participants did ask for outcome and practical implementation advices (recommendation for action) as important need, even though there is a variety of existing water management concepts. That indicates poor knowledge exchange as well.</p>", "<p id=\"Par41\">The inclusion of all stakeholders and agreements made in water management are time-consuming, yet it is necessary to consider both, hydrological and ecological needs in management practices. Four out of five participants who did not select any answer for clarification of the occurrence of especially/strongly protected species at managed waterbodies stated to not examine the waterbody ecologically before water management, with regard to flora and fauna. Nevertheless, this is true for the minority, as we hypothesize that no clarification in any way leads to water management considering no or barely ecological purposes, even when approximately 97% of the participants state to consider species conservation when selecting and applying actions in water management. Keeping that in mind, a good ecological potential or status are however set goals in the EU Water Framework Directive, as well as a favorable conservation status of the Habitats Directive when the species live in an EU protected flowing water habitat (3260).</p>", "<p id=\"Par42\">Municipalities and the corresponding department responsible for water management do often perform several other tasks as road and green structure maintenance as well, struggling with time resources. The implementation of water associations according to river basins/catchments is one possible solution, replacing municipalities as water management authorities and centralize water management tasks. Water associations are already present in half of the federal states in Germany, having responsibility for water management. Specific tasks as water management facilitate a holistic approach including agreements with stakeholders (e.g. the lower nature conservation authority). The lower nature conservation authority communicates, in turn, with (monitoring) scientists and seeking exchange with scientific associations. It already has major significance with regard to the clarification of the occurrence of especially/strongly protected species at managed waterbodies, especially since it represents the link between policy and science.</p>", "<p id=\"Par43\">To reconcile both interests, the main challenge is to exchange knowledge, to map stakeholders and to work altogether on management plans. Water management practices can have positive effects on abundance and diversity of species, as it is the case for Odonata as the damselfly <italic>C. mercuriale</italic>. This can result in collaboration rather than working alone or in the worst-case reproaching and working against each other – especially since there is a great ecological potential in water management, and interests in reducing climate change effects also usually coincide.</p>", "<title>Consequences for the Habitats Directive</title>", "<p id=\"Par44\">Improved communication contributes to the Habitats Directive by implementing water management plans for conservation areas and beyond. Knowledge exchange about occurrence of species listed under the Habitats Directive as <italic>C. mercuriale</italic>, <italic>U. crassus</italic> or <italic>M. fossilis</italic> attracts attention and can promote change in the status quo of water management to an ecological point of view. Typical species of the protected habitat type 3260 under the Habitats Directive are threatened i.a due to frequent water management (Ssymank et al. ##UREF##53##2021##).</p>", "<p id=\"Par45\">The habitat type 3260 provides habitats for fish, invertebrates, birds, amphibians, reptiles and mammals, as well as food availability for birds, bats and other mammals, indicating the importance of considering consequences when performing water management. Some habitat requirements of protected species are in conflict with the general goal of wood growth, e.g. the development from habitat type 3260 to habitat type 91E0 (Alluvial forests with <italic>Alnus glutinosa</italic> and <italic>Fraxinus excelsior</italic> (Alno-Padion, Alnion incanae, Salicion albae)). Wood growth is a threat to species that are dependent on a partly open water surface as the protected damselfly <italic>C. mercuriale</italic>. Therefore, communication and knowledge exchange are crucial to reach a favorable conservation status for protected species.</p>", "<p id=\"Par46\">According to the state of nature report 2013–2018, legal site protection actions mostly concentrate on keeping the status quo, avoiding a decline rather than improving actively the conservation status (European Environment Agency ##UREF##20##2020##). Existing concepts, such as these in water management, should yet be reviewed according to their consideration of positive and negative effects on biodiversity. By exchanging knowledge of both sites, practice and research, adaptions in water management could be made, challenging improvements besides stabilization actions.</p>", "<p id=\"Par47\">By managing small lotic waterbodies in an ecological feasible way in the agricultural landscape, those habitats contribute to the European Biodiversity Strategy for 2030 where “at least 10% of agricultural area is under high-diversity landscape features” (European Commission, Directorate-General for Environment ##UREF##19##2021##). In addition, water management considering species listed under the Habitats Directive contributes to the key commitment of the EU Biodiversity Strategy that “at least 30% of those not already in favorable conservation status reach that category or show a positive trend” by the year 2030 (European Commission, Directorate-General for Environment ##UREF##19##2021##). Improved communication, collaboration and consideration of conservation key goals can result in a higher relevance of conservation interests than it is the case for the current status of water management.</p>" ]

[ "<title>Conclusions and Limitations</title>", "<p id=\"Par48\">The present study reveals the current status of water management and knowledge about several aspects of water management is gained which has not yet been available to this extend. These are necessary to improve water management with regard to nature conservation of small lotic waterbodies. However, this research has some limitations that should be considered. First, the application area is limited to Germany. In addition, the detection of responsible authorities turned out to be challenging, so that there is a small possibility that not all the authorities were contacted. During the survey, there were a few participants who answered that they only practice close-to-nature methods, so there might be smaller deviations.</p>", "<p id=\"Par49\">In conclusion, the present study demonstrates that challenges in water management mainly result in the balancing act between water management interests (i.e. especially the preservation of the water bed/protection of water runoff) and conservation interests. It demonstrates that the implementation of available knowledge in practice is still a challenge, even when ecological performance due to the goal of a good ecological potential/status according to the Water Framework Directive has given increasing priority (Bączyk et al. ##REF##29426140##2018##; European Parliament and European Council ##UREF##21##2000## [EU Water Framework Directive]). However, small lotic waterbodies need special attention due to their function as biodiversity hotspots of vast amount.</p>", "<p id=\"Par50\">There are improvements that can easily be adapted, as it is the case for communication, seasonality, choice of equipment and frequency, which exhibit a multiplicity of studies. However, there are still challenging factors in water management as the handling with accruing material, which need further notice. Yet, water management, performed in close communion with nature, can contribute to nature conservation, especially in the context of the conservation status of protected species under the Habitats Directive.</p>" ]

[ "<p id=\"Par1\">Small lotic waterbodies are abundant and species rich habitats, offering refuges and microhabitats to protected species of the European Union Habitats Directive. Highly impacted by water management actions, it is essential to reveal the current status and challenges of water management. The present study aims to identify relevant issues by conducting a survey concerning water management authorities. Authorities were selected according to their involvement in the management of small lotic waterbodies within the actual range of a threatened species, <italic>Coenagrion mercuriale</italic> (Odonata), which is highly dependent on water management actions and protected by the Habitats Directive. The survey involved three sets of questionnaires, (1) socio-demographic (personal) questions (2) specific questions about water management and (3) questions on the biological background. Out of 181 selected authorities, 75 participated in the survey. The results showed that though nature conservation interests are partially considered, they represented a minor factor in water management decision-making. In addition, knowledge exchange is insufficient between involved stakeholders from policy, management practice and science, which was especially reflected in the case of equipment use and accruing material. The reconciliation of both, water management and nature conservation interests, can contribute to enhance the conservation status of key protected species of small lotic waterbodies under the Habitats Directive.</p>", "<title>Keywords</title>" ]

[ "<title>Supplementary Information</title>", "<p>\n\n</p>" ]

[ "<title>Supplementary information</title>", "<p>The online version contains supplementary material available at 10.1007/s00267-023-01904-y.</p>", "<title>Acknowledgements</title>", "<p>We thank the authority conducting the pretest. We are grateful to Leila Maria Kehl, Louisa Rothmeier and Benedikt Taiber for their reviews and suggestions. We thank the water management authorities participating in our study and spending their time. Many thanks to two anonymous reviewers, whose comments have greatly improved this article.</p>", "<title>Author Contributions</title>", "<p>II wrote the main manuscript text and prepared the figures. All authors reviewed the manuscript.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>", "<title>Compliance with Ethical Standards</title>", "<title>Conflict of Interest</title>", "<p id=\"Par51\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Water management authorities in Germany according to the territories of the federal states. In the federal state marked as green, the territory is divided into local water associations. In the northern federal state Schleswig-Holstein, water associations are usually responsible, occasionally municipalities and cities. For federal states marked as blue, the territory is not divided into water associations. There, governing authorities are responsible, yet they can devote the management responsibility to associations or companies</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Responses of participants (<italic>N</italic> = 75) concerning reasons for water management and their relevance. Greenish colors indicate higher and greyish colors lower values, i.e. the more greenish the more participants selected the reason with a specific relevance</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Frequency classification is given with a six-point scale (never, every &lt;3 years, every 2–3 years, 1x/year, 2x/year, &gt;2x/year). The height of the bars indicates the count, the dashed lines the medians and the arrow the difference between those medians of frequently/far-from-nature managed waterbodies and rarely/close-to-nature managed waterbodies. Yellow bars indicate frequently/far-from-nature managed waterbodies, blue bars indicate rarely/close-to-nature managed waterbodies. On the left-hand side, actions (highlighted in gray) taking place in the bed are present. On the right-hand side, actions (highlighted in gray) taking place at the bank are present</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Number of counts of the equipment used in water management by the participants. The question was multiple choice. For water management in bed, equipment was suggested from “mowing bucket” to “using a spacer”, followed by an additional free text field for additional equipment. Therefore, only small numbers are present for the additional equipment which numbers are not shown to receive a better readability. For water management at the shore/bank, equipment was suggested from “scythe” to “bar mower”, followed by an additional free text field for additional equipment which are not shown to receive a better readability</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>The count of numbers across four main actions in water management are plotted. The different colors indicate the four seasons, the ordinate the count of answers that specific actions are performed in the respective season</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>The counts for the destinations of four materials accruing due to water management are plotted. Participants’ answers were categorized into seven (mowing, weeding material) or six (dug-out, pruning material) categorizes, which are additionally highlighted by “left at site” (red), “disposal” (black) and “utilization” (green). Diagram (<bold>A</bold>) shows the destinations of the mowing material, (<bold>B</bold>) the destinations of the dug-out material, (<bold>C</bold>) the destinations of the weeding material and (<bold>D</bold>) the destinations of the pruning material</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><p>Clarification of the occurrence of strongly/especially protected species when water management is performed at the specific waterbody sites</p></caption></fig>", "<fig id=\"Fig8\"><label>Fig. 8</label><caption><p>Clarification of the occurrence of strongly/especially protected species, plotted by the count of answers of the participants regarding the type of clarification (<italic>n</italic> = 67, see Fig. 7 “yes”). The first two providers of information were by default, whereas the other four providers have been mentioned by the participants in the “additional free text field” of the question</p></caption></fig>" ]

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[ "<fn-group><fn><p><bold>Publisher’s note</bold> Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par13\">It is known that tendon disorders are linked to disturbances in tendon vasculature, which result in insufficiency in blood circulation (Jarvinen et al. ##REF##9211609##1997##). As a result of local tissue hypoxia and inadequate nutrition brought on by decreased blood circulation within the tendons, tendon degeneration is likely to occur (Ahmed et al. ##REF##9820283##1998##; Carr and Norris ##UREF##0##1989##; Stein et al. ##REF##10743995##2000##; Zantop et al. ##REF##12712360##2003##). In the medical field, acupuncture and acupressure are known to be effective in treating tendon disorders (e.g., Alim et al. ##REF##28668970##2018##; Kleinhenz et al. ##REF##10534595##1999##). The healing mechanisms of tendon disorders with these therapies included improved blood circulation of the tendons (Chen et al. ##REF##11352511##2001##; Greve et al. ##REF##22591506##2012##; Praxitelous et al. ##REF##28378372##2018##). In fact, our studies showed that blood volume and oxygen saturation of the human tendons increased after acupuncture and acupressure (Kubo et al. ##REF##20140448##2010##, ##REF##21618161##2011##, ##UREF##6##2020a##, ##REF##32351663##b##; Yasuda et al. ##UREF##7##2022##). In all of these studies, acupuncture and acupressure were directly applied to the tendons. In the medical field, however, these therapies are generally performed at a distance from the affected area, i.e., the remote acupoint (Haker and Lunderberg ##REF##2135016##1990##; Fink et al. ##REF##11886971##2002##).</p>", "<p id=\"Par14\">Many previous studies have shown that muscle and skin blood flow increased with acupuncture and acupressure of acupoints (Hsiu et al. ##REF##20479520##2010##; Li et al. ##REF##17243026##2007##; Litscher et al. ##REF##11845364##2002##; Sandberg et al. ##REF##12827364##2003##). To our knowledge, no studies animal or human studies have examined the effects of acupuncture and acupressure of remote acupoints on tendon blood circulation. Although the acupoints have not been fully elucidated, histochemical studies reported that acupoints were sites of dense concentrations of Aδ and C afferent sensory nerve fibers (Li et al. ##REF##15158172##2004##). To apply our findings in a medical setting, we need to investigate the effects of acupuncture and acupressure of the acupoints, i.e., at points distant from the tendons, on the blood circulation of the human tendons in vivo.</p>", "<p id=\"Par15\">From the results of animal experiments (Kagitani et al. ##UREF##2##2005##, ##REF##20494626##2010##), acupuncture of acupoints on the lower leg has been shown to cause activation of Aδ and C fibers in the dorsal root ganglion of the lumbar region. In human experiments, acupuncture and acupressure of acupoints have been shown to decrease heart rate and alter the autonomic nervous system (as assessed by heart rate variability) (Arai et al. ##REF##18955366##2011##; Haker et al. ##REF##10683506##2000##; Matsubara et al. ##REF##20953433##2011##; Nishijo et al. ##REF##9185676##1997##). Our previous studies demonstrated that blood circulation of the tendons in the treated and non-treated sides increased after acupuncture and acupressure of the Achilles tendon (Kubo et al. ##REF##21618161##2011##, ##UREF##6##2020a##, ##REF##32351663##b##). These results suggested that acupuncture and acupressure of tendons elicited a systemic response. In light of the above, acupuncture and acupressure of acupoints is also expected to produce a systemic reaction (i.e., an increase in tendon blood circulation in the treated and non-treated sides) through the sensory nerves distribution to the acupoints.</p>", "<p id=\"Par16\">The purpose of this study was to compare the effects of acupuncture and acupressure of acupoints on tendon blood circulation with those of both types of stimulation of tendons. We hypothesized that acupuncture and acupressure of acupoint would enhance blood circulation of the tendon on both the treated and non-treated sides due to a systemic response during the recovery period after stimulation, as is the case with stimulation of the tendon, because of the dense concentration of sensory nerves at the acupoint as described above.</p>" ]

[ "<title>Methods</title>", "<title>Participants</title>", "<p id=\"Par17\">The sample size was estimated according to our previous studies in which the increases in the blood volume of the Achilles tendon by acupuncture and acupressure were determined (0.63 ± 0.56 µmol·L⁻¹ in Kubo et al. ##REF##20140448##2010##, 0.65 ± 0.56 µmol·L⁻¹ in Kubo et al. ##REF##21618161##2011##, 0.87 ± 1.05 µmol·L⁻¹ in Kubo et al. ##UREF##6##2020a##). Based on an α level of 0.05 and a power (1 – ß) of 0.8, it was shown that at least eleven participants per group were necessary for the present study. Twenty-six healthy volunteers (23 males and 3 females; age: 27.8 ± 9.7 years, height: 170.9 ± 6.7 cm, body mass: 69.2 ± 14.0 kg, mean ± SD) participated in this study. Twelve and fourteen volunteers participated in the acupuncture and acupressure experiments (Fig. ##FIG##0##1##). Exclusion criteria included a history of injuries and surgery on the Achilles tendon and cardiovascular diseases related to blood circulation. The participants were fully informed of the procedures to be utilized and the purpose of this study. Written informed consent was obtained from all participants. This study was approved by the office of the Department of Sports Sciences, The University of Tokyo, and complied with their requirements for human experimentation, and was performed by the Declaration of Helsinki. One part of the data in our previous study (n = 13, tendon blood circulation during and after acupuncture of the tendon in Kubo et al. ##UREF##6##2020a##) diverted to the data in the present study (n = 12; tendon blood circulation during and after acupuncture of the tendon), because 12 of the 13 participants in our previous study (Kubo et al. ##UREF##6##2020a##) took part in the measurement of the changes in tendon blood circulation with acupuncture of the acupoint due to scheduling limitations.</p>", "<title>Acupuncture and acupressure</title>", "<p id=\"Par18\">The participants lay prone on a test bench to acclimate to the laboratory conditions for 15 min before the experiment. Initially, the participants lay in a prone position for a 20 min rest period (baseline). After that, a needle was inserted (acupuncture stimulation experiment) or acupressure was applied (acupressure stimulation experiment) to the right Achilles tendon or acupoint (BL57 Chengshan). BL57 was chosen as an acupoint and was located in the myotendinous junction of the triceps surae, which is continuous with the Achilles tendon (Zhang et al. ##REF##14698480##2004##). After the needle was removed or the acupressure was stopped, the participants remained relaxed in the same position for 40 min. Each participant received two treatments (stimulation of tendon and acupoint) on two separate days, with at least one week between sessions and no longer than two weeks separating the two sessions. The entire experimental protocol is described in Fig. ##FIG##0##1##. The order of the two experimental conditions was randomized for each participant.</p>", "<p id=\"Par19\"><italic>Acupuncture</italic> Acupuncture was performed by one of the authors (H.Y.), an experienced (more than 25 years) licensed acupuncturist (Fig. ##FIG##1##2##A). A stainless steel needle of 0.16 mm in diameter and 40 mm in length was inserted vertically into the skin at 40 mm proximal to the calcaneus (stimulation of the tendon experiment) or the acupoint (stimulation of the acupoint experiment). To locate the acupoint (BL57), ultrasonography (SSD-3500, Aloka, Tokyo, Japan) was used to identify the boundary between the medial and lateral gastrocnemius muscles and the myotendinous junction between the Achilles tendon and gastrocnemius muscle. After insertion of the needle to a targeted depth (4 mm for the tendon, 10 mm for the acupoint), it was left for 5 min without manipulation (Acu-1). Then, the tip of the needle was moved up and down from the targeted depth (up-and-down manipulation) at an approximately 1-mm amplitude and 2 Hz for 3 min (Acu-2). During Acu-2, the needle tip was moved at an approximately constant speed and frequency with the aid of a metronome, and the insertion depth was confirmed visually. After this technique, the needle was left for 2 min without manipulation (Acu-3).</p>", "<p id=\"Par20\"><italic>Acupressure</italic> Acupressure was applied by one of the authors (A.Y.) (Fig. ##FIG##1##2##B). In the present study, we used a modified wooden stick (Tubo, Lieb Corporation, Japan) with a force sensor to monitor the pressing force during acupressure (Yasuda et al. ##UREF##7##2022##). This stick was pressed perpendicularly to the skin at 40 mm proximal to the calcaneus (stimulation of the tendon experiment) or the acupoint (stimulation of the acupoint experiment). Acupressure was performed at a frequency of 1.5 Hz for 3 min with a pressing force of 50 N, as described in our previous study (Yasuda et al. ##UREF##7##2022##).</p>", "<title>Blood circulation of the Achilles tendon</title>", "<p id=\"Par21\">During the experimental period, the blood circulation (oxyhemoglobin; Oxy, deoxyhemoglobin; Deoxy, total hemoglobin; THb, oxygen saturation; StO₂) of the Achilles tendon was measured on both the treated and non-treated sides using a previously described procedure (Kubo et al. ##REF##21618161##2011##, ##UREF##6##2020a##, ##REF##32351663##b##). First, a probe (SF-DS, Omega Wave, Tokyo, Japan) was positioned at 20 mm proximal to the calcaneus to measure the blood circulation of the tendon using red laser lights (BOM-L1TRSF, Omega Wave, Tokyo, Japan). This instrument uses three red laser lights (635, 650, and 690 nm) and calculates the relative tissue levels of Oxy, Deoxy, and THb (corresponding to the blood volume) according to the Beer-Lambert law. Oxy, Deoxy, THb, and StO₂ at a specific depth (measurement depth of 3–5 mm) of the tissue could be measured by changing the location of the two detectors (Kashima ##UREF##4##2003##; Kubo et al. ##UREF##5##2008##).</p>", "<p id=\"Par22\">In the present study, the units of Oxy, Deoxy, and THb are expressed as µmol / l, although this does not represent the actual physical volume. StO₂ was calculated using the formula from Oxy and THb values: StO₂ (%) = 100 · Oxy · THb⁻¹. Our data were input into a personal computer at a sampling frequency of 10 Hz via an A/D transducer (Power Lab, AD Instruments, Australia). The mean values over a given duration (Acu-1, Acu-2, Acu-3, and every 10 min during the recovery period) were calculated using analytical software (Chart ver. 7.1, AD Instruments, Australia). Oxy, Deoxy, THb, and StO₂ data are presented as the increase from the resting level. The repeatability of measurement of tendon blood circulation (Oxy, Deoxy, THb, and StO₂) had been investigated in our previous studies (Kubo et al. ##UREF##5##2008##).</p>", "<title>Statistical analysis</title>", "<p id=\"Par23\">Values are reported as means ± SD. Two-way (site x time) analysis of variance (ANOVA) with repeated measures was used to detect significant differences in the measured variables from the resting level. One-way ANOVA was used to detect a significant difference in mean changes in THb during the recovery period among the four conditions (the treated and non-treated tendons due to the treatments of the tendon and acupoint). The F ratios for main effects and interactions were considered significant at <italic>p</italic> &lt; 0.05. Significant differences among means at <italic>p</italic> &lt; 0.05 were detected using the Tukey’s HSD <italic>post-hoc</italic> test. In ANOVA, Mauchly's sphericity test was performed to assess the homogeneity of variance. Greenhouse–Geisser correction was applied where the assumption of sphericity was violated. The effect size was calculated using partial eta-squared (<italic>pη</italic>²) for two-way ANOVA. Pearson product-moment correlations were computed to assess the associations among the measured variables. The level of significance was set at <italic>p</italic> &lt; 0.05.</p>" ]

[ "<title>Results</title>", "<p id=\"Par24\">The changes in the blood circulation of the treated and non-treated tendons due to acupuncture of the tendon are shown in Fig. ##FIG##2##3##A–D. For Oxy, THb, and StO₂, the effect of time was significant (<italic>p</italic> = 0.024 <italic>pη</italic>² = 0.299 for Oxy, <italic>p</italic> = 0.030 <italic>pη</italic>² = 0.294 for THb, <italic>p</italic> = 0.024 <italic>pη</italic>² = 0.264 for StO₂), although the effects of site (<italic>p</italic> = 0.377 <italic>pη</italic>² = 0.071 for Oxy, <italic>p</italic> = 0.514 <italic>pη</italic>² = 0.040 for THb, <italic>p</italic> = 0.433 pη² = 0.057 for StO₂) and the interaction between site and time (<italic>p</italic> = 0.081 <italic>pη</italic>² = 0.211 for Oxy, <italic>p</italic> = 0.144 <italic>pη</italic>² = 0.169 for THb, <italic>p</italic> = 0.160 <italic>pη</italic>² = 0.148 for StO₂) were not significant. The <italic>post-hoc</italic> analysis identified significant increases for Oxy and THb at 20, 30, and 40 min points during the recovery period, although that did not identify significant differences for StO₂ at any point. For Deoxy, the effects of site (<italic>p</italic> = 0.853 <italic>pη</italic>² = 0.003) and time (<italic>p</italic> = 0.377 <italic>pη</italic>² = 0.084) and the interaction between site and time (<italic>p</italic> = 0.851 <italic>pη</italic>² = 0.011) were not significant.</p>", "<p id=\"Par25\">The changes in the blood circulation of the treated and non-treated tendons due to acupuncture of the acupoint are shown in Fig. ##FIG##2##3##E–H. For Oxy, Deoxy, THb, and StO₂, the effects of site (<italic>p</italic> = 0.949 <italic>pη</italic>² = 0.000 for Oxy, <italic>p</italic> = 0.739 <italic>pη</italic>² = 0.010 for Deoxy, <italic>p</italic> = 0.848 <italic>pη</italic>² = 0.004 for THb, <italic>p</italic> = 0.931 <italic>pη</italic>² = 0.001 for StO₂) and the interaction between site and time (<italic>p</italic> = 0.757 <italic>pη</italic>² = 0.021 for Oxy, <italic>p</italic> = 0.702 <italic>pη</italic>² = 0.027 for Deoxy, <italic>p</italic> = 0.791 <italic>pη</italic>² = 0.015 for THb, <italic>p</italic> = 0.811 <italic>pη</italic>² = 0.017 for StO₂) were not significant. The effect of time for Oxy (<italic>p</italic> = 0.052 <italic>pη</italic>² = 0.253), THb (<italic>p</italic> = 0.063 <italic>pη</italic>² = 0.242), and StO₂ (<italic>p</italic> = 0.109 <italic>pη</italic>² = 0.195) tended to be significant, although that for Deoxy was not (<italic>p</italic> = 0.691 <italic>pη</italic>² = 0.019).</p>", "<p id=\"Par26\">No significant difference in the changes in THb during the recovery period after acupuncture of the tendon and acupoint for the treated and non-treated tendons was found among the four conditions (<italic>p</italic> = 0.492 <italic>pη</italic>² = 0.069; Fig. ##FIG##3##4##). The changes in THb on the treated tendons during the latter half of the recovery period (21–40 min) were not correlated with the changes in THb on the non-treated tendons after acupuncture of the tendon (<italic>r</italic> = 0.459, <italic>p</italic> = 0.133) and acupoint (<italic>r</italic> = 0.382, <italic>p</italic> = 0.221) (Fig. ##FIG##4##5##).</p>", "<p id=\"Par27\">The changes in the blood circulation of the treated and non-treated tendons due to acupressure of the tendon are shown in Fig. ##FIG##5##6##A–D. For Oxy, Deoxy, and THb, the effects of site (<italic>p</italic> = 0.002 <italic>pη</italic>² = 0.538 for Oxy, <italic>p</italic> = 0.030 <italic>pη</italic>² = 0.313 for Deoxy, <italic>p</italic> = 0.001 <italic>pη</italic>² = 0.574 for THb) and time (<italic>p</italic> = 0.002 <italic>pη</italic>² = 0.384 for Oxy, <italic>p</italic> = 0.002 <italic>pη</italic>² = 0.389 for Deoxy, <italic>p</italic> &lt; 0.001 <italic>pη</italic>² = 0.437 for THb) and the interaction between site and time (<italic>p</italic> &lt; 0.001 <italic>pη</italic>² = 0.454 for Oxy, <italic>p</italic> = 0.014 <italic>pη</italic>² = 0.318 for Deoxy, <italic>p</italic> &lt; 0.001 <italic>pη</italic>² = 0.490 for THb) were significant. Regarding the treated tendon due to acupressure of the tendon, the <italic>post-hoc</italic> analysis identified significant increases for Oxy, Deoxy, and THb at all time points during the recovery period (except for Deoxy at 10 min). For StO₂, the effect of site (<italic>p</italic> = 0.525 <italic>pη</italic>² = 0.032) and the interaction between site and time (<italic>p</italic> = 0.120 <italic>pη</italic>² = 0.161) were not significant. Although the effect of time for StO₂ was significant (<italic>p</italic> = 0.031 <italic>pη</italic>² = 0.229), the <italic>post-hoc</italic> analysis did not identify significant differences at any point.</p>", "<p id=\"Par28\">The changes in the blood circulation of the treated and non-treated tendons due to acupressure of the acupoint are shown in Fig. ##FIG##5##6##E–H. For Oxy, Deoxy, THb, and StO₂, the effects of site (<italic>p</italic> = 0.233 <italic>pη</italic>² = 0.107 for Oxy, <italic>p</italic> = 0.799 <italic>pη</italic>² = 0.005 for Deoxy, <italic>p</italic> = 0.280 <italic>pη</italic>² = 0.089 for THb, <italic>p</italic> = 0.204 <italic>pη</italic>² = 0.121 for StO₂) and time (<italic>p</italic> = 0.273 <italic>pη</italic>² = 0.095 for Oxy, <italic>p</italic> = 0.620 <italic>pη</italic>² = 0.028 for Deoxy, <italic>p</italic> = 0.260 <italic>pη</italic>² = 0.099 for THb, <italic>p</italic> = 0.458 <italic>pη</italic>² = 0.054 for StO₂) and the interaction between site and time (<italic>p</italic> = 0.154 <italic>pη</italic>² = 0.140 for Oxy, <italic>p</italic> = 0.854 <italic>pη</italic>² = 0.007 for Deoxy, <italic>p</italic> = 0.175 <italic>pη</italic>² = 0.130 for THb, <italic>p</italic> = 0.235 <italic>pη</italic>² = 0.107 for StO₂) were not significant.</p>", "<p id=\"Par29\">The change in THb during the recovery period after acupressure of the tendon for the treated tendon was significantly greater than that of the tendon (<italic>p</italic> &lt; 0.001) and acupoint (<italic>p</italic> &lt; 0.001) for the non-treated tendon and that of the acupoint for the treated tendon (<italic>p</italic> = 0.005) (Fig. ##FIG##6##7##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par30\">Consistent with our previous studies (Kubo et al. ##REF##20140448##2010##, ##REF##21618161##2011##, ##UREF##6##2020a##, ##REF##32351663##b##), acupuncture stimulation of the tendon showed a rapid change in blood circulation on the treated tendon during acupuncture with up-and-down manipulation (Acu-2), with no change on the contralateral side (non-treated tendon). These changes during acupuncture with up-and-down manipulation are thought to be due to the release of neurotransmitters (e.g., substance P), resulting in axon reflex (Kashiba and Ueda ##UREF##3##1991##; Sato et al. ##REF##10739894##2000##). During the recovery period after removal of the needle, tendon blood volume significantly increased on both the treated and non-treated sides (Fig. ##FIG##2##3##C). Unfortunately, no significant correlation was found between tendon blood volume on the treated and non-treated sides (Fig. ##FIG##4##5##), although several of our previous studies found significant correlations between the two (Kubo et al. ##REF##21618161##2011##, ##REF##32351663##2020b##). However, regarding acupuncture of the tendon, the increase in tendon blood volume of the treated tendon was significantly correlated with that of the non-treated one, if the outlier of one participant was excluded (<italic>r</italic> = 0.729, <italic>p</italic> = 0.011; Fig. ##FIG##4##5##A). Reasons for the discrepancies may include the number of participants (n = 17 in Kubo et al. ##REF##21618161##2011##, n = 21 in Kubo et al. ##REF##32351663##2020b##, n = 12 in the present study). In any case, the present results may be attributed to central effects via cholinergic vasodilator fibers (Inoue et al. ##UREF##1##2001##). On the other hand, both during and after acupuncture stimulation, Oxy increased, and Deoxy did not change (Fig. ##FIG##2##3##). These results are presumably due to increased blood inflow to the tendon via the axon reflex (primarily during acupuncture with up-and-down manipulation) and cholinergic vasodilator fibers (primarily during the recovery period). Thus, acupuncture of tendons altered blood circulation of the treated tendon by peripheral and central effects and the non-treated tendon by central effect.</p>", "<p id=\"Par31\">Acupuncture of the acupoint did not change tendon blood circulation during acupuncture with up-and-down manipulation, unlike acupuncture of the tendon. Our inference that the increased blood circulation in the Achilles tendon with a needle insertion to this tendon is due to the axon reflex (Kashiba and Ueda ##UREF##3##1991##; Sato et al. ##REF##10739894##2000##) is supported by the present finding that blood circulation in the Achilles tendon did not increase with a needle insertion to the acupoint. On the other hand, during the recovery period after the removal of the needle, blood volume tended to increase on both treated and non-treated tendons (effect of time <italic>p</italic> = 0.063; Fig. ##FIG##2##3##G). This result suggested that acupuncture of the acupoint acted to enhance blood inflow to tendons by cholinergic vasodilator fibers through the central nervous system (Inoue et al. ##UREF##1##2001##). However, the increase in tendon blood volume due to acupuncture of the acupoint did not show a significant correlation between the treated and non-treated sides as in the case of acupuncture of the tendon in the latter half of the recovery period (Fig. ##FIG##4##5##). Therefore, there may be a greater abundance of sensory nerves (related to cholinergic vasodilation) in the Achilles tendon than in the acupoint (Chengshan, BL57). Regardless, further studies using isolated animal tendons are needed to clarify this point.</p>", "<p id=\"Par32\">We recently reported that acupressure of the tendon increased blood volume on both the treated and the non-treated tendons (Kubo et al. ##UREF##6##2020a##). In the present study, however, no change in blood volume on the non-treated tendon was observed. In this previous study (Kubo et al ##UREF##6##2020a##), no significant correlation was found between the increase in blood volume on the treated and non-treated tendons as in the case of acupuncture of tendons (data not shown in Kubo et al. ##UREF##6##2020a##). Furthermore, in Yasuda et al. (##UREF##7##2022##), we obtained a similar result in which blood volume on the non-treated tendon did not change when acupressure was applied to the Achilles tendon (data not shown in Yasuda et al. ##UREF##7##2022##). Although the reasons for these discrepancies in results are unknown, the possible reason is the method of acupressure, i.e., 5-mm amplitude and 1.5 Hz in Kubo et al. (##UREF##6##2020a##) and 50 N and 1.5 Hz in the present study. In any case, it can be said that, unlike acupuncture, acupressure in this study does not produce centrally mediated changes in tendon blood circulation. Regarding the difference in hemodynamic changes caused by both types of stimulation, it is speculated that the nociceptive stimulation of tissues by acupuncture causes peripheral vasodilatation through the autonomic nervous system at the spinal level by ascending Aδ and C fibers (Chae et al. ##REF##23395475##2013##). Furthermore, unlike acupuncture, acupressure of the tendon increased Deoxy on the treated side, resulting in no significant increase in StO₂. Therefore, it is likely that acupressure of the tendon alters tendon blood circulation by enhancing the metabolism of the treated tendon, which is due to a local rather than a systemic response.</p>", "<p id=\"Par33\">Acupressure of the acupoint did not produce changes in blood circulation on either the treated or non-treated tendons, although acupuncture of the acupoint tended to change tendon blood circulation. These results indicated that the sensory nerves present in acupoints could be stimulated by acupuncture but not by acupressure. In this regard, it has been pointed out that the excitation by nociceptive stimulation with acupuncture may ascend Aδ and C fibers and cause a vasodilating effect via the autonomic nervous system at the level of the spinal cord (Pomeranz and Chui ##REF##187888##1976##; Pomeranz and Warma ##REF##3401731##1988##). Thus, the microscopic tissue damage caused by acupuncture may be related to differences between acupuncture and acupressure in their effects on tendon blood circulation.</p>", "<p id=\"Par34\">Based on the results of this study, in acupuncture, when there is pain in the affected area immediately after the injury, therapeutic effects can be expected by applying the treatment to acupoints that are distant from the affected area. Acupuncture treatment on Chengshan (BL57), the acupoint employed in the present study, has actually been shown to be effective in the treatment of Achilles tendon disorders (Zhang et al. ##REF##29231427##2017##). In addition, experiments with animals reported that acupuncture with a low voltage electrical current at BL57 increased the concentration of collagen and the collagen fibril diameters in rat Achilles tendons, indicating the strengthening of the tendons (Almeida et al. ##REF##22891942##2012##, ##REF##25138672##2015##). Unfortunately, it is inferred that acupressure of acupoints is not effective in curing tendon disorders. However, acupressure may be useful as maintenance to prevent injury by increasing the metabolism of the tendon.</p>", "<p id=\"Par35\">In the present study, we must draw attention to the limitations associated with the methodology followed. Firstly, the locations of acupoints are defined (by WHO) by the bone, muscle, blood vessels, etc. as indicators, but the locations as acupoints in individuals may differ from the difference of these anatomical landmarks. If so, differences in the location of acupoints in different individuals may affect the results of acupuncture and acupressure of acupoints. In this study, we used ultrasonography to define the stimulation location while confirming the boundary between the medial gastrocnemius muscle and lateral gastrocnemius muscle and the muscle–tendon junction of the gastrocnemius muscle with images. Secondly, changes in the blood circulation of the Achilles tendon were only measured 40 min after both acupuncture and acupressure. Further observation over a longer post-stimulation period is needed to examine the therapeutic effect on tendon disorders. Thirdly, all of the participants in this study were healthy and were not patients with tendon disorders. It cannot be ruled out that changes in tendon blood circulation in response to acupuncture or acupressure may differ between healthy participants and patients with tendon disorders. Future studies should be conducted on patients with tendon disorders to verify the therapeutic effects of acupuncture and acupressure treatment.</p>", "<p id=\"Par36\">In conclusion, the main results of the present study were that (1) acupuncture of tendon and acupoint acted centrally to enhance blood circulation of both the treated and non-treated tendons during the recovery period after stimulation, and (2) acupressure of tendon locally increased tendon blood circulation by enhancing the metabolism of the treated tendon only, whereas acupressure of acupoint did not alter tendon blood circulation.</p>" ]

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[ "<p>Communicated by Olivier Seynnes.</p>", "<title>Purpose</title>", "<p id=\"Par1\">The purpose of this study was to compare the effects of acupuncture and acupressure of acupoints on tendon blood circulation with those of both types of stimulation of tendon itself.</p>", "<title>Methods</title>", "<p id=\"Par2\">Before, during (except for acupressure), and after acupuncture and acupressure of the tendon and acupoint, blood circulation of the Achilles tendon was measured using red laser lights.</p>", "<title>Results</title>", "<p id=\"Par3\">The blood volume of the treated and non-treated tendons increased after acupuncture of the tendon (effect of time p = 0.030), whereas that tended to increase after acupuncture of the acupoint (effect of time p = 0.063). In addition, no significant difference in the increases in blood volume was found among the four conditions, i.e., after acupuncture stimulation of the tendon and acupoint for the treated and non-treated tendons (p = 0.492). The blood volume of the treated tendon significantly increased after acupressure of the tendon (effect of time p &lt; 0.001), but not of the acupoint (effect of time p = 0.260), whereas that of the non-treated tendon did not change after acupressure of both the tendon and acupoint.</p>", "<title>Conclusion</title>", "<p id=\"Par4\">These results suggested that acupuncture of the tendon and acupoint acted centrally to enhance blood circulation of both the treated and non-treated tendons during the recovery period, whereas acupressure of the tendon locally increased blood circulation of the treated tendon only, but not the non-treated tendon and both the treated and non-treated tendons after acupressure of acupoint.</p>", "<title>Keywords</title>", "<p>Open access funding provided by The University of Tokyo.</p>" ]

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[ "<title>Acknowledgements</title>", "<p>This study was supported by a Grant-in-Aid for Scientific Research (B) (17H02149 and 20H04070 to K. Kubo) from the Japan Society for the Promotion of Science. The authors thank Mr. Iizuka Y. for his technical assistance with the measurements and Dr. Takeshita D. (The University of Tokyo) for help with statistics.</p>", "<title>Author contributions</title>", "<p>KK: conception of this study, drafting the manuscript. Ayaka Yasuda; acquisition of data, analysis data. HY: acquisition of data. MT: drafting the manuscript. NT: conception of this study, drafting the manuscript.</p>", "<title>Funding</title>", "<p>Open access funding provided by The University of Tokyo.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par37\">I have no conflict of interest with this work.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Experimental protocol (see <xref rid=\"Sec2\" ref-type=\"sec\">Methods</xref> for a detailed description of the protocol)</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Views of acupuncture (<bold>A</bold>) and acupressure (<bold>B</bold>) stimulation experiments</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p><bold>A</bold>–<bold>D</bold> The changes in oxyhemoglobin (Oxy), deoxyhemoglobin (Deoxy), total hemoglobin (THb), and oxygen saturation (StO₂) of treated (open circle) and non-treated (closed circle) tendons during acupuncture of the tendon and recovery periods. <bold>E</bold>–<bold>H</bold> The changes in oxyhemoglobin (Oxy), deoxyhemoglobin (Deoxy), total hemoglobin (THb), and oxygen saturation (StO₂) of treated (open circle) and non-treated (closed circle) tendons during acupuncture of the acupoint and recovery periods. *Significantly different from the resting level (*p &lt; 0.05, **p &lt; 0.01, ***p &lt; 0.001)</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Comparison of mean ∆THb during the recovery period after acupuncture among the four conditions</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Relationships between mean ∆THb of treated and non-treated tendons during the latter half of the recovery period after acupuncture of the tendon (<bold>A</bold>) and acupoint (<bold>B</bold>)</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p><bold>A</bold>–<bold>D</bold> The changes in oxyhemoglobin (Oxy), deoxyhemoglobin (Deoxy), total hemoglobin (THb), and oxygen saturation (StO₂) of treated (open circle) and non-treated (closed circle) tendons before (rest) and after acupressure of the tendon (recovery). <bold>E</bold>–<bold>H</bold> The changes in oxyhemoglobin (Oxy), deoxyhemoglobin (Deoxy), total hemoglobin (THb), and oxygen saturation (StO₂) of treated (open circle) and non-treated (closed circle) tendons before (rest) and after acupressure of the acupoint (recovery). *Significantly different from the resting level (**p &lt; 0.01, ***p &lt; 0.001) ^#significantly different from the non-treated side (^#p &lt; 0.05, ^##p &lt; 0.01, ^###p &lt; 0.001)</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><p>Comparison of mean ∆THb during the recovery period after acupressure among the four conditions. *Significantly different among the conditions (**p &lt; 0.01, ***p &lt; 0.001)</p></caption></fig>" ]

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{ "acronym": [ "Acu", "ANOVA", "Deoxy", "Oxy", "pη2", "SD", "StO2", "THb" ], "definition": [ "Acupuncture", "Analysis of variance", "Deoxyhemoglobin", "Oxyhemoglobin", "Partial eta-squared", "Standard deviation", "Oxygen saturation", "Total hemoglobin" ] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Visuospatial neglect is a frequent consequence of unilateral, most commonly right hemispheric, brain damage (Becker and Karnath ##REF##17962601##2007##). It is characterised by visuospatial deficits, such as failing to attend, orient, or respond to stimuli on the contralesional side of space. Therefore, neglect patients “ignore” events or objects on their contralesional side. This spatial asymmetry appears to be associated with asymmetrical attentional representations of body and space as an expression of human brain lateralization (Heilmann et al. ##UREF##3##2003##; Karnath and Rorden ##REF##21756924##2012##). Importantly, these deficits cannot be attributed to sensory or motor impairments and are instead commonly explained by an allocation or shift of spatial attention resources towards the ipsilesional side (Bartolomeo and Chokron ##REF##11856560##2002##; Karnath ##REF##26004064##2015##).</p>", "<p id=\"Par3\">In the clinical setting, severe neglect patients are also typically described as showing a delayed reaction and a reduced state of alertness (Corbetta and Shulman ##REF##21692662##2011##). There is mounting evidence that spatial neglect is not just a disorder of spatial attention, but also associated with a more general non-spatial form of impaired sustained attention linked to a reduced state of arousal or alertness (Husain and Rorden ##REF##12511859##2003##). The concepts arousal and alertness both indicate a readiness to respond to stimulation (Posner and Petersen ##REF##2183676##1990##). Arousal is commonly seen as a general physiological and cognitive state of readiness, whereas alertness is typically seen as a more cognitive state of readiness (Brown and Bowman ##UREF##0##2002##). However, there is considerable overlap and interdependence between these concepts. For example, a lowered state of physiological readiness will generally be accompanied by a lower state of cognitive readiness. As a result, the concepts of arousal and alertness (and the related concepts of vigilance and sustained attention) have often been used interchangeably (Lindsley ##UREF##4##1988##; Oken et al. ##REF##16581292##2006##). Studies have shown that inducing a heightened state of arousal in neglect patients with a warning signal can ameliorate their ipsilesional spatio-attentional bias (e.g., Robertson et al. ##REF##7650103##1995##, ##REF##9744274##1998##). Moreover, research suggests that both spatial and sustained attention rely on overlapping brain areas (Corbetta and Shulman ##REF##21692662##2011##; Kanwisher and Wojciulik 2000). These findings suggest that spatial and sustained attention are closely associated, both behaviourally and neuroanatomically.</p>", "<p id=\"Par4\">This association has also been demonstrated in neurotypical participants. For example, after a 50-min vigilance task, more right-sided and less left-sided letters of a letter recognition task were reported in the decreased alertness session compared to an alert baseline before the task (Matthias et al. ##REF##19682470##2009##). This suggests that a reduction in alertness led to a rightward spatio-attentional bias, similar to that shown by neglect patients. Manly et al. (##REF##16154447##2005##) found similar effects using a landmark task when comparing shift workers in a sleep-deprived and well-rested state. In this study, participants were presented with a pre-bisected horizontal line and instructed to indicate which side is longer. When participants were well-rested, they made more errors when the line was bisected to the left, i.e., when the right side was longer. This suggests a leftward spatial bias, consistent with previous observations of the so-called “pseudoneglect” in neurotypical participants (Jewel and McCourt ##REF##10617294##2000##). However, when participants were sleep-deprived, they made less errors when the line was bisected to the left. In other words, they showed a reduction of their leftward spatial bias. Moreover, they now made more errors when the line was bisected to the right, i.e., when the left side was longer. This suggests that decreased alertness led to an underestimation of the left side of the line and an overestimation of the right side. In a second experiment, alert participants estimated evenly bisected lines as bisected to the left, but over the course of several blocks shifted their estimates rightwards. This illustrates the time-on-task effect and reflects the expected rightward shift in spatial attention with decreasing alertness. These observations have since been replicated repeatedly, using a wide variety of tasks in visual and auditory modalities (e.g., Bareham et al. ##REF##24867667##2014##; Benwell et al. ##REF##28887893##2018##; Benwell et al. ##REF##22270326##2013a##, ##REF##24076376##b##; Dodds et al. ##REF##18590365##2008##; Dufour et al. ##REF##17146643##2007##; Fimm et al. ##REF##16530231##2006##; Golob et al. ##REF##34342887##2021##; Jagannathan et al. ##REF##34815316##2022##; Matthias et al. ##REF##19682470##2009##; Newman et al. ##REF##25234646##2014##; Peers et al. ##REF##16522325##2006##; Pérez et al. ##REF##18789956##2009##; Xu et al. ##REF##38187733##2023##; see Chandrakumar et al. ##REF##31075552##2019##, for a review). Therefore, there is firm evidence for a connection between spatial attention and alertness.</p>", "<p id=\"Par5\">However, in neurotypical populations, the effect of alertness on spatial attention has mostly been examined in artificial settings with an emphasis on speeded reaction tasks (Chandrakumar et al. ##REF##31075552##2019##). To our knowledge, no one so far has attempted to find the effects of alertness on spatial attention with a real-life unspeeded bedside tool used to diagnose visuospatial neglect in clinical settings. There are several bedside tools classically used to measure spatio-attentional biases in clinical settings, such as cancellation tasks (e.g., Gauthier et al. ##UREF##1##1989##), copying tasks (e.g., Johannsen and Karnath ##REF##15202544##2004##), or line bisection tasks (e.g., Schenkenberg et al. ##REF##7189256##1980##). In line bisection tasks, a horizontally presented line on a sheet of paper should be centrally divided into two equal parts with a pen. When used as a diagnostic tool to assess abnormal spatial attention, the line bisection task has predominantly been used in clinical settings. However, a large body of research exists examining line bisection performance in neurotypical populations, including, among others, elderly populations (Learmonth and Papadatou-Pastou ##REF##33890188##2022##), children (Kaul et al. ##REF##36416485##2023##), or even to study cultural differences in line bisection behaviour (Marinelli et al. ##UREF##5##2019##). Consistent with the idea of pseudoneglect (Jewell and McCourt ##REF##10617294##2000##), neurotypical participants in left-to-right reading cultures typically bisect a line in the very middle or slightly to the left. Many neglect patients (60% in Ferber and Karnath ##REF##11778637##2001##), on the other hand, bisect the line considerably to the right of the true middle, which is typically attributed to neglect patients ignoring the most contralesional part of the line (e.g., Ishiai et al. ##REF##2597992##1989##; McIntosh et al. ##UREF##7##2005##, ##REF##28923304##2017##), or a compression of perception of contralesional space in neglect patients (e.g., Bisiach et al. ##REF##8673497##1996##).</p>", "<p id=\"Par6\">However, a problematic assumption underlying these models of line bisection is that all patients take into consideration the entire line and then provide a (biased) estimate of the middle. However, eye-tracking studies have shown that some patients fixate towards an arbitrary point to the right of the middle of the line and make exploratory eye movements on the line to the right of that point, but not to the left (e.g., Ishiai et al. ##REF##2597992##1989##, ##REF##7561964##1995##). Then, they place a mark at the leftmost area they could fixate. In other words, they do not genuinely try to “bisect” the line, but make a wild guess based on the right endpoint position (see McIntosh et al. ##UREF##7##2005##, for a more in-depth explanation of this account). To address this, McIntosh and colleagues provide a new approach to implement and analyse line bisection that is potentially more sensitive to a spatial bias by taking into account non-spatial influences on line bisection (McIntosh ##REF##28807326##2018##; McIntosh et al. ##UREF##7##2005##, ##REF##28923304##2017##). Importantly, their approach does not rely on the assumption that all patients can truly bisect the line. McIntosh et al. (##UREF##7##2005##) frame the ends of the line as “endpoints”, which receive “attentional weights”. In neglect patients, the right endpoint is weighted in an extreme manner compared to the left endpoint. They then estimate the middle of the line relative to this highly weighted endpoint rather than truly bisecting it. McIntosh and colleagues put forward two dependent measures based on endpoints: the endpoint weightings bias (EWB) is derived by subtracting the left endpoint weighting from the right endpoint weighting and reflects lateral spatial attention. A positive EWB reflects a bias to the right, while a negative EWB reflects a bias to the left. The endpoint weightings sum (EWS) is the sum of the endpoint weightings and is said to reflect general attentional resources or arousal. Higher EWS values reflect a higher level of arousal or attentional resources dedicated to the task, with optimal arousal levels yielding an EWS = 1. Therefore, this method of line bisection can capture both a specific spatial component as well as a more general component of attention. For a detailed description and derivation of the formalism, see McIntosh et al. (##UREF##7##2005##). It has been shown in patients that EWB can provide a measure of spatio-attentional biases that is highly sensitive to the presence of neglect, with the endpoint weightings bias correlating highly with performance on the cancellation and copying task in patients (McIntosh et al. ##REF##28923304##2017##).</p>", "<p id=\"Par7\">The first aim of our study is to assess whether a reduction in alertness is capable of eliciting a rightward bias in spatial attention in the endpoint weightings task, a task very similar to the traditional bedside task used to assess spatial biases in patients. We expect that decreasing participants’ alertness by administering a dull, 50-min vigilance task (see Matthias et al. ##REF##19682470##2009##) will lead to a rightward shift in spatial attention (indicated by increased EWB values) as well as a reduction in non-spatial attention (indicated by decreased EWS values).</p>", "<p id=\"Par8\">The second aim of our study is to assess whether or not a pre-existing spatial bias is a pre-requisite for the effect of alertness on spatial attention. Whereas there is a considerable body of work suggesting that there is a close link between alertness and spatial attention, with reductions in alertness reliably resulting in a rightward shift of spatial attention in neurotypical participants, other work suggests that a decrease in alertness may not always affect spatial attention. Specifically, several studies found an effect of alertness on spatial attention only when a rightward spatial bias was already pre-existing, such as in neglect patients (Bellgrove et al. 2013; Bonato et al. 2010; Russell et al. 2013). Furthermore, Benwell et al. (##REF##24076376##2013b##) suggest that there is a difference between neurotypical participants showing typical leftward pseudoneglect and those with an initial bias to the right: The former showed an expected rightward shift during a prolonged landmark task indicative of the time-on-task effect, while participants initially presenting with a rightward bias showed a ‘reversed’ time-on-task effect towards the left. Newman et al. (##REF##25234646##2014##), however, argue that those findings could reflect regression to the mean, as Benwell et al. (##REF##24076376##2013b##) grouping of participants was based on the initial extreme values, which were then also included in the analysis of time-on-task effect. Given these conflicting findings, our study additionally aims to explicitly assess whether the effect of a reduction of alertness on spatial attention depends on whether there is a pre-existing spatial bias or not. If the effect of alertness on spatial attention, that is, the effect of decreasing participant's alertness by administering a vigilance task on the endpoint weightings bias, depends on a pre-existing spatial bias, we expect that it would be modulated by cueing participants to one side of the line before performing the bisection.</p>" ]

[ "<title>Methods</title>", "<title>Participants</title>", "<p id=\"Par9\">See <ext-link ext-link-type=\"uri\" xlink:href=\"https://aspredicted.org/blind.php?x=2CN_5BF\">https://aspredicted.org/blind.php?x=2CN_5BF</ext-link> for our pre-registered data collection and analysis plan. We aimed for a medium-effect size for the main effect of the reduction in alertness on the endpoint weightings bias (EWB) and the endpoint weightings sum (EWS), which according to Schaefer and Schwarz (2019) is approximately an <italic>r</italic> = 0.3 (this corresponds roughly to <italic>d</italic> = 0.6) and above. Therefore, an initial power analysis with <italic>d</italic> = 0.6, <italic>β</italic> = 0.8 and <italic>α</italic> = 0.05 for a within-subjects t test using MorePower (Campbell and Thompson 2012) yielded an estimated sample size of 90. To ensure perfect counterbalancing of the cued and uncued line bisection conditions before and after the vigilance task, we aimed for a sample size of 92. As such, we had a power of 0.87 to detect an effect of a reduction of alertness on EWB and EWS of medium-effect size in a within-subject design (<italic>r</italic> = 0.31). For each excluded participant (due to, e.g., aborting the task), another one was recruited to ensure 92 participants. Because several experimenters tested in parallel, we unintentionally tested 98 participants. (<italic>M</italic>_age = 22.24; SD_age = 11.49; range: 18–36 years; 64 females, 34 males). Of these, 45 participants were recruited at the University of Tübingen and received 8 €/h as compensation. Fifty-three participants were recruited at Brunel University London and, if applicable, received course credits for participation. None of them reported suffering from any psychiatric or neurological illness, taking any medication that affects the central nervous system, or suffering from non-correctible visual deficits (e.g., astigmatism). All participants gave informed written consent. The study was approved by both the ethics committees of the University Clinic of Tuebingen (774/2019BO2) as well as Brunel University (18784-LR-Nov/2019-21016-1).</p>", "<title>Materials and procedure</title>", "<p id=\"Par10\">All participants were required to carry out the line bisection task according to McIntosh et al. (##UREF##7##2005##) with and without a spatial cue on a desktop computer or a laptop running Windows OS (high alertness condition). Line bisection was carried out using a computer mouse. Lines were either 8, 12, or 16 cm in length and 0.2 cm wide. They were either presented centrally (the 8 and 16 cm lines) or 2 cm to the left or right of centre (12 cm lines). From this task, we derived values for endpoint weightings bias (EWB) and endpoint weightings sum (EWS) as derived from McIntosh et al. (##UREF##7##2005##). The directional bisection error (DBE; the absolute distance of the bisection from the middle of the line in cm) is commonly used in the line bisection literature to assess spatial bias. Thus, to allow comparison with the previous line bisection literature, we also derived the DBE.</p>", "<p id=\"Par11\">In the uncued line bisection task, participants had to bisect 32 randomly presented lines, 8 of each type (see McIntosh ##UREF##7##2005##). In the cued line bisection task, we decided to use a different form of cueing than McIntosh et al. (##REF##28807326##2018##), as it can be argued that a letter printed closely to the line does not just induce attentional processes but may lead to a different perception of the line (Chieffi et al ##REF##22576681##2012##; Fischer ##REF##8043264##1994##; Porac et al. ##REF##16527384##2006##). Instead, we used a method similar to Harvey et al. (##REF##10617289##2000##): In this study, participants were biased towards one side when the experimenter pointed at one of the line’s ends, while no other items were presented apart from the line itself. In the current study, these spatial cues were made up of vertical red bars appearing briefly at the presentation of the line. This should only affect the spatial measure, but not the measure of general attention. In the cued version of the line bisection task, red vertical lines (2 cm) flashed up for a random time (between 300 and 500 ms) at the start of the presentation of the line on either the left or the right endpoint of the line. In the cued line bisection task, participants bisected 64 lines; 32 were cued on the right and 32 were cued on the left. In both line bisection tasks, participants were instructed to draw a vertical line through the horizontal line, as centrally and accurately as possible from top to bottom using a computer mouse, closely mimicking the paper and pencil line bisection typically used in clinical settings to evaluate spatio-attentional biases. Participants started each trial by clicking on a centred rectangular button saying “[Please click here]” at the top of the screen to ensure that participants could not use their previous bisection to inform the next one.</p>", "<p id=\"Par12\">Subsequently, alertness was manipulated using a 50-min vigilance task based on the task used by Matthias et al. (##REF##19682470##2009##): It consisted of a static horizontal red line and a smaller black line which randomly moved up and down, occassionally going above the red line. Whenever this happened (approximately one-to-three times a minute), participants had to quickly press the space button. If participants did not react quickly enough, they received a warning message that they reacted too slow. If this message came up three times in a row, they were required to contact the experimenter who explicitly reminded them to stay concentrated and respond as quickly as possible. This purposely dull task was used to decrease alertness, which was measured by the Stanford Sleepiness Scale before each line bisection condition (SSS) (Hoddes et al. ##REF##4719486##1973##), a Likert-type scale ranging from 1 (“Feeling active, vital, alert, or wide awake”) to 7 (“No longer fighting sleep, sleep onset soon; having dream-like thoughts”), as well as the difference in reaction times in the first and last 10 min of the vigilance task. This provided one subjective and one objective measure of alertness. For participants recruited at the University of Tübingen, a German translation of the Stanford Sleepiness Scale was used. After the vigilance task, participants carried out the uncued and cued line bisection tasks again (low alertness condition). The order of the cued and uncued line bisection tasks before and after the vigilance task was counterbalanced across participants. The overall duration of the experiment was approximately 75 min.</p>" ]

[ "<title>Analyses and results</title>", "<p id=\"Par13\">Analyses were pre-registered on AsPredicted <ext-link ext-link-type=\"uri\" xlink:href=\"https://aspredicted.org/blind.php?x=2CN_5BF\">https://aspredicted.org/blind.php?x=2CN_5BF</ext-link>. The data and analysis code underlying this study are openly available on OSF at <ext-link ext-link-type=\"uri\" xlink:href=\"https://doi.org/10.17605/OSF.IO/X9MKY\">https://doi.org/10.17605/OSF.IO/X9MKY</ext-link>.</p>", "<title>Participant exclusion and manipulation check</title>", "<p id=\"Par14\">We predicted that participants would be more tired after the vigilance task, which should be displayed in terms of greater SSS values. As described in our preregistration, we intended to exclude participants who showed no difference in either the Stanford Sleepiness Scale or in RT to the vigilance task before and after the vigilance task. Specifically, for RT, we originally planned to run an individual t test for each participant comparing reaction times in the first and last 10 min of the vigilance task. In hindsight, however, we realised this would have led to comparisons of roughly 10–20 data points per person, which would have resulted in severely underpowered and unreliable results. As the SSS is a scale containing only 7 values, we planned to accept an increase of 1 to indicate a decrease in vigilance, as implied by the wordings of the response possibilities in the SSS. However, due to a translation error that was only discovered shortly before data collection was already complete, the SSS data from most participants recruited at the University of Tuebingen could not be used. Specifically, the original text of level 2 of the SSS which states \"Functioning at a high level, but not at peak; able to concentrate” was incorrectly translated to state “Functioning at a high level, but not at peak; not able to concentrate” in German. As this phrasing may have confused some participants, we deviated from the previously planned data exclusion criteria (see asPredicted) and decided not to use the SSS values or RT in the vigilance task as an exclusion criterium. McIntosh et al. (##UREF##7##2005##, p.842, Eq. (3)), however, also provide a regression equation to examine the quality of the derived measures of endpoint weightings. It has been suggested that the derived <italic>r</italic>² can be used as an sensible exclusion criterion, whereby an <italic>R</italic>-square of below 0.7 can be deemed as an indicator for inconsistent participant behaviour (see Mitchell et al. ##REF##35940957##2022##). In our data set, one participant had an <italic>r</italic>² of below 0.7 in one of six conditions (in the left-cued condition post-vigilance task). Additionally, this participant was the only one to indicate the highest score on the SSS questionnaire (“No longer fighting sleep…”), therefore we excluded them. As such, 97 participants were used for the analyses. A groupwise analysis of SSS (from participants recruited at Brunel University London) and RT in the vigilance task (from all participants recruited) indicated that, overall, alertness decreased (see Matthias et al. ##REF##19682470##2009##): A paired-samples t test on the reaction times of the first and last 10 min of the vigilance task for the entire group suggests that reaction times were slower during the last 10 min of the vigilance task, suggesting decreased alertness, <italic>t</italic>(96) = − 4.57, <italic>p</italic> &lt; 0.001. The difference between SSS pre- and post-vigilance task was also significant, <italic>t</italic>(51) = − 10.374, <italic>p</italic> &lt; 0.001, with SSS scores overall higher after the vigilance task. This suggests that the vigilance task was overall effective in reducing alertness levels in our participants. We also performed our analyses using the Brunel sample only, applying the originally planned exclusion criteria as described in our preregistration. This did not fundamentally change the results and conclusions reported below.</p>", "<title>The effect of alertness reduction in the uncued line bisection task</title>", "<p id=\"Par15\">To assess the effect of alertness on spatial and non-spatial components of attention, the EWB, EWS, and DBE values of the uncued line bisection task before and after the vigilance task were compared via a separate paired-samples t test for each, with condition (pre-/post-vigilance task) as the independent variable and EWB, EWS, and DBE as dependent variables, respectively (see Fig. ##FIG##0##1##).</p>", "<p id=\"Par16\">There was no difference in EWB before (mean = 0.000, SD = 0.041) and after (mean = − 0.004, SD = 0.040) the vigilance task, <italic>t</italic>(96) = 0.81, <italic>p</italic> = 0.417, <italic>d</italic> = 0.09. There was a significant effect of the vigilance task on EWS, <italic>t</italic>(96) = 3.53, <italic>p</italic> &lt; 0.001, <italic>d</italic> = 0.34, which remained significant after correcting for multiple comparisons using Bonferroni correction for three tests. EWS before the vigilance task (mean = 1.031, SD = 0.066) was larger than after the vigilance task (mean = 1.007, SD = 0.075), suggesting lower levels of general attentional resources after the vigilance task than before, in line with the SSS and RT data. We additionally examined whether there was a difference in DBE before (mean = − 0.04, SD = 0.15) and after (mean = − 0.04, SD = 0.15) the vigilance task. A paired-samples t test showed that there was no significant difference, <italic>t</italic>(96) = − 0.10, <italic>p</italic> = 0.917, <italic>d</italic> = − 0.01 (see Fig. ##FIG##0##1##, right graph), suggesting that alertness did not affect DBE values.</p>", "<p id=\"Par17\">As described in our preregistration, if the effect of alertness on either EWB or EWS was significant, we planned to run an exploratory MANOVA including time (pre- or post-vigilance task) as an independent variable and EWB and EWS as dependent variables, to compare the effect of alertness on spatial and non-spatial components of attention. However, while there was a significant difference in the EWS values before and after the vigilance task, the assumptions for an MANOVA were not met. More specifically, a multivariate Shapiro–Wilk test was significant (<italic>W</italic> = 0.972, <italic>p</italic> = 0.001), suggesting that multivariate normality was not given. Moreover, the two dependent variables, EWB and EWS, were not significantly correlated. Yet, MANOVA requires low-to-moderate correlations between dependent variables (Maxwell ##UREF##6##2001##). Therefore, we decided against running a MANOVA.</p>", "<title>The effect of alertness reduction in the cued line bisection task</title>", "<p id=\"Par18\">We also examined the effect of alertness on spatial attention when participants were cued either to the right or the left side of the horizontal line. Repeated measures 2 (condition: pre- or post-vigilance task) × 2 (cue: left or right) ANOVAs were carried out to assess the effect of alertness and cueing side on EWB, EWS, and DBE values. EWB, EWS, and DBE were again dependent variables in separate tests. For EWB, both the main effect of condition, <italic>F</italic>(1,96) = 1.61, <italic>p</italic> = 0.208, <italic>η</italic>^{<italic>2</italic>} = 0.003 and the main effect of cue, <italic>F</italic>(1,96) = 0.55, <italic>p</italic> = 0.459, <italic>η</italic>^{<italic>2</italic>} = 0.001, as well as the interaction, <italic>F</italic>(1,96) = 1.48, <italic>p</italic> = 0.223, <italic>η</italic>^{<italic>2</italic>} = 0.002, were non-significant (see Fig. ##FIG##1##2##). This suggests neither the cue nor alertness had an effect on the spatio-attentional bias, and that the effect of alertness on spatio-attentional bias did not differ as a function of whether the line was cued on the left or right side. For EWS, the main effects of both condition, <italic>F</italic>(1,96) = 9.95, <italic>p</italic> = 0.002, <italic>η</italic>^{<italic>2</italic>} = 0.016 and cue, <italic>F</italic>(1,96) = 11.62, <italic>p</italic> &lt; 0.001, <italic>η</italic>^{<italic>2</italic>} = 0.014, were significant, but the interaction was not, <italic>F</italic>(1,96) = 0.01, <italic>p</italic> = 0.941, <italic>η</italic>^{<italic>2</italic>} &lt; 0.001. EWS decreased after the vigilance task, and EWS was lower in left-cued compared to right-cued trials (see Fig. ##FIG##1##2##). As for the uncued line bisection task, this suggests lower levels of general attentional resources after the vigilance task than before, in line with the SSS and RT data. Moreover, these results suggest that general attentional resources were lower when lines were cued on the left than when lines were cued on the right. Finally, for DBE, there was a main effect of cue side, <italic>F</italic>(1,96) = 78.50, <italic>p</italic> &lt; 0.001, <italic>η</italic>^{<italic>2</italic>} = 0.096, where participants showed a minimal bisection deviation to the left when cued to the right, and a minimal bisection deviation to the right when cued to the left. Neither the main effect of condition, <italic>F</italic>(1,96) = 0.23, <italic>p</italic> = 0.631, <italic>η</italic>^{<italic>2</italic>} &lt; 0.001 nor the interaction, <italic>F</italic>(1,96) = 3.12, <italic>p</italic> = 0.080, <italic>η</italic>^{<italic>2</italic>} = 0.001, effect however reached significance.</p>", "<title>Comparison of the effect of alertness reduction in the cued and uncued line bisection task</title>", "<p id=\"Par19\">Finally, to assess whether the effect of alertness on spatial attention is modulated by the presence of a pre-existing spatio-attentional bias, we directly compared the effect of a reduction of alertness on all measures between both versions of the line bisection task (with and without cueing). This was done by calculating the difference between the pre- and post-vigilance task values in EWB, EWS, or DBE scores for both cue conditions with the uncued condition and comparing them via repeated measures ANOVAs. All three ANOVAs remained non-significant (all <italic>p</italic>’s &gt; 0.05). Therefore, the differences of pre- versus post-vigilance task were not significantly different between the cued and uncued versions of the line bisection task for EWB, EWS, or DBE.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par20\">This experiment examined the effects of a vigilance task as well as the use of spatial cues on performance in a line bisection task. While including the classical directional bisection error, our examination focused on the endpoint weightings bias (McIntosh et al. ##UREF##7##2005##), which has been suggested to more sensitively assess spatio-attentional biases (McIntosh et al. ##UREF##7##2005##, ##REF##28923304##2017##; McIntosh ##REF##28807326##2018##). We predicted that the EWB of participants would become larger following the vigilance task, reflecting an attentional shift to the right. The current results could not corroborate this. This suggests that one or more of the following were true: (1) The vigilance task did not decrease participant alertness sufficiently to be reflected in the task; (2) a reduction in alertness had no effect on spatial attention; (3) the version of the line bisection task we used is not sensitive enough to recognise vigilance-based changes in line bisection behaviour in neurotypical participants, or (4) the spatial attention involved in line bisection is affected differently by an individual’s alertness than spatial attention as measured by more fast-paced tasks with objects shortly flashing up.</p>", "<p id=\"Par21\">Due to the faulty translation of the SSS into German and thus missing SSS data for half of the participants, it could not be determined with certainty whether the vigilance task successfully reduced alertness in each individual participant. Nonetheless, the t tests for RTs and SSS suggested that, over all participants, alertness indeed decreased, ruling out an unsuccessful manipulation from the vigilance task. Moreover, the EWS was significantly reduced after the vigilance task. This strongly suggests that the vigilance task did in fact result in a reduction of alertness and that our line bisection task was able to pick this up.</p>", "<p id=\"Par22\">Thus, our results suggest that this reduction in alertness did not elicit a rightward shift in spatial bias. This seemingly contradicts a considerable body of previous research, where a reduction in alertness has been found to result in a rightward shift of spatial attention (e.g., Manly et al. ##REF##16154447##2005##; Matthias et al. ##REF##19682470##2009##; Robertson et al. ##REF##7650103##1995##, ##REF##9744274##1998##; see Chandrakumar et al. ##REF##31075552##2019## for a meta-analysis). In the current study we examined both the EWB, as well as the classical DBE, finding an effect of alertness reduction on spatial attention in neither. McIntosh and colleagues (McIntosh et al. ##UREF##7##2005##, ##REF##28923304##2017##; McIntosh ##REF##28807326##2018##; Mitchell et al. ##REF##35940957##2022##) convincingly show that the EWB is sensitive to shifts in spatial attention. Moreover, in our the task, the EWS was clearly able to pick up on the effect of a reduction in alertness. Our findings cannot easily be explained by insufficient statistical power. Our sample size of 97 participants was considerably larger than the sample size used in the previous studies. Finally, in contrast to the paper and pencil line bisection task used in, e.g., clinical settings, participants in our study used the computer mouse to bisect the line. This creates a misalignment between the position of the bisection mark on the line and hand position, which could have affected our participants' line bisection performance. However, several previous studies that similarly asked participants to use the mouse to bisect the lines were able to detect spatio-attentional biases, such as those associated with pseudoneglect (Learmonth et al. ##REF##26378925##2015##; Mitchell et al. ##REF##35940957##2022##) and hemispatial neglect (Halligan and Marshall ##UREF##2##1989##), as well as shifts in spatial attention such as those associated with non-invasive brain stimulation (Sparing et al. ##REF##19528092##2009##; Varnava et al. ##REF##23823975##2013##). This suggests that our findings cannot easily be explained by our use of a computerised line bisection task where participants used the mouse to bisect the lines. Taken together, it is unlikely that our task was not sensitive enough to recognise vigilance-based changes in line bisection behaviour in neurotypical participants.</p>", "<p id=\"Par23\">Instead, the most likely explanation for the current null results is that reductions in alertness have no measurable effect on line bisection performance in young, neurotypical adults. As previous research in young neurotypical adults did find an effect of alertness on spatial attention, our results suggest that alertness may only affect spatial attention in situations where a quick reaction to stimuli is required. For example, the landmark task (e.g., Benwell et al. ##REF##22270326##2013a##, ##REF##24076376##b##; Dufour et al. ##REF##17146643##2007##; Manly et al. ##REF##16154447##2005##) presents participants with a pre-bisected line, to which they must react as quickly as possible via push-button response. Similar effects have been found in experiments with briefly presented stimuli (e.g., Fimm et al. ##REF##16530231##2006##; Matthias et al. ##REF##19682470##2009##; Newman et al. ##REF##25234646##2014##). On the other hand, active line bisection requires a more in-depth examination of the object to find its exact middle. This provides participants with enough time to examine the line and make a well-informed decision, in contrast to the previous studies in which alertness effects were found.</p>", "<p id=\"Par24\">Interestingly, line bisection has been shown to be affected by spatial cues in patients (e.g., Harvey et al. ##REF##10617289##2000##; McIntosh ##REF##28807326##2018##) and neurotypical participants (Chieffi et al. ##REF##24496492##2014##; Harvey et al. ##REF##10617289##2000##). While no such effect was observed in our task when examining EWB, there was an effect of cue side when examining the DBE. In the uncued line bisection condition, participants tended to bisect lines slightly to the left of the middle, reflective of pseudoneglect (Jewell and McCourt ##REF##10617294##2000##). Yet, when one of the line ends was cued, participants tended to bisect the lines towards the side opposite of the cue, in contrast to what was observed by Harvey et al. (##REF##10617289##2000##). This suggests some form of ‘attentional repulsion’ (Chieffi et al. ##REF##24496492##2014##; Suzuki and Cavanagh ##REF##9104004##1997##; Toba ##REF##21110990##2011##). The attentional repulsion effect states that participants shift their attention away from the cued end of the line towards the uncued end. As a result, the uncued side of the line is attentionally magnified, which in turn leads to an overestimation of its length compared to the cued side. In other words, the uncued side appears longer than it actually is, \"pushing\" the perceived middle of the line towards it Thus, it appears that the effect of spatial cues works in separate directions in patients with neglect and neurotypical participants. In patients with neglect, spatial cueing leads to a bias towards the cue (Harvey et al. ##REF##10617289##2000##; McIntosh ##REF##28807326##2018##), while healthy participants tend to bisect away from the cue (e.g., Chieffi et al. ##REF##24496492##2014##).</p>", "<p id=\"Par25\">Finally, the observation that the effect of vigilance condition on line bisection performance was not significantly different between the cued and the uncued versions of our line bisection task suggests that the effect of alertness on spatio-attentional biases was not exacerbated by a pre-existing spatial bias. Previous work reporting the modulation of the effect of alertness on spatial biases by a pre-existing spatial bias was mostly in neglect patients or children with ADHD (Bellgrove et al. 2013; Bonato et al. 2010; Russell et al. 2013). The current results suggest that this modulation may only occur in certain patient populations and not, or to a lesser extent, in neurotypical participants. While there is work suggesting that neurotypical participants can react differentially to changes in alertness depending on subtle differences in pre-existing biases (Benwell et al. ##REF##24076376##2013b##), this is most likely due to regression to the mean (see Newman et al. ##REF##25234646##2014##). In our case, the attempt at eliciting pre-existing spatial biases did not modulate the non-effect of alertness on a spatial bias line bisection, implying that alertness has no meaningful effect on line bisection in young, neurotypical participants. More generally, the heterogeneous results from studies with neurotypical participants, including the current one, imply findings made in patients do not necessarily generalise to neurotypical participants and vice versa, highlighting the importance of testing different populations on the same task to fully understand the cognitive mechanisms underlying them.</p>" ]

[]

[ "<p>Communicated by Bill J Yates.</p>", "<p id=\"Par1\">Alertness, or one’s general readiness to respond to stimulation, has previously been shown to affect spatial attention. However, most of this previous research focused on speeded, laboratory-based reaction tasks, as opposed to the classical line bisection task typically used to diagnose deficits of spatial attention in clinical settings. McIntosh et al. (Cogn Brain Res 25:833–850, 2005) provide a form of line bisection task which they argue can more sensitively assess spatial attention. Ninety-eight participants were presented with this line bisection task, once with and once without spatial cues, and both before and after a 50-min vigilance task that aimed to decrease alertness. A single participant was excluded due to potentially inconsistent behaviour in the task, leaving 97 participants for the full analyses. While participants were, on a group level, less alert after the 50-min vigilance task, they showed none of the hypothesised effects of reduced alertness on spatial attention in the line bisection task, regardless of with or without spatial cues. Yet, they did show the proposed effect of decreased alertness leading to a lower level of general attention. This suggests that alertness has no effect on spatial attention, as measured by a line bisection task, in neurotypical participants. We thus conclude that, in neurotypical participants, the effect of alertness on spatial attention can be examined more sensitively with tasks requiring a speeded response compared to unspeeded tasks.</p>", "<title>Keywords</title>" ]

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[ "<title>Acknowledgements</title>", "<p>The authors would like to thank Sophia Nestmann, Axel Lindner and Lisa Röhrig for their helpful feedback. Moreover, the authors would like to thank the 4 BSc Psychology students at Brunel University London, Amber Stokes, Simran Deol, Vinusha Anandarajah, and Hardeep Chana, for their support with data collection as part of their BSc dissertation project. This work was supported by an internal Brunel Research Initiative &amp; Enterprise Fund (BRIEF) award (1073 to BdH) as well as the Deutsche Forschungsgemeinschaft (KA 1258/23-1 AOBJ 632333).</p>", "<title>Author contribution</title>", "<p>All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by SS, DB, and BdH. The first draft of the manuscript was written by SS and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.</p>", "<title>Funding</title>", "<p>This work was supported by an internal Brunel Research Initiative &amp; Enterprise Fund (BRIEF) award (1073 to BdH) as well as the Deutsche Forschungsgemeinschaft (KA 1258/23-1 AOBJ 632333).</p>", "<title>Data availability</title>", "<p>The data and analysis code underlying this study are openly available on OSF at <ext-link ext-link-type=\"uri\" xlink:href=\"https://doi.org/10.17605/OSF.IO/X9MKY\">https://doi.org/10.17605/OSF.IO/X9MKY</ext-link></p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par26\">The authors have no competing interests to declare that are relevant to the content of this article.</p>", "<title>Ethical approval</title>", "<p id=\"Par27\">The study was performed in accordance with the ethical standards laid down in the 2013 Declaration of Helsinki. The study was approved by both the ethics committees of the University Clinic of Tuebingen (774/2019BO2) as well as Brunel University (18784-LR-Nov/2019-21016-1).</p>", "<title>Consent to participate</title>", "<p id=\"Par28\">All participants gave informed written consent to participate. Participants consented to the publication of their data in scientific journals and to the storing and sharing of their anonymised data for use in future projects.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>EWB (left), EWS (middle), and DBE (right) values before and after the vigilance task for the no-cue task</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>EWB, EWS, and DBE values before and after the vigilance task when cued left or right. Error bars denote 95% CIs</p></caption></fig>" ]

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[ "<title>Introduction</title>", "<p id=\"Par13\">Power output at the boundaries between the moderate, heavy, and severe intensity domains are routinely used to assess performance capability, regulate training load and competition intensities, and to quantify adaptations to training (Burnley and Jones ##REF##27806677##2018##; Jones et al. ##REF##31758668##2019##; Maunder et al. ##REF##33886100##2021##). However, we and others have observed that the power outputs observed at these intensity transitions decreases over time during prolonged exercise (Clark et al. ##REF##29521722##2018a##, ##REF##31295069##2019a##, ##REF##30995104##b##; Stevenson et al. ##REF##36127418##2022##). This has implications for the application of physiological profiling data collected in well-rested athletes to prolonged training sessions (Maunder et al. ##REF##33886100##2021##).</p>", "<p id=\"Par14\">Identification of a physiological marker that changes over time during prolonged exercise in accordance with changes in the intensity domain transitions would be useful for within-session intensity regulation, and could result in a more precise calculation of training intensity distribution (Maunder et al. ##REF##33886100##2021##). We previously observed that the classic upward drift in heart rate during prolonged cycling was proportionally greater than the downward drift in power output at the moderate-to-heavy intensity transition (Stevenson et al. ##REF##36127418##2022##). This indicates that the heart rate observed at the moderate-to-heavy intensity transition during a physiological profiling assessment in a well-rested athlete may not provide useful information regarding the athlete’s proximity to the transition following multiple hours of exercise. Therefore, investigation of other markers of exercise intensity for this purpose are warranted.</p>", "<p id=\"Par15\">Expired minute ventilation (), and its underlying parameters respiratory frequency (F_R) and tidal volume (V_T), can be measured non-invasively by endurance athletes in real-time (Clarenbach et al. ##REF##16162719##2005##; Witt et al. ##REF##16503424##2006##; Nicolò et al. ##REF##28154536##2017b##). These ventilatory parameters are highly-responsive to exercise intensity (Nicolò et al. ##REF##28560751##2017a##, ##REF##30393984##2018##). The and F_R typically rise linearly with exercise intensity up to the respiratory compensation point, after which non-linear increases occur; whereas V_T typically plateaus at higher intensities (Nicolò et al. ##UREF##4##2020##). There is emerging suggestion that V_T may be regulated primarily by stimulation of central and peripheral chemoreceptors and skeletal muscle metaboreceptors by exercise-induced changes in CO₂, pH, and skeletal muscle metabolites, whereas F_R may be primarily regulated by fast inputs such as group III/IV muscle afferents and central command (Tipton et al. ##REF##28650070##2017##; Nicolò et al. ##UREF##4##2020##). Accordingly, monitoring changes in ventilatory parameters during exercise may have the potential to provide endurance athletes with useful information regarding their physiological status in real-time. This contention is further supported by the upward drift in ventilatory parameters that may be observed during prolonged, constant-work rate exercise (Phillips et al. ##REF##26271678##2016##; Katagiri et al. ##REF##37184224##2023##). If prolonged exercise-induced changes in these ventilatory parameters align with prolonged exercise-induced changes in the intensity domain transitions; that is, if one or more ventilatory parameters coincident with the intensity domain transitions remains constant over time during prolonged exercise, despite reductions in external work rates achieved at the transition, then monitoring ventilatory parameters during exercise may provide athletes with useful information regarding their real-time proximity to the intensity domain transitions.</p>", "<p id=\"Par16\">Accordingly, the purpose of the present investigation was to quantify the effects of prolonged cycling on the , F_R, and V_T associated with the moderate-to-heavy intensity transition. The data presented here were collected as part of a previously-published study (Stevenson et al. ##REF##36127418##2022##).</p>" ]

[ "<title>Methods</title>", "<title>Ethical approval</title>", "<p id=\"Par17\">This study was performed in accordance with the standards of the Declaration of Helsinki, 2013. The Auckland University of Technology Ethics Committee approved all procedures (21/253), and all participants provided written informed consent prior to participation. This study was not registered in a database. Data associated with this study are available from the corresponding author upon reasonable request.</p>", "<title>Participants</title>", "<p id=\"Par18\">Fourteen endurance-trained cyclists and triathletes took part in the present investigation (13 males, 1 female; age, 34 ± 10 y; height, 178.1 ± 5.6 cm; mass, 71.2 ± 6 kg; peak oxygen uptake [O₂peak], 59.9 ± 6.8 mL^.kg^−1.min⁻¹; training volume, 9 ± 3 h^.week⁻¹). A priori sample size estimation indicated that a total sample size of 15 was required to detect a large magnitude (ES = 0.7) reduction in power output at the moderate-to-heavy intensity transition with 80% statistical power using the G*Power software package. A large magnitude effect size was used for this calculation based on previous studies showing the effect of prolonged exercise on the heavy-to-severe intensity transition (Clark et al. ##REF##29521722##2018b##, ##REF##31295069##2019a##, ##REF##30995104##b##). A one-tailed test was used as it seemed implausible that the moderate-to-heavy intensity power output would increase following acute prolonged exercise. One participant dropped out of the study. All participants were free of recent (&lt; 3 months) musculoskeletal injury and chronic disease and habitually training &gt; 5 h^.week⁻¹ in cycling-based endurance sports.</p>", "<title>Study design</title>", "<p id=\"Par19\">The data presented here were collected as part of a previously-published study (Stevenson et al. ##REF##36127418##2022##). Briefly, participants reported to the laboratory following an overnight fast on two occasions: (i) a characterisation trial for measurement of O₂peak and initial estimation of the moderate-to-heavy intensity transition, (ii) a prolonged trial for measurement of the moderate-to-heavy intensity transition before and after two hours of cycling at 90% of the initial estimate of the moderate-to-heavy intensity transition. The first ventilatory threshold (VT₁) was used as the marker of the moderate-to-heavy intensity transition.</p>", "<title>Characterisation trial</title>", "<p id=\"Par20\">Participants initially reported to the laboratory for an incremental cycling test. Participants arrived after a 10-h overnight fast having refrained from vigorous exercise for 24 h and having ingested ~ 1 L of plain water ~ 2 h beforehand. Height and body mass was first measured. Cycling subsequently commenced on an electromagnetically-braked ergometer at 95 W, and the power output initially increased by 35 W every 3 min (Excalibur Sport, Lode BV, Groningen, NET). Expired gases were collected continuously using indirect calorimetry (TrueOne 2400, ParvoMedics, UT, USA). Once the respiratory exchange ratio exceeded 1.0 and clear signs of increased . O₂⁻¹ emerged, power output was increased by 35 W every minute until task failure. The O₂peak was identified as the highest 15-s average O₂, and VT₁ was identified as the O₂ at which a systematic rise in ^.O₂⁻¹ occurred. This O₂ was converted to a power output by linear fit of the power output vs. O₂ relationship, using the last minute of O₂ data from each 3-min stage.</p>", "<title>Prolonged trial</title>", "<p id=\"Par21\">Participants arrived for the prolonged trial after a 10-h overnight fast, having refrained from vigorous exercise for 24 h, and having ingested ~ 1 L of plain water ~ 2 h beforehand. Following measurement of body mass, the experimental trial commenced on the same electromagnetically-braked ergometer as the initial assessment with a 5-min warm-up at 100 W, followed by a five-stage incremental assessment to determine the power output and heart rate at the moderate-to-heavy intensity transition (PRE). The incremental test began with 4-min at 50 W below the previously estimated VT₁ power output, and power output increased by 25 W per increment. Expired gases were measured continuously during the incremental test (TrueOne 2400, ParvoMedics, UT, USA; Tickr, Wahoo Fitness, Atlanta, USA). Participants then cycled for 5 min at 100 W, and then at 90% of the previously estimated power output at VT₁ for 2 h. Participants consumed plain water ad libitum. Following the two-hour constant work-rate phase, participants again cycled for 5 min at 100 W before repeating the five-step incremental exercise assessment (POST).</p>", "<p id=\"Par22\">The moderate-to-heavy intensity transitions in PRE and POST were estimated using the VT₁ method in accordance with the procedures described above for the initial assessment. The O₂ at VT₁ was converted to a power output by linear fit of the power output vs. O₂ relationship, using the last minute of O₂ data from each of the five 4-min stages. The VT₁ was then matched to a corresponding , F_R, and V_T value by linear fit of the relationship between these variables and power output using the last minute of data from each stage. The linear fit of individual (R² = 0.977 ± 0.015), F_R (R² = 0.927 ± 0.061), and V_T (R² = 0.829 ± 0.278) against power output curves were strong.</p>", "<p id=\"Par23\">The validity of our VT₁ data for estimating the moderate-to-heavy intensity transition is supported by its alignment with the blood lactate-derived LoglogLT estimate (within-subject coefficient or variation, ~ 6.9%) and lack of significant difference between VT₁ and LoglogLT (<italic>P</italic> = 0.18), as reported in our previous publication related to this data collection (Stevenson et al. ##REF##36127418##2022##). Specifically, we collected capillary blood lactate samples in the last 30-s of each stage, and the blood lactate concentration vs. power output relationship was used to quantify LoglogLT. The LoglogLT method models a blood lactate concentration vs. power output curve using two segments, and the intersection point of the two lines with the lowest residuals sum of squares is taken as the moderate-to-heavy intensity transition (Jamnick et al. ##UREF##2##2018##). Whilst no accepted gold-standard estimate of the moderate-to-heavy intensity transition exists, the alignment of these two separate estimates supports their validity.</p>", "<title>Statistical analysis</title>", "<p id=\"Par24\">Data are presented as mean ± standard deviation (SD), unless otherwise stated. Normality of data distributions were assessed using the Shapiro–Wilk test. The effect of prolonged exercise on VT₁, expressed as power output (previously reported (Stevenson et al. ##REF##36127418##2022##)), , F_R, and V_T, was assessed using paired t-tests (or non-parametric equivalents). These analyses were performed in GraphPad Prism Version 9.3.1. The consistency of values between PRE and POST was assessed using within-subject coefficient of variation (CV) statistics calculated using the within-standard deviation method and Pearsons’s product-moment correlations, both expressed with 95% confidence intervals. These analyses were performed in R (version 4.4.0) with RStudio (version 1.1463). Significance was inferred when <italic>P</italic> ≤ 0.05.</p>" ]

[ "<title>Results</title>", "<p id=\"Par25\">Power output at VT₁ significantly decreased from PRE to POST (217 ± 42 W vs. 196 ± 42 W, ∆ − 21 ± 12 W, ∆ − 10 ± 6%, <italic>P</italic> &lt; 0.001) (Stevenson et al. ##REF##36127418##2022##). During the moderate-intensity, constant-work rate phase between PRE and POST, (<italic>P</italic> = 0.065), F_R (<italic>P</italic> = 0.068), and V_T (<italic>P</italic> = 0.266) did not significantly change with time (Fig. ##FIG##0##1##). The at VT₁ was unchanged from PRE to POST (72 ± 12 vs. 69 ± 13 L^.min⁻¹, ∆ − 3 ± 5 L^.min⁻¹, ∆ − 4 ± 8%, <italic>P</italic> = 0.075, Fig. ##FIG##1##2##a), whereas F_R at VT₁ increased (27.6 ± 5.8 vs. 31.9 ± 6.5 breaths^.min⁻¹, ∆ 4.3 ± 3.1 breaths^.min⁻¹, ∆ 16 ± 11%, <italic>P</italic> &lt; 0.001, Fig. ##FIG##1##2##b) and V_T decreased (2.62 ± 0.43 vs. 2.19 ± 0.36 L^.breath⁻¹, ∆ − 0.44 ± 0.22 L^.breath⁻¹, ∆ − 16 ± 7%, <italic>P</italic> &lt; 0.001, Fig. ##FIG##1##2##c) from PRE to POST. The within-subject CV for at VT₁ between PRE and POST was 5.4% (3.7, 8.0%), and the PRE and POST values were strongly associated (r = 0.928 [0.782, 0.977], <italic>P</italic> &lt; 0.001) (Fig. ##FIG##2##3##). Data from a representative participant is shown in Fig. ##FIG##3##4##.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par26\">The aim of the present investigation was to assess the effect of prolonged exercise on the , and its underlying parameters F_R and V_T, associated with the moderate-to-heavy intensity transition. Our primary observations were, concomitant with a reduction in the power output associated with the moderate-to-heavy intensity transition: (i) the associated with the transition was unchanged, whilst (ii) the associated F_R increased and (iii) V_T decreased. These data suggest that real-time monitoring of may be a useful means of assessing proximity to the moderate-to-heavy intensity transition during prolonged exercise.</p>", "<p id=\"Par27\">We previously observed that the heart rate associated with the moderate-to-heavy intensity transition increased following prolonged cycling (Stevenson et al. ##REF##36127418##2022##). These data indicated that heart rate thresholds, measured in traditional, well-rested athlete physiological profiling assessments, may not readily translate to prolonged exercise. Specifically, adherence to heart rate zones derived from well-rested athlete physiological profiling assessments may risk undertraining an athlete during prolonged exercise as the heart rate associated with the intensity transition drifts upwards over time. Here we present evidence that may be an alternative physiological metric that can be used to provide information regarding the proximity to the moderate-to-heavy intensity transition during exercise, as the associated with the transition was unchanged following prolonged cycling. Whilst not statistically significant (<italic>P</italic> = 0.075), our data does show a numeric decrease in the associated with VT₁ from PRE to POST (Fig. ##FIG##1##2##a). However, even if this effect was statistically significant, we consider this numeric reduction to be practically insignificant in terms of magnitude (∆ − 4 ± 8%), given the reported day-to-day variation associated with gas exchange-derived estimates of (~ 4–7%) (Carter and Jeukendrup ##REF##11882930##2002##). Therefore, estimates of the associated with the moderate-to-heavy intensity transition during traditional physiological profiling assessments may translate effectively to prolonged exercise, and therefore to within-session intensity regulation and calculation of training intensity distribution. That is, if an athlete’s moderate-to-heavy intensity transition power output in a well-rested physiological assessment is determined as 215 W with a concomitant of 70 L^.min⁻¹, our data suggests their moderate-to-heavy intensity transition power output after prolonged exercise may fall, but the at the moderate-to-heavy transition would remain constant at 70 L^.min⁻¹. Therefore, if this athlete intends to undertake a prolonged training session in the moderate domain, they could guide their effort according to keeping below 70 L^.min⁻¹, although the values used in practice should acknowledge the day-to-day variation in exercise .</p>", "<p id=\"Par28\">Our observation that is tightly linked with physiologically-based intensity domain transitions is highly-plausible, given the physiological stresses associated with increased exercise intensity regulate (Tipton et al. ##REF##28650070##2017##; Nicolò et al. ##UREF##4##2020##). For example, transition from the moderate to heavy intensity domain sees perturbations in muscle metabolic homeostasis, including increased lactate and H⁺ accumulation and depletion of PCr stores (Black et al. ##REF##28008101##2017##). Disturbed muscle metabolic homeostasis drives hyperpnoea via stimulation of muscle metaboreceptors (Piepoli et al. ##UREF##5##1995##; Stickland et al. ##REF##23720327##2013##). The increased F_R and decreased V_T used to produce the constant rate of at the moderate-to-heavy intensity transition in POST vs. PRE might reflect fatigue in the respiratory musculature, and therefore a shift in the most efficient ventilatory pattern to produce a given rate of , following prolonged exercise. This would align with the so-called ‘principle of minimal effort’ (Otis et al. ##REF##15436363##1950##; Mead ##UREF##3##1960##), but requires examination in specific work to be confirmed.</p>", "<p id=\"Par29\">The translation of these data to practical settings requires wearable technology that can accurately and reliably measure ventilatory parameters during training. Several technologies exist that allow for accurate estimation of F_R in real-time during exercise (Nicolò et al. ##REF##28154536##2017b##), including through sensors embedded in straps or clothes sensitive to thoracic or abdominal strain (Hailstone and Kilding ##UREF##1##2011##; Kim et al. ##REF##23175181##2013##; Liu et al. ##REF##23259751##2013##; Villar et al. ##REF##26360814##2015##), or ventilation-induced changes in the electrocardiogram or photoplethysmography signals (Bailón et al. ##UREF##0##2006##; Meredith et al. ##REF##22185462##2012##; Schumann et al. ##UREF##6##2016##). Respiratory-inductive plethysmography has been used to estimate F_R, V_T and , with some success (Clarenbach et al. ##REF##16162719##2005##; Witt et al. ##REF##16503424##2006##). Therefore, development of technologies that can be used by endurance athletes to estimate real-time during exercise, with data integrated onto bicycle computers and/or smart watches such that it can be viewed in real-time, may allow for improved within-session intensity regulation when coupled with quantification of the associated with the moderate-to-heavy intensity transition during routine physiological profiling assessments. However, as indicated above, intensity-related decisions using measurements of in practice would need to acknowledge the day-to-day variation in exercise measured using said device.</p>", "<p id=\"Par30\">Additionally, translation of these data to applied settings requires further research to address the limitations of our study. For example, our observations are specific to our exercise protocol; that is, a submaximal incremental test followed by two hours of initially moderate-intensity exercise. It is possible that the main effects observed here do not translate to intermittent or higher-intensity exercise protocols, or longer exercise durations. Similarly, our data were collected during exercise in a fasted state without feeding during exercise, and (primarily) in male athletes. Thus, further research is warranted to determine if at the moderate-to-heavy intensity transition remains constant over time during prolonged exercise across a broader range of ecologically-valid exercise scenarios.</p>", "<p id=\"Par31\">In summary, the data presented here indicate that real-time monitoring of during prolonged exercise might provide a useful means of assessing proximity to the moderate-to-heavy intensity transition. This would require prior assessment of the associated with the moderate-to-heavy intensity transition during routine physiological profiling assessments, and technologies that allow accurate, real-time monitoring of during exercise.</p>" ]

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[ "<p>Communicated by Susan Hopkins.</p>", "<title>Purpose</title>", "<p id=\"Par1\">To quantify the effects of prolonged cycling on the rate of ventilation (), frequency of respiration (F_R), and tidal volume (V_T) associated with the moderate-to-heavy intensity transition.</p>", "<title>Methods</title>", "<p id=\"Par2\">Fourteen endurance-trained cyclists and triathletes (one female) completed an assessment of the moderate-to-heavy intensity transition, determined as the first ventilatory threshold (VT₁), before (PRE) and after (POST) two hours of moderate-intensity cycling. The power output, , F_R, and V_T associated with VT₁ were determined PRE and POST.</p>", "<title>Results</title>", "<p id=\"Par3\">As previously reported, power output at VT₁ significantly decreased by ~ 10% from PRE to POST. The associated with VT₁ was unchanged from PRE to POST (72 ± 12 vs. 69 ± 13 L^.min⁻¹, ∆ − 3 ± 5 L^.min⁻¹, ∆ − 4 ± 8%, <italic>P</italic> = 0.075), and relatively consistent (within-subject coefficient of variation, 5.4% [3.7, 8.0%]). The associated with VT₁ was produced with increased F_R (27.6 ± 5.8 vs. 31.9 ± 6.5 breaths^.min⁻¹, ∆ 4.3 ± 3.1 breaths^.min⁻¹, ∆ 16 ± 11%, <italic>P</italic> = 0.0002) and decreased V_T (2.62 ± 0.43 vs. 2.19 ± 0.36 L^.breath⁻¹, ∆ − 0.44 ± 0.22 L^.breath⁻¹, ∆ − 16 ± 7%, <italic>P</italic> = 0.0002) in POST.</p>", "<title>Conclusion</title>", "<p id=\"Par4\">These data suggest prolonged exercise shifts ventilatory parameters at the moderate-to-heavy intensity transition, but remains stable. Real-time monitoring of may be a useful means of assessing proximity to the moderate-to-heavy intensity transition during prolonged exercise and is worthy of further research.</p>", "<title>Keywords</title>", "<p> Open Access funding enabled and organized by CAUL and its Member Institutions</p>" ]

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[ "<title>Author contributions</title>", "<p>JDS, EM, AEK, and DJP conceived and designed the research. JDS and EM conducted experiments and collected the data. JDS and EM analysed the data. JDS and EM drafted the manuscript. All authors read, revised, and approved the manuscript.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by CAUL and its Member Institutions. No sources of funding were used in the completion of this study.</p>", "<title>Data availability</title>", "<p>Data is available from the corresponding author upon reasonable request.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par32\">The authors declare no competing interests associated with this manuscript.</p>", "<title>Ethical approval</title>", "<p id=\"Par33\">The Auckland University of Technology Ethics Committee approved all procedures (21/253).</p>", "<title>Consent to participate</title>", "<p id=\"Par34\">All participants provided written informed consent.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p><bold>a</bold> Rate of ventilation (), <bold>b</bold> frequency of respiration (F_R), and <bold>c</bold> tidal volume (V_T) during constant-work rate cycling between PRE and POST</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p><bold>a</bold> Rate of ventilation (), <bold>b</bold> frequency of respiration (F_R), and (<bold>c</bold>) tidal volume (V_T) at the first ventilatory threshold (VT₁) before (PRE) and after (POST) prolonged cycling. *** denotes <italic>P</italic> ≤ 0.001</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Rate of ventilation () at the first ventilatory threshold (VT₁) before (PRE) and after (POST) prolonged cycling. The dashed line indicates x = y</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Data from a representative participant. Estimates of the rate of oxygen consumption (O₂) at the first ventilatory threshold (VT₁) are shown for PRE and POST, as are the linear fittings of the rate of ventilation (), frequency of respiration (F_R), and tidal volume (V_T) against power output</p></caption></fig>" ]

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\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}$$\\end{document}</tex-math><mml:math id=\"M48\"><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq29\"><alternatives><tex-math id=\"M49\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M50\"><mml:msub><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq30\"><alternatives><tex-math id=\"M51\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M52\"><mml:msub><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq31\"><alternatives><tex-math id=\"M53\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} 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accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq33\"><alternatives><tex-math id=\"M57\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M58\"><mml:msub><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq34\"><alternatives><tex-math id=\"M59\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} 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accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq36\"><alternatives><tex-math id=\"M63\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M64\"><mml:msub><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq37\"><alternatives><tex-math id=\"M65\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} 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accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq39\"><alternatives><tex-math id=\"M69\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M70\"><mml:msub><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq40\"><alternatives><tex-math id=\"M71\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M72\"><mml:msub><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq41\"><alternatives><tex-math id=\"M73\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M74\"><mml:msub><mml:mover 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\n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M84\"><mml:msub><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover><mml:mtext>E</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>", "<inline-formula id=\"IEq47\"><alternatives><tex-math id=\"M85\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}</tex-math><mml:math id=\"M86\"><mml:msub><mml:mover 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{ "acronym": [ "FR", "HR", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}\\text{CO}}_{{2}}$$\\end{document}V˙CO2", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}_{{\\text{E}}}$$\\end{document}V˙E", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}\\text{O}}_{{2}}$$\\end{document}V˙O2", "\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}\\text{O}}_{{2}} {\\text{peak}}$$\\end{document}V˙O2peak", "VT", "VT1" ], "definition": [ "Frequency of respiration", "Heart rate", "Rate of carbon dioxide production", "Expired minute ventilation", "Rate of oxygen consumption", "Peak rate of oxygen consumption", "Tidal volume", "First ventilatory threshold" ] }

[ "<title>Introduction</title>", "<p id=\"Par5\"><italic>Streptomyces peucetius</italic> produces a number of bioactive secondary metabolites including daunorubicin (DNR), doxorubicin (DXR) (Arcamone and Cassinelli ##REF##9756981##1998##; Arcamone et al. ##REF##5365804##1969##), flaviolin (Ghimire et al. ##REF##18612244##2008##), geosmin (Singh et al. ##REF##19557446##2009##), peucechelin (Park et al. ##REF##22825833##2013##) (Kodani et al. ##REF##26085470##2015##), and hopene (Ghimire et al. ##REF##25406531##2015##). Furthermore, a new 14-membered macrolide (peucemycin) with a γ-pyrone ring was purified and assigned its structure (Pham et al. ##REF##35424263##2021##). The compound exhibited antibacterial activities against some pathogens and suppressed the viability of various cancer cell lines (Pham et al. ##REF##35424263##2021##). Recently, a new peucemycin derivative and its putative biosynthetic gene cluster were identified, providing insight into the biosynthesis of peucemycin and its derivatives (Magar et al. ##REF##36680588##2023##). The newly identified derivative was 25-hydroxy peucemycin (peucemycin A) and had antibacterial activities against some pathogens (Magar et al. ##REF##36680588##2023##).</p>", "<p id=\"Par6\">The peucemycin biosynthetic gene cluster (Peu BGC) has two cluster-situated regulators (pathway-specific regulators). Among the two, PeuR was identified as a <italic>Streptomyces</italic> antibiotic regulator protein (SARP) regulator having a helix-turn-helix (HTH) DNA-binding domain motif at the N-terminal and a bacterial transcriptional activator domain (BTAD) at their C terminus (Hindra and Elliot ##REF##20675485##2010##; Magar et al. ##REF##36680588##2023##). It is currently unknown how PeuR controls the production of peucemycin and its derivatives.</p>", "<p id=\"Par7\">The regulation of biosynthetic pathways by regulatory genes functions as pathway-specific regulators (also known as cluster-situated regulators) and/or pleiotropic (or global) regulators (Lu et al. ##UREF##2##2017##). Some biosynthetic gene clusters necessitate the participation of both regulators, such as pathway-specific regulatory gene <italic>actII-</italic>ORF4 and global regulatory gene <italic>cprB</italic> (Fernández-Moreno et al. ##REF##1878971##1991##) in the production of actinorhodin (ACT) from <italic>S. coelicolor</italic> (Onaka et al. ##REF##9643542##1998##). Similarly, the production of polyketide can be improved by controlling the regulatory mechanism (Chen et al. ##REF##20091304##2010##). For instance, overexpression of SARP regulator in <italic>Streptomyces</italic> sp. KCCM11116P resulted in a higher production titer of tacrolimus (FK506) compared to the wild type (Chen et al. ##UREF##0##2015##). Furthermore, overexpression of the SARP regulator can activate a silent gene cluster. One example is the activation of the undecylprodigiosin (Red) gene cluster by the overexpression of the <italic>papR2</italic> from <italic>S. pristinaespiralis</italic> in <italic>S. lividans</italic> (Krause et al. ##REF##32082274##2020##).</p>", "<p id=\"Par8\">In addition to the pathway-specific regulator, a global regulator BldA also participates in the regulation of biosynthetic pathways. The <italic>bldA</italic> encodes tRNA required for the translation of a rare UUA codon for leucine (Chater and Chandra ##REF##18337685##2008##). Hence, the BldA affects the translation of genes having this rare codon. It also plays an important role in the regulation of antibiotic production (Hackl and Bechthold ##REF##25917027##2015##) like undecylprodigiosin (RED) biosynthesis in <italic>S. coelicolor</italic> (White and Bibb ##REF##9006013##1997##) and landomycin E in <italic>S. globisporus</italic> 1912 (Rebets et al. ##REF##16487316##2006##).</p>", "<p id=\"Par9\">In this study, we successfully isolated another peucemycin derivative and determined its structure. The impact of overexpressing <italic>peuR</italic>, a SARP regulator, on biosynthesis of peucemycin and its derivatives was also thoroughly investigated. Furthermore, the effect of heterologous expression of <italic>bldA</italic>, a pleiotropic regulator, on biosynthesis of peucemycin and its derivatives was investigated.</p>" ]

[ "<title>Materials and methods</title>", "<title>Bacterial strains, media, and culture conditions</title>", "<p id=\"Par10\"><italic>Escherichia coli</italic> XL1-Blue MRF (Stratagene) was used as the cloning host, while <italic>E. coli</italic> ET12567 (John Innes Centre, UK) was used as the demethylating host. They were cultured in Luria–Bertani (LB) media at 37 °C with ampicillin (100 µg/mL) when necessary. For cloning PCR fragments, pGEM®–T Easy vector (Promega) was used. As an expression vector for <italic>S. peucetius</italic>, pIBR25 (Sthapit et al. ##REF##15147895##2004##) was used. Standard protocols were used for manipulating DNA in <italic>E. coli</italic> (Sambrook and Russell ##UREF##3##2001##). <italic>S. peucetius</italic> and its derived strains were grown in R2YE media at 28 °C with thiostrepton (15 µg/mL) when necessary. Their protoplasts were prepared in tryptic soya broth (TSB) following the standard protocol (Kieser et al. ##UREF##1##2000##). Peucemycin and its derivatives were produced by growing <italic>S. peucetius</italic> strains in Hickey-Tresner (HT) media at 18 °C for 3 days (Hickey and Tresner ##REF##13011167##1952##). All wild-type and recombinant strains along with vectors developed during this study are listed in Table ##SUPPL##0##S1##.</p>", "<title>Construction of recombinant vectors and generation of mutant strains</title>", "<p id=\"Par11\">Standard protocols were followed for DNA manipulations and the production of mutants (Kieser et al. ##UREF##1##2000##; Sambrook and Russell ##UREF##3##2001##). The <italic>peuR</italic> and <italic>bldA</italic> were amplified from genomic DNAs of <italic>S. peucetius</italic> DM07 and <italic>S. coelicolor</italic> A3, respectively, using primer pair listed in Table ##SUPPL##0##S2##. Conditions for PCR amplification were 95 °C for 7 min; by 30 cycles of 95 °C for 30 s, 55–68 °C for 30 s, 72 °C for 60–90 s; and final extension at 72 °C for 7 min. DNA amplification was performed using PrimeSTAR HS DNA Polymerase (Takara) according to the manufacturer’s instructions. Following ligation into the pGEM-T Easy vector, sequences were verified.</p>", "<p id=\"Par12\">After <italic>peuR</italic> and <italic>bldA</italic> were ligated separately into pIBR25 at <italic>Xb</italic>aI-<italic>Hin</italic>dIII and <italic>Bam</italic>HI-<italic>Xba</italic>I sites, respectively, the combination of both genes was produced using <italic>Bam</italic>HI-<italic>Hin</italic>dIII sites of pIBR25. All recombinant vectors were demethylated by <italic>E. coli</italic> ET12567 and subsequently transferred into <italic>S. peucetius</italic> using polyethylene glycol (PEG)-mediated protoplast transformation (Malla et al. ##REF##19619853##2009##). Transformants were selected using R2YE plates with thiostrepton. Confirmation of the transformation was done by isolating recombinant vectors from positive clones that were resistant to thiostrepton. A single colony from each mutant was taken to study the production of peucemycin and its derivatives.</p>", "<title>Analysis of growth rate and production of peucemycin and its derivatives</title>", "<p id=\"Par13\">To determine the optimal time for producing 19-hydroxypeucemycin (peucemycin B), a seed culture was prepared by growing <italic>S. peucetius</italic> DM07 in R2YE media for 48 h at 28 °C. Then 1 mL seed culture was added to 50 mL HT media and cultured for 168 h at 18 °C. At every 24-h time interval, 1 mL of culture broth was collected for 168 h. The remaining culture broths were used for quantification of peucemycin B. Samples were centrifuged at 12,000 rpm and washed twice with sterile distilled water. Pellets were finally dried at 70 °C for 4 days, and dry cell weight (DCW) for each sample was measured. Measurements were taken for three biological replicates. Peucemycin B was quantified after the remaining culture broths were extracted with ethyl acetate at double volume. The organic phase was dried using a rotary evaporator under reduced pressure. Each extract was then dissolved in 1 mL of methanol.</p>", "<p id=\"Par14\">Samples were analyzed by Thermo HPLC series 1100 with a Thermo-C₁₈ column (5 µm, 4.6 mm × 250 mm) which was equilibrated with 90% solvent A (water + 0.1% trifluoroactetic acid (TFA)) and 10% acetonitrile (ACN). The condition for analysis was a linear gradient of 1–25 min with 10% to 90% B, 25–28 min with 90% to 50% B, and 28 − 30 min with 50% to 10% B at a flow rate of 1 mL/min with UV detection at 268 nm. A standard curve was prepared with different concentrations of peucemycin B. Concentration of peucemycin B was calculated based on the peak area. Compound mass was analyzed by ultra-high-performance liquid chromatography electrospray ionization quadrupole time-of-flight high-resolution mass spectrometry (UPLC − ESI − Q − TOF − HRMS) using an Acquity column (UPLC; Waters Corp., Milford, MA, USA) coupled with a SYNAPT G2-S (Waters Corp) with a gradient of solvent mobile phase of 0.1% TFA in water and 100% ACN (0 to 12 min) at 35 °C. The sample volume used for injection was 10 µL. LC − MS analysis was performed using a high-resolution mass spectrometer equipped with an electrospray ionization source under the following conditions: 3 kV of capillary voltage, 300 °C of desolvation gas temperature, and 600 L/h of desolvation gas flow rate.</p>", "<p id=\"Par15\">Growth rate and peucemycin production for all other mutants were studied by taking samples for 3 days and performing similar steps as mentioned above. Calibration curves were prepared for peucemycin and peucemycin A. All the data were generated from three experimental samples, and a student <italic>t</italic>-test was performed with GraphPad Prism 6 for significance tests.</p>", "<title>Isolation and purification of peucemycin B</title>", "<p id=\"Par16\">For sample preparation, <italic>S. peucetius</italic> DM07 was grown in HT media for 72 h at 18 °C in a 4 L fermenter. A total of 12 L of HT medium was used to isolate peucemycin B. Double volume of ethyl acetate was added to the sample and the organic phase was dried using a rotary evaporator under reduced pressure. This crude extract was washed twice with autoclaved distilled water followed by washing once with hexane. The sample was then washed with dichloromethane and dried. The final extract was dissolved in 150 mL of methanol. The extract was filtered and purified using Dionex Ultimate 3000 UPLC (Thermo Fisher Scientific) with a C₁₈ column (YMC − Pack ODS − Aq, 150 × 20 mm²) connected to a UV detector (220 and 268 nm). The condition for binary gradient of mobile phase was 100% water (solvent A) and 100% acetonitrile (solvent B) (0–5 min, 0 to 20% B; 5–10 min, 20 to 40% B, 10–20 min, 40 to 60% B; 20–28 min, 60 to 100% B; 28–30 min, 100% B; and 30–35 min, 100 to 0% B) at a flow rate of 10 mL/min. The purified compound was dried, lyophilized, and dissolved in dimethyl sulfoxide (DMSO-<italic>d</italic>_{<italic>6</italic>}), and then subjected to 700 MHz analyses using a Bruker BioSpin nuclear magnetic resonance (NMR) spectrometer (Billerica, USA), including one-dimensional (1D) ¹H- NMR,¹³C-NMR, two-dimensional (2D) correlated spectroscopy (COSY), rotational frame nuclear overhauser effect (NOE) spectroscopy (ROESY), heteronuclear single quantum correlation (HSQC) analysis, and heteronuclear multiple bond correlation (HMBC) analysis (Ochang, Republic of Korea).</p>", "<title>Transcriptional level analysis</title>", "<p id=\"Par17\">Total RNAs were isolated from 48 h bacterial cultures using an RNeasy Mini Kit (Qiagen Inc., USA) following the manufacturer’s protocols. DNA contamination was removed using RNase-Free DNase (Qiagen Inc., USA). Total RNA concentration and purity were determined using a spectrophotometer at 260 nm. Finally, cDNA was prepared by QuantiTect® Reverse Transcription kit (Qiagen) with an equal amount of RNA. RT-PCR conditions were cDNA synthesis at 50 °C for 30 min; initial denaturation at 95 °C for 10 min followed by 45 cycles of denaturation for 1 min at 95 °C, annealing at 1 min for 64 °C, and elongation at 72 °C for 1 min for PCR. Finally, PCR products were visualized using 1% agarose gel. Primers used for this study are listed in Table ##SUPPL##0##S2##.</p>", "<title>Biological assays</title>", "<p id=\"Par18\">The paper disk method was used to evaluate the antibacterial activities of peucemycin B against Gram-positive bacteria including both MRSA and MSSA strains of <italic>Staphylococcus aureus</italic> and Gram-negative bacteria <italic>Proteus hauseri</italic> NBRC 3851. The compound dissolved in DMSO was used for the test along with DMSO as a negative control and erythromycin as a positive control. The antibacterial effect was assessed after incubating plates at 37 °C for 16 − 24 h (Weinstein et al. ##UREF##5##2018##; Poudel et al. ##REF##36080320##2022##).</p>", "<p id=\"Par19\">Five different human cancer cell lines were obtained from the Korean Cell Line Bank (Seoul, Korea). MKN45 gastric cancer and NCI-H1650 lung cancer cell lines were grown in RPMI-1640 media (Corning Cellgro, Manassas, VA, USA) supplemented with 10% fetal bovine serum (FBS; R&amp;D systems, Minneapolis, MN, USA). Hep3B liver cancer cells, MDA-MB-231 breast cancer cells, and MRC-5 lung normal cells were grown in DMEM medium (Corning Cellgro) supplemented with 10% FBS. U87MG brain cancer cell line was cultured with MEM medium (Corning Cellgro) supplemented with 10% FBS. All cells were cultured at 37 °C in a humidified CO₂ incubator with 5% CO₂ (Thermo Fisher Scientific, Vantaa, Finland). For cell viability assay, a CellTiter-Glo® luminescent assay system (Promega, Madison, WI, USA) was used according to the manufacturer’s instructions. Briefly, cells were seeded into a 96-white well culture plate at a density of 3 × 10³ cells/well and treated with peucemycin or its derivative at 0–400 µM for 72 h. After adding 20 µL of substrate solution to each well, culture plates were shaken for 2 min. They were then incubated at room temperature in the dark for 10 min. Luminescence was measured using a multimode microplate reader. Finally, IC₅₀ values were determined with acquired data utilizing GraphPad Prism 6.</p>" ]

[ "<title>Results</title>", "<title>Identification of a new peucemycin derivative</title>", "<p id=\"Par20\">Mass analysis and UV absorption pattern for the peak at 15.31 min indicated that it was likely a derivative of peucemycin (Fig. ##FIG##0##1##). The structure was supported by LC–MS/MS analysis of the compound with <italic>m/</italic>z 431.2071 [M + H]⁺ (expected mass <italic>m/</italic>z 431.2064), <italic>m/</italic>z 413.1956 [M-OH + H]⁺ (expected mass <italic>m/</italic>z 413.1959), <italic>m/</italic>z 175.1104 [M-B + H]⁺ (expected mass <italic>m/</italic>z 175.1117), and <italic>m/</italic>z 239.0910 [M-A + H]⁺ (expected mass <italic>m/</italic>z 239.0914) (Fig. ##SUPPL##0##S1##). These findings led to the conclusion that the newly discovered compound was hydroxylated peucemycin. Furthermore, the compound had absorbance maxima of 200.7346, 215.7346, and 265.7347 nm similar to peucemycin and peucemycin A (Magar et al. ##REF##36680588##2023##; Pham et al. ##REF##35424263##2021##) (Fig. ##FIG##0##1##).</p>", "<title>Growth rate analysis and production of peucemycin B</title>", "<p id=\"Par21\">The maximum peucemycin B production occurred at 72 h, while the maximum growth occurred at 144 h (Fig. ##SUPPL##0##S2##). At 72 h, the yield of peucemycin B was found to be 11.48 mg/L. Therefore, <italic>S. peucetius</italic> DM07 was cultured for 72 h to isolate the compound and determine its structure.</p>", "<title>Structure elucidation of peucemycin B</title>", "<p id=\"Par22\">The compound was isolated as a yellow powder that could readily dissolve in dimethylsulfoxide (DMSO). The structure of the compound was examined using NMR spectroscopy. Results are summarized in Table ##TAB##0##1##, Fig. ##FIG##1##2##, and Fig. ##SUPPL##0##S3##. Compared to the structure of peucemycin (Pham et al. ##REF##35424263##2021##), a chemical shift (δ_C) of C-19 from 21.24 ppm of peucemycin to 62.89 ppm of peucemycin B was found. Similarly, a chemical shift (δ_C) of C-20 from 14.01 ppm of peucemycin to 24.35 ppm of peucemycin B was found. 2D NMR data further supported the structure of peucemycin B. Correlation between carbon and proton of peucemycin B is summarized in Fig. ##FIG##1##2##. COSY correlations were observed between H-25/Me-26, H23/H24, H-19/Me-20, H-21/Me-22, and H-19/H-18 (Fig. ##SUPPL##0##S3##c). Similarly, HMBC correlations were found between Me-20 to C-19, 18, Me-22 to C-21, C-17, and Me-26 to C-25, C24 (Fig. ##SUPPL##0##S3##f). These results revealed the existence of three methyl groups in the structure. The presence of methine groups was identified from COSY correlations as seen among H-7 and H-8, and H-23 and H-24 while similar HMBC correlations were seen among H-23 and H-24 to C-25 and, H-7 and H-8 to H-9 and H-6. ROESY correlations among protons of C-9, C-8, and C-7 revealed that they were all present on the same side. Figure ##SUPPL##0##S3##d gives information on additionally observed correlations. All of these results supported that the structure was 19-hydroxy peucemycin (peucemycin B).\n</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par29\">In this work, a new peucemycin derivative (peucemycin B) was isolated, and both the pathway-specific regulator (PeuR) and global regulator (BldA) were investigated as targets for the improvement of the production of peucemycin and its derivatives. The newly identified derivative is synthesized from the hydroxylation at C-19 of peucemycin suggesting a separate hydroxylation step distinct from the C-25 hydroxylation of peucemycin A biosynthesis (Magar et al. ##REF##36680588##2023##). The Peu BGC analysis provides insight into the likelihood that the PeuK is involved in the biosynthesis of peucemycin B (Magar et al. ##REF##36680588##2023##).</p>", "<p id=\"Par30\">The peucemycin B produced higher anticancer activity towards some cancer cell lines when compared to peucemycin and peucemycin A (Fig. ##FIG##2##3## and Fig. ##SUPPL##0##S5##) (Pham et al. ##REF##35424263##2021##; Magar et al. ##REF##36680588##2023##). The IC₅₀ values of peucemycin B for MKN45 and NCI-H1650 cell lines were less than 100 µM, whereas those for MDA-MB-231, Hep3B, and U87MG cancer cell lines were higher than 100 µM. In comparison with some anticancer drugs that have very low IC₅₀ values (Table ##SUPPL##0##S4##), the compound is characterized as mildly active to weakly active against these cell lines (Table ##SUPPL##0##S3##) (Jin et al. ##REF##27499633##2016##; Abbasi et al. ##REF##32180814##2020##; Wan et al. ##UREF##4##2021##; Choi et al. ##REF##18468633##2008##; Zhan et al. ##UREF##6##2018##). The reduced solubility of the compound could be the cause of low anticancer activity. Therefore, enhancing solubility might help to improve activity.</p>", "<p id=\"Par31\">Analysis of <italic>peuR</italic> revealed three TTA codons. TTA codon is regarded as a rare codon since the tRNA required for this UUA (leucine) is very rare in <italic>Streptomyces</italic> (Chater and Chandra ##REF##18337685##2008##; Zaburannyy et al. ##REF##19574286##2009##). The <italic>S. peucetius</italic> was found to be deficient in tRNA required for the UUA codon (Chater and Chandra ##REF##18337685##2008##; Pokhrel et al. ##REF##27664727##2016##). Hence, the combined effects of overexpression of <italic>peuR</italic> and heterologous expression of <italic>bldA</italic> were studied.</p>", "<p id=\"Par32\">Similar patterns of peucemycin and its derivatives production were seen in the <italic>S. peucetius</italic> bldA25 and <italic>S. peucetius</italic> R25 strains, both of which had higher titers than the <italic>S. peucetius</italic> DM07 and <italic>S. peucetius</italic> P25 <bold>(</bold>Fig. ##FIG##3##4## and Fig. ##FIG##4##5##). The results were also supported by the transcription level of some genes (Fig. ##FIG##6##7##). As predicted, overexpression of SARP gene contributed to higher production titer (Chen et al. ##UREF##0##2015##). Furthermore, the production results of <italic>S. peucetius</italic> DM07 and <italic>S. peucetius</italic> P25 suggest that a mistranslation of <italic>peuR</italic> mRNA may have resulted in a lower level of functional PeuR that regulates Peu BGC.</p>", "<p id=\"Par33\">The final strain, <italic>S. peucetius</italic> bldAR25 produced the highest level of peucemycin derivatives (Fig. ##FIG##3##4## and Fig. ##FIG##4##5##). The strain had the highest transcriptional levels of <italic>peuA</italic>, <italic>peuG</italic>, and <italic>peuJ</italic>, indicating that a functional copy of PeuR was synthesized in the presence of BldA (Fig. ##FIG##6##7##). Similarly, the results conclude that higher expression of <italic>peuJ</italic> is linked to the highest level of peucemycin A production. However, the gene responsible for the hydroxylation of peucemycin to peucemycin B is yet unknown and hence, the reason for the higher titer cannot be concluded from the existing results. All of these findings ultimately lead to the conclusion that the <italic>peuR</italic> is responsible for the regulation of Peu BGC, while BldA helps in producing a functional copy of PeuR.</p>", "<p id=\"Par34\">In summary, we identified another peucemycin derivative and named it peucemycin B, 19-hydroxy peucemycin. Compared to peucemycin, the production of peucemycin derivatives was lower. Hence, in this study, we increased the production of peucemycin derivatives by using two regulators, a pathway-specific SARP regulator (PeuR) and a global regulator (BldA). We are now working on the gene responsible for the formation of peucemycin B.</p>" ]

[]

[ "<title>Abstract</title>", "<p id=\"Par1\"><italic>Streptomyces peucetius</italic> ATCC 27952 is known to produce a variety of secondary metabolites, including two important antitumor anthracyclines: daunorubicin and doxorubicin. Identification of peucemycin and 25-hydroxy peucemycin (peucemycin A), as well as their biosynthetic pathway, has expanded its biosynthetic potential. In this study, we isolated a new peucemycin derivative and identified it as 19-hydroxy peucemycin (peucemycin B). Its antibacterial activity was lower than those of peucemycin and peucemycin A. On the other hand, this newly identified peucemycin derivative had higher anticancer activity than the other two compounds for MKN45, NCI-H1650, and MDA-MB-231 cancer cell lines with IC₅₀ values of 76.97 µM, 99.68 µM, and 135.2 µM, respectively. Peucemycin biosynthetic gene cluster revealed the presence of a SARP regulator named PeuR whose role was unknown. The presence of the TTA codon in the <italic>peuR</italic> and the absence of global regulator BldA in <italic>S. peucetius</italic> reduced its ability to regulate the peucemycin biosynthetic gene cluster. Hence, different mutants harboring these genes were prepared. <italic>S. peucetius</italic> bldA25 harboring <italic>bldA</italic> produced 1.75 times and 1.77 times more peucemycin A (11.8 mg/L) and peucemycin B (21.2 mg/L), respectively, than the wild type. On the other hand, <italic>S. peucetius</italic> R25 harboring <italic>peuR</italic> produced 1.86 and 1.79 times more peucemycin A (12.5 mg/L) and peucemycin B (21.5 mg/L), respectively, than the wild type. Finally, strain <italic>S. peucetius</italic> bldAR25 carrying <italic>bldA</italic> and <italic>peuR</italic> produced roughly 3.52 and 2.63 times more peucemycin A (23.8 mg/L) and peucemycin B (31.5 mg/L), respectively, than the wild type.</p>", "<title>Key points</title>", "<p id=\"Par2\">\n<italic>• This study identifies a new peucemycin derivative</italic>, <italic>19-hydroxy peucemycin</italic> (<italic>peucemycin B</italic>).</p>", "<p id=\"Par3\"><italic>• The SARP regulator</italic> (<italic>PeuR</italic>)<italic> acts as a positive regulator of the peucemycin biosynthetic gene cluster</italic>.</p>", "<p id=\"Par4\">• <italic>The overexpression of peuR and heterologous expression of bldA increase the production of peucemycin derivatives</italic>.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00253-023-12923-4.</p>", "<title>Keywords</title>" ]

[ "<title>Biological activities</title>", "<p id=\"Par23\">Antibacterial activities of peucemycin B were weaker than those of peucemycin and peucemycin A. For <italic>Proteus hauseri</italic> NBRC 3851, peucemycin produced about two times higher antibacterial effect than peucemycin B when equivalent amounts of compounds were used (Fig. ##SUPPL##0##S4##b). The growth of some <italic>S. aureus</italic> strains like <italic>S. aureus</italic> CCARM 0204 (MSSA) and <italic>S. aureus</italic> CCARM 3090 (MRSA) was inhibited by the compound at a high amount (Fig. ##SUPPL##0##S4##a). These data showed that the compound had less antibacterial effects than peucemycin and peucemycin A.</p>", "<p id=\"Par24\">Five different cancer cell lines were used to evaluate the anticancer activities of the compound (Fig. ##FIG##2##3##). IC₅₀ values for MKN45 and NCI-H1650 were found to be 76.97 µM and 99.68 µM, respectively (Table ##SUPPL##0##S3##). These results showed that the compound has mild activity against these cell lines. Similarly, for three other cell lines MDA-MB-231, U87MG, and Hep3B, its IC50 values were found to be 135.2 µM, 150.0 µM, and 175.4 µM, respectively (Table ##SUPPL##0##S3##). These results showed that the compound was weakly active against these cell lines.</p>", "<title>Heterologous expression of <italic>bldA</italic> and overexpression of <italic>peuR</italic></title>", "<p id=\"Par25\">The nucleotide sequence of <italic>peuR</italic> was found to have three rare TTA codons at the 13th, 52nd, and 74th codon positions that code for leucine (Fig. ##SUPPL##0##S6##). <italic>S. peucetius</italic> does not have tRNA for this codon. Hence, <italic>bldA</italic> from <italic>S. coelicolor</italic> was heterologously expressed along with overexpression of <italic>peuR</italic>. At first, 873 bp <italic>bldA</italic> was amplified from <italic>S. coelicolor</italic> and ligated into pIBR25 at <italic>Bam</italic>HI and <italic>Xba</italic>I sites to generate pbldA25 (Fig. ##SUPPL##0##S7##). Then, 963 bp <italic>peuR</italic> was amplified from <italic>S. peucetius</italic> DM07 and ligated into pIBR25 at <italic>Xba</italic>I and <italic>Hin</italic>dIII sites to generate pR25 (Fig. ##SUPPL##0##S7##). Finally, pbldAR25 vector having both genes was constructed by ligating <italic>peuR</italic> at <italic>Xba</italic>I and <italic>Hin</italic>dIII sites of pbldA25. The observation of a fragment with a size of 1836 bp in the gel after digesting with <italic>Bam</italic>HI and <italic>Hin</italic>dIII confirmed the presence of both genes in pIBR25. Transformation of these vectors resulted in mutants <italic>S. peucetius</italic> R25, <italic>S. peucetius</italic> bldA25, <italic>S. peucetius</italic> bldAR25, and <italic>S. peucetius</italic> P25.</p>", "<title>Analysis of the production of peucemycin and its derivatives as well as growth rate</title>", "<p id=\"Par26\">The impact of heterologously expressed <italic>bldA</italic> and overexpressed <italic>peuR</italic> on the production of peucemycin and its derivatives were examined in all five strains (<italic>S. peucetius</italic> DM07, <italic>S. peucetius</italic> R25, <italic>S. peucetius</italic> bldA25, <italic>S. peucetius</italic> bldAR25, and <italic>S. peucetius</italic> P25) (Fig. ##FIG##3##4##). There was no significant difference in the production of peucemycin or its derivatives between <italic>S. peucetius</italic> DM07 and <italic>S. peucetius</italic> P25 as evidenced by their HPLC profiles (Fig. ##FIG##3##4##). With less variation in the production of peucemycin than the wild type, <italic>S. peucetius</italic> bldA25 strain produced peucemycin A (11.8 mg/L) and peucemycin B (21.2 mg/L) at 1.75 and 1.77 times higher levels than the wild type, respectively. Similarly, <italic>S. peucetius</italic> R25 produced a 1.86 times higher level of peucemycin A (12.5 mg/L) and 1.79 times higher level of peucemycin B (21.5 mg/L) with less variation in production of peucemycin (Fig. ##FIG##4##5##). On the other hand, <italic>S. peucetius</italic> bldAR25 significantly altered the production of peucemycin and its derivatives when compared with the wild type (Fig. ##FIG##4##5##). This strain produced 3.52 times more peucemycin A (23.8 mg/L) and 2.63 times more peucemycin B (31.5 mg/L) than the wild type. In addition, the amount of peucemycin (5.8 mg/L) in <italic>S. peucetius</italic> bldAR25 was 3.92 times lower than the wild type, indicating that, in contrast to the other four strains, peucemycin was converted to its derivatives at a significant rate in this strain (Fig. ##FIG##4##5##).</p>", "<p id=\"Par27\">Next, we sought to determine how genes affected bacterial growth. When compared to the wild type, <italic>S. peucetius</italic> P25 did not exhibit any significant growth differences. Among the five strains, <italic>S. peucetius</italic> bldA25 exhibited reduced growth (Fig. ##FIG##5##6##). On the other hand, <italic>S. peucetius</italic> R25 strain had a slight reduction in growth, whereas <italic>S. peucetius</italic> bldAR25 grew similarly to the wild type (Fig. ##FIG##5##6##).</p>", "<title>RT-PCR analysis of different strains</title>", "<p id=\"Par28\">Transcriptional levels of <italic>peuA</italic>, <italic>peuG</italic>, and <italic>peuJ</italic> in several strains were examined. RNA polymerase subunit gene (<italic>rpoB</italic>) was used as a positive internal control. <italic>S. peucetius</italic> DM07 and <italic>S. peucetius</italic> P25 showed lower transcriptional levels of <italic>peuA</italic>, <italic>peuG</italic>, and <italic>peuJ</italic> (Fig. ##FIG##6##7##). On the other hand, heterologous expression of <italic>bldA</italic> resulted in higher transcriptional levels of <italic>peuA</italic>, <italic>peuG</italic>, and <italic>peuJ</italic> in <italic>S. peucetius</italic> bldA25 as compared with the wild-type strain (Fig. ##FIG##6##7##). Similarly, overexpression of <italic>peuR</italic> produced a higher transcriptional level of <italic>peuA</italic> as seen for <italic>S. peucetius</italic> R25 while showing similar transcriptional levels of other genes as that of <italic>S. peucetius</italic> bldA25 (Fig. ##FIG##6##7##). Finally, the highest transcriptional levels of <italic>peuG</italic> and <italic>peuJ</italic> were seen in <italic>S. peucetius</italic> bldAR25, while similar transcriptional levels were seen for <italic>peuA</italic> and <italic>peuR</italic> as compared with <italic>S. peucetius</italic> R25 (Fig. ##FIG##6##7##).</p>", "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Author contribution</title>", "<p>RTM conceived and conducted the research and wrote the manuscript. RTM and VTTP designed the research. PBP assisted with carrying out the antimicrobial test. AFB helped in preparing some reagents and media. JKS conceived and supervised the research, helped in writing the manuscript, and edited the manuscript to the final version.</p>", "<title>Funding</title>", "<p>This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (NRF-2021R1A2C2004775).</p>", "<title>Data availability</title>", "<p>All data generated or analyzed during this study are included in this published article (and its supplementary information files).</p>", "<title>Declarations</title>", "<title>Ethical approval</title>", "<p id=\"Par35\">This article does not contain any studies with human participants or animals performed by any of the authors.</p>", "<title>Conflict of interest</title>", "<p id=\"Par36\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>HPLC and mass analyses of the culture extract of <italic>S. peucetius</italic> DM07. <bold>a</bold> HPLC profile of culture extract, red asterisk represents the probable peucemycin derivative. <bold>b</bold> UV absorption and HRMS spectrum of peucemycin B</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Two-dimensional NMR correlation of peucemycin B. <bold>a</bold>\n¹H-¹H COSY (green bold line) and HMBC (arrow). <bold>b</bold>\n¹H-¹H ROESY (blue arrow)</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Anticancer activities of peucemycin B for various cancer cell lines. Standard deviation was calculated and represented as error bars from three experimental replicates for each sample</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>HPLC profiles of culture extracts. <bold>a</bold>\n<italic>S. peucetius</italic> DM07, <bold>b</bold>\n<italic>S. peucetius</italic> P25, <bold>c</bold>\n<italic>S. peucetius</italic> bldA25, <bold>d</bold>\n<italic>S. peucetius</italic> R25, and <bold>e</bold>\n<italic>S. peucetius</italic> bldAR25. Dark blue asterisk is for peucemycin. Sky blue asterisk is for peucemycin A. Red asterisk is for peucemycin B</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Comparison of the production of peucemycin and its derivatives. DM07, <italic>S. peucetius</italic> DM07; P25, <italic>S. peucetius</italic> P25; bldA25, <italic>S. peucetius</italic> bldA25; R25, <italic>S. peucetius</italic> R25; bldAR25, <italic>S. peucetius</italic> bldAR25. Standard deviation was calculated and represented as error bars from three experimental replicates for each sample. Student’s <italic>t</italic>-test is used to determine the <italic>p</italic>-values. Statistical significance: <bold>**</bold>\n<italic>p</italic> &lt; 0.01, <bold>***</bold>\n<italic>p</italic> &lt; 0.001</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Comparison of mycelial density. DM07, <italic>S. peucetius</italic> DM07; P25, <italic>S. peucetius</italic> P25; bldA25, <italic>S. peucetius</italic> bldA25; R25, <italic>S. peucetius</italic> R25; bldAR25, <italic>S. peucetius</italic> bldAR25. Standard deviation was calculated and represented as error bars from three experimental replicates for each sample</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><p>RT-PCR profiles of <italic>rpoB</italic>, <italic>peuA</italic>, <italic>peuG</italic>, <italic>peuJ</italic>, and <italic>peuR</italic>. DM07, <italic>S. peucetius</italic> DM07; P25, <italic>S. peucetius</italic> P25; bldA25, <italic>S. peucetius</italic> bldA25; R25, <italic>S. peucetius</italic> R25; bldAR25, <italic>S. peucetius</italic> bldAR25</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>¹H- and ¹³C-NMR data of peucemycin B in DMSO-<italic>d</italic>₆</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">No</th><th align=\"left\">δ_C, type</th><th align=\"left\">δ_H, (<italic>J</italic>, Hz)</th><th align=\"left\">No</th><th align=\"left\">δ_C, type</th><th align=\"left\">δ_H, (<italic>J</italic>, Hz)</th></tr></thead><tbody><tr><td align=\"left\">1</td><td align=\"left\">160.25, C</td><td align=\"left\"/><td align=\"left\">14</td><td align=\"left\">114.46, CH</td><td align=\"left\">6.21 (1 H, s)</td></tr><tr><td align=\"left\">2</td><td align=\"left\">39.17, CH₂</td><td align=\"left\">3.65 (1 H, d, <italic>J</italic> 15.8) 3.73 (1 H, d, <italic>J</italic> 15.8)</td><td align=\"left\">16</td><td align=\"left\">136.17, CH</td><td align=\"left\">6.06 (1 H, s)</td></tr><tr><td align=\"left\">3</td><td align=\"left\">167.33, CO</td><td align=\"left\"/><td align=\"left\">17</td><td align=\"left\">131.71, C</td><td align=\"left\"/></tr><tr><td align=\"left\">5</td><td align=\"left\">60.70, CH₂</td><td align=\"left\">5.00 (1 H, d, <italic>J</italic> 11.9) 5.04 (1 H, d, <italic>J</italic> 12.0)</td><td align=\"left\">18</td><td align=\"left\">135.84, CH</td><td align=\"left\">5.12 (1 H, d, <italic>J</italic> 8.2)</td></tr><tr><td align=\"left\">6</td><td align=\"left\">133.28, C</td><td align=\"left\"/><td align=\"left\">19</td><td align=\"left\">62.89, CH</td><td align=\"left\">4.43 (1 H, m)</td></tr><tr><td align=\"left\">7</td><td align=\"left\">129.26, CH</td><td align=\"left\">6.02 (1 H, d, <italic>J</italic> 15.8)</td><td align=\"left\">20</td><td align=\"left\">24.35, CH₃</td><td align=\"left\">1.12 (3 H, d, <italic>J</italic> 6.0)</td></tr><tr><td align=\"left\">8</td><td align=\"left\">130.65, CH</td><td align=\"left\">5.71 (1 H, dd, <italic>J</italic> 15.6, 4.9)</td><td align=\"left\">21</td><td align=\"left\">23.79, CH₂</td><td align=\"left\">2.04 (2 H, m)</td></tr><tr><td align=\"left\">9</td><td align=\"left\">74.54, CH</td><td align=\"left\">4.33 (1 H, d, <italic>J</italic> 4.8)</td><td align=\"left\">22</td><td align=\"left\">13.54, CH₃</td><td align=\"left\">0.90 (3 H, t, <italic>J</italic> 7.4)</td></tr><tr><td align=\"left\">10</td><td align=\"left\">72.14, CH</td><td align=\"left\">4.92 (1 H, s)</td><td align=\"left\">23</td><td align=\"left\">118.82, CH</td><td align=\"left\">6.27 (1 H, d, <italic>J</italic> 16.4)</td></tr><tr><td align=\"left\">11</td><td align=\"left\">162.89, C</td><td align=\"left\"/><td align=\"left\">24</td><td align=\"left\">138.65, CH</td><td align=\"left\">6.81 (1 H, dt, <italic>J</italic> 13.87, 6.34, 6.34)</td></tr><tr><td align=\"left\">12</td><td align=\"left\">122.54, C</td><td align=\"left\"/><td align=\"left\">25</td><td align=\"left\">26.79, CH₂</td><td align=\"left\">2.11 (2 H, m)</td></tr><tr><td align=\"left\">13</td><td align=\"left\">178.41, CO</td><td align=\"left\"/><td align=\"left\">26</td><td align=\"left\">13.66, CH₃</td><td align=\"left\">1.00 (3 H, t, <italic>J</italic> 7.4)</td></tr></tbody></table></table-wrap>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Borderline personality disorder (BPD) is characterized by instability in self, emotion dysregulation, and dysfunctional interactional processes. Altered facial emotion processing, threat hypersensitivity, and increased rejection sensitivity have been described as possible underlying impairments [##REF##24574071##1##–##REF##26269211##3##] and may lead to particular challenges when individuals with BPD are parents and interact with their children. Mothers with BPD seem to experience increased levels of parenting distress in self-report and feel less competent in their parenting [##UREF##0##4##]. They tend to show more intrusive behaviors, less reciprocal mother–child interactions on a dyadic level and reveal altered oxytocin and cortisol reactivity, which could indicate a lack of reward and of relief of stress in the interaction with their child [##REF##35709662##5##].</p>", "<p id=\"Par3\">More and more research tries to understand the neurobiological underpinnings of the disorder, bringing up the theory of fronto-limbic imbalance [##REF##33414379##6##, ##REF##25935068##7##]. The general model of cognitive control of emotion (MCCE) aims to explain emotion regulation—a central topic in BPD—by integrating knowledge on behavior and experience, information processing, and neural systems [##REF##23025352##8##]. It describes mechanisms involved in generating an emotion (affect system) as well as mechanisms involved in cognitive control, and, thus, can help to understand neural alterations in BPD. According to the MCCE, the amygdala, anterior insula (AINS), ventral striatum (VS) and orbitofrontal cortex are involved in emotion generation [##REF##23025352##8##]. These areas—especially the amygdala and insula [##UREF##1##9##, ##REF##22906520##10##]—have often been reported to show increased activity in BPD in various contexts, especially in between-groups contrasts for negative—neutral experimental conditions [##REF##22906520##10##, ##REF##30581154##11##], but also during a social inclusion condition as compared to a passive watching condition [##UREF##1##9##]. This could relate to an emotional over-involvement, increased processing and augmented negative appraisal of emotional stimuli in BPD in areas involved in emotion regulation (MCCE) [##REF##22906520##10##, ##REF##30581154##11##] and the symptom of intense and instable emotions. Additionally, especially the AINS and the dorsal anterior cingulate cortex (ACC) are also involved in the salience network, which detects, classifies and re-evaluates salient stimuli out of the broad range of information (one perceives) and which could play an important role in emotion regulation in BPD [##REF##34611112##12##, ##REF##29961363##13##]. An exaggerated sensitization to emotionally salient situations, an increased experience of emotions, and reduced or dysfunctional emotion regulation abilities could be reasons for increased experienced distress in individuals with BPD [##REF##29961363##13##, ##REF##31784065##14##].</p>", "<p id=\"Par4\">Furthermore, the MCCE describes the ACC, the dorsolateral, ventrolateral, and dorsomedial prefrontal cortex (PFC) as important regions for emotion processing, regulation and cognitive control with modulating effects on the affect system [##REF##23025352##8##]. In BPD, meta-analyses reported enhanced activity in the ventrolateral prefrontal cortex (PFC) [##REF##30581154##11##], reduced activity in dorsolateral prefrontal areas [##REF##25935068##7##], and heterogeneous results with hypo- and hyperactivations in comparison with healthy controls probably depending on the study design and stimuli used for the ACC [##REF##33414379##6##, ##REF##22906520##10##]. Individuals with BPD also seem to have a reduced striatal neural response to reward and loss anticipation in response to monetary rewards compared to healthy controls [##REF##27766203##15##]. Such a result could indicate alterations in the neural processing of reward and could also affect social interactions, if similar patterns apply to social rewards.</p>", "<p id=\"Par5\">The concept of the “maternal brain” highlights neural systems—that have also been shown to be altered in BPD—including (among others) emotion processing and salience of social cues (amygdala, insula, ACC), emotional and cognitive control (ventrolateral and dorsolateral PFC, ACC), and reward and motivation (VS), which are described to be critical for parenting [##REF##26268151##16##, ##REF##33038383##17##]. These systems might serve to increase neural and behavioral sensitivity to child cues, as well as self- and co-regulative processes in the context of (distressful) interactions in healthy mothers [##REF##33038383##17##]. For emotion processing and control, the maternal brain concept relates well to the MCCE as effective emotion regulation with a well-regulated prefrontal and cingulate control system, which can modulate activity in (para-)limbic affect systems, is highly important for sensitive parenting. Healthy mothers showing intrusive maternal behaviors demonstrated an overactivation of the amygdala, which has been interpreted as an explanation for non-matched excessive maternal behavior [##REF##21881566##18##]. An excessive activity in the AINS can lead to high maternal distress, an emotional over-involvement in the child’s distress, and reduced maternal abilities to co-regulate the child’s distress [##REF##33038383##17##, ##REF##29947610##19##]. Stress in turn can negatively affect maternal response behavior and emotion regulation capacity and impacts the maternal brain adaptation [##REF##33038383##17##]. Reward-related mechanisms seem to be essential underlying factors in maternal behavior and motivate mothers to contact and care for their child [##REF##26268151##16##]. Functional magnetic resonance imaging (fMRI) studies have shown that sounds, pictures, or videos of the child activate areas in the reward system of healthy mothers [##REF##17686467##20##–##REF##26236256##22##]. Stronger activations of the nucleus accumbens were shown in mothers with sensitive maternal behavior compared to mothers with intrusive maternal behavior [##REF##21881566##18##]. Up to now, brain activity in mothers with BPD has not been studied.</p>", "<p id=\"Par6\">Here, we analyzed neural activity in significant areas of the maternal brain with a focus on stress and reward in mothers with BPD compared to healthy mothers using a script-driven imagination-based fMRI paradigm. Scripts described stressful or rewarding mother–child interactions, or situations in which the mother was alone. We expected altered activity in areas of (1) emotion processing and salience (amygdala, insula, ACC), (2) emotional and cognitive control (ventrolateral and dorsolateral PFC, ACC), and (3) reward and motivation (ventral striatum) in mothers with BPD compared to healthy mothers. These alterations could be specifically pronounced for mother–child interactions. We further investigated in an explorative approach neural activity in the different phases of stimulation (audio phase, imagination phase), as well as associations with the quality of real-life mother–child interactions.</p>" ]

[ "<title>Materials and methods</title>", "<title>Participants</title>", "<p id=\"Par7\">Twenty-five mothers with a current diagnosis of BPD (M_{number of BPD symptoms} = 6.4 ± 1.1; M_age = 31.2 ± 7.0 years) and 28 healthy mothers without a current or lifetime psychiatric diagnosis (HC; M_age = 31.9 ± 5.0 years; t₅₁ = − 0.44, <italic>p</italic> = 0.663) were included in the study. Mothers did not differ in intelligence estimation (BPD: M = 26.4 ± 9.8; HC: M = 29.5 ± 8.9; t₅₁ = − 1.21; <italic>p</italic> = 0.233). The participants’ children were between 18- and 36-months old (BPD: M_age = 27.2 ± 7.0 months; HC: M_age = 27.4 ± 6.0 months; t₅₁ = − 0.13, <italic>p</italic> = 0.897; BPD/HC: 12/13 girls, 13/15 boys; Χ²₁ = 0.01, <italic>p</italic> = 0.909); please also see Table ##TAB##0##1##. General exclusion criteria were age &lt; 18 and &gt; 50 years, MRI contraindications, neurological disorders, organic brain damage, severe medical illness, alcohol or drug (nicotine excluded) dependence over the last 24 months, left-handedness, mother and child not living together, pregnancy, and breast-feeding. Comorbidities in mothers with BPD were as follows: posttraumatic stress disorder: <italic>n</italic> = 6, major depression: <italic>n</italic> = 9, anxiety disorder: <italic>n</italic> = 6, obsessive–compulsive disorder: <italic>n</italic> = 1. Six mothers with BPD took psychotropic medication (SSRI: <italic>n</italic> = 4; SSNRI: <italic>n</italic> = 1; Ritalin: <italic>n</italic> = 1). Originally, 26 mothers with BPD and 30 healthy mothers were assessed; however, one mother with BPD and two healthy mothers had to be excluded due to excessive head motion (BPD, HC) and a brain lesion (HC). Participants were screened via telephone and participated in a diagnostic interview and a behavioral observation [##REF##35709662##5##].</p>", "<title>Measures</title>", "<p id=\"Par8\">We assessed current and lifetime axis I disorders using the International Neuropsychiatric Interview (M.I.N.I.; [##REF##9881538##23##]) and BPD using the International Personality Disorder Examination (IPDE; [##REF##8122958##24##]). Intelligence was estimated using the mini-q [##UREF##2##25##], a reliable and validated screening for cognitive abilities based on the reasoning test in English presented by Baddeley [##UREF##3##26##].</p>", "<p id=\"Par9\">Mother–child interaction was assessed by behavioral observation in a 10-min free-play situation of a sub-sample (BPD: <italic>n</italic> = 22; HC: <italic>n</italic> = 28). Interactions were rated for maternal, child, and dyadic behavior using the well validated “Coding Interactive Behavior” manual (CIB [##UREF##4##27##]). Composite scores were computed for maternal sensitivity, intrusiveness, and limit setting, child involvement and withdrawal, as well as dyadic reciprocity and negative states. A CIB total score, which included maternal, child, and dyadic behavior (((maternal sensitivity + maternal limit setting + child involvement + dyadic reciprocity) /4) / ((maternal intrusiveness + child withdrawal + dyadic negative states) /3))), was used to judge the overall quality of the interaction (0 = low, 5 = high). Two coders were trained to 90% agreement and rated the videos blind to groups and all other information. Interrater reliability was at 95% (intraclass <italic>r</italic> = 0.95) based on 12 video-taped interactions (24%) which were rated separately by the two coders. More information on the method and data of a largely overlapping sample is available at [##REF##35709662##5##].</p>", "<title>FMRI paradigm</title>", "<p id=\"Par10\">We used a script-driven imagination-based paradigm based on Neukel et al. [##REF##29947610##19##], which consisted of 24 acoustically presented pseudorandomized scripts depicting everyday situations presented in two sessions with a structural MR scan in between. At the beginning of the paradigm, mothers were instructed to listen to the scripts and imagine the situation as vividly as possible. After a 15 s baseline, a 15 s long script, read by a professional actress, was played [audio phase (AP)]. Then, mothers were asked to imagine the mother–child interaction for 15 s [imagination phase (IP)]. After that, participants rated their affect as a subjective evaluation of emotion (1 = negative to 5 = positive), arousal as a subjective evaluation of affective physiological reactions (1 = relaxed to 5 highly aroused), and the experienced vividness (1 = not at all to 5 = very good) in order to investigate associated affective states (Fig. ##FIG##0##1##). For the baseline, participants received the instruction to close their eyes, to lie still and think of nothing in particular. Phases were separated by audio signals. Scripts were divided into 8 scripts describing a rewarding mother–child interaction (rMCI; e.g., “I was outside and finally I am getting back to my daughter. When she sees me, she runs towards me and stretches her arms towards me. She smiles happily.”), 8 scripts describing a stressful mother–child interaction (sMCI; e.g., “I was outside and finally I am getting back to my daughter. When she sees me, she runs away from me and tries to hide. My daughter starts to cry and avoids my gaze.”) and 8 scripts of a comparable situation without the child (nonMCI; e.g., “I was outside and finally I am getting back home. I open the door and take off my shoes. I put the shoes next to the door. Then I take off my jacket.”). Scripts were all parallelized regarding the content, had the same length and same volume. For further information on validation of the stimuli and all scripts, please see online resource 1 and 2 in the supplementary materials.</p>", "<title>FMRI data acquisition</title>", "<p id=\"Par11\">MRI scans were conducted using a 3 T whole body MR-scanner with a 32-channel head coil. After 22 participants (BPD: 11; HC: 11), the scanner was updated from a Magnetom TIM Trio to a Magnetom Prisma (Siemens). Thirty-three transverse slices (slice thickness: 3 mm) were acquired with a T2*-weighted echo-planar imaging sequence (TR: 2000 ms, TE: 30 ms; flip angle = 78°; field of view: 192 mm; in-plane resolution 3 × 3 mm). Structural images were recorded using a T1-weighted, sagittal oriented MPRAGE sequence with isotropic high-resolution (1 × 1 × 1 mm³). Prior to the paradigm, participants underwent a ~ 6 min resting-state scan. The paradigm lasted ~ 28 min. Participants were asked to move as little as possible and to follow the instructions described above (2.3).</p>", "<title>Data analyses</title>", "<p id=\"Par12\">For demographic data, independent t-tests for continuous variables and Χ²-tests for categorical variables were used. Since CIB data were not normally distributed, a Mann–Whitney <italic>U</italic> test was used. The rating of vividness was used to document the successful completion of the task and was compared for possible group differences. Individual means were expected to be between 4 and 5, which was fulfilled by all participants. For ratings of affect and arousal, repeated-measure analyses of variance (rmANOVA) with group (BPD, HC) as between-subjects factor and condition (rMCI, sMCI, nonMCI) as within-subject factor with Dunn’s multiple comparisons with Bonferroni correction for multiple testing as post-hoc tests were used. Results were considered to be significant at <italic>p</italic> &lt; 0.05. Partial eta squared (η_p²) was used as a measure of effect sizes. Data analysis was performed using IBM SPSS Statistics 28.0 (IBM, Armonk, NY).</p>", "<p id=\"Par13\">FMRI data were analyzed using Statistical Parametric Mapping 12 software (SPM 12; The Wellcome Centre for Human Neuroimaging, London, UK) implemented in MATLAB (R2017a, The MathWorks, Natick, MA, USA). Preprocessing included realignment, co-registration to the mean structural image, spatial normalization including segmentation, and smoothing with a 6 mm full width at half-maximum (FWHM) Gaussian filter. Motion parameters were assessed by calculating the framewise displacement (FD; [##REF##22019881##28##]). Datasets with excessive head movements (FD &gt; 3 mm) in more than 10% of the trials were excluded (<italic>n</italic> = 2). Otherwise, motion scrubbing was performed in order to eliminate functional volumes during which a FD &gt; 3 mm occurred during the relevant phases from the statistical analysis (BPD: <italic>n</italic> = 3; HC: <italic>n</italic> = 2; maximum number of scrubbed scans: 2). The threshold of 3 mm was chosen with regard to the voxel size of the T2*-weighted echo-planar imaging sequence being 3 × 3 × 3 mm. On a first level, a general linear model was defined for each participant for the baseline, AP, IP, and rating phase as separate regressors for the three conditions (rMCI, sMCI, nonMCI), as well as six movement parameters. Each data set was high-pass filtered (cutoff 128 s) and first-order autoregressive processes corrected for temporal autocorrelations. Contrast images (rMCI-baseline, sMCI-baseline, nonMCI-baseline) were calculated for each participant for the AP and IP. On a second-level, a 2 × 3 full factorial design with group (BPD, HC) and condition (rMCI, sMCI, nonMCI) was used with type of scanner and use of medication as covariates of no interest. As our primary interest was the imagination phase, a first model was calculated for the IP. Since imagination already starts with the listening to the script, we also calculated a model for the audio phase to capture possible first reactions to the presented scripts. Due to our specific hypotheses on the maternal brain with a focus on stress and reward, we performed region-of-interest (ROI) analyses with a single mask including bilateral amygdala, insula, anterior cingulate cortex, ventral striatum, inferior frontal gyrus, and middle frontal gyrus. We used SPM small volume correction (SVC) of p_FWE &lt; 0.05 on the respective <italic>p</italic> &lt; 0.01 uncorrected whole-brain statistical maps. The regions for ROI analyses were chosen based on a review of Kim et al. [##REF##26268151##16##], describing these areas as part of the “maternal brain,” and defined by the Neuromorphometrics atlas (Neuromorphometrics, Inc. (Somerville, MA, USA) <ext-link ext-link-type=\"uri\" xlink:href=\"http://Neuromorphometrics.com/\">http://Neuromorphometrics.com/</ext-link>, accessed on 02/05/21 under academic subscription). For comparison, results of a whole brain analysis can be found in the supplements (online resource 3).</p>", "<p id=\"Par14\">Since we were also interested, if neural activity differences between groups were associated with real-life mother–child interaction, we analyzed Spearman’s correlations between significant neural clusters and the CIB-score. The MarsBaR Toolbox (0.44) [##UREF##5##29##] was used to extract parameter estimates form these clusters. Additionally, these parameter estimates were used to depict differences between AP and IP.</p>" ]

[ "<title>Results</title>", "<title>Behavioral data</title>", "<p id=\"Par15\">Mothers with BPD showed lower scores at the CIB-score (BPD: M = 2.9 ± 0.8; HC: M = 3.4 ± 0.4; U_51.16 = 442.5, <italic>p</italic> = 0.009; Table ##TAB##0##1##). There was no significant group difference regarding the rating of vividness of imagination (t₅₁ = − 0.56, <italic>p</italic> = 0.576).</p>", "<p id=\"Par16\">Analyses of the affect ratings revealed a significant effect of condition (F_2,102 = 115.60, <italic>p</italic> &lt; 0.001, η_p² = 0.69) with highest affect ratings for rMCI (rMCI &gt; nonMCI &gt; sMCI), and a significant group effect (F_1,51 = 5.24, <italic>p</italic> = 0.026, η_p² = 0.09) with lower affect ratings in BPD compared to HC. A significant interaction effect (F_2,102 = 4.38, <italic>p</italic> = 0.023, η_p² = 0.08) showed lower affect ratings in the rMCI in BPD compared to HC but not for the sMCI or nonMCI (Fig. ##FIG##1##2##, Table ##TAB##0##1##).</p>", "<p id=\"Par17\">Analyses of the arousal ratings revealed a significant effect of condition (F_2,102 = 164.27, <italic>p</italic> &lt; 0.001, η_p² = 0.76) with highest arousal during sMCI (sMCI &gt; rMCI = nonMCI), and a significant group effect (F_1,51 = 10.25, <italic>p</italic> = 0.002, η_p² = 0.17) with higher arousal ratings in BPD compared to HC (Fig. ##FIG##1##2##, Table ##TAB##0##1##). The interaction effect was not significant (F_2,102 = 1.57, <italic>p</italic> = 0.217, η_p² = 0.03).</p>", "<title>ROI-analyses</title>", "<p id=\"Par18\">In the imagination phase, analyses revealed a significant group difference with a stronger activation in the left AINS within a cluster extending to the left posterior insula (PINS), as well as a stronger activation in the right AINS extending to the right PINS in BPD compared to HC. Mothers with BPD also showed a stronger activation in the left pregenual ACC within a cluster extending from sub- to supragenual. A significant main effect of condition or group x condition interaction effect could not be found. Please see Table ##TAB##1##2## and Fig. ##FIG##2##3## for further information.</p>", "<p id=\"Par19\">The exploratory analysis of the audio phase revealed a significant group effect with a stronger activation in the left AINS in mothers with BPD compared to healthy mothers. Healthy mothers showed a significantly stronger activation in a cluster in the left ACC extending from pre- and subgenual to supragenual and to the right side in conditions with the child (rMCI, sMCI) compared to the condition without the child (nonMCI), but not in mothers with BPD. Please also see Table ##TAB##2##3##.</p>", "<title>Associations between fMRI and mother–child interaction</title>", "<p id=\"Par20\">There was no significant correlation of clusters with the CIB-score during the imagination phase in mothers with BPD or in healthy mothers. During the audio phase, stronger activations in the left AINS correlated with lower values in the CIB-score in mothers with BPD (<italic>r</italic> = − 0.44, <italic>p</italic> = 0.042), but not in healthy mothers (<italic>r</italic> = 0.01, <italic>p</italic> = 0.967), who did not show much variance in the CIB-score (see also Fig. ##FIG##3##4##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par21\">In the present study, we investigated neural activities in regions of the so-called maternal brain with a focus on stress and reward in a sample of mothers with BPD that has not been studied before. Mothers with BPD expressed a hyperactivation of the bilateral insula and ACC compared to healthy mothers during the imagination of stressful and rewarding mother–child interactions and non-mother–child-interactions (being with oneself). Additionally, during the audio phase, mothers with BPD showed stronger activity in the left AINS, but not in the ACC, compared to healthy mothers. Activity in the left AINS correlated negatively with the quality of real-life mother–child interactions in mothers with BPD. Interestingly, healthy mothers but not mothers with BPD showed increased activation in the ACC in response to listening to scripts describing an interaction with their child compared to nonMCI scripts. Mothers with BPD reported significantly lower affect, especially in the rMCI condition, and higher arousal during imagination of the scripts.</p>", "<p id=\"Par22\">Firstly, the subjective ratings of affect and arousal underline that the experimental manipulation aiming at inducing emotional states occurring in mother–child interactions, worked: In line with the validation of the scripts (see online resource 1 in the supplement), rMCI elicited the highest (i.e., most positive) affect ratings and sMCI elicited the lowest affect (i.e., most negative) ratings overall, while sMCI elicited the highest arousal ratings across all participants. Interestingly, mothers with BPD reported lower affect ratings in response to rMCI scripts than healthy mothers, indicating group differences in emotional perception of rMCI that are in line with previous results, showing that patients with BPD rate the intensity of happiness in happy faces lower [##UREF##6##30##] and report less positive emotion (amusement, affection, contentment; [##REF##18533129##31##]) than healthy controls. Regarding the arousal ratings, a significant group effect indicated higher arousal in mothers with BPD than in healthy mothers across all conditions.</p>", "<p id=\"Par23\">As expected, we found altered neural activity in regions involved in emotion processing and salience, as well as emotional and cognitive control in response to everyday situations in mothers with BPD. As these alterations were not more pronounced during imagination of stressful or rewarding MCI compared to nonMCI, they may indicate a more general neural dysfunctioning in BPD, which could be an underlying mechanism in reaction to various stimuli. The interpretation matches reported exaggerated sensitization to emotionally salient situations, an increased experience of emotions, and dysfunctional emotion regulation abilities in BPD [##REF##29961363##13##, ##REF##31784065##14##]. Furthermore, it is possible that self-perception triggered by the imagination of being by oneself may be experienced as aversive by women with BPD [##REF##33029307##32##, ##UREF##7##33##] and therefore, may also be associated with increased neural activity.</p>", "<p id=\"Par24\">The AINS is part of the salience network and known to be involved in the processing of emotions [##REF##19096369##34##–##REF##28644199##36##]. The PINS is involved in the processing of emotional states, too, while a main focus seems to lie on the integration of sensory information [##REF##34461066##35##]. Furthermore, the PINS is implicated in the remembering of interoceptive states [##REF##29724684##37##] and, hence, could play a role in the imagination of the internal state during the presented scripts. In patients with BPD, the AINS and the PINS have been shown to be hyperactivated in response to negative emotional stimuli [##REF##25935068##7##]. Increased AINS activity was also found in response to negative as well as positive stimuli in patients with BPD [##REF##29252164##38##]. These activations might indicate a general increase in emotional sensitivity in patients with BPD (reflected in hyperactivation of the AINS). Our findings from the imagination phase showing increased bilateral insula activity point in the same direction underlining the notion of a general emotional hyperarousal across different stimuli and situations. Accordingly, in the present study mothers with BPD reported greater arousal compared to healthy mothers across all scripts. Such exaggerated sensitization to emotionally salient situations and strong experience of emotions could affect mother–child interactions by leading to an emotional over-involvement in the child’s affective state and especially the child’s distress, impeding a sensitive response to different signals of the child and mother’s (co)-regulative abilities [##REF##33038383##17##, ##REF##21881566##18##].</p>", "<p id=\"Par25\">Furthermore, mothers with BPD showed increased activation of a large cluster including the dorsal and pregenual ACC during the imagination phase. As the ACC is involved in top-down regulation encompassing emotional and cognitive control [##REF##23025352##8##, ##REF##21167765##39##], this might indicate that hyperarousal in response to everyday situations with and without the child is associated with more regulative effort in mothers with BPD, while, ultimately, they do not seem to succeed in reducing their arousal to a level as experienced by healthy mothers. Moreover, regarding the exaggerated sensitization to salient situations and possible emotional overinvolvement, regulatory capacities might indeed be more challenged in mothers with BPD. This neural response pattern might contribute to mothers with BPD perceiving interactions with their children as more stressful and interacting more intrusively [##REF##30637488##40##]. It is in line with previous results showing reduced cortisol levels in healthy mothers after mother–child interaction, while cortisol levels remained unchanged in mothers with BPD, which could indicate a lack of stress relief [##REF##35709662##5##].</p>", "<p id=\"Par26\">We then examined neural activity during the initial audio phase, in which the scripts were presented and participants may have already started imagining the situations. In this phase, we also found increased activity in the AINS in response to everyday situations in mothers with BPD compared to healthy mothers, albeit in a smaller cluster limited to the left hemisphere. Importantly, we found a significant negative correlation between activation in the left AINS and the CIB-score (a marker for the overall quality of mother–child interaction) in mothers with BPD suggesting the AINS to have relevance for parenting behavior. However, this correlation was only found in the audio phase and not in the imagination phase. Although we did not find an overall group effect regarding ACC activity in the audio phase, healthy mothers showed stronger activation of the ACC in response to MCI than nonMCI scripts, which was observed in healthy mothers only. This could indicate that healthy mothers utilize more regulative capacities during a situation of emotional involvement in stressful and rewarding situations with the child compared to nonMCI and are able to regulate their arousal when initially presented with the situation. As our paradigm does not allow to map temporal processes exactly or to directly compare the imagination and the audio phases, it should be investigated in future studies how insula and ACC activations may change over time and how such changes may implicate maternal behavior.</p>", "<p id=\"Par27\">Mothers with BPD reported lower affect ratings in response to rMCI scripts than healthy mothers, indicating a more negative emotional perception of rMCI in mothers with BPD. However, contrary to our expectations we did not find altered neural activity in the reward system in mothers with BPD compared to healthy mothers. In previous studies, activation of the reward system in healthy mothers has been observed mainly in response to visual stimuli but not as consistently in response to auditive stimuli of the own child [##REF##33038383##17##]. Hence, the type of presented stimuli could have influenced the activation of the reward system, and therefore, the present results from a script-based imagination paradigm may not be transferable to other types of stimuli. Furthermore, while comorbid psychiatric disorders might have exerted an effect on the maternal brain, the presence of comorbidities is very common in patients with BPD (e.g., [##REF##29930242##41##, ##UREF##8##42##]), cannot be precisely separated from BPD psychopathology itself [##REF##29930242##41##, ##UREF##8##42##], and effects of comorbid psychiatric disorders on the maternal brain cannot be meaningfully separated from the effect of BPD.</p>", "<title>Limitations</title>", "<p id=\"Par28\">Despite the strengths of the present study such as the combination of neural and behavioral data in a sample of mothers with BPD with young children that has not been studied before and the use of a carefully designed fMRI paradigm, we want to acknowledge some limitations of the study. First, participants were asked to imagine mother–child interactions and situations in which the mother is alone; therefore, neural data are not available during real-life mother–child interaction. Importantly, vividness ratings of the imagination were high and did not differ between the two groups included in the study. Furthermore, there is accumulating evidence that the imagination of behavior evokes neural responses that are similar to neural responses to actual behavior, albeit using more simple stimuli than the scripts applied in the present study [##REF##25863237##43##–##REF##15563729##47##]. Nevertheless, the neural activation pattern observed in this study might also be influenced by different ways of achieving a vivid imagination of the situation described in the scripts and, hence, different neural avenues which cannot (yet) be addressed using our current technical possibilities. Second, although participants may have already started imagination during the audio phase, the paradigm does not allow to directly compare the imagination and the audio phases and, thus, cannot address temporal processes exactly. Third, results cannot be generalized to mothers with children in other age groups and especially not to fathers. Fathers are dramatically underrepresented in research on parenting and the parental brain and should be considered in future studies. Fourth, the results should be replicated in a bigger sample. Additionally, healthy mothers had overall high CIB values with little variability in the group, which could be causal for the missing associations in this group. Future studies should also investigate other aspects besides the processing of stress and re-ward, e.g., the hyperactivation in regions belonging to the social cognition network probably suggesting a compensatory mechanism.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par29\">Results from this first study investigating the maternal brain with a focus on stress and reward in mothers with BPD indicate that an exaggerated sensitization to different, emotionally salient situations together with dysfunctional emotion regulation abilities, as reflected by increased insula and ACC activation, might hinder sensitive maternal behavior in mothers with BPD. AINS activation was associated with maternal behavior in a real-life mother–child interaction and may hence be of relevance for parenting behavior. These results underline the importance for psychotherapeutic interventions to decrease emotional hyperarousal and improve difficulties in emotion regulation in patients with BPD, especially in affected mothers caring for young children. In order to be able to target specific neural dysfunctions in BPD, future research needs to concentrate on temporal processes in mother–child interaction and should use different stimulus modalities to further elucidate neural mechanisms underlying or mediating difficulties in maternal behavior.</p>" ]

[ "<p id=\"Par1\">Borderline personality disorder (BPD) is associated with altered neural activity in regions of salience and emotion regulation. An exaggerated sensitization to emotionally salient situations, increased experience of emotions, and dysfunctional regulative abilities could be reasons for increased distress also during parenting. Mothers with BPD tend to have less reciprocal mother–child interactions (MCI) and reveal altered cortisol and oxytocin reactivity in the interaction with their child, which could indicate altered processing of stress and reward. Here, we studied underlying neural mechanisms of disrupted MCI in BPD. Twenty-five mothers with BPD and 28 healthy mothers participated in a script-driven imagery functional magnetic resonance imaging (fMRI)-paradigm. Scripts described stressful or rewarding MCI with the own child, or situations in which the mother was alone. Mothers with BPD showed larger activities in the bilateral insula and anterior cingulate cortex (ACC) compared to healthy mothers during the imagination of MCI and non-MCI. Already in the precursory phase while listening to the scripts, a similar pattern emerged with stronger activity in the left anterior insula (AINS), but not in the ACC. This AINS activity correlated negatively with the quality of real-life MCI for mothers with BPD. Mothers with BPD reported lower affect and higher arousal. An exaggerated sensitization to different, emotionally salient situations together with dysfunctional emotion regulation abilities, as reflected by increased insula and ACC activity, might hinder sensitive maternal behavior in mothers with BPD. These results underline the importance for psychotherapeutic interventions to improve emotional hyperarousal and emotion regulation in patients with BPD, especially in affected mothers caring for young children.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00406-023-01634-6.</p>", "<title>Keywords</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Author contributions</title>", "<p>Conceptualization was contributed by IS, SCH. Methodology was contributed by IS, CN, SCH. Formal analysis and investigation were contributed by IS, CN, KU. Writing—original draft preparation, was contributed by IS, CN. Writing—review and editing, was contributed by IS, CN, KU, SCH. Funding acquisition was contributed by IS.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL. The study was supported by Grants from the Medical Faculty Heidelberg and the Hoffmann–Klose Foundation.</p>", "<title>Data availability</title>", "<p>Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data are not available.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par30\">The authors have no competing interests to declare that are relevant to the content of this article.</p>", "<title>Ethics approval</title>", "<p id=\"Par31\">The study was conducted according to the ethical standards of the relevant national and institutional committees on human experimentation and with the Declaration of Helsinki of 1975, as revised in 2008. It was approved by the Ethics Committee of the Medical Faculty at Heidelberg University, Germany (approval number: S-707/2018).</p>", "<title>Consent statement</title>", "<p id=\"Par32\">All participants gave written informed consent prior to inclusion and received equal monetary compensation for their participation.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>FMRI paradigm</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Rating of affect and arousal. <bold>a</bold> Significant group × condition interaction with lower ratings of affect in mothers with borderline personality (BPD) compared to healthy mothers (HC) in positive mother–child interactions (pMCI). <bold>b</bold> Significant group effect with higher ratings of affect in mothers with BPD compared to healthy mothers. <italic>rMCI</italic> rewarding mother–child interaction, <italic>sMCI</italic> stressful mother–child interaction, <italic>nonMCI</italic> no mother–child interaction. Significant comparisons are marked with an asterisk indicating <italic>p</italic> &lt; 0.05 at the post-hoc test</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Significant neural clusters in the group comparison during the imagination phase. Mothers with borderline personality disorder show larger activity in bilateral insula and bilateral anterior cingulum compared to healthy mothers</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Associations between fMRI and mother–child interaction. Scatter plot of CIB-scores and β-weights of left anterior insula during audio phase for mothers with BPD</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Descriptive data for group characteristics and behavioral data of mothers with BPD and healthy mothers (HC)</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" colspan=\"2\">BPD</th><th align=\"left\" colspan=\"2\">HC</th><th align=\"left\" rowspan=\"2\">F/t/U_df</th><th align=\"left\" rowspan=\"2\"><italic>p</italic></th></tr><tr><th align=\"left\">M</th><th align=\"left\">SD</th><th align=\"left\">M</th><th align=\"left\">SD</th></tr></thead><tbody><tr><td align=\"left\">Age</td><td char=\".\" align=\"char\">31.2</td><td char=\".\" align=\"char\">7.0</td><td char=\".\" align=\"char\">31.9</td><td char=\".\" align=\"char\">5.0</td><td align=\"left\">− 0.44₅₁</td><td char=\".\" align=\"char\">0.663</td></tr><tr><td align=\"left\">Age child</td><td char=\".\" align=\"char\">27.2</td><td char=\".\" align=\"char\">7.0</td><td char=\".\" align=\"char\">27.4</td><td char=\".\" align=\"char\">6.0</td><td align=\"left\">− 0.13₅₁</td><td char=\".\" align=\"char\">0.897</td></tr><tr><td align=\"left\">Intelligence</td><td char=\".\" align=\"char\">26.4</td><td char=\".\" align=\"char\">9.8</td><td char=\".\" align=\"char\">29.5</td><td char=\".\" align=\"char\">8.9</td><td align=\"left\">− 1.21₅₁</td><td char=\".\" align=\"char\">0.233</td></tr><tr><td align=\"left\">CIB-score</td><td char=\".\" align=\"char\">2.9</td><td char=\".\" align=\"char\">0.8</td><td char=\".\" align=\"char\">3.5</td><td char=\".\" align=\"char\">0.4</td><td align=\"left\">442.5_51.16</td><td char=\".\" align=\"char\">0.009</td></tr><tr><td align=\"left\">Affect ratings</td><td char=\".\" align=\"char\">3.2</td><td char=\".\" align=\"char\">0.3</td><td char=\".\" align=\"char\">3.4</td><td char=\".\" align=\"char\">0.4</td><td align=\"left\">5.24_1,51</td><td char=\".\" align=\"char\">0.026</td></tr><tr><td align=\"left\">rMCI</td><td char=\".\" align=\"char\">4.0</td><td char=\".\" align=\"char\">0.7</td><td char=\".\" align=\"char\">4.5</td><td char=\".\" align=\"char\">0.4</td><td align=\"left\">− 3.39₅₁</td><td char=\".\" align=\"char\">&lt; 0.050*</td></tr><tr><td align=\"left\">sMCI</td><td char=\".\" align=\"char\">2.4</td><td char=\".\" align=\"char\">0.9</td><td char=\".\" align=\"char\">2.2</td><td char=\".\" align=\"char\">0.7</td><td align=\"left\">0.88₅₁</td><td char=\".\" align=\"char\">&gt; 0.050</td></tr><tr><td align=\"left\">Non-MCI</td><td char=\".\" align=\"char\">3.2</td><td char=\".\" align=\"char\">0.5</td><td char=\".\" align=\"char\">3.6</td><td char=\".\" align=\"char\">0.6</td><td align=\"left\">− 2.44₅₁</td><td char=\".\" align=\"char\">&gt; 0.050</td></tr><tr><td align=\"left\">Arousal ratings</td><td char=\".\" align=\"char\">2.2</td><td char=\".\" align=\"char\">0.4</td><td char=\".\" align=\"char\">1.8</td><td char=\".\" align=\"char\">0.5</td><td align=\"left\">10.25_1,51</td><td char=\".\" align=\"char\">0.002</td></tr><tr><td align=\"left\">rMCI</td><td char=\".\" align=\"char\">1.6</td><td char=\".\" align=\"char\">0.5</td><td char=\".\" align=\"char\">1.3</td><td char=\".\" align=\"char\">0.5</td><td align=\"left\">1.86₅₁</td><td char=\".\" align=\"char\">&lt; 0.050*</td></tr><tr><td align=\"left\">sMCI</td><td char=\".\" align=\"char\">3.2</td><td char=\".\" align=\"char\">0.7</td><td char=\".\" align=\"char\">2.6</td><td char=\".\" align=\"char\">0.6</td><td align=\"left\">3.26₅₁</td><td char=\".\" align=\"char\">&lt; 0.050*</td></tr><tr><td align=\"left\">Non-MCI</td><td char=\".\" align=\"char\">1.8</td><td char=\".\" align=\"char\">0.6</td><td char=\".\" align=\"char\">1.4</td><td char=\".\" align=\"char\">0.7</td><td align=\"left\">2.35₅₁</td><td char=\".\" align=\"char\">&lt; 0.050*</td></tr><tr><td align=\"left\">Rating of vividness</td><td char=\".\" align=\"char\">4.6</td><td char=\".\" align=\"char\">0.3</td><td char=\".\" align=\"char\">4.7</td><td char=\".\" align=\"char\">0.3</td><td align=\"left\">− 0.56₅₁</td><td char=\".\" align=\"char\">0.576</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Significant group differences between mothers with BPD and healthy mothers (HC) during the imagination phase</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Contrast</th><th align=\"left\">Cluster size (k)</th><th align=\"left\"><italic>T</italic> value</th><th align=\"left\"><italic>p</italic> value peak</th><th align=\"left\"><italic>p</italic> value cluster FWE</th><th align=\"left\" colspan=\"3\">Peak voxel MNI: x y z (mm)</th><th align=\"left\">Anatomical location of peak voxel</th><th align=\"left\">Anatomical location of cluster</th></tr></thead><tbody><tr><td align=\"left\">BPD &gt; HC</td><td char=\".\" align=\"char\">187</td><td char=\".\" align=\"char\">5.84</td><td char=\".\" align=\"char\">&lt; 0.001</td><td char=\".\" align=\"char\">0.023</td><td align=\"left\">39</td><td align=\"left\">17</td><td align=\"left\">− 13</td><td align=\"left\">R AINS</td><td align=\"left\">R AINS, R PINS</td></tr><tr><td align=\"left\"/><td char=\".\" align=\"char\">182</td><td char=\".\" align=\"char\">4.76</td><td char=\".\" align=\"char\">&lt; 0.001</td><td char=\".\" align=\"char\">0.026</td><td align=\"left\">− 27</td><td align=\"left\">26</td><td align=\"left\">− 4</td><td align=\"left\">L AINS</td><td align=\"left\">L AINS, L PINS</td></tr><tr><td align=\"left\"/><td char=\".\" align=\"char\">220</td><td char=\".\" align=\"char\">4.48</td><td char=\".\" align=\"char\">&lt; 0.001</td><td char=\".\" align=\"char\">0.011</td><td align=\"left\">− 3</td><td align=\"left\">29</td><td align=\"left\">− 4</td><td align=\"left\">L ACC (pre)</td><td align=\"left\">L ACC (sup, sub), R ACC (pre, sup, sub)</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Significant group differences between mother with BPD and healthy mothers (HC) during the audio phase</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Contrast</th><th align=\"left\">Cluster size (k)</th><th align=\"left\"><italic>T</italic> value</th><th align=\"left\"><italic>p</italic> value peak</th><th align=\"left\"><italic>p</italic> value cluster FWE</th><th align=\"left\" colspan=\"3\">Peak voxel MNI: x y z (mm)</th><th align=\"left\">Anatomical location of peak voxel</th><th align=\"left\">Anatomical location of cluster</th></tr></thead><tbody><tr><td align=\"left\">BPD &gt; HC</td><td align=\"left\">147</td><td align=\"left\">5.07</td><td align=\"left\">&lt; 0.001</td><td align=\"left\">0.040</td><td align=\"left\">− 27</td><td align=\"left\">26</td><td align=\"left\">5</td><td align=\"left\">L AINS</td><td align=\"left\">L AINS</td></tr><tr><td align=\"left\">HC: r/sMCI &gt; nonMCI</td><td align=\"left\">360</td><td align=\"left\">4.40</td><td align=\"left\">&lt; 0.001</td><td align=\"left\">&lt; 0.001</td><td align=\"left\">3</td><td align=\"left\">44</td><td align=\"left\">8</td><td align=\"left\">L ACC (pre)</td><td align=\"left\">L ACC (sup, sub); R ACC (pre, sub, sup)</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p><italic>r/sMCI</italic> rewarding/stressful mother–child interaction, <italic>nonMCI</italic> no mother–child interaction, *according to Dunn’ post hoc test</p></table-wrap-foot>", "<table-wrap-foot><p><italic>R</italic> right, <italic>L</italic> left, <italic>AINS</italic> anterior insula, <italic>PINS</italic> posterior insula, <italic>ACC</italic> anterior cingulate cortex</p></table-wrap-foot>", "<table-wrap-foot><p><italic>r/sMCI</italic> rewarding/stressful mother–child interaction, <italic>nonMCI</italic> no mother–child interaction, <italic>R</italic> right, <italic>L</italic> left, <italic>AINS</italic> anterior insula, <italic>ACC</italic> anterior cingulate cortex</p></table-wrap-foot>" ]

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[ "<media xlink:href=\"406_2023_1634_MOESM1_ESM.pdf\"><caption><p>Supplementary file1 (PDF 73 KB)</p></caption></media>" ]

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[ "<title>Introduction</title>", "<p id=\"Par13\">In the Netherlands, approximately 120,000 patients are diagnosed with cancer every year [##UREF##0##1##]. These patients often undergo a long and intensive healthcare trajectory from the moment of diagnosis through to long-term follow-up. Patients’ opinions about the care provided are an important quality measure as they can offer different perspectives and provide insights into aspects of healthcare that professionals are unaware of. Consequently, there is increasing attention given to the use of patient-reported experience measures (PREMs) in seeking to improve quality as part of value-based healthcare (VBHC) [##REF##36123114##2##–##REF##31606809##4##]. In the Netherlands, most tertiary hospitals measure patients’ experiences with the Picker Institute’s patient experience questionnaire [##REF##33312007##5##]. This experience measure is based on “Picker’s principles of patient-centered care” and determines generic experiences of the care process using topics such as experience with “waiting time” and “friendliness of personnel” [##REF##33312007##5##]. These generic PREMs are convenient for general quality improvements at the hospital level or for integrated care. Since the delivered care and logistic processes will differ between departments within a hospital (for example in “the use of volunteers on the diagnostic day” or “the use of prediction models to inform patients in decision making”), patients’ experiences with such care-specific processes are useful for improving quality at the department level [##REF##35934546##3##].</p>", "<p id=\"Par14\">Although there are potential advantages, the effectiveness of routine PREM assessments in clinical practice in enhancing healthcare services is uncertain as the evidence is inconclusive [##REF##16326789##6##–##REF##21862449##9##]. These inconsistent findings may be due to heterogeneity in the PREMs used. Healthcare is dynamic and contains a wide range of aspects that contribute to quality of care. To further enhance the healthcare process within a department, it is important to respond to opportunities for improvement identified through the PREM data. At a certain moment, when the items in the PREM are fully satisfied, it is no longer possible to further improve on these items and it is no longer useful to assess them. A more dynamic approach would offer the opportunity to switch to including other items covering another or new aspects of the healthcare process in seeking continuous improvement.</p>", "<p id=\"Par15\">Based on this idea, we have developed a PREM-item bank for improving cancer-specific VBHC. This PREM-item bank complements the generic PREM (Picker) by providing opportunities to add specific or detailed questions about care experiences. This PREM item bank can be dynamically used to measure patients’ experiences with their care at the outpatient clinic.</p>" ]

[ "<title>Methods</title>", "<p id=\"Par16\">In a co-creation process with patients, we took the following steps to create the PREM-item bank: (1) a literature search to identify existing PREMs, (2) the identification of themes through focus group discussions in an approach based on patient journeys, (3) combining themes from the literature and themes from the qualitative analysis, (4) mapping by healthcare professionals of items within themes, (5) prioritizing the items seen as most important by patients and by healthcare professionals, and (6) rewriting items in a language understandable for most people (level B1) (Fig. ##FIG##0##1##).</p>", "<title>1. Explorative literature search</title>", "<p id=\"Par17\">An explorative literature search was performed using the PubMed, Embase, and Medline databases in August 2019 to obtain details of available generic and cancer-specific PREMs. For the search strategy, the words “patient reported experience measure” OR “experience measure” AND “cancer” were used. Articles were included when they described a PREM validated in the Dutch language that contained items assessing experience with the healthcare process covering both emotional and cognitive evaluation of the delivered care. We included generic and cancer-specific PREMs. Exclusion criteria were studies describing patient-reported outcomes measures (PROMs) and other questionnaires that did not include any patient-reported experience measures.</p>", "<title>2a. Patient journey: focus group</title>", "<p id=\"Par18\">Together with patients and healthcare professionals, we gathered relevant themes for the PREM-item bank. We asked (ex-) patients (<italic>n</italic> = 8) and healthcare professionals (<italic>n</italic> = 3) to participate in a focus group meeting during which a “patient journey of outpatient clinic experiences” was evaluated (Figs. ##FIG##1##2## and ##FIG##2##3##). From our previous experience with focus groups and qualitative research, we know that a group size of 6–10 participants is ideal for ensuring a trusted environment and that everyone has a chance to speak, while also obtaining diverse input from different individuals. Creating a patient journey is a method to obtain the patient’s perspective on all (possible) activities and contact moments between patients and healthcare professionals. We focused on two moments in the outpatient clinic in this full patient journey: the diagnostic phase and the follow-up phase, as these specific contact periods contribute to how the total provided cancer care is experienced. The diagnostic phase was defined as the time between the moment of referral through to the consultation in which treatment options are discussed. Contact moments were grouped within four phases: referral, registration procedure, contact with healthcare professionals on intake to the hospital, and consultation about treatment options. The follow-up phase started with the first regular follow-up visit after treatment and ended at the last follow-up visit, five years after treatment. Contact moments were arranged in three phases: before the follow-up visit, during the registration procedure, and later contact with several healthcare professionals. Each possible contact moments was visualized and discussed separately. Patients were asked if they thought there were missing aspects in the proposed patient journey. Following this, all the steps were evaluated using the following questions: “What were positive experiences with the provided care?”, “What were negative experiences with the provided care?”, “What did you miss in the provided care?”, “Do you have suggestions to improve our care?”, and “Who or what was indispensable in the provided care?”. Data saturation was reached when no new themes were opted.</p>", "<title>2b. Qualitative data analysis</title>", "<p id=\"Par19\">An inductive approach for coding the data was followed by three researchers (MO, KD, and HW) who independently performed thematic analysis on the data. Consensus on the themes present was achieved through discussion, with verification by a fourth researcher (KH).</p>", "<title>3. Combining themes from the literature and from the qualitative analysis</title>", "<p id=\"Par20\">Three researchers (MO, KD, and HW) compared the themes identified from the literature with the themes from the focus group and formed eight new themes that covered different aspects of the intake or diagnostic phase and of the follow-up phase.</p>", "<title>4. Mapping items within themes</title>", "<p id=\"Par21\">After identifying suitable PREMs in step 1, all the individual items included in the PREMs were listed. Duplicates were removed. Items provided by the focus group that were not covered by the list of existing PREM questions were added. Following this, all the items were independently mapped on to the formulated themes by two senior researchers (MO and KD) and one junior researcher (HW). Consensus was achieved through later discussion.</p>", "<title>5. Prioritizing</title>", "<p id=\"Par22\">In order to select the most important items for each theme, a prioritization exercise was completed by both patients (<italic>n</italic> = 7) and 11 healthcare professionals (e.g., head and neck surgeons, psychologists, and oncology nurses). For themes with a fairly limited number of items (##SUPPL##0##1##, ##SUPPL##0##2##, ##SUPPL##0##5##, ##SUPPL##0##7##, and ##SUPPL##0##8##), a top-five list was compiled, while for more extensive themes (##SUPPL##0##3##, ##SUPPL##0##4##, and ##SUPPL##0##6##), a top-ten was generated. Items were weighted based on their ordering (i.e., first place = 5 and second place = 4). Final prioritization was based on the square root of the frequency of occurrence of an item multiplied by the weight of that item: . The outcome was adjusted for group size such that both groups (patients and experts) had an equal influence on the outcome. Both healthcare professionals and patients were asked whether items were relevant, understandable, and whether important items were missing.</p>", "<title>6. Qualitative analysis open comments</title>", "<p id=\"Par23\">After the prioritization, three researchers (MO, KD, and HW) reviewed the open comments in which participants could formulate missing items. After discussion, the researchers reached a consensus on the items to be added when they had been mentioned multiple times and fit within the themes formulated from the previously conducted focus groups.</p>", "<title>7. Rewriting items in Dutch language level B1 (intermediate level)</title>", "<p id=\"Par24\">Next, all the items were rewritten using B1 language, i.e., put in a form that patients with limited health literacy could understand. Following the method applied with the Picker questionnaire, questions were partly repeated in the answer options to make them easier to understand [##REF##33312007##5##]. The reformulated items were again sent to the participating patients to check for understandability.</p>" ]

[ "<title>Results</title>", "<title>1. Explorative literature search</title>", "<p id=\"Par25\">Two previously validated generic PREMs (Consumer Quality Index (CQI) [##REF##28218984##10##], Picker questionnaire [##REF##12389801##11##]) plus five cancer-specific PREMs (FACE-Q head and neck [##REF##30500993##12##], PREM VBHC head and neck [##REF##32808370##13##], EORTC-INFO25 [##REF##20674333##14##], and EORTC-COMU26 [##REF##28025709##15##]) were included in the review. In addition, a PREM concerning the diagnostic day at the outpatient clinic constructed by the Department of Head and Neck Oncology of Erasmus Medical Center was included [##UREF##2##16##]. After removing duplications, 141 items were identified from the above instruments (Table ##TAB##0##1##). Additionally, six themes were derived from the included PREMs: (1) organization, (2) treatment by healthcare providers, (3) expertise of healthcare providers, (4) patient empowerment, (5) end of treatment process, and (6) outpatient clinic.</p>", "<title>2. Qualitative analyses of patient journey: focus group</title>", "<p id=\"Par26\">In the focus group, the patient journey was discussed with head and neck cancer patients and healthcare professionals. Two key points in the full patient journey were visualized (the diagnostic stage and the follow-up phase), and additional contact moments were added. Six themes were derived from this qualitative analysis: (1) “Communication,” (2) “Information,” (3) “Shared decision-making,” (4) “Provided care,” (5) “Environment,” and (6) “Technology.” The topics considered important by the focus-group participants in the first phase are included in Fig. ##FIG##1##2## and in the second phase in Fig. ##FIG##2##3##.</p>", "<title>3. Combining themes from literature and themes from qualitative analysis</title>", "<p id=\"Par27\">After comparing our themes resulting from the focus group with those derived from the literature, we proposed eight final themes: (1) organization, (2) competence of healthcare professionals, (3) communication, (4) information and services, (5) patient empowerment, (6) continuity of provided care, (7) environment, and (8) technology (Table ##TAB##1##2##). Further, during the qualitative analysis, 19 additional items were formulated that were not covered in the 141 items that were identified in the existing PREMs.</p>", "<title>4 &amp; 5. Mapping and prioritizing</title>", "<p id=\"Par28\">Subsequently, 160 items were mapped within the eight themes. Following this, 7 (ex-)patients and 11 healthcare professionals participated in prioritizing the items within each theme. The top-five items selected by the two groups, from each of the smaller themes (##SUPPL##0##1##, ##SUPPL##0##2##, ##SUPPL##0##5##, ##SUPPL##0##7##, and ##SUPPL##0##8##), and the top-ten from the larger themes (##SUPPL##0##3##, ##SUPPL##0##4##, and ##SUPPL##0##6##) were included in the item-bank (<italic>n</italic> = 57). In most cases, the prioritizations of the (ex-)patients and healthcare professionals were similar: 72% of the selected items were in the top five/ten of both groups, and 25% of the selected items were in the top five/ten of one group and in the top 11/16 respectively of the other group (Δ &lt; 6 places). Only two items were selected in which the prioritization of (ex-)patients and healthcare professionals differed widely: “Were you satisfied with the communication between you and the specialist nurse?” (theme ##SUPPL##0##3##) was put in fifth place by the (ex-)patients but only 24th by the healthcare professionals. Further, “Did you receive information about the effects of smoking and alcohol on your illness?” (theme ##SUPPL##0##4##) was placed 11th and 22nd, respectively.</p>", "<title>6. Qualitative analysis open comments</title>", "<p id=\"Par29\">Eventually, the open comments were evaluated and discussed. An additional 19 items were added to the PREM-item bank after consensus of all three researchers. In total, 76 items were included in the final PREM-item bank (Table ##TAB##1##2##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par30\">To the best of our knowledge, there is currently no patient-reported experience measure (PREM) item bank applicable to cancer care at an outpatient clinic. In this mixed-method study, we proposed a PREM-item bank that can be used to dynamically evaluate the provided care at a cancer outpatient clinic. Through the discussion of a patient journey with patients and professionals, which assessed the key contact moments of care during the intake and diagnostic phase and the follow-up phase, eight themes were derived. Together with patients and healthcare professionals, the most important items from existing PREMs were chosen and missing relevant items were added. Eventually, an item bank with 76 items was formed (Table ##TAB##1##2##).</p>", "<p id=\"Par31\">Since the introduction of value-based healthcare (VBHC) in 2006, there has been increasing interest in the patient’s perspective on healthcare [##REF##21142528##17##, ##REF##31029136##18##]. Both the perspective of patients on their own functioning (PROMs) and their experiences with the provided care (PREMs) are seen as important instruments for quality improvement [##REF##35934546##3##]. As the World Health Organization (WHO) notes, person-centered care is a key component of providing high-quality healthcare [##UREF##3##19##]. Furthermore, patient-reported experiences are associated with higher patient safety and clinical effectiveness [##UREF##1##7##, ##REF##25142685##20##].</p>", "<p id=\"Par32\">To date, most PREMs that are used are generic so that results can be compared between departments and hospitals (e.g., the patient experience monitor (PEM) [##REF##33312007##5##]). Although the PEM is used in all academic university hospitals in the Netherlands, it can be difficult to pinpoint concrete actions to improve the care quality in specific departments based on the results of this generic PREM. Some of the evaluated items are outside the control of a department, such as how parking is experienced. The review by Gleeson et al. similarly noted the problem of a lack of specificity in national surveys, and that staff often thought that such data were not applicable or relevant to their daily work [##REF##27531733##8##].</p>", "<p id=\"Par33\">Furthermore, there are problems with the PEM in that there appears to be a ceiling effect: the overall experience is often rated as good (score of 8 out of 10) in all participating university hospitals [##UREF##4##21##]. This makes it difficult to further improve healthcare based on these already good scores. While we acknowledge the importance of this generic measurement for benchmarking experiences with the provided care, our PREM-item bank can complement this generic measurement with a department-specific measurement, in which the care delivered by a specific department can be evaluated. Each department has its own care pathways and may provide care in ways that are not seen in other departments (e.g., the use of volunteers on the first day).</p>", "<p id=\"Par34\">In particular, the use of VBHC during consultations and remote care is relatively a new aspect of healthcare, and the ways these are provided often differ between departments. For patients to actively take part in VBHC, they have to contribute by completing questionnaires or using a web application. Since we can only request this of patients, it is particularly important that we continuously assess their experiences. On one hand, we want to identify areas where we can further improve the care we provide while, on the other hand, we want to know what patients already value. From an earlier study in which we used a department-specific PREM, we learned that patients did not see completing these PROMs as a burden, and, further, that filling in and discussing PROMs during consultations enhanced patient empowerment [##REF##32808370##13##]. These appreciated aspects can be used to convince other stakeholders that VBHC leads to quality improvements from the patient’s perspective [##REF##36459251##22##]. Although quality improvements based on PREM data have often been described, only a few studies report a quantitative impact as a result of using PREM-data [##REF##35934546##3##]. It is our hypothesis that with the introduction of this dynamic manner of collecting department-specific PREM-data, identifying potential quality improvements will be more straightforward and applicable for a specific care pathway. When items are given the highest possible rating or it is not possible to further improve an aspect, PREM items could be changed in order to focus on another aspect of care. In this way, patients’ experiences will be able to optimally contribute to improving the quality of various aspects of healthcare. In the future, we intend to evaluate the impact of using aggregated PREM-data on patient-reported outcomes and experiences.</p>", "<title>Strengths and limitations</title>", "<p id=\"Par35\">A strength of this study is its mixed-method design. Furthermore, inputs from both patients and healthcare professionals were taken into account when forming the PREM-item bank. Both groups prioritized similar items that they considered important to include in the PREM-item bank. This item bank could be used at any oncology department worldwide, and additional items can be added to enable the constantly evolving healthcare to be structurally evaluated. The questions were phrased in an easily understandable way so that patients with low health literacy could participate. A limitation is that our study only included head and neck cancer patients and healthcare professionals who were working in this area. Nevertheless, to make this item bank applicable to all cancer departments, we included both generic and cancer-specific PREMs based on our explorative literature search. Another limitation is that the literature search was explorative, limited to known PREMs, meaning that some relevant PREMs might have been overlooked. Furthermore, only PREMs validated in the Dutch language were included. In this phase, the item bank is not psychometrically validated, and we added non-validated items from our focus group analysis. However, this is the first step and validation will be performed in the upcoming paper.</p>", "<title>Future perspectives</title>", "<p id=\"Par36\">In order to evaluate the VBHC offered in various oncology departments, we intend, in co-creation with other departments and patients, to develop a PREM-VBHC that will be structurally embedded in the provided care. We aim for the associated questionnaire to be limited to approximately 15 fixed items and 5 dynamic items. In this way, oncology departments can be compared, while department-specific care can be dynamically evaluated. The PREM-VBHC will be part of our electronic patient-reported outcome system so it will not increase the workload of healthcare professionals during their daily practice, which has been reported as a barrier to the use of PREMs [##REF##36459251##22##]. The PREM-VBHC results will not be used during consultations as this could affect patients’ honesty [##REF##36459251##22##]. Rather, the aggregated data will be discussed during regular meetings with all involved healthcare professionals following a plan-do-study-act cycle. Ideally, the aggregated PREM data will be complemented with aggregated PROM results. Although the use of aggregated PROMs is still in its infancy, their combination with PREMs for quality improvement seems promising [##REF##35978425##23##]. The PREM-item bank can additionally be used as a basis when a specific topic needs to be addressed (e.g., acute care).</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par37\">In collaboration with patients and healthcare professionals, we have developed a bank of patient-reported experience measure (PREM) items to evaluate patients’ experiences while receiving cancer care in an outpatient clinic. This PREM-item bank is the first step to dynamically assess the quality of cancer care provided in an outpatient setting. The questions were formulated in straightforward language so that patients with limited health literacy could understand them. We will use the PREM-item bank to develop a PREM that is purposefully designed to evaluate the value-based healthcare that is offered in various oncology departments in our institute and could be used elsewhere.</p>" ]

[ "<title>Objective</title>", "<p id=\"Par1\">Since the implementation of value-based healthcare, there has been a growing emphasis on utilizing patient-reported experience measures (PREMs) to enhance the quality of care. However, the current PREMs are primarily generic and static, whereas healthcare is constantly evolving and encompasses a wide variety of aspects that impact care quality. To continuously improve care requires a dynamic PREM. The aim of this study was to propose an item bank for the establishment of a dynamic and care-specific patient-reported evaluation.</p>", "<title>Methods</title>", "<p id=\"Par2\">In co-creation with patients, a mixed methods study was conducted involving: (1) an explorative review of the literature, (2) a focus group analysis with (ex-)patients, (3) qualitative analyses to formulate themes, and (4) a quantitative selection of items by patients and experts through prioritization.</p>", "<title>Results</title>", "<p id=\"Par3\">Eight existing PREMs were evaluated. After removing duplicates, 141 items were identified. Through qualitative analyses of the focus group in which the patient journey was discussed, eight themes were formulated: “Organization of healthcare,” “Competence of healthcare professionals,” “Communication,” “Information &amp; services,” “Patient empowerment,” “Continuity &amp; informal care,” “Environment,” and “Technology.” Seven patients and eleven professionals were asked to prioritize what they considered the most important items. From this, an item bank with 76 items was proposed.</p>", "<title>Conclusion</title>", "<p id=\"Par4\">In collaboration with patients and healthcare professionals, we have proposed a PREM-item bank to evaluate the experiences of patients’ receiving cancer care in an outpatient clinic. This item bank is the first step to dynamically assess the quality of cancer care provided in an outpatient setting.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00520-023-08266-5.</p>", "<title>Keywords</title>" ]

[ "<title>Supplementary information</title>", "<p>\n</p>" ]

[ "<title>Acknowledgements</title>", "<p>We would like to thank Hester van Willigen and Peter Koemans for their valuable contributions to this study.</p>", "<title>Author contribution</title>", "<p>K.H., K.D., and M.O. contributed to the study conception and design. Material preparation, data collection, and analysis were performed by M.O. and K.D. The first draft of the manuscript was written by K.H. and K.D.; A.S., R.B., and M.O commented on previous versions of the manuscript. All authors read and approved the final manuscript.</p>", "<title>Funding</title>", "<p>Zorginstituut Nederland (2018017074).</p>", "<title>Data availability</title>", "<p>Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.</p>", "<title>Declarations</title>", "<title>Ethics approval and informed consent</title>", "<p id=\"Par38\">This study is in accordance with the Declaration of Helsinki. This study was approved by the Medical Ethical Committee of the Erasmus Medical Center.</p>", "<title>Consent to participate</title>", "<p id=\"Par39\">Written informed consent was obtained from all participants.</p>", "<title>Competing interest</title>", "<p id=\"Par40\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Development of the PREM-item bank. PREM, patient-reported experience measure; B1 language level, intermediate level</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Contact moments in the diagnostic phase of the patient journey for HNC patients. HNC, head and neck cancer</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Contact moments in the follow-up phase of the patient journey for HNC patients. HNC, head and neck cancer; PROMs, patient-reported outcome measure; ePRO structure, electronic patient-reported outcome structure</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Included patient-reported experience measures (PREMs)</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Included PREMs</th><th>Items extracted</th><th>Items in<break/>item bank</th></tr></thead><tbody><tr><td>Consumer Quality Index (CQI) [##REF##28218984##10##] (59 items)</td><td>23</td><td>16</td></tr><tr><td>Picker questionnaire [##REF##12389801##11##] (22 items)</td><td>19</td><td>13</td></tr><tr><td>FACE-Q head and neck [##REF##30500993##12##] (103 items)</td><td>25</td><td>8</td></tr><tr><td>PREM VBHC head and neck [##REF##32808370##13##] (35 items)</td><td>24</td><td>10</td></tr><tr><td>EORTC-INFO25 [##REF##20674333##14##] (25 items)</td><td>22</td><td>1</td></tr><tr><td>EORTC-COMU26 [##REF##28025709##15##] (26 items)</td><td>20</td><td>6</td></tr><tr><td>Intern evaluation outpatient clinic (20 items) [##UREF##2##16##]</td><td>8</td><td>2</td></tr><tr><td>Formulated extra items</td><td>19</td><td>20</td></tr><tr><td>Total</td><td>160</td><td>76</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Final PREM-item bank</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th>Themes</th><th>Description</th><th>Items</th><th>Original questionnaire</th></tr></thead><tbody><tr><td rowspan=\"7\">1. Organization</td><td rowspan=\"7\">Experience with the practical organization of healthcare. For example: time to consultation, accessibility of care, and waiting times</td><td>1. Were you satisfied with the time between the diagnostic tests and the diagnosis?</td><td>[##REF##28218984##10##]</td></tr><tr><td>2. Were you satisfied with the waiting time between the first consultation and the diagnosis?</td><td>-</td></tr><tr><td>3. Did you like it that (if possible) several appointments for examination and/or treatment were scheduled on one day?</td><td>[##REF##28218984##10##]</td></tr><tr><td>4. Was your medical doctor available when you had questions or problems?</td><td>[##REF##30500993##12##]</td></tr><tr><td>5. Were the administrative staff friendly when you had questions or problems?</td><td>[##REF##12389801##11##]</td></tr><tr><td>6. Were you satisfied with the time between the consultation where treatment options were explained and the start of your treatment?</td><td>[##UREF##2##16##]</td></tr><tr><td>7. Was the guidance of a volunteer on the first day in the hospital of added value?</td><td>[##REF##32808370##13##]</td></tr><tr><td rowspan=\"6\">2. Competence of healthcare professionals</td><td rowspan=\"6\">Experience with the professionalism and expertise of healthcare professionals in order to provide optimal care</td><td>1. Did you trust your medical doctor?</td><td>[##REF##12389801##11##]</td></tr><tr><td>2. Did you trust the supportive care professionals at the outpatient clinic, such as speech therapists, physiotherapists, and social workers?</td><td>[##REF##12389801##11##]</td></tr><tr><td>3. Did your medical doctor have a professional attitude?</td><td>[##REF##30500993##12##]</td></tr><tr><td>4. Did your medical doctor consult other doctors or refer you if additional expertise was needed?</td><td>[##REF##28218984##10##]</td></tr><tr><td>5. Did your medical doctor or other healthcare providers read your file carefully?</td><td>[##REF##28218984##10##]</td></tr><tr><td>6. Did your medical doctor take action in response to your complaints (e.g., by prescribing medication for pain)?</td><td>[##REF##32808370##13##]</td></tr><tr><td rowspan=\"15\">3. Communication</td><td rowspan=\"15\">Experience of the communication between healthcare professionals and patient and the social and communicative skills of the healthcare professionals</td><td>1. Did your medical doctor listen to you and understand your concerns?</td><td>[##REF##30500993##12##]</td></tr><tr><td>2. Did your medical doctor answer all your questions?</td><td>[##REF##30500993##12##]</td></tr><tr><td>3. Did your medical doctor put you at ease?</td><td>[##REF##30500993##12##]</td></tr><tr><td>4. If you had questions for other professionals at the outpatient clinic, did you get answers that you could understand?</td><td>[##REF##12389801##11##]</td></tr><tr><td>5. Was there enough time to talk about your illness or problems with the medical doctor or other professionals at the outpatient clinic?</td><td>[##REF##12389801##11##]</td></tr><tr><td>6. Were you satisfied with the communication between you and the specialist nurse?</td><td>[##REF##28025709##15##]</td></tr><tr><td>7. Did your medical doctor speak to you in a way you could understand?</td><td>[##REF##30500993##12##]</td></tr><tr><td>8. Did you feel free to ask questions to healthcare providers at the outpatient clinic?</td><td>[##REF##28025709##15##]</td></tr><tr><td>9. Was there mutual trust between you and your healthcare providers?</td><td>[##REF##28025709##15##]</td></tr><tr><td>10. Did your doctor discuss the answers you filled in on the health questionnaires with you?</td><td>-</td></tr><tr><td>11. Did your healthcare provider seem honest to you?</td><td>[##REF##28025709##15##]</td></tr><tr><td>12. Did your healthcare provider try to understand your current situation?</td><td>[##REF##28025709##15##]</td></tr><tr><td>13. Did your medical doctor discuss the health problems that bother you the most?</td><td>[##REF##32808370##13##]</td></tr><tr><td>14. Did your healthcare providers pay enough attention to your wishes?</td><td>[##REF##28218984##10##]</td></tr><tr><td>15. Were you properly assisted by telephone by the secretariat or desk employee?</td><td>-</td></tr><tr><td rowspan=\"12\">4. Information and services</td><td rowspan=\"12\">Experience with the provided information so that patients are able to optimally communicate with their healthcare professionals</td><td>1. Did your medical doctor clearly explain what will happen during treatment?</td><td>[##REF##20674333##14##]</td></tr><tr><td>2. Were you satisfied with the information that you received about unexpected problems that could occur during treatment?</td><td>[##REF##28218984##10##]</td></tr><tr><td>3. Were you satisfied with the information that you received about possible complaints that could occur after treatment?</td><td>[##REF##28218984##10##]</td></tr><tr><td>4. Was it clear to you that you had cancer during treatment?</td><td>-</td></tr><tr><td>5. Were you encouraged to take someone with you to the consultation where your treatment options discussed?</td><td>-</td></tr><tr><td>6. Did you receive information about the existence of a patient organization?</td><td>[##REF##28218984##10##]</td></tr><tr><td>7. Was it clear for you with whom in the hospital you could discuss questions or problems once the treatment was finished?</td><td>[##REF##28218984##10##]</td></tr><tr><td>8. Was the provided written information about the diagnostic tests and treatments clear?</td><td>[##REF##28218984##10##]</td></tr><tr><td>9. Were you asked the way(s) you preferred to receive information?</td><td>-</td></tr><tr><td>10. When you had to wait for your consultation, was it clear how long the waiting time was going to be?</td><td>[##REF##12389801##11##]</td></tr><tr><td>11. Did the letter you received at home clearly explain what the day at the hospital would be like?</td><td>[##UREF##2##16##]</td></tr><tr><td>12. Did you receive information about the effects of smoking and alcohol on your illness?</td><td>[##REF##28218984##10##]</td></tr><tr><td rowspan=\"8\">5. Patient empowerment</td><td rowspan=\"8\">Experience with the opportunity to participate in shared decision making, which will enhance patient empowerment and autonomy for the patient</td><td>1. Did you feel better prepared for the consultation with your medical doctor by filling in the health questionnaires?</td><td>[##REF##32808370##13##]</td></tr><tr><td>2. Did your medical doctor help you to decide what was best for you?</td><td>[##REF##30500993##12##]</td></tr><tr><td>3. Did your medical doctor treat you as an equal?</td><td>[##REF##28025709##15##]</td></tr><tr><td>4. Were you able to participate in decisions about your diagnostic tests or treatment?</td><td>[##REF##12389801##11##]</td></tr><tr><td>5. Were your family or friends able to think along and discuss your diagnostic tests or treatment?</td><td>[##REF##12389801##11##]</td></tr><tr><td>6. Did you have enough information to make a choice for treatment?</td><td>-</td></tr><tr><td>7. Did someone clearly explain the advantages and disadvantages of the treatment to you?</td><td>[##REF##12389801##11##]</td></tr><tr><td>8. Did you have enough time to let the information you received sink in?</td><td>-</td></tr><tr><td rowspan=\"10\">6. Continuity of provided care</td><td rowspan=\"10\">Experience with the continuity of care (before or after treatment), when more medical specialties were involved</td><td>1. Did you have a permanent contact person to arrange your appointments?</td><td>[##REF##28218984##10##]</td></tr><tr><td>2. Did you see the same healthcare providers during your examinations and treatments (when possible)?</td><td>[##REF##28218984##10##]</td></tr><tr><td>3. Did you have a consultation with a specialist nurse after your diagnosis was confirmed by the medical doctor/breaking bad news?</td><td>[##REF##28218984##10##]</td></tr><tr><td>4. Did your healthcare provider, besides your illness, also look at your overall health?</td><td>-</td></tr><tr><td>5. Was the necessary care and additional help for the home situation arranged in time?</td><td>[##REF##28218984##10##]</td></tr><tr><td>6. Was it clear who to contact with questions?</td><td>-</td></tr><tr><td>7. Was there a healthcare provider in this hospital that you could call 24 h a day?</td><td>[##REF##28218984##10##]</td></tr><tr><td>8. Was there someone at the outpatient clinic you could talk to about your problems and fears?</td><td>[##REF##12389801##11##]</td></tr><tr><td>9. Were there moments when healthcare providers at the outpatient clinic told you contrary things, which left you confused?</td><td>[##REF##12389801##11##]</td></tr><tr><td>10. Did the healthcare providers involved in your care worked well together at the outpatient clinic?</td><td>[##REF##30500993##12##]</td></tr><tr><td rowspan=\"8\">7. Environment</td><td rowspan=\"8\">Experience with the ambiance and decor of the outpatient clinic, including attention to privacy</td><td>1. Did you like the atmosphere in the waiting room?</td><td>-</td></tr><tr><td>2. Were there drinks available in the waiting room?</td><td>-</td></tr><tr><td>3. Did you like the temperature in the waiting room?</td><td>-</td></tr><tr><td>4. Was your privacy handled well at the outpatient clinic?</td><td>-</td></tr><tr><td>5. Was the route to the toilets at the outpatient clinic well marked?</td><td>-</td></tr><tr><td>6. Were the toilets in the outpatient clinic clean?</td><td>-</td></tr><tr><td>7. Was there enough space in the waiting room?</td><td>-</td></tr><tr><td>8. Were you called in by name by the medical doctor?</td><td>-</td></tr><tr><td rowspan=\"6\">8. Technology</td><td rowspan=\"6\">Experience with the technology that is imbedded in the regular care. For example: experience with the use of an electronic patient reported outcome system</td><td>1. Was the help of the volunteer with the health questionnaires on the first day in the hospital of added value?</td><td>[##REF##32808370##13##]</td></tr><tr><td>2. Was the explanation by the specialist nurse about the health questionnaires of added value?</td><td>[##REF##32808370##13##]</td></tr><tr><td>3. Were you able to view your own results from the health questionnaires on the internet?</td><td>[##REF##32808370##13##]</td></tr><tr><td>4. Was it clear to you how you needed to register at the digital check-in point at the outpatient clinic?</td><td>-</td></tr><tr><td>5. Do you have any comments or tips about our way of working with the health questionnaires ?</td><td>[##REF##32808370##13##]</td></tr><tr><td>6. Are you satisfied with the time it took you to complete the health questionnaires ?</td><td>[##REF##32808370##13##]</td></tr><tr><td rowspan=\"4\">Other</td><td rowspan=\"4\">General experience</td><td>1. How would you rate your visit to the outpatient clinic?</td><td>[##REF##12389801##11##]</td></tr><tr><td>2. Would you recommend the department to others?</td><td>-</td></tr><tr><td>3. Did you feel any topics were overlooked during the check-up visit to your medical doctor?</td><td>[##REF##32808370##13##]</td></tr><tr><td>4. Would you like to tell us anything else about the outpatient clinic? This can be positive or negative.</td><td>[##REF##12389801##11##]</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p>Health questionnaires = patient-reported outcome measures (PROMs)</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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{ "acronym": [ "PREM", "PROM", "VBHC", "CQI", "PEM", "EORTC-INFO25", "EORTC-COMU26", "WHO" ], "definition": [ "Patient-reported experience measure", "Patient-reported outcome measure", "Value-based healthcare", "Consumer Quality Index", "Picker experience measure", "EORTC information module", "EORTC communication module", "World Health Organization" ] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Regenerative endodontic treatments (RETs) are considered biologically based procedures designed to regenerate and replace damaged structures, including the pulp-dentin complex in necrotic immature teeth following dental caries or trauma [##REF##17368324##1##]. According to the guideline of the American Association of Endodontists (AAE) and European Society of Endodontology (ESE) [##UREF##0##2##, ##REF##26990236##3##], RETs include disinfection of the root canal space, the invocation of the stem cells and growth factors, and the generation of a scaffold that promotes the new tissue by creating a blood clot. Crucial steps for regenerative procedures are root canal disinfection and preventing reinfection. Due to the short and open apexes and thin dentin walls of the necrotic immature teeth, mechanical instrumentation is not suggested, and the absence of preparation may result in unremovable bacterial biofilm [##REF##36890739##4##]. Therefore, it is essential to use effective irrigation solutions and intracanal medicaments that have superior antibacterial properties to ensure a suitable environment for regeneration through the removal of biofilms [##REF##36169591##5##].</p>", "<p id=\"Par3\">Triple antibiotic paste (TAP) that contains equal portions of metronidazole, ciprofloxacin, and minocycline; double antibiotic paste (DAP) obtained by removing minocycline from TAP; and calcium hydroxide (CH) are the most widely used medicaments for root canal disinfection [##REF##35852919##6##]. Although using these medicaments is essential to provide bacteria-free root canal space, they have been associated with some detrimental effects such as being cytotoxic [##REF##24666903##7##], causing discoloration [##REF##25069927##8##], resulting in bacterial resistance [##REF##29480932##9##], and reducing the bond strength of barrier materials to the dentin [##REF##35852919##6##]. Therefore, the complete removal of intracanal medicaments from root canal walls is one of the important factors for the long-term success of RETs [##REF##25069927##8##].</p>", "<p id=\"Par4\">Intracanal medicaments can be removed with the aid of irrigation solutions and the action of mechanical instrumentation [##REF##30803540##10##]. However, the absence of mechanical instrumentation in RETs might jeopardize the removal of intracanal medicaments and consequently prevent the formation of desirable conditions for stem cell survival, proliferation, and differentiation. Based on present guidelines, intracanal medicaments are removed by syringe-needle irrigation (SNI) with ethylene diamine tetra acetic acid (EDTA) solution in routine regenerative treatments [##UREF##0##2##, ##REF##26990236##3##]. However, since SNI could compromise the effective delivery of solution into the root canal space, various irrigation activation systems have been introduced to improve agitation [##REF##25146028##11##]. One of these activation systems, passive ultrasonic irrigation (PUI), relies on the transmission of acoustic energy from an oscillating file or smooth wire to an irrigation solution in the root canal and can be activated from 25 to 30 kHz [##REF##17442017##12##]. EDDY (VDW, Munich, Germany) is another irrigation activation system that is used in endodontic treatments by application of sonic energy. EDDY has a flexible polyamide tip that triggers cavitation and acoustic streaming in the irrigation solution and can be operated between 5 and 6 kHz [##REF##28185091##13##]. It was shown that both PUI and EDDY are effective systems for removing intracanal medicaments in routine endodontic treatments [##REF##30803540##10##, ##REF##35028030##14##].</p>", "<p id=\"Par5\">Laser-activated irrigation has been developed to improve the irrigation and disinfecting efficacy of irrigation solutions. One of the latest laser technology in endodontics, photon-induced photoacoustic streaming (PIPS, FOTONA, Ljubljana, Slovenia, EU), uses the Er:YAG laser to ensure a three-dimensional (3D) flow of the irrigation solution within root canal space and, subsequently, provides advance disinfection by creating cavitation and photoacoustic shock waves [##REF##36804946##15##]. In recent years, shock wave–enhanced mission photo-acoustic streaming (SWEEPS, FOTONA, Ljubljana, Slovenia, EU) lasers have been introduced in endodontics to increase the debridement efficiency of the PIPS [##UREF##1##16##]. SWEEPS technology uses the erbium laser with ultra-short pulses for collapsing of laser-induced bubbles by placing its fiber tip in the pulp chamber similar to the PIPS [##REF##36595139##17##]. As the initially formed bubble collapse, energy is emitted to form the secondary bubble, and expansion of the secondary bubble accelerates the collapse of the primary bubble, leading to advanced shockwave emission even inside the narrowest root canals [##REF##36804946##15##].</p>", "<p id=\"Par6\">Although the efficacy of SWEEPS technology in removing intracanal medicaments has been demonstrated in the literature [##REF##34662526##18##, ##REF##33961503##19##], its effectiveness in RETs without mechanical preparation has not been investigated and compared with currently used irrigation activation systems. Therefore, the aim of this study is to evaluate the removal of DAP and CH from the canal space using SNI, PUI, EDDY, and SWEEPS techniques. The null hypothesis was the different irrigation activation systems used in RETs would not differ regarding the removal of intracanal medicaments from the root canal space.</p>" ]

[ "<title>Materials and methods</title>", "<title>Sample selection, preparation, and placement of intracanal medicaments</title>", "<p id=\"Par7\">The study design (no. 2023-144) was approved by the Research Ethics Committee of the University. The required sample size was calculated using G*Power software (G*Power 3.1.9.4, Heinrich-Heine, Dusseldorf, Germany) and 10 teeth per group were allowed for comparison of the quantitative variables between groups at alpha error probability of 0.05 and power of 0.80 [##REF##35852919##6##]. Teeth with caries-free, single-rooted, and closed apex were collected and evaluated under a stereo microscope for any possible fractures or anatomical malformations. Accordingly, the periodontal tissues of selected 80 teeth were removed from the external root surfaces with periodontal curettes, and teeth were stored in 0.1% thymol solution at 4°C until used.</p>", "<p id=\"Par8\">The immature teeth models were created based on a similar study in the literature [##REF##32139265##20##]. Following 3-mm resection of the apical ends, the root lengths were adjusted to 14±1 mm. Since the critical apical diameter in RETs is 1.1 mm, the root canal spaces of selected teeth were enlarged up to #100 (Dentsply Tulsa) to obtain a standard intracanal diameter [##REF##34115394##21##]. Between each file, irrigation procedures were performed with SNI using a sterile saline solution. Subsequently, the root canals were irrigated with 20 mL 1.5% sodium hypochlorite (NaOCl) for 5 min in accordance with regenerative protocols proposed by AAE and ESE [##UREF##0##2##, ##REF##26990236##3##], rinsed with 20 mL saline, and dried with paper points. The apical ends of roots were sealed with modeling wax and vacuum suction was used during irrigation procedures to mimic clinical conditions. Afterwards, teeth were divided into 2 main groups based on the type of intracanal medicaments. Intracanal medicaments were prepared as the manufacturer’s recommendations and applied using lentulo spiral (VDW, Munich, Germany). The modeling waxes were removed to ensure that intracanal medicaments could be placed in the whole root canal lumen through the apical foramen. Preparations were performed as described below:</p>", "<p id=\"Par9\">DAP (<italic>n</italic> = 40): Equal portions of metronidazole (Flagyl, Sanofi, Istanbul, Turkey) and ciprofloxacin (Cipro, Biofarma, Istanbul, Turkey) were mixed with distilled water to a final concentration of 1–5 mg/mL.</p>", "<p id=\"Par10\">CH (<italic>n</italic> = 40): CH powder (Kalsin, Aktu Tic, Izmir, Turkey) was mixed with distilled water at a 1:1 ratio.</p>", "<p id=\"Par11\">After observing the intracanal medicaments that had been placed properly, the modeling waxes were re-placed, and access cavities were restored with a temporary filling material (Cavitimi, Imicryl Dental, Turkey). Teeth were stored at 37°C in %95 relative humidity for 3 weeks to simulate RET protocol.</p>", "<title>Removal of intracanal medicaments</title>", "<p id=\"Par12\">After 3 weeks, all dressed teeth in DAP and CH groups were randomly divided into four subgroups (<italic>n</italic>=10) in terms of the irrigation activation system and irrigated with 20 mL 17% EDTA and saline solution based on present guidelines by ESE, respectively [##REF##26990236##3##]. While EDTA solution can significantly increase the release of growth factors, which promote stem cell differentiation from the dentine matrix, the saline solution was also recommended in order to reduce possible adverse effects of irrigants on target cells [##REF##26990236##3##]. All irrigation procedures were performed by the same operator in the same conditions to ensure standardization. Additionally, the irrigation process was completed with modeling waxes to mimic clinical conditions, and waxes were kept until teeth were longitudinally sectioned. Used irrigation systems were activated according to the manufacturer’s recommendations as follows:</p>", "<p id=\"Par13\">SNI: The tip of a 30-gauge side-vented closed-ended needle (Endo-Top, Cerkamed, Stalowa Wola, Poland) was placed 1 mm short of the root apex and moved in an up-and-down motion. Each 5 mL solution was delivered into the root canal for 20 s.</p>", "<p id=\"Par14\">PUI: A stainless steel (#25) file (Irri-Safe; Acteon, Merignac, France) driven by an ultrasonic device (Suprasson PMax de Satelec Acteon, Merignac, France) was placed 1 mm short of the root apex and every 5 mL solution was activated for 20 s.</p>", "<p id=\"Par15\">EDDY: A non-cutting polyamide tip (#25) operated by an air-driven handpiece (Kavo Kerr, Detroit, USA) was placed 1 mm short of the root apex and each 5 mL solution was activated for 20 s at maximum intensity.</p>", "<p id=\"Par16\">SWEEPS: Er:YAG laser with a wavelength of 2940 nm and a pulse length of 50 μs equipped with the handpiece H14 was adjusted using a special mode for SWEEPS (LightWalker AT, Fotona, Ljubljana, Slovenia; 0.3 W, 15 Hz, and 20 mJ, without water or air). The 9-mm-long and tapered 600-μm fiber tip (PIPS 600/9) was placed in the access cavity and activated at a fixed position during the procedures. Every 5 mL solution was activated for 20 s.</p>", "<title>Evaluation of the remaining intracanal medicaments</title>", "<p id=\"Par17\">Following the irrigation procedures, modeling waxes were removed and teeth were longitudinally sectioned into two halves using a diamond disk. During this procedure, special care was taken to avoid penetration of the disk in the root canal system. After obtaining enough space for the separation of the teeth, an enamel chisel was inserted in the grooves, and a smooth pressure was applied to separate the two parts [##UREF##2##22##]. Root samples were examined under a stereo microscope (Olympus SZ61, Olympus, Tokyo, Japan) at a 20× magnification, and images were taken with a digital camera (Olympus DP12, Olympus, Tokyo, Japan) connected to the microscope. Each image was evaluated using the Image J software program (Image J 1.47V, National Institute of Health, USA). Firstly, the border of the whole root canal space was determined and measured and this measurement corresponded to 100%. Subsequently, the area of the remaining intracanal medicament was measured and these two measurements were proportioned to each other. According to the obtained results as a percentage, each value was also independently scored by 2 calibrated and blinded investigators according to the scoring system that has been proposed in the literature previously [##REF##28084647##23##]. The used scores were as follows: 0 = empty cavity, 1 = &lt;50% of the cavity is filled with intracanal medicaments, 2 = &gt;50% of the cavity is filled with intracanal medicaments, and 3= the cavity is completely filled with intracanal medicaments (Fig. ##FIG##0##1##). Scores of the selected 40 samples (25%) were re-evaluated after 1 week to ensure accuracy.</p>", "<title>Statistical analysis</title>", "<p id=\"Par18\">Statistical Package for Social Sciences software (SPSS 26, Chicago, IL, USA) was used for statistical analysis. The Cohen kappa test was used to analyze the inter-examiner agreement. The Shapiro-Wilk test served to check the normality of the variables. The Kruskal-Wallis test and Mann-Whitney <italic>U</italic> test with Bonferroni correction were used to compare the remnant of CH and DAP within different medicament groups. The Mann-Whitney <italic>U</italic> test was used to compare two independent groups. The significance level was 5%.</p>" ]

[ "<title>Results</title>", "<p id=\"Par19\">The Cohen kappa value was calculated as 0.921 for inter-examiner agreement. Table ##TAB##0##1## shows the percentages of the remaining intracanal medicaments based on different irrigation activation systems. The distribution of the scores for each group is also demonstrated in Fig. ##FIG##1##2##.</p>", "<p id=\"Par20\">Regardless of the used irrigation activation systems, there was no statistically significant difference between the removal of the CH and DAP from the root canal system (<italic>P</italic> &gt; 0.05). Moreover, while the efficiency of SWEEPS regarding the removal of both used intracanal medicaments from the root canal system was significantly higher (<italic>P</italic> &lt; 0.05), the SNI group showed the lowest effectiveness compared to the other used systems (<italic>P</italic> &lt; 0.05). No statistically significant difference was found between PUI and EDDY systems in terms of intracanal medicament removal (<italic>P</italic> &gt; 0.05).</p>", "<p id=\"Par21\">Within each type of intracanal medicament group, SWEEPS also removed the highest amount of medicaments and SNI removed the least (<italic>P</italic> &lt; 0.05). PUI and EDDY groups indicated similar effectiveness regarding the medicament removal (<italic>P</italic> &gt; 0.05).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par22\">It has been showed that overall success rates for the regenerative endodontic treatments ranged from 50 to 98% and the survival rates were between 94% and 100% through development of used materials and techniques [##REF##36704087##24##]. Especially using intracanal medicaments to eliminate microorganisms is the crucial part of regenerative treatments in order to achieve enhanced disinfection and increased the success rates [##REF##34033820##25##]. However, due to the some adverse effects of currently used intracanal medicaments on the viability of stem cells and the bond strength of the barrier materials, their application in RETs presents limitations [##REF##28844309##26##]. Therefore, based on the knowledge that the complete removal of intracanal medicaments from the root canal system is essential [##REF##35852919##6##, ##REF##25069927##8##], this study aimed to compare the effect of different irrigation activation methods on the removal of CH and DAP in RETs. The null hypothesis was rejected since SWEEPS removed significantly higher amounts of intracanal medicaments compared to the other used systems.</p>", "<p id=\"Par23\">The remaining intracanal medicaments in the root canal system have been evaluated with several techniques in previous studies such as digital photographs [##REF##16728252##27##], stereomicroscopy [##REF##35852919##6##], scanning electron microscopy [##REF##24279657##28##], and micro-computed tomography (micro CT) [##UREF##3##29##]. This study assessed the amount of the remaining medicament in the root canal space with a 4-grade scoring system by evaluating the images under a stereo microscope at a 20× magnification [##REF##28084647##23##] since the scoring system has several advantages such as ease of application and repeatability and high rates of intra-examiner agreement used [##REF##28299554##30##]. On the other hand, it has been stated that measuring the surface layer of intracanal medicaments poses a risk in demonstrating the three-dimensional (3D) evaluation of the removal depth [##REF##36463133##31##], and therefore volumetric analysis with micro-CT could demonstrate more accurate results. However, three-dimensional imaging with micro-CT has low availability and high cost [##REF##36463133##31##]. In addition, the radiopacity level of CH and DAP can be a challenge for their complete visualization with micro-CT [##REF##35478706##32##].</p>", "<p id=\"Par24\">Berkhoff et al. [##REF##25069927##8##] showed that CH was more effectively removed compared to the TAP regardless of the used irrigation techniques. They have attributed this result to the high diffusion capacity of TAP into the dentinal tubules. On the contrary, Eymirli et al. demonstrated that the remaining CH in the root canal system was significantly higher than TAP with a laser-activated system and they claimed that the small particle size of CH which leads to direct penetration of CH into the dentinal tubules [##REF##27623238##33##]. In this study, two routinely used intracanal medicaments, CH and DAP, could not be removed entirely from the root canal space, and there was no statistically significant difference among those medicaments regarding retrievability with SNI, PUI, EDDY, and SWEEPS systems. This result is consistent with some studies in the literature that compare the removal of calcium and antibiotic pastes from the root canal system [##REF##35852919##6##, ##UREF##4##34##]. Divergent results in the literature can be explained by the different irrigation activation systems, tooth morphologies, irrigation solutions and protocols, and evaluation methods.</p>", "<p id=\"Par25\">EDDY and PUI have significantly increased the retrievability of intracanal medicaments from root canals compared to SNI; however, their superiority over each other has not been exhibited in this study in line with other studies in the literature [##REF##30803540##10##, ##REF##35028030##14##]. The higher velocity of irrigation solution created by PUI with enhanced fresh irrigant replacement could explain the larger amount of the removed intracanal medicaments [##REF##24565670##35##]. Furthermore, improved irrigant fluid flow through higher frequency of EDDY system also leads to higher intracanal medicament removal from the root canal system [##REF##30803540##10##]. Additionally, EDDY creates three-dimensional movement that triggers cavitation and acoustic streaming similar to the PUI, and therefore, similar efficiency of these irrigation activation systems might have been observed in terms of medicament removal.</p>", "<p id=\"Par26\">Although the efficiency of SWEEPS technology regarding calcium hydroxide removal has been demonstrated in different clinical scenarios in the literature, there is a lack of information on its effectiveness in RETs. Kırmızı et al. [##REF##34662526##18##] showed that although SWEEPS significantly increased the calcium hydroxide removal from the resorption cavities compared to the sonic and ultrasonic irrigation activation systems, there was no significant difference between the SWEEPS and PIPS groups. Moreover, Yang et al. [##REF##33961503##19##] also found that the remnants of the calcium hydroxide were lesser in SWEEPS and PIPS groups than ultrasonic activation system, especially in the cervical third of the root canal system. According to the present findings, although complete removal could not be achieved with any of the irrigation activation systems, SWEEPS significantly improved the removal of CH and DAP in all experimental groups. This result can be explained by the unique activation mechanism of SWEEPS. It creates a sudden expansion of the second bubble produced by the second laser pulse, causing the primary bubble to collapse violently by applying additional pressure to the first bubble. This powerful shock wave generated by the secondary cavitation bubbles can be emitted in all root canal surfaces during the irrigation activation procedure. Accordingly, it can constitute the shear stress and vertical flows that can remove intracanal medicaments as well as debris, the smear layer, and biofilm effectively from the root canal surface [##UREF##1##16##, ##REF##36595139##17##].</p>", "<p id=\"Par27\">This study has some limitations that should be addressed. The vehicle used to mix the CH powder is an essential factor influencing the removal rate of CH from the root canal walls. Distilled water was selected as a vehicle in this study; however, if glycerin had been used, the removal of CH could have been more challenging [##REF##34782506##36##]. In addition, the loss of medicament may have been occurred during the sectioning process of teeth. Moreover, irrigation activation systems may lead to structural changes and weakening of dentin when they are used in combination with EDTA [##REF##27769680##37##]. Finally, since this study is the first study that evaluate the intracanal medicament efficiency of SWEEPS technology, removal amounts of medicaments have not been investigated regarding different parts of the teeth. This may lead to a lack of information, especially in the coronal part of the root, where the bond strength of barrier materials is important. Future detailed studies are needed to explore the efficiencies of these irrigation methods in terms of intracanal medicament removal and dentin erosion and/or demineralization in regenerative endodontics.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par28\">The complete removal of intracanal medicaments from root canal space in RETs poses a risk. SWEEPS technology removed significantly higher amounts of CH and DAP compared to the other activation systems whereas SNI was the less effective system. PUI and EDDY showed similar effectiveness in terms of the ability to remove medicaments from root canal walls.</p>" ]

[ "<p id=\"Par1\">This study aimed to compare the syringe-needle irrigation (SNI), passive ultrasonic irrigation (PUI), EDDY, and shock wave–enhanced emission photoacoustic streaming (SWEEPS) techniques regarding calcium hydroxide and double antibiotic paste removal from the root canal in regenerative endodontic treatments. Eighty single-rooted human teeth were decoronated and enlarged up to #100 to stimulate the immature tooth model. Root canals were irrigated with 1.5% sodium hypochlorite followed by saline solution according to the regenerative endodontic treatment protocol. Dressed teeth were divided into 2 main groups regarding the used intracanal medicaments. Calcium hydroxide and double antibiotic paste were introduced to the canals, and teeth were stored for 3 weeks. Each medicament group was divided into 4 subgroups according to the activation techniques. Medicaments were removed using a 17% EDTA solution. Teeth were split longitudinally into two parts. The remaining medicaments were evaluated under a stereo microscope with a scoring system. Data were analyzed with the Kruskal-Wallis and Mann-Whitney <italic>U</italic> tests. Regardless of the used irrigation activation systems, there was no statistically significant difference between the removal of the CH and DAP from the root canal (<italic>P</italic>&gt;0.05). While SWEEPS had the highest ability regarding the removal of intracanal medicaments, syringe-needle irrigation had the lowest (<italic>P</italic>&lt;0.05). There was no statistically significant difference between PUI and EDDY (<italic>P</italic>&gt;0.05). Complete removal of intracanal medicaments could not be achieved with any techniques. SWEEPS technology was more effective in removing intracanal medicaments in regenerative endodontic treatments compared to the sonic and ultrasonic irrigation activation systems.</p>", "<title>Keywords</title>", "<p>Open access funding provided by the Scientific and Technological Research Council of Türkiye (TÜBİTAK).</p>" ]

[]

[ "<title>Author contributions</title>", "<p>Conceptualization: Sıla Nur Usta, Mustafa Gündoğar; data curation: Sıla Nur Usta, Berat Akın Erdem; formal analysis: Sıla Nur Usta; investigation: Sıla Nur Usta, Berat Akın Erdem, Mustafa Gündoğar; methodology: Sıla Nur Usta, Mustafa Gündoğar; software: Sıla Nur Usta; supervision: Mustafa Gündoğar; validation: Sıla Nur Usta, Berat Akın Erdem, Mustafa Gündoğar; visualization: Sıla Nur Usta, Berat Akın Erdem, Mustafa Gündoğar; writing—original draft: Sıla Nur Usta; writing—review and editing: Sıla Nur Usta, Berat Akın Erdem, Mustafa Gündoğar.</p>", "<title>Funding</title>", "<p>Open access funding provided by the Scientific and Technological Research Council of Türkiye (TÜBİTAK).</p>", "<title>Data availability</title>", "<p>The data that support the findings of this study are available from the corresponding author upon reasonable request.</p>", "<title>Declarations</title>", "<title>Ethical approval</title>", "<p id=\"Par29\">This study was performed in line with the principles of the Declaration of Helsinki. The study protocol was approved by the Ethics Committee of the University where the study was conducted (no. 2023-144).</p>", "<title>Consent to participate</title>", "<p id=\"Par30\">Informed consent was obtained from all individual participants included in the study.</p>", "<title>Competing interests</title>", "<p id=\"Par31\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Demonstrative images of score 0 (<bold>a</bold>), score 1 (<bold>b</bold>), score 2 (<bold>c</bold>), and score 3 (<bold>d</bold>)</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>The distributions of the scores based on the experimental groups</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>The percentages of the remaining intracanal medicaments for four different irrigation activation systems.</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th/><th>SNI</th><th>PUI</th><th>EDDY</th><th>SWEEPS</th></tr></thead><tbody><tr><td>CH</td><td>66.17^a,1</td><td>31.54^b,1</td><td>29.32^b,1</td><td>11.74^c,1</td></tr><tr><td>DAP</td><td>64.33^a,1</td><td>27.67^b,1</td><td>25.04^b,1</td><td>12.84^c,1</td></tr></tbody></table></table-wrap>" ]

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[ "<table-wrap-foot><p>Different superscript lowercase letters in the same row indicate a statistically significant difference (<italic>P</italic> &lt; 0.05)</p><p>The same superscript numbers in the same column indicate no statistically significant difference (<italic>P</italic> &gt; 0.05)</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher’s Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"10103_2024_3980_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"10103_2024_3980_Fig2_HTML\" id=\"MO2\"/>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par2\">Fibromyalgia is a clinical syndrome that mainly affects women [##UREF##0##1##], characterized by a chronic presence of widespread pain, accompanied by a conglomerate of physical and psychological symptoms. These include fatigue, sleep disturbances, and cognitive dysfunction [##REF##19962494##2##]. Furthermore, depression and anxiety are common comorbidities, with a lifetime prevalence of depression estimated to be higher than 50%, and up to 33% for anxiety [##REF##33383293##3##]. A common finding in fibromyalgia is an imbalance in the presence of positive and negative affect, meaning that patients experience positive affect less frequently than controls, while negative affect is more frequent [##UREF##1##4##, ##REF##15673637##5##]. This imbalance is not only associated with an increase in the prevalence of depression and anxiety [##UREF##2##6##], it is also related to higher intensity of pain [##REF##17600456##7##, ##REF##15251076##8##], lower cognitive performance [##UREF##3##9##], and overall higher severity of fibromyalgia [##REF##25596699##10##]. Because of its relevance for symptomatology, understanding and improving affect in fibromyalgia is an important clinical goal.</p>", "<p id=\"Par3\">Disturbances in emotion processing and regulation have been related to affective instability [##REF##18399953##11##, ##REF##12916575##12##] and might help explain the high comorbidity of fibromyalgia with depression and anxiety. It has been described that patients with fibromyalgia experience emotions with higher intensity and arousal than controls [##REF##26186433##13##, ##REF##18222129##14##]. Additionally, fibromyalgia patients use expressive suppression more frequently as an emotion regulation strategy when compared to controls [##REF##18222129##14##, ##REF##31019693##15##]. Expressive suppression is a strategy frequently associated with psychopathology [##UREF##4##16##], and it is considered to be maladaptive because when compared to reappraisal, it fails to effectively reduce negative affect and results in increased arousal [##REF##26186433##13##, ##REF##18222129##14##, ##REF##23622762##17##], although findings are not fully consistent [##REF##23622762##18##]. Also, difficulties to identify and describe one's own feelings, known as alexithymia, have been shown to be associated with fibromyalgia and impaired emotion regulation [##REF##27750065##19##–##REF##10742872##21##]. Alexithymia has been related to higher impact of the fibromyalgia [##REF##22200522##22##], depression, anxiety, [##REF##28577473##23##, ##REF##25511201##24##] and pain [##REF##27750065##19##, ##REF##19379959##25##], although not all studies report this relationship [##UREF##6##26##]. In general, emotion processing and regulation disturbances affect emotional state in fibromyalgia patients and are thought to facilitate the development of depression and anxiety.</p>", "<p id=\"Par4\">Recent advances in the understanding of the physiopathology of fibromyalgia can help elucidate the origin of the emotional difficulties that characterize this disorder. One of the current theories describes fibromyalgia as a central sensitization condition [##REF##12746916##27##, ##UREF##7##28##], which is triggered by neuro-inflammation [##REF##30223011##29##–##REF##33556139##31##]. The brain areas that have been associated with neuro-inflammation encompass the precuneus, posterior cingulate cortex, midcingulate cortex, supramarginal gyrus, superior parietal lobe, frontal operculum, dorsolateral prefrontal cortex, precentral and postcentral gyrus, medial prefrontal cortex, and the superior frontal gyrus, including the supplementary motor area [##REF##30223011##29##, ##REF##33556139##31##]. Interestingly, many of these brain areas are related to emotion processing and regulation. Roughly, the amygdala, hippocampus, insula, and midcingulate cortex are associated with the generation of the primary emotional response and salience detection. The ventrolateral prefrontal cortex has been associated with signaling the need for control and calling for additional regulatory resources [##REF##24220041##32##–##REF##30773147##34##]. Finally, the dorsolateral prefrontal cortex, supplementary motor area, anterior cingulate cortex, superior parietal lobe, and angular gyrus are related to the implementation of regulation strategies, such as cognitive reappraisal and suppression [##REF##24220041##32##, ##REF##25425765##35##, ##REF##27998996##36##]. Thus, multiple brain regions are orchestrated, to execute a set of cognitive functions that underpin the adequate emotion processing and regulation.</p>", "<p id=\"Par5\">A few previous studies have addressed alterations of brain activity during the processing of emotional stimuli in fibromyalgia [##REF##26186433##13##, ##UREF##9##37##, ##REF##33539799##38##]. Some of these studies relied on electroencephalography, and one functional magnetic resonance imaging (fMRI) study investigated brain activation associated to the influence of emotions on the processing of painful stimuli [##REF##23752177##39##]. In the current study, we aimed to investigate brain activation and functional connectivity (FC) during emotion processing and regulation in fibromyalgia using fMRI. Specifically, we studied the differences between female fibromyalgia patients and healthy controls (HC) in whole-brain activation and in FC of structures in networks associated with emotional processing and regulation. We focused on female participants because of the higher prevalence of fibromyalgia in this group. Furthermore, we investigated whether individual variation in the clinical presentation of fibromyalgia relates to FC, particularly alexithymia, pain, depression, and anxiety owing to the hypothesized inter-relation between these variables mentioned earlier. To this end, we compared fMRI data acquired from fibromyalgia patients and HC during emotional processing and regulation. We hypothesized higher brain activation in fibromyalgia in the prefrontal cortex, pregenual anterior cingulate cortex (pACC), insula, and amygdala, as well as higher FC between the anterior insula, amygdala and cortical areas involved in emotion processing and regulation, with larger abnormalities in those displaying higher alexithymia and pain, regulated by depression and anxiety.</p>" ]

[ "<title>Materials and methods</title>", "<title>Participants</title>", "<p id=\"Par6\">The current analysis is part of a bigger project from the National Institute of Psychiatry in Mexico (internal Research Committee registry number: IC18080.0) which aims to study clinical and neuroimaging correlates of emotion processing and regulation in fibromyalgia. For the present analysis, we included participants who performed an emotion processing and regulation task (EPRT) during fMRI: 34 fibromyalgia patients and 33 HC (all females). After fMRI quality control (see <italic>fMRI preprocessing</italic> in the Online Resource document), data from 30 patients with fibromyalgia (mean age = 41.8 years; years of education = 15.5) and 31 HC (mean age = 41.2 years; years of education = 16.8) were analyzed. For details on recruitment and selection criteria, see Online Resource. All participants were right-handed and the groups were matched with respect to age and years of education. All participants provided written informed consent. The protocol was approved by Research Ethics Committee of the National Institute of Psychiatry “Ramon de la Fuente Muñiz” in Mexico City.</p>", "<title>Clinical measures</title>", "<p id=\"Par7\">A series of scales and interviews were administered to assure the compliance with inclusion and exclusion criteria, and to characterize the sample. To confirm right laterality, the Edinburgh Handedness Inventory Short Form was administered [##UREF##10##40##]. All participants with fibromyalgia had previously received the diagnosis by a rheumatologist or an internist. To confirm (or exclude for HC) the diagnosis of fibromyalgia, we used the American College of Rheumatology 2016 criteria [##REF##27916278##41##]. To exclude major psychiatric disorders in the sample or any disorder in HC, as well as to document other psychiatric comorbidities in the fibromyalgia group (such as depression and anxiety), the Mini International Neuropsychiatric Interview-Plus [##REF##9881538##42##] was administered by a trained psychiatrist. To measure severity of depressive and anxiety, we applied the 17-items Hamilton Depression Rating Scale (HAMD) [##UREF##11##43##, ##REF##3397906##44##] and the Hamilton Anxiety Rating Scale (HAMA) [##REF##11975886##45##]. Other clinical variables were measured using self-rating scales: the tendency to employ cognitive reappraisal or suppression with the Emotional Regulation Questionnaire [##REF##12916575##12##], alexithymia with the Toronto Alexithymia Scale [##REF##8126686##46##, ##UREF##12##47##], regular affective state in the past week with the Positive and Negative Affect Schedule [##REF##3397865##48##, ##UREF##13##49##]. Participants filled the Socio-economic levels Questionnaire of the Mexican Association of Market Research and Public Opinion Agencies Questionnaire (AMAI NSE 8 × 7), which is a standardized instrument to measure socio-economic level in Mexican households, and filled a form with sociodemographic data and clinical characteristics of fibromyalgia (i.e., duration and treatment). Finally, the Fibromyalgia Impact Questionnaire [##REF##1865419##50##] and the McGill Pain Questionnaire [##REF##1235985##51##, ##UREF##14##52##] were administrated to participants in the fibromyalgia group to evaluate the severity of fibromyalgia and the characteristics of pain, respectively.</p>", "<title>Procedure and fMRI task</title>", "<p id=\"Par8\">Evaluations for each participant were conducted over two sessions with a median time interval of 8 days (range 0–20). During the first session, the interviews and scales mentioned were applied. On the second session, participants were trained to perform the EPRT, and next they underwent the MRI session. Depression, anxiety and affect measurements were updated during the second interview when time interval between sessions was longer than eight days.</p>", "<p id=\"Par9\">For the EPRT, three regulation instructions were implemented: Attend, Reappraise, and Suppress. During the Attend conditions, participants were asked to observe the pictures and allow themselves to experience any emotional response elicited by the stimuli without trying to manipulate the emotional experience. The Reappraise condition had two variants depending on the valence of the stimuli: Increase for positive pictures and Decrease for negative ones. In the case of Increase, participants were asked to boost the positive emotional experience elicited by the stimuli by reinterpreting the presented picture in a more positive self-related manner. In the case of Decrease, participants were asked to reduce the negative emotion elicited by the stimuli by interpreting it as something distant and not dangerous for them or by changing the meaning of the situation to something less negative. For the Suppress conditions (positive and negative), participants were asked to avoid any emotional expression elicited by the stimuli, so that someone watching them would not be able to infer their emotional state. In total, there were seven conditions: Attend neutral, Attend negative, Attend positive, Reappraise negative, Reappraise positive, Suppress negative, and Suppress positive. The task was implemented in a block design (Fig. ##FIG##0##1##). After each block, participants rated on a visual analog scale the intensity of the emotion elicited, arousal and physical pain. See Online Resource for details on the task.</p>", "<title>fMRI data acquisition</title>", "<p id=\"Par10\">Whole-brain functional and anatomical images were acquired using a 3.0T Philips Ingenia Magnetic Resonance Imaging scanner with a 32-channel phased array head coil. See Online Resource for details on the sequences.</p>", "<title>Clinical and behavioral analyses</title>", "<p id=\"Par11\">Demographic and clinical characterization of the sample was evaluated using non-parametric (Wilcoxon test) and parametric tests. Permutation tests with 1000 iterations were executed for analyzing the behavioral data from the EPRT. Behavioral analyses were done first comparing the ratings (emotional intensity, arousal, and pain intensity) for the combination of all instructions (Regulate, Suppress, and Attend) and valences (neutral, positive, and negative), leading to compare the seven conditions. In consideration of the lack of intra-group effects of conditions on ratings and brain activation (see “<xref rid=\"Sec14\" ref-type=\"sec\">Behavioral</xref>” and “<xref rid=\"Sec15\" ref-type=\"sec\">Whole-brain activation</xref>” “<xref rid=\"Sec12\" ref-type=\"sec\">Results</xref>” sections), we analyzed behavioral data across instructions, leading effectively to comparing the effect of valence (neutral, positive, and negative). To assess the differences between groups in emotion intensity, arousal, and pain, we performed a non-parametric contrast between groups for each variable per task condition (and valence across instructions). Because depression and anxiety may relate to intensity of the emotion, arousal, and pain, we performed Spearman’s correlation between ratings during each valence and the scores of HAMD and HAMA for the fibromyalgia group. Statistics were performed using R 3.6.2 (R Core Team, 2019).</p>", "<title>fMRI preprocessing</title>", "<p id=\"Par12\">The quality of the acquired image sequences was assessed using MRIQC Toolbox [##REF##28945803##53##]. Preprocessing and first-level analysis were executed with SPM12 (Statistical Parametric Mapping, Wellcome Institute for Cognitive Neurology, London, UK) [##UREF##15##54##]. For details, see the Online Resource.</p>", "<p id=\"Par13\">For the first-level analysis, data was analyzed in the context of the general linear model, with the time series of each participant convolved with the canonical hemodynamic response function and a 128 s high-pass filter applied. The model included the seven conditions (onsets of each picture and durations) plus the instructions, the visual analog scales and, the temporal and dispersion derivatives as regressors. Brain activation during fixation was modeled as implicit baseline.</p>", "<title>Whole-brain activation analysis</title>", "<p id=\"Par14\">Group analyses were performed at the whole-brain level. We planned two repeated measures ANCOVAs: one with the negative conditions (Attend negative, Reappraise negative, and Suppress negative) and one with the positive conditions (Attend positive, Reappraise positive, and Suppress positive) as the within-subject factor. Group (fibromyalgia and HC) was set as the between-subjects factor, and age and education were entered as covariates. Because exploration of the data across all participants revealed lack of significant activations for the main effect of conditions (across groups, and within HC and fibromyalgia separately; even at uncorrected threshold, which was in line with the behavioral results; see “<xref rid=\"Sec7\" ref-type=\"sec\">Clinical and behavioral analyses</xref>” and “<xref rid=\"Sec12\" ref-type=\"sec\">Results</xref>”), we set up a 2 × 2 ANCOVA model with valence (positive and negative, across instructions) as the within-subject factor, groups (fibromyalgia and HC) as the between-subjects factor, and age and education as covariates. In this model, the first-level contrasts used were all negative &gt; implicit baseline, and all positive &gt; implicit baseline. This decision allowed us to assess emotion processing and regulation according to the valence of the stimuli, but without differentiating processing from regulation. We modeled the main effect of group, and valence × group interaction. To explore relations of depression and anxiety, the peak activation of the significant clusters was extracted and correlated with the HAMD and HAMA scores.</p>", "<title>Functional connectivity: psychophysiological interaction analysis</title>", "<p id=\"Par15\">The FC was estimated using a generalized Psychophysiological interaction (gPPI) approach. We chose the following seeds (left and right) based on their affiliation with the amygdala–hippocampal network and salience network: hippocampus, amygdala, and anterior insula from the Hammers atlas [##REF##28179166##55##, ##REF##12874777##56##], and pACC five mm spheres were created based on literature about anterior cingulate cortex coordinates relevant for emotion regulation (MNI ± 6 36 10) [##REF##27998996##36##, ##REF##23409009##57##]. In total, eight seeds were defined.</p>", "<p id=\"Par16\">To perform the gPPI analyses, the time series for each seed was extracted and deconvolved to uncover neural activity. Next, the interaction term was created by multiplying the deconvolved seed time series and the task design time series. This interaction term was convolved with the hemodynamic response function to form the gPPI regressor, and the resulting time series was regressed against the rest of the brain to obtain the valence specific FC estimates. Thus, for each seed, a general linear model was estimated in the first-level analysis. In these models, the psychological terms for the gPPI consisted of the contrast between each task condition (i.e., Attend positive) and the implicit baseline, similar to the whole-brain activation analysis model. The other regressors were the time series of the seed and the interaction term. Additionally, temporal and dispersion derivatives were included. Following the across-instruction approach of the main brain activity analyses, the contrasts used in the second-level analysis were: all negative &gt; implicit baseline, and all positive &gt; implicit baseline. To test for the main effects of group and the valence x group effect, we performed an ANCOVA 2 × 2 (valence x group). Next, to test whether depression and anxiety severity moderated the relation between alexithymia, pain, and FC, we extracted the mean connectivity term from the clusters with significant correlation with the clinical variables and performed a partial correlation analysis to control for the contribution of depression and anxiety. The SPM 12 gPPI toolbox was used to perform the gPPI analyses and R for the partial correlations.</p>", "<title>Statistical significance</title>", "<p id=\"Par17\">For all analyses (clinical, behavioral, and fMRI), significant level was set to <italic>p</italic> &lt; 0.05 two-tailed, and False discovery rate (FDR) corrected for multiple comparisons, at a cluster-level for the fMRI data. For the gPPI analysis, an additional Bonferroni correction was applied to account for the number of seeds that were explored.</p>" ]

[ "<title>Results</title>", "<title>Demographic and clinical characteristics</title>", "<p id=\"Par18\">The demographic characteristics of the 30 fibromyalgia and 31 HC participants are summarized in Table ##TAB##0##1##. Among the fibromyalgia participants, 56.67% used medication daily (pregabalin being the most prescribed) and 63% fulfilled criteria for at least one current psychiatric disorder, being major depressive disorder the most common (46.7%). For clinical and psychiatric details specific to the fibromyalgia group, see Tables 2S and 3S in the Online Resource. As shown in Table ##TAB##1##2##, in comparison to HC, fibromyalgia participants presented more pain (<italic>W = 925.5, p</italic> &lt; <italic>0.001</italic>), depressive and anxious symptoms (<italic>W</italic> = <italic>914.0, p</italic> &lt; <italic>0.001</italic>, and <italic>W</italic> = <italic>926.0, p</italic> &lt; <italic>0.001</italic>, respectively), alexithymia (<italic>W</italic> = <italic>720.0 p</italic> &lt; <italic>0.001</italic>), negative affect (<italic>W</italic> = <italic>774.0, p</italic> &lt; <italic>0.001</italic>), and less positive affect (<italic>W</italic> = <italic>190.0, p</italic> &lt; <italic>0.001</italic>). The use of cognitive reappraisal in daily life did not differ between groups (<italic>t(59)</italic> = <italic>− 0.4, p</italic> = <italic>0.73</italic>); for suppression, a non-significant tendency for higher use was found in fibromyalgia (<italic>W</italic> = <italic>590.0, p</italic> = <italic>0.073</italic>).</p>", "<title>Behavioral</title>", "<p id=\"Par19\">We only observed an effect of valence (neutral, positive, and negative), and not of condition (e.g., Reappraise positive, as summarized in Fig. ##FIG##1##2## and 1S. Based on this result, we decided to continue the analyses with valence as the independent variable. For effects on pain in fibromyalgia, pain intensity was higher during negative valence compared to neutral (<italic>Z</italic> = <italic>2.31 p</italic> = <italic>0.03</italic>) and positive (<italic>Z</italic> = <italic>3.44 p</italic> = <italic>0.002</italic>) as shown in Fig. ##FIG##1##2## panel C; depression (and possibly anxiety) might explain pain during negative valence as these two variables were positively correlated (<italic>r</italic>(26) = 0.43, <italic>p</italic> = 0.02, and <italic>r</italic>(26) = 0.36, <italic>p</italic> = 0.06, respectively). Pain did not differ between valence for HC (mean = 0.8 points, <italic>X</italic>^{<italic>2</italic>}<italic>(2)</italic> = <italic>1.0, p</italic> = <italic>0.6)</italic>.</p>", "<p id=\"Par20\">For emotional intensity, fibromyalgia patients experienced emotions more negatively than HC, both for negative (<italic>Z</italic> = <italic>8.0, p</italic> &lt; <italic>0.001</italic>), and positive stimuli (<italic>Z</italic> = 3.0, <italic>p</italic> = 0.009). The arousal was also higher in fibromyalgia for negative stimuli (<italic>Z</italic> = <italic>− 4.0 p</italic> &lt; <italic>0.001</italic>). Depression and anxiety were not correlated to emotional intensity nor arousal in fibromyalgia (Online Resource Table 4S).</p>", "<title>Whole-brain activation</title>", "<p id=\"Par21\">For the 2 × 2 ANCOVA (valence x group) model, we found a significant cluster for the group main effect in the left superior lateral occipital cortex (MNI coordinates: -30 -79 23; F = 26.53, <italic>p</italic> = 0.028). The post hoc <italic>t</italic>-test for the contrast fibromyalgia &gt; HC was significant for that cluster (Fig. ##FIG##2##3##; <italic>t</italic>(116) = 5.15, <italic>p</italic> = 0.023, <italic>k</italic> = 77). The BOLD activation of this cluster correlated positively with depression (<italic>r</italic>(25) = 0.58, <italic>p</italic> = 0.001), and anxiety (<italic>r</italic>(25) = 0.66, <italic>p</italic> &lt; 0.001) in fibromyalgia.</p>", "<title>Functional connectivity: psychophysiological interactions</title>", "<p id=\"Par22\">We explored the task-modulated FC of hippocampus, amygdala, anterior insula, and pACC during processing and regulation of emotions. In our analysis, only the left pACC seed showed a valence x group interaction (Table ##TAB##2##3##). The right post- and precentral cortex, and the left central operculum, premotor and postcentral cortex showed higher FC with the left pACC in fibromyalgia participants than HC during the processing of positive valence stimuli, while during the processing of negative valence stimuli, the FC was lower in these regions (Fig. ##FIG##3##4##). In fibromyalgia, the FC of left pACC with significant clusters did not correlate with depression nor anxiety (Table ##TAB##3##4##). The rest of the seeds (bilateral hippocampus, amygdala, anterior insula, and right pACC) did not show significant effects of group nor a valence × group interaction.</p>", "<p id=\"Par23\">Finally, a correlation analysis was performed between the FC of each seed and the clinical variables alexithymia and pain in the fibromyalgia group. The <italic>Difficulty to identify feelings</italic> (<italic>DIF</italic>) subscale was the only alexithymia measure that correlated to the FC between right anterior insula and a cluster encompassing parts of the right superior frontal gyrus, the supplementary motor area and the dorsal anterior cingulate cortex (MNI coordinates: <italic>x</italic> = 18, <italic>y</italic> = 5, <italic>z</italic> = 47, size: 43 voxels, <italic>r</italic>(28) = 0.61, <italic>p</italic> = 0.01). Adding depression in a partial correlation moderated the relation between right insula seeded FC and <italic>DIF</italic>, so it was no longer significant (<italic>r</italic>(27) = 0.49, <italic>p</italic> = 0.23). When the correlation analysis was repeated including the control group, no correlation was found. The FC of other seeds did not correlate with alexithymia nor pain.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par24\">In this study, we investigated brain activation and FC during emotion processing and regulation in fibromyalgia, using fMRI. We found higher activation of lateral occipital cortex in fibromyalgia during processing of emotional pictures, irrespective of valence. We also found altered valence-dependent FC of the left pACC with the opercular, premotor, post- and precentral cortex during the processing and regulation of emotional stimuli in fibromyalgia. More specifically, we observed higher pACC seeded FC during positive emotion processing and lower FC during negative emotion processing. Our behavioral analysis showed more negative emotions in fibromyalgia than in HC. Taken together, these results suggest that higher negative mood and pain in fibromyalgia are associated with abnormal processing of negative and positive emotional stimuli, which might underpin the emotional difficulties present in fibromyalgia and its effect on pain.</p>", "<p id=\"Par25\">The lateral occipital cortex was found to be hyper-activated in fibromyalgia compared to HC, irrespective of valence, but with variations according to the severity of depression. The lateral occipital cortex has been related to visual attention [##REF##33941755##58##], object perception [##REF##17055298##59##, ##REF##11322983##60##], but also to pain modulation [##REF##20418174##61##]. A recent study found that the decrease in resting-state FC between the occipital cortex and the pACC following transcranial magnetic stimulation relates to a reduction in the affective dimension of pain in fibromyalgia [##REF##34785365##62##], suggesting the occipital cortex has functional relevance for the affective processing of pain. Hypo-activation of visual areas has been already described in other populations with high levels of alexithymia during subliminal emotional stimuli [##REF##28099136##63##]. Here, the observed higher activation of the occipital gyrus during overt emotional stimuli may suggest higher use of visual cues to process and regulate emotions (in opposition to cognitive processes). Additional to pain modulation and alexithymia, emotion processing or depression could explain the differences in occipital activation since this region was found affected in a previous study using a similar emotion processing and regulation task in patients with remitted depression [##REF##35298997##64##], and from our results in the correlation with severity of depression.</p>", "<p id=\"Par26\">Besides the lateral occipital cortex, no other regions showed activation differences, including those from the hypothesis (insula, amygdala, prefrontal and pACC). This could be due to a compensation mediated by changes in the FC as found for the pACC. For the other hypothesized regions, amygdala and prefrontal cortex could be less involved with the emotion processing and regulation difficulties, while the insula alterations seem to depend more on psychological characteristics of the fibromyalgia group, as found in the correlation of FC and clinical variables.</p>", "<p id=\"Par27\">In regard to the pACC, it is an integrative hub associated with the convergence of salient interoceptive, sensitive and emotional stimuli for further processing and coordination of potential motor responses [##UREF##16##65##]. Furthermore, it is an area rich in opioid receptors [##REF##1650933##66##], thereby participating in the affective assessment of pain [##REF##24887007##67##]. Finally, pACC activation, connectivity, and structure have been implicated in the top-down regulation of negative affect and pain [##UREF##17##69##–##REF##21697947##70##]. Previously, pACC FC with other structures from a pain inhibitory network was found to be reduced in fibromyalgia [##REF##22537768##71##], and its activation during pain has been related to the availability of μ-opioid receptors and to the affective intensity of pain [##REF##27420606##72##].</p>", "<p id=\"Par28\">We found a hyper-connectivity of pACC during positive stimuli processing and a reduced connectivity during negative stimuli processing with the precentral gyrus, postcentral gyrus, central operculum, and superior frontal gyrus. The precentral and postcentral gyri have been found important for the discrimination of emotions and the representation of valence [##REF##29973874##73##, ##REF##21801839##74##], and to be activated during reappraisal and suppression [##REF##24220041##32##, ##REF##34391808##75##]. It has been reported that these areas are hypoactive in women with premenstrual dysphoric disorder [##REF##29145910##76##], a condition characterized also by emotional dysregulation and pain. The central operculum has been implicated in emotion and pain processing in pathological conditions. For example, in functional dystonia and alcohol dependence, pACC was found hypoactive while performing emotion regulation tasks [##REF##29124784##77##, ##UREF##18##78##], and in masochist patients, its FC was impaired during a task that involved emotional and painful stimuli [##REF##26808014##79##]. The valence-related alteration of the pACC FC to areas related to interoception and emotion processing and regulation that we found might help explain the relationship between negative affect and higher pain intensity [##REF##17600456##7##, ##REF##32112278##80##], and the deficient pain modulation by positive emotional stimuli [##REF##23752177##39##] in fibromyalgia.</p>", "<p id=\"Par29\">In consideration of the mentioned evidence from the literature and our results, where negative conditions were characterized by higher pain intensity in fibromyalgia and more negative emotional experience (between-groups comparison), we interpret that in fibromyalgia, the processing of emotional stimuli is disrupted according to its valence, given by the affected FC between areas involved in the processing of valence and internal representations encoding. In other words, the pACC FC is affected in fibromyalgia during the processing of emotional stimuli and how it is affected depends on whether the valence of the stimuli is positive or negative.</p>", "<p id=\"Par30\">The involvement of the pACC in linking negative affect and pain is not exclusive from fibromyalgia and might be related to neuro-inflammation. A metabolic marker of neuro-inflammation in the pACC was related to negative affect in patients with chronic low back pain [##REF##31138890##81##]. Although the studies on neuro-inflammation in fibromyalgia [##REF##30223011##29##, ##REF##33556139##31##, ##REF##31990749##82##] have not shown neuro-inflammation this region, neuro-inflammation has been found in areas connected to the pACC such as the midcingulate cortex [##REF##17928332##83##]. Thus, one possibility is that neuro-inflammation affects the pACC through its connection to areas with neuro-inflammation. Alternatively, neuro-inflammation is present in the pACC in fibromyalgia, but it has not been observed due to the employed methodology. Whether neuro-inflammation affects the pACC in fibromyalgia requires further research. In case it is proved, neuro-inflammation could become a treatment target to improve affect and pain modulation in patients with fibromyalgia.</p>", "<p id=\"Par31\">Given the involvement of the anterior insula in emotion processing and regulation [##REF##34391808##75##] and in fibromyalgia symptomatology [##UREF##19##84##], we studied its FC. We found that in fibromyalgia, during the regulation of negative stimuli, the anterior insula FC to the superior frontal gyrus, supplementary motor area, and dorsal anterior cingulate cortex, areas that are important for emotion regulation, was positively correlated with the <italic>DIF</italic>, a factor of the alexithymia construct. This finding is in accordance to previously described negative correlation of anterior insula activation with alexithymia [##UREF##20##85##]. Notably, the <italic>DIF</italic> relation to anterior insula connectivity was explained by depression according to our partial correlation analysis results.</p>", "<title>Limitations and future directions</title>", "<p id=\"Par32\">Some limitations need to be taken into account. As for most of the studies in fibromyalgia, our results are limited to women. This is a limitation insofar that we do not know if the findings extend to men. Nevertheless, as a first study, we limited the sample to women to enhance homogeneity, taking into account that the prevalence is considerably larger in women (3.98%, for women vs. 0.01% for men) [##UREF##0##1##]. Furthermore, participants over 50 years old were excluded to ease task-training, in spite of representativity of elderly patients where the prevalence of fibromyalgia is high [##REF##23801009##86##]. Another limitation pertaining our sample is the presence of physical and mental health comorbidities in the fibromyalgia group with some patients being medicated with drugs that affect central nervous system such as antidepressants. Nevertheless, we required participants to have a stable dose of their medication and to avoid rescue doses 24 h before the brain scan. Although the medication and the mental health disorders could affect the task performance and brain activity, mental comorbidities are highly prevalent among patients with fibromyalgia, which make our findings more generalizable [##REF##33383293##3##, ##REF##32383318##87##], exempting for those using opioids since they were excluded from the study. Furthermore, we performed analyses to control for depression and anxiety.</p>", "<p id=\"Par33\">An important limitation is the lack of effects of condition in the behavioral and the ANCOVA 3 × 2 analyses (condition [reappraise, suppress, attend] x group) in the fMRI analysis. This task has been successfully applied without the suppress condition in a Dutch sample of people with remitted depression [##REF##35298997##64##]. One possible explanation for the lack of clear differences could be that it may have been difficult for our sample to follow the three different regulation instructions (even after training them), as it is suggested by a study using a similar task in a Mexican sample where differences in the effect size of cognitive reappraisal were found according to the procedures to instructing participants [##UREF##21##88##]. Another possibility is that it may be more difficult for people with fibromyalgia to adequately perform the different emotion regulation strategies than for people with remitted depression. Furthermore, our fMRI results must be taken cautiously, especially the whole-brain activation analysis, since the multiple comparison correction approach was relatively liberal (<italic>p</italic> &lt; 0.05 FDR). In regard to the FC analysis, an additional correction to account for the number of seeds was applied. Finally, our interpretations concerning pain intensity were conceived based on the behavioral results of the task. However, to assess how emotion regulation affects the neural underpinnings of pain, tasks that include painful stimuli along with emotional ones should be applied.</p>" ]

[ "<title>Conclusions</title>", "<p id=\"Par34\">Taken together, our findings suggest that difficulties in emotion processing and regulation in fibromyalgia are related to alterations in activation of lateral occipital cortex, and in FC of the pACC, a central hub for emotion and pain processing, to other important emotion processing and regulation areas. These alterations might imply that a stronger involvement of regions associated with pain modulation is needed to process emotional stimuli (including valence and pain) in fibromyalgia. As standardized treatment and pharmacotherapy in fibromyalgia are often unsuccessful [##UREF##22##89##], psychotherapeutic strategies are being used more frequently to treat pain as well as the emotional difficulties and psychiatric comorbidities. Some of these therapies emphasize emotional awareness and regulation [##REF##31019693##15##, ##REF##22110946##90##, ##REF##28796118##91##]. Other therapeutic strategies include neuromodulation techniques [##REF##27977465##92##, ##REF##31982685##93##]. Longitudinal studies are needed to better understand the neural mechanisms of improvement with those therapies. The findings of the current study highlight some of the brain structures for which activation or connectivity might change after treatment.</p>" ]

[ "<p id=\"Par1\">Fibromyalgia, a condition characterized by chronic pain, is frequently accompanied by emotional disturbances. Here we aimed to study brain activation and functional connectivity (FC) during processing of emotional stimuli in fibromyalgia. Thirty female patients with fibromyalgia and 31 female healthy controls (HC) were included. Psychometric tests were administered to measure alexithymia, affective state, and severity of depressive and anxiety symptoms. Next, participants performed an emotion processing and regulation task during functional magnetic resonance imaging (fMRI). We performed a 2 × 2 ANCOVA to analyze main effects and interactions of the stimuli valence (positive or negative) and group (fibromyalgia or HC) on brain activation. Generalized psychophysiological interaction analysis was used to assess task-dependent FC of brain regions previously associated with emotion processing and fibromyalgia (i.e., hippocampus, amygdala, anterior insula, and pregenual anterior cingulate cortex [pACC]). The left superior lateral occipital cortex showed more activation in fibromyalgia during emotion processing than in HC, irrespective of valence. Moreover, we found an interaction effect (valence x group) in the FC between the left pACC and the precentral and postcentral cortex, and central operculum, and premotor cortex. These results suggest abnormal brain activation and connectivity underlying emotion processing in fibromyalgia, which could help explain the high prevalence of psychopathological symptoms in this condition.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00406-023-01578-x.</p>", "<title>Keywords</title>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Acknowledgements</title>", "<p>We thank Jan-Bernard Marsman and Remco Renken for their assistance in the MRI analysis; Francisco Pellicer Graham, José Sánchez-Sosa, Jorge González-Olvera for their academic assistance; Xochitl Duque for her support to obtain part of the software used [fund CONACYT-FOSISS number 289831]; Raúl Osorio and Lourdes Martínez from the Neuroimaging Department of the National Institute of Psychiatry “Ramón de la Fuente Muñiz”. We are grateful Isabel Barrera and the Mexican Foundation for Fibromyalgia for their help to recruit participants. Finally, and overall we thank our participants. This article is a requirement to T.B. to obtain the grade of Doctor in Science from the Programa de Maestría y Doctorado en Ciencias Médicas y Odontológicas y de la Salud from the National Autonomous University of Mexico.</p>", "<title>Funding</title>", "<p>Thania Balducci was funded by the National Council of Science and Technology of Mexico (CONACYT) [scholarship number 547524/577656, CVU 547524]; and the University of Groningen.</p>", "<title>Data availability</title>", "<p>The dataset is described in Scientific Data [##REF##36138036##94##] and publicly available.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par35\">None declared.</p>", "<p id=\"Par36\">\n<bold>Ethical standards</bold>\n</p>", "<p id=\"Par37\">This study was approved by the Research Ethics Committee of the National Institute of Psychiatry “Ramon de la Fuente Muñiz” in Mexico City, and it was performed in accordance with the ethical standards from the Declaration of Helsinki. All participants gave their informed consent prior to their inclusion in the study.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Task design for a single block</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Behavioral results of the emotion regulation task. <bold>A</bold> Intensity of emotion per condition: the visual analog scale (VAS) points represent the valence and intensity of the emotion experienced with 0 corresponds to the most intense negative emotion, 5 is a neutral state and 10 is the most intense positive emotion. <bold>B</bold> Arousal per condition: The visual analog scale (VAS) points represent the arousal with 0 being the minimum level and 10 is the most intense. <bold>C</bold> Pain per condition: the visual analog scale (VAS) points represent the pain intensity with 0 being no pain and 10 is the most intense pain. Mean and SD in the boxes. * Intergroup significant differences (all differences were significant at <italic>p</italic> &lt; 0.001)</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Significant cluster for the fibromyalgia &gt; healthy controls contrast in the whole-brain analysis, located in the left superior lateral occipital cortex (MNI coordinates: − 30 − 79 23), <bold>A</bold> sagittal, <bold>B</bold> axial and <bold>C</bold> correlation of depression/anxiety and cluster activation in FM (<italic>r</italic>(25) = 0.58, <italic>p</italic> = 0.001)</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Left ACC task-modulated functional connectivity during emotion regulation. Three clusters were significative for the valence x group interaction effect: <bold>A</bold> right precentral/postcentral cortex, <bold>B</bold> right frontal operculum, and <bold>C</bold> left central operculum, posterior insula, premotor and postcentral cortex. ACC, anterior cingulate cortex; FM, fibromyalgia group; HC, control group; +, regulation of positive valence stimuli; −, regulation of negative valence stimuli</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Demographic characteristics of the study participants</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">FM<break/>(<italic>n</italic> = 30)</th><th align=\"left\">HC<break/>(<italic>n</italic> = 31)</th><th align=\"left\"><italic>t/W</italic> value*</th><th align=\"left\"><italic>p</italic> value</th></tr></thead><tbody><tr><td align=\"left\">Age, years (SD)</td><td align=\"left\">41.9 (6.3)</td><td align=\"left\">41.2 (6.1)</td><td align=\"left\">498.5</td><td char=\".\" align=\"char\">0.633</td></tr><tr><td align=\"left\" colspan=\"5\">Education, <italic>n</italic> (%)</td></tr><tr><td align=\"left\"> Elementary</td><td align=\"left\">2 (6.7)</td><td align=\"left\">1 (3.2)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> High school or technical</td><td align=\"left\">9 (30.0)</td><td align=\"left\">7 (22.6)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Bachelor</td><td align=\"left\">13 (43.3)</td><td align=\"left\">14 (45.2)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Postgraduate</td><td align=\"left\">6 (20.0)</td><td align=\"left\">9 (29.0)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\">Years of study, years (SD)</td><td align=\"left\">15.4 (3.9)</td><td align=\"left\">16.8 (4.0)</td><td align=\"left\">− 1.361</td><td char=\".\" align=\"char\">0.179</td></tr><tr><td align=\"left\" colspan=\"4\">Marital status, <italic>n</italic> (%)</td><td char=\".\" align=\"char\">0.700</td></tr><tr><td align=\"left\"> Single</td><td align=\"left\">10 (29.4)</td><td align=\"left\">7 (21.2)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Married/cohabitating</td><td align=\"left\">17 (50.0)</td><td align=\"left\">21 (63.6)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Divorced/separated</td><td align=\"left\">5 (14.7)</td><td align=\"left\">4 (12.1)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Widow</td><td align=\"left\">2 (5.9)</td><td align=\"left\">1 (3.0)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" colspan=\"5\">Occupation, <italic>n</italic> (%)</td></tr><tr><td align=\"left\"> Employed</td><td align=\"left\">17 (56.7)</td><td align=\"left\">23 (74.2)</td><td align=\"left\"/><td char=\".\" align=\"char\">0.395</td></tr><tr><td align=\"left\"> Unemployed/Housewife</td><td align=\"left\">11 (36.7)</td><td align=\"left\">7 (22.6)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Student</td><td align=\"left\">2 (6.7)</td><td align=\"left\">1 (3.2)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" colspan=\"4\">Occupation pattern^†, <italic>n</italic> (%)</td><td char=\".\" align=\"char\">0.088</td></tr><tr><td align=\"left\"> Full time</td><td align=\"left\">10 (47.6)</td><td align=\"left\">16 (61.5)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Half time, fixed schedule</td><td align=\"left\">1 (4.8)</td><td align=\"left\">5 (19.2)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Half time, irregular schedule</td><td align=\"left\">10 (47.6)</td><td align=\"left\">5 (19.2)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\" colspan=\"4\">Menstrual cycle phase, <italic>n</italic> (%)^‡</td><td char=\".\" align=\"char\">0.500</td></tr><tr><td align=\"left\"> Follicular</td><td align=\"left\">14 (46.7)</td><td align=\"left\">15 (48.5)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Luteal</td><td align=\"left\">8 (26.7)</td><td align=\"left\">12 (38.7)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Postmenopause</td><td align=\"left\">4 (13.3)</td><td align=\"left\">1 (3.2)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Unknown^§</td><td align=\"left\">4 (13.3)</td><td align=\"left\">3 (9.7)</td><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\">BMI, mean (sd)</td><td align=\"left\">26.9 (4.2)</td><td align=\"left\">24.8 (3.2)</td><td align=\"left\">2</td><td char=\".\" align=\"char\">0.030</td></tr><tr><td align=\"left\">Economic status^¶, median (range)</td><td align=\"left\">C + (AB−D+)</td><td align=\"left\">C + (AB−D)</td><td align=\"left\">388</td><td char=\".\" align=\"char\">0.300</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Clinical characteristics of the study participants</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">FM<break/>(<italic>n</italic> = 30)</th><th align=\"left\">HC<break/>(<italic>n</italic> = 31)</th><th align=\"left\"><italic>F/W/t*</italic> value</th><th align=\"left\"><italic>p</italic> value</th><th align=\"left\">Effect size</th></tr></thead><tbody><tr><td align=\"left\">VAS for pain during the interview, mean (SD)</td><td char=\"(\" align=\"char\">45.7 (19.8)</td><td char=\"(\" align=\"char\">1.2 (3.5)^†</td><td char=\".\" align=\"char\">925.5</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.88</td></tr><tr><td align=\"left\">Widespread pain index, mean (SD)</td><td char=\"(\" align=\"char\">11.8 (4.3)</td><td char=\"(\" align=\"char\">0.9 (1.4)</td><td char=\".\" align=\"char\">922.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.86</td></tr><tr><td align=\"left\">Symptom severity scale score, mean (SD)</td><td char=\"(\" align=\"char\">8.3 (2.5)</td><td char=\"(\" align=\"char\">1.4 (1.5)</td><td char=\".\" align=\"char\">904.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.82</td></tr><tr><td align=\"left\">HAMD total score, mean (SD)</td><td char=\"(\" align=\"char\">15.2 (6.5)</td><td char=\"(\" align=\"char\">1.3 (2.0)</td><td char=\".\" align=\"char\">914.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.84</td></tr><tr><td align=\"left\">HAMA total score, mean (SD)</td><td char=\"(\" align=\"char\">21.2 (7.0)</td><td char=\"(\" align=\"char\">2.3 (2.5)</td><td char=\".\" align=\"char\">926.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.85</td></tr><tr><td align=\"left\">Positive affect—last week, mean (SD)</td><td char=\"(\" align=\"char\">25.3 (7.6)</td><td char=\"(\" align=\"char\">32.5 (4.9)</td><td char=\".\" align=\"char\">− 4.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">1.00</td></tr><tr><td align=\"left\">Negative affect—last week, mean (SD)</td><td char=\"(\" align=\"char\">22.9 (8.6)</td><td char=\"(\" align=\"char\">14.0 (4.4)</td><td char=\".\" align=\"char\">774.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.57</td></tr><tr><td align=\"left\">ERQ reappraisal score, mean (SD)</td><td char=\"(\" align=\"char\">31.6 (6.6)</td><td char=\"(\" align=\"char\">32.3 (6.5)</td><td char=\".\" align=\"char\">− 0.4</td><td char=\".\" align=\"char\">0.729</td><td char=\".\" align=\"char\">0.10</td></tr><tr><td align=\"left\">ERQ suppression score, mean (SD)</td><td char=\"(\" align=\"char\">14.7 (6.8)</td><td char=\"(\" align=\"char\">11.8 (5.0)</td><td char=\".\" align=\"char\">590.0</td><td char=\".\" align=\"char\">0.073</td><td char=\".\" align=\"char\">0.49</td></tr><tr><td align=\"left\">TAS difficulty identifying feelings, mean (SD)</td><td char=\"(\" align=\"char\">23.0 (10.0)</td><td char=\"(\" align=\"char\">12.0 (6.1)</td><td char=\".\" align=\"char\">776.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.58</td></tr><tr><td align=\"left\">TAS difficulty describing feelings, mean (SD)</td><td char=\"(\" align=\"char\">14.8 (6.5)</td><td char=\"(\" align=\"char\">11.0 (4.6)</td><td char=\".\" align=\"char\">617.0</td><td char=\".\" align=\"char\">0.032</td><td char=\".\" align=\"char\">0.28</td></tr><tr><td align=\"left\">TAS externally oriented thinking, mean (SD)</td><td char=\"(\" align=\"char\">20.9 (8.4)</td><td char=\"(\" align=\"char\">16.6 (5.7)</td><td char=\".\" align=\"char\">2.0</td><td char=\".\" align=\"char\">0.023</td><td char=\".\" align=\"char\">0.60</td></tr><tr><td align=\"left\">TAS total score, mean (SD)</td><td char=\"(\" align=\"char\">58.7 (21.9)</td><td char=\"(\" align=\"char\">39.5 (12)</td><td char=\".\" align=\"char\">720.0</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.47</td></tr><tr><td align=\"left\">Alexithymia, <italic>n</italic> (%)</td><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"/><td char=\".\" align=\"char\"> &lt; 0.001</td><td char=\".\" align=\"char\">0.46</td></tr><tr><td align=\"left\"> No alexithymia</td><td char=\"(\" align=\"char\">14 (46.7)</td><td char=\"(\" align=\"char\">26 (83.9)</td><td char=\".\" align=\"char\"/><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Possible alexithymia</td><td char=\"(\" align=\"char\">4 (13.3)</td><td char=\"(\" align=\"char\">4 (12.9)</td><td char=\".\" align=\"char\"/><td align=\"left\"/><td char=\".\" align=\"char\"/></tr><tr><td align=\"left\"> Alexithymia</td><td char=\"(\" align=\"char\">12 (40.0)</td><td char=\"(\" align=\"char\">1 (3.2)</td><td char=\".\" align=\"char\"/><td align=\"left\"/><td char=\".\" align=\"char\"/></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Brain regions per cluster that showed significant task-modulated functional connectivity to the left anterior cingulate cortex during emotion regulation</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Region</th><th align=\"left\" rowspan=\"2\">Size^a</th><th align=\"left\" rowspan=\"2\"><italic>F</italic></th><th align=\"left\" rowspan=\"2\"><italic>p</italic></th><th align=\"left\" colspan=\"3\">MNI coordinates</th></tr><tr><th align=\"left\"><italic>x</italic></th><th align=\"left\"><italic>y</italic></th><th align=\"left\"><italic>z</italic></th></tr></thead><tbody><tr><td align=\"left\" colspan=\"7\">Valence × group interaction</td></tr><tr><td align=\"left\"> R precentral/postcentral cortex</td><td align=\"left\">253</td><td char=\".\" align=\"char\">33.7</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td align=\"left\">57</td><td align=\"left\">− 4</td><td align=\"left\">29</td></tr><tr><td align=\"left\"> L central operculum/premotor/postcentral cortex</td><td align=\"left\">284</td><td char=\".\" align=\"char\">23.9</td><td char=\".\" align=\"char\"> &lt; 0.001</td><td align=\"left\">− 54</td><td align=\"left\">− 13</td><td align=\"left\">14</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Results of correlation tests between functional connectivity of left anterior cingulate cortex with significant clusters and depression and anxiety in fibromyalgia</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Cluster</th><th align=\"left\" rowspan=\"2\">Stimuli valence</th><th align=\"left\" colspan=\"2\">Depression</th><th align=\"left\" colspan=\"2\">Anxiety</th></tr><tr><th align=\"left\"><italic>r</italic></th><th align=\"left\"><italic>p</italic></th><th align=\"left\"><italic>r</italic></th><th align=\"left\"><italic>p</italic></th></tr></thead><tbody><tr><td align=\"left\" colspan=\"6\">Valence × group interaction</td></tr><tr><td align=\"left\" rowspan=\"2\"> R precentral/postcentral cortex</td><td align=\"left\">Positive</td><td char=\".\" align=\"char\">0.14</td><td char=\".\" align=\"char\">0.6</td><td char=\".\" align=\"char\">0.18</td><td char=\".\" align=\"char\">0.6</td></tr><tr><td align=\"left\">Negative</td><td char=\".\" align=\"char\">0.01</td><td char=\".\" align=\"char\">1.0</td><td char=\".\" align=\"char\">0.09</td><td char=\".\" align=\"char\">0.7</td></tr><tr><td align=\"left\" rowspan=\"2\"> L central operculum/premotor/postcentral cortex</td><td align=\"left\">Positive</td><td char=\".\" align=\"char\">0.30</td><td char=\".\" align=\"char\">0.4</td><td char=\".\" align=\"char\">0.35</td><td char=\".\" align=\"char\">0.4</td></tr><tr><td align=\"left\">Negative</td><td char=\".\" align=\"char\">0.12</td><td char=\".\" align=\"char\">0.7</td><td char=\".\" align=\"char\">0.17</td><td char=\".\" align=\"char\">0.6</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p>FM, fibromyalgia; HC, healthy controls; BMI, body mass index</p><p>^*W for age and economic status; t for years of study and BMI; Fisher´s Exact Test for marital status, occupation and menstrual cycle phase</p><p>^†Among those who work, FM = 21, HC = 26 participants</p><p>^‡Probable phase according to self-reported last menstrual period date</p><p>^§Six because of hysterectomy, 1 lost data</p><p>^¶The instrument used was the AMAI rule 8 × 7 created for Mexican homes, where A/B is the highest economic status category and E is the lowest</p></table-wrap-foot>", "<table-wrap-foot><p>ERQ: Emotion regulation questionnaire, FM, fibromyalgia group; HC, healthy controls; HAMA, Hamilton Anxiety Rating Scale; HAMD, Hamilton Depression Rating Scale; TAS, Toronto Alexithymia Scale; VAS, visual analog scale</p><p>*W for VAS for pain during the interview, Widespread pain index, Symptom severity scale, painful tender points (ACR90), HAMD, HAMA, ERQ suppression, TAS total and subscales (except externally oriented thinking), negative effect; Fisher´s Exact Test for alexithymia categories; T for TAS externally oriented thinking, positive effect, ERQ reappraisal</p><p>^†Five healthy controls reported some pain during the interview. This pain was due high physical activity during previous days. Precautions were taken for avoid this kind of pain during the fMRI session</p></table-wrap-foot>", "<table-wrap-foot><p>^aVoxels</p></table-wrap-foot>" ]

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[ "<media xlink:href=\"406_2023_1578_MOESM1_ESM.docx\"><caption><p>Supplementary file1 (DOCX 293 kb)</p></caption></media>" ]

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[ "<title>Introduction</title>", "<p id=\"Par5\">Although fungal infections are mostly unknown to the public, their total annual mortality is comparable to or exceeds that of malaria, tuberculosis, or HIV. The impact of fungal infections has been worsened by the steady increase of antifungal drug-resistant strains and species, which indicates the widespread consumption of antifungals for preventive measures and treatment and has been related, in the case of azole resistance in <italic>Aspergillus</italic>, to antifungal use in agriculture (Gow et al. ##UREF##25##2022##). The COVID-19 pandemic exacerbated the present situation by predisposing patients in intensive care units (ICUs) to secondary deadly fungal infections, making accurate diagnosis more challenging (Li and Denning ##REF##36852004##2023##). Mucormycosis, also known as “Black Fungus,” has been linked to COVID-19 patients, making up approximately 70% of all mucormycosis cases reported earlier (Dam et al. ##REF##36805033##2023##). When the pre- and post-COVID-19 eras are compared, there is an increased rate of <italic>Candida albicans</italic> coinfections during COVID-19 with impaired immune response to such infections (Moser et al. ##REF##33717195##2021##; Zand et al. ##REF##36597074##2023##). Furthermore, <italic>Aspergillus fumigatus</italic> has been identified as the most common cause of fungal infections in severely ill COVID-19 patients (Szabo et al. ##UREF##48##2021##).</p>", "<p id=\"Par6\">For the treatment of medical cases and superficial skin infections, dermatologists favor topical semisolid formulations which provide effective delivery of drugs to the preparation methods and vehicles used, which have an impact on the pace at which the drugs permeate the skin (Akhtar et al. ##REF##25925110##2015##). Additionally, they have a number of advantages over parenteral or peroral dosage forms, such as enhanced patient compliance due to their simplicity of use and noninvasive design, on-site delivery that minimizes systemic side effects, and efficient targeting properties (Wong et al. ##UREF##52##2023##). Out of the topical dosage forms, hydrogels are getting popularity due to their swelling ability in conjunction with their adhesion strength and potential to regulate drug release (Dattilo et al. ##REF##36826854##2023##). The use of polysaccharide biopolymers in medicine is urgent because they are non-carcinogenic, non-allergenic, non-irritant, and non-toxic. β-Cyclodextrins (β-CD) are biodegradable, non-toxic materials and are gaining popularity because of their capacity to bind non-covalently to medication molecules (Santos et al. ##REF##36722254##2023##).</p>", "<p id=\"Par7\">Nanosponges (NS) are an innovative formulation that consists of a sponge-like structure that is non-collapsible and porous and is used to encapsulate nanoparticles (Das et al. ##REF##35619316##2023##). It is mainly used in the pharmaceutical industry because it combines the benefits of nanoscale vesicular structures and microsponges making it ideal for cosmetic and cosmeceutical applications (Kandekar et al. ##REF##36748244##2023##). The porous structure affects the release pattern in addition to allowing us to entrap a wide range of active molecules (Kandekar et al. ##REF##36748244##2023##). Cyclodextrin nanosponges have excellent properties such as the simple method of preparation, the ability to form inclusion complexes, which incorporate less water-soluble molecules into their core cavities, improving drug aqueous solubility while also increasing bioavailability, biocompatibility, and stability and minimizing undesirable side effects (Lee and Poh ##REF##36735107##2023##). When NS and hydrogel are combined together, this provides remarkable benefits due to its three-dimensional porous structure, the most significant of which is improved skin retention, improved patient compliance, decreased dose, and less adverse effects (Tiwari and Bhattacharya ##REF##35244808##2022##).</p>", "<p id=\"Par8\">To create an optimized product with superior attributes and quality, software-based optimization methods are used (Thirunavukkarasu et al. ##UREF##49##2023##). Response surface methodology (RSM) is an efficient statistical tool that uses lower-order polynomial equations to develop, improve, and optimize a process with many factors that influence the response (Chen et al. ##UREF##11##2023##). RSM reduces the overall number of possible combinations, saving time and materials during experimentation (El-Sayed et al. ##UREF##20##2020b##).</p>", "<p id=\"Par9\">In our previous study, octadecyl 3-(3,5-di-tert-butyl-4-hydroxyphenyl) propanoate (ODHP) was extracted from <italic>Alcaligenes faecalis</italic> culture broth as an antifungal agent and was optimized for its maximum yield production (El-Sayed et al. ##REF##33090249##2020a##). The toxic lipophilic phenol moiety 2,4-di-tert-butylphenol (DTBP) has been found in at least 169 species of organisms, including nitrogen-fixing cyanobacteria (Zhao et al. ##REF##31935944##2020##), food-borne and hot spring Gram-positive bacteria (Aissaoui et al. ##UREF##3##2019##) and freshwater and soil Gram-negative bacteria (Dharni et al. ##REF##24934765##2014##; Padmavathi et al. ##REF##25377484##2014##), and fungi (11 species of eight families) (Zhao et al. ##REF##31935944##2020##). Hence, our study was intended to optimally formulate ODHP into a nanosponge hydrogel and evaluate the effectiveness of the developed formulation in vitro and pre-clinically to be used as a potential formula for the treatment of topical mycotic infections.</p>" ]

[ "<title>Materials and methods</title>", "<title>Chemicals, media, and antifungals used</title>", "<p id=\"Par10\">β-Cyclodextrin (β-CD), diphenyl carbonate (DPC), carbopol 940, and poloxamer 188 were purchased from Middle East Company (Cairo, Egypt). Carboxymethyl cellulose (CMC), sodium alginate, hydroxylpropyl methylcellulose (HPMC E4), and Tween 80 were purchased from El-Nasr Pharmaceuticals (ADWIC, Cairo, Egypt). Triethanolamine (TEA), dichloromethane, methyl paraben, propylene glycol, and polyvinyl alcohol (PVA) were purchased from Sigma-Aldrich (St. Louis, MO, USA). Other materials used are as follows: Sabouraud Dextrose Agar (SDA) (Oxoid Ltd, England), collagenase 0.6 IU (Iruxol®, Abbott Co., and Wiesbaden, Germany); fluconazole (SEDICO Pharmaceutical Company, Giza, Egypt), and isoconazole (ISN) 1% (Candicure®, Al-Esraa Pharmaceutical Optima Co., Egypt).</p>", "<title>Extraction of ODHP</title>", "<p id=\"Par11\">ODHP was optimized for its maximum yield production, extracted and purified from <italic>Alcaligenes faecalis</italic> culture broth in our lab as previously reported (El-Sayed et al. ##REF##33090249##2020a##). The <italic>Alcaligenes faecalis</italic> MT332429 was previously identified using 16S ribosomal RNA (NCBI GenBank accession number MT332429) (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ncbi.nlm.nih.gov/nuccore/MT332429\">https://www.ncbi.nlm.nih.gov/nuccore/MT332429</ext-link>) (accessed on 23 July 2023), and the isolate was deposited in the Culture Collection Ain Shams University (CCASU) belonging to the World Data Centre for Microorganisms (WDCM) under the code, <italic>Alcaligenes faecalis</italic> CCASU-MT332429 (<ext-link ext-link-type=\"uri\" xlink:href=\"http://ccinfo.wdcm\">http://ccinfo.wdcm</ext-link>. org/collection/by_id/1186) (accessed on 23 July 2023).</p>", "<title>Preparation of ODHP-loaded nanosponges (NS) by emulsion solvent diffusion method and optimization using RSM</title>", "<p id=\"Par12\">Using the emulsion solvent diffusion approach, batches of nanosponges (NS) were formulated using varied ratios of β-cyclodextrin and diphenyl carbonate, as previously described (Sharma and Pathak ##UREF##46##2011##). In brief, two phases were adopted in this process, namely a continuous phase and a dispersed phase. The dispersed phase was prepared ultrasonically by stirring different molar ratios of β-cyclodextrin and cross-linking diphenyl carbonate with 105 µg ODHP in 20 mL dichloromethane for 10 min; this solution was prepared using a homogenizer (Ultra-Turrax, Germany). Then, 0.5% w/v PVA was dissolved in 150 mL of distilled water to make a continuous aqueous phase by stirring in a 60 °C water bath. The dispersed phase was slowly incorporated in the continuous phase using a syringe, while the reaction mixture was being emulsified at 35 °C using probe sonication (Fisher Scientific, Waltham, MA, USA) for 10 min and then left to homogenize. The dispersion produced (the nanosponges formed) was filtered using 0.45-µm filter paper to separate the solid mass and washed with deionized water and ethanol/methanol (50:50) in order to remove the free/un-reacted β-CD residues. It was then filtered once more, transferred to glass vials, and pre-frozen at − 80 °C for 12 h then lyophilized to remove any residual solvent (CHRIST, Osterode, Germany) using mannitol as cryoprotectant and under conditions of temperature equal to − 48 °C and pressure 0.37 mbar for 2 days to get the freely flowing powder (Fonte et al. ##REF##26805517##2016##; Prabhu et al. ##UREF##41##2021##). The finished product was a fine white powder which was packaged and stored in airtight containers (Ghose et al. ##REF##33287406##2020##). The Box-Behnken design was employed for the optimization process. Independent process parameters included β-cyclodextrin (polymer) and diphenyl carbonate (cross-linker) ratio, homogenization time (min), homogenization speed (rpm), and polyvinyl alcohol (PVA) % (w/v %). The optimization process dependent parameters were PDI, PS (nm), and entrapment efficiency% (EE) (Nait Bachir et al. ##REF##30388376##2019##; Srivastava et al. ##REF##34293406##2021##). The levels of independent parameters and goals of dependent ones are presented in Table ##TAB##0##1##. As shown in Table ##TAB##1##2##, the Box-Behnken design specified 29 experimental runs yielding quadratic equations that define the models.</p>", "<title>Characterization of the prepared ODHP-NS</title>", "<title>Percent yield of ODHP-NS</title>", "<p id=\"Par13\">By weighing the nanosponges and the original excipients utilized in their synthesis, the % yield of nanosponges was estimated as shown in Eq. (##FORMU##0##1##) (Omar et al. ##REF##32194337##2020##):</p>", "<title>Evaluation of particle size, PDI, and zeta potential (ZP)</title>", "<p id=\"Par14\">The dynamic light scattering (DLS) technique was utilized to evaluate the average PS, PDI, and ZP of the formulated ODHP-loaded NSs using Malvern Nano ZS Zetasizer (Malvern Instruments Ltd., Worcestershire, UK). Prior to analysis, each sample was appropriately diluted with distilled water and ultrasonically processed for 3 min to break up agglomerates and dissociate adherents. At 25 ± 0.5 °C, samples were measured in triplicate, and the results were demonstrated as a mean value with a standard deviation (± SD) (Anwer et al. ##REF##30880967##2019##).</p>", "<title>Entrapment efficiency (%EE)</title>", "<p id=\"Par15\">The %EE of ODHP-NS was evaluated by direct method through centrifuging the ODHP-NS in methanol at 10,000 rpm for 30 min (Centurion Scientific-K240R) to separate nanosponge particles. The content of free drug in the supernatant was measured by a UV spectrophotometer (Shimadzu, 1700, Japan) at <italic>λ</italic> max of ODHP (285 nm) (Sharma and Pathak ##UREF##46##2011##), and the concentration was determined from the standard curve of ODHP (Fig. ##SUPPL##0##S1##) (Monica and Gautami ##UREF##34##2014##; Priyanka et al. ##UREF##42##2018##). All the measurements were made three times, and average results were recorded. The %EE and drug loading capacity % (DL%) of ODHP loaded NS were calculated using Eq. ##FORMU##1##2## (Penjuri et al. ##UREF##39##2016##) and Eq. ##FORMU##2##3## (Kumar et al. ##REF##33321649##2021##), respectively, as follows:</p>", "<title>Scanning electron microscopy (SEM) analysis</title>", "<p id=\"Par16\">A scanning electron microscope (JEOL JSM-SEM, model: JSM6330 LV, Tokyo, Japan) was employed to show the surface morphology of the optimized ODHP-NS formula. The optimized ODHP-NS was placed carefully on the SEM stubs and covered with gold. At various magnifications, scanning was done, and areas were recorded and processed to determine the spherical 3D structure of the NS formed (Penjuri et al. ##UREF##39##2016##).</p>", "<title>Fourier transform infrared (FTIR) spectroscopy analysis</title>", "<p id=\"Par17\">FTIR was done to ensure that there would be no interaction between the ODHP and the polymer. FTIR spectrometer (Shimadzu, Japan) was utilized to analyze the FTIR spectra of pure ODHP and optimized ODHP-loaded NSs. Before being pressed into translucent film, the sample was suitably diluted with crystalline potassium bromide (1:10 w/w). A sample holder was used to mount the film, and several different frequencies of spectra were captured ranging from 4000 to 400 cm⁻¹ using spectral manager software (Almutairy et al. ##REF##34301030##2021##).</p>", "<title>Differential scanning calorimetry</title>", "<p id=\"Par18\">Differential scanning calorimetry of ODHP and optimized ODHP-loaded NS was performed using TA instruments, California (Discovery DSC25 series), equipped with a Refrigerated Cooling System 90 (RCS 90), TA Instruments, New Castle, USA, and TRIOS software. The DSC was graduated with indium for the enthalpy heat and melting point. A heating rate (10 °C/min) was used with 30–400 °C (temperature range), under nitrogen purge (350 mL/min). For reference, the standard aluminum empty pan was employed (Kumar et al. ##REF##33321649##2021##).</p>", "<title>Formulation of topical hydrogel containing optimized ODHP-NS formula</title>", "<p id=\"Par19\">To incorporate the optimized ODHP-loaded NS into a hydrogel formula, carbopol 940, sodium alginate, CMC, poloxamer 188, and HPMC E4 were all explored as gel formers in different quantities (0.2, 0.5, 0.8, 1, 1.2, 1.5 w/v %) to select the best gel former (Ahmed et al. ##REF##34135673##2021##). A specified amount of the gelling agent in grams was introduced in portions and dissolved in 100 mL of a 30:70 propylene glycol:distilled water mixture and homogeneously distributed using a magnetic stirrer at 600 rpm followed by a 15-min stagnation process to release trapped air. To achieve transparency and a pH of 6.7–6.9, 2 mL triethanolamine was added (Yang et al. ##UREF##54##2016##). Then, 1 g of methyl paraben was added as a preservative, and the gel was completed to 100 mL with distilled water. To obtain a smooth gel with no lumps, the dispersion was continually swirled on a magnetic stirrer at 600 rpm for around 6 h until formed, and it was allowed to stand overnight to accomplish complete hydration (Moglad et al. ##UREF##33##2020##). The hydrogel formulations were then stored at 5 °C in firmly closed screw-capped containers for further studies (Aldawsari et al. ##REF##25673986##2015##).</p>", "<title>Evaluation of the selected prepared nanosponge-loaded hydrogels</title>", "<title>Homogeneity, spreadability, extrudability, swelling study, pH determination, and viscosity measurement</title>", "<p id=\"Par20\">All of the prepared nanosponge gels were visually inspected for homogeneity (Gangadharappa et al. ##UREF##24##2017##). The spreadability of the hydrogel was also evaluated. A glass plate (5 × 5 cm) was filled with 100 mg of the generated hydrogel. A glass plate of the same size was dropped upon the first one from a height of 5 cm. A steady weight (0.5 kg) was placed on the glass plate surface and held in place for 1 min. Following weight removal, the diameter of the spread circle in centimeter was measured (Ahmed et al. ##REF##34135673##2021##; Moglad et al. ##UREF##33##2020##). To verify the capability of a hydrogel to flow from collapsible tubes after a constant weight (500 g) was applied for 10 s. For each formula, this examination was carried out in triplicate; extrudability was recorded in g/s (El-Gayar et al. ##REF##34989907##2022##). The hydrogel’s swelling behavior was investigated by inserting 0.5 g of hydrogel in previously weighed perforated aluminum foil. The weight growth as a function of soaking duration in 10 mL of phosphate buffer 6.8 at 37 °C was assessed in the experiment. Prior to measurement, an aluminum foil was hung up for approximately 15 min to remove the excess swelling media. Measurements were made until the hydration degree approached equilibrium, which was reached when three successive measurements yielded the same weight. The samples were withdrawn from the beakers at varied time intervals (30 min, 60 min, and 120 min) and placed on a dry surface for some time before being reweighed and calculated according to Eq. (##FORMU##3##4##)(Ambala and Vemula ##UREF##6##2015##):where (SW) % denotes the equilibrium swelling percentage, <italic>W</italic>_t denotes the swollen gel weight after time <italic>t</italic>, and <italic>W</italic>_o is the weight of hydrogel before swelling at zero time.</p>", "<p id=\"Par21\">The pH of the selected ODHP-loaded NS-based topical hydrogel was estimated by a standardized pH meter (Edge pH series, Hanna instruments) at a temperature of 25 °C.To investigate the rheology of the optimized ODHP-NS-HG formulation, Brookfield DV-III ultra-programmable rheometer (AMETEK Brookfield, East Lyme, CT, USA) was employed (Kumar et al. ##REF##33321649##2021##).</p>", "<title>Determination of drug content</title>", "<p id=\"Par22\">In 100 mL phosphate buffer (pH 7.4), about 50 mg of the best formulated HG was dissolved and agitated for 2 h before bath sonication for 2 min. This strategy is aimed at maximizing drug solubility under mechanical shaking. The absorbance of the solution was calculated at 285 nm after filtration. The drug amount contained in the hydrogel was calculated using the standard curve (Fig ##SUPPL##0##S1##) (Zakaria et al. ##UREF##55##2016##).</p>", "<title>In vitro drug release studies</title>", "<p id=\"Par23\">The release of ODHP from ODHP-NS-HG was performed using the USP dissolution apparatus II by the paddle technique. To mimic the human skin state, the paddles revolved at 50 rpm, and the temperature was fixed at 37 ± 0.5 °C (Ng et al. ##UREF##37##2010##; Singh et al. ##REF##32548372##2020##). In dialysis bags, 10 mg of the optimized ODHP-NS-HG was added. The dialysis bags were linked with paddles and inserted in the release medium (phosphate buffer of physiological pH = 7.4) (Ghose et al. ##REF##33287406##2020##). After 0, 1, 3, 5, 7, 9, 11, 13, 15, and 24 h time intervals, 3 mL samples were extracted and substituted with an equal volume of fresh phosphate buffer pH 7.4 solution. The samples were filtered and spectrophotometrically analyzed for drug concentration at <italic>λ</italic> 285 nm. The drug release mechanism from the porous nanosponge matrix and kinetics was calculated by fitting the data into various kinetic models. The mechanism of drug release from nanosponges was determined via the correlation coefficient (<italic>R</italic>²) value as previously reported (Gaber et al. ##REF##36744372##2023##).</p>", "<title>Photodegradation study</title>", "<p id=\"Par24\">At room temperature (25 ± 2 °C), photodegradation experiments were carried out using a UVA lamp with a wavelength range of 254–365 nm. The optimized ODHP-NS-HG formulation was the system under investigation. An aliquot (40 mg) of test gels was equally placed around the bottom of a beaker and then irradiated for 4 h. Following the exposure interval, the beaker was withdrawn, its contents quantitatively transferred into a 20-mL calibrated flask, and sonication was performed for 15 min. The resultant sample was volume adjusted (20 mL), filtered (0.45-mm membrane filters), and quantified using a UV spectrophotometer. The degree of photodegradation was determined by comparing the ODHP peak regions from irradiated samples to those obtained from evaluating an equivalent amount of non-exposed formulations (previously tested for drug content). Each sample was evaluated three times, and the findings were demonstrated as mean value standard deviation (± SD) (Kumar et al. ##UREF##32##2022##).</p>", "<title>Stability study</title>", "<p id=\"Par25\">The chosen medicated NS-HG formula was kept in amber glass containers at both room temperature and refrigerated at 5 ± 3 °C for 3 months followed by examining the physical appearance, rheological behavior, pH, and drug content (Pushpalatha et al. ##UREF##43##2019##).</p>", "<title>In vitro antifungal activity</title>", "<p id=\"Par26\">In Sabouraud Dextrose Agar (SDA) plates previously seeded with 100 µL of 0.5 McFarland <italic>C. albicans</italic> ATCC10231, wells were filled with 100 µL ODHP-NS-HG. Placebo HG, positive (fluconazole 105 µg/mL), and negative (DMSO) controls were also included. Inhibition zones in different petri dishes were measured in triplicate (Agrawal et al. ##REF##33740733##2021##).</p>", "<title>Cytotoxicity assay</title>", "<p id=\"Par27\">Vero cells (kidney epithelial cells of African green monkey (<italic>Cercopithecus aethiops</italic>)) were seeded in 96-well plates (Thermo Scientific™ PCR Plate, 96-well, Waltham, MA, USA) at a density of 5000 cells/well. After 1-day incubation, 10 µL of ODHP-NS-HG and FLC dilutions (7.8, 15.6, 31.25, 62.5, 125, 250, 500, and 1000 µg/mL) were added to each well for 24 h. The 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl-2H-tetrazolium bromide (MTT) assay was done after 37 °C incubation in a humidified 5% CO₂ environment (Espíndola et al. ##UREF##21##2022##). The IC₅₀ was calculated as previously determined (Korbášová et al. ##UREF##31##2022##).</p>", "<title>In vivo studies</title>", "<p id=\"Par28\">All rates received the standard care according to the standard guidelines during all the stages of the experiment.</p>", "<title>Animals</title>", "<p id=\"Par29\">Forty adult male Wistar albino rats weighing 200–220 g were used. They were purchased from the animal house facility of Faculty of Pharmacy, Ahram Canadian University, Giza, Egypt. Prior to the start of the study, the animals were acclimatized for 15 days. Animals were handled and were housing in accordance with the Care and Use of Laboratory Animals recommendations and ARRIVE guidelines (<ext-link ext-link-type=\"uri\" xlink:href=\"https://arriveguidelines.org\">https://arriveguidelines.org</ext-link>) (accessed on 20 March 2023). The whole study was reviewed and approved by the research ethical committee of the Faculty of Pharmacy, Ain Shams University, Egypt (Protocol approval number: ACUC-FP-ASU-RHDIRB2020110301-REC#39).</p>", "<title>Experimental design and thermal injury model</title>", "<p id=\"Par30\">A third-degree burn wound infection with <italic>C. albicans</italic> ATCC10231 (containing about 7.5 × 10⁷ CFU) was induced in rats as previously reported (Okur et al. ##REF##32194336##2020##). Briefly, the rats were divided into eight groups (Groups A–H; 5 rats each) as follows:</p>", "<p id=\"Par31\">Group (A): Unburned, uninfected, treated with ODHP-NS-HG (skin irritation test).</p>", "<p id=\"Par32\">Group (B): Control, burned, infected, untreated.</p>", "<p id=\"Par33\">Group (C): Control, burned, uninfected, untreated.</p>", "<p id=\"Par34\">Group (D): Control, burned, infected, treated with vehicle (negative control hydrogel).</p>", "<p id=\"Par35\">Group (E): Burned, infected, treated with ODHP-NS-HG.</p>", "<p id=\"Par36\">Group (F): Positive control-1, burned, infected, treated with collagenase 0.6 IU (Iruxol®, Abbott Co., Wiesbaden, Germany).</p>", "<p id=\"Par37\">Group (G): Positive control-2, burned, infected, treated with isoconazole hydrogel (ISN) 1% (Candicure®, Al-Esraa Pharmaceutical Optima Co., Egypt).</p>", "<p id=\"Par38\">Group (H): Normal control group (intact, unburned, uninfected, untreated).</p>", "<title>Survival rate study</title>", "<p id=\"Par39\">The tested formulations (1 g of hydrogel) were first applied 2 h after the induced infection to the burned skin and continued twice daily for 14 days. Three days after infection, the survival rate of the animals was determined. Dead animals were removed and calculated when calculating mortality rates. The animals were euthanized by cervical dislocation after being anaesthetized intraperitoneally with a cocktail of 60 mg kg⁻¹ ketamine and 10 mg kg⁻¹ xylazine, and the dorsal skin at the site of the lesion was carefully removed and kept in 10% formalin solution for histological investigation (Abdellatif et al. ##REF##34819785##2021##).</p>", "<title>Wound size measurement</title>", "<p id=\"Par40\">Progression of the wound was photographed, and according to the wound diameter at different days of injury, the wound contraction % was calculated by Eq. (##FORMU##4##5##) (Abdellatif et al. ##REF##34819785##2021##):where <italic>W</italic>_t denotes the measured wound area at a given time interval and <italic>W</italic>_o is the initial wound area at the onset of the experiment (Tang et al. ##REF##33817423##2021##).</p>", "<title>Skin irritation studies</title>", "<p id=\"Par41\">Dermal responses such as erythema and edema were reported for animals in group A (unburned, uninfected treated with 1 g ODHP-NS-HG) based on a visual scoring scale as previously described (Wairkar et al. ##UREF##50##2022##).</p>", "<title>Histopathological examination</title>", "<p id=\"Par42\">As previously reported, all conventional methods for sample fixation and staining were adhered to in accordance with standard practices (Al-Sabaawy et al. ##UREF##5##2021##). The Masson’s trichrome staining technique was employed to assess the quantity of collagen fibers within the tissues and perform an unbiased histological analysis. In accordance with established methods, six distinct and non-overlapping sections from the dermal layers of each sample were randomly selected and subjected to scanning in order to quantify the proportionate area occupied by collagen fibers (Negm et al. ##UREF##35##2022##).</p>", "<title>Ex vivo skin permeation analysis</title>", "<p id=\"Par43\">The investigation of skin permeation involved the use of normal abdominal albino rat skin, and the assessment was conducted using the Franz diffusion cells with a receptor volume of 22.5 mL and a diffusion area of 3.104 cm (Hussain et al. ##UREF##29##2016##). The positive control ISN1% and 100 mg of the formulation were both evenly applied to the skin. Throughout the experiment, the lower receptor chamber, which contained phosphate buffer (pH 7.4) and 2% v/v DMSO, was mixed continuously using a magnetic bead to approximate skin temperature. Samples were collected at predetermined intervals of 0.5, 1, 2, 4, 6, 8, 10, 12, 16, and 24 h and replaced with the same buffer media. The samples were filtered, and the contents of each were identified by spectrophotometric analysis at 285 nm for ODHP-NS-HG and 279.8 nm for ISN1%. Any residual formulation present on the skin surface was washed with PBS (pH 7.4) to assess drug penetration into rat skin (Hussain et al. ##UREF##29##2016##; Khurana et al. ##REF##23353874##2013##).</p>", "<title>Collection of blood samples</title>", "<p id=\"Par44\">Blood samples were taken from retro-orbital plexus under lidocaine (4%) local anesthesia from each animal in all groups 3 days after the beginning of the study and before the rats were euthanized (Moustafa et al. ##REF##29572844##2018##). The serum was utilized to measure levels of some immunological markers such as pro-inflammatory cytokines (tumor necrosis factor alpha (TNF-α), nuclear factor-kappa (NF-κB)-p105, interleukin-6 (IL-6) and interleukin-1 beta (IL-1β)) and the inflammatory marker cyclooxygenase (COX-2) prostaglandin-endoperoxide synthase (PTGS-2) and to state the level of angiogenesis by vascular endothelial growth factor (VEGF) (Nonoguchi et al. ##REF##35892413##2022##).</p>", "<title>Angiogenesis, inflammatory markers, and pro-inflammatory cytokine measurements</title>", "<p id=\"Par45\">ELISA kit(s) based on the sandwich ELISA principle (Elabscience®) were utilized to assess inflammatory markers and pro-inflammatory cytokines. These kits include pre-coated micro-ELISA plates with antibodies specific to rat COX-2, TNF-α, VEGF, NF-κB-p105, IL-6, and IL-1. The relevant antibody was mixed with the samples (or standards) before being added to the micro-ELISA plate wells. Following that, an avidin-horseradish peroxidase (HRP) combination and a biotinylated detection antibody specific for the observed parameter were added successively to each microplate well and incubated at 37 °C for 30 min. After adding the substrate, wells containing the measured parameter, the biotinylated detection antibody, and the avidin-HRP conjugate will turn blue. The optical density (OD) was calculated spectrophotometrically at 450 nm ± 2 nm using a plate reader (BMG Labtech, FLUOstar Omega, Germany). For rats, the OD value is inversely proportional to the concentration of the parameter being measured (Alvarez et al. ##REF##32882817##2020##; Navaei-Alipour et al. ##REF##33751689##2021##).</p>", "<title>Statistical analysis</title>", "<p id=\"Par46\">For the calculation of <italic>p</italic>-values and standard deviation, a one-way ANOVA test was applied followed by Tukey’s multiple comparison test (GraphPad Software Inc., San Diego, CA, USA). The results were presented as average values ± standard deviation. Data analysis, response surface generation, and model diagnostic plots were accomplished using Design-Expert® v. 11.0. The experimental data were statistically validated through analysis of variance (ANOVA), which determined the significance of each parameter.</p>" ]

[ "<title>Results</title>", "<title>Optimization of ODHP-loaded nanosponges (NS)</title>", "<p id=\"Par47\">The actual values of the investigated factors, design, observed versus the predicted results are displayed in Table ##TAB##1##2##. The resulting quadratic BBD model equations obtained from the software are as follows:</p>", "<p id=\"Par48\">Table ##TAB##2##3## shows the ANOVA results for the different responses, the <italic>F</italic>-values were 90.03, 84.26, and 123.90 (<italic>p</italic>-value &lt; 0.0001) for PS, PDI, and EE%, respectively, which proves the models are significant. The model terms (<italic>A</italic>, <italic>B</italic>, <italic>A</italic>², <italic>B</italic>², <italic>D</italic>²) for PS, (<italic>A</italic>, <italic>B</italic>, <italic>A</italic>², <italic>B</italic>², <italic>C</italic>², <italic>D</italic>²) for PDI, and (<italic>A</italic>, <italic>B</italic>, <italic>D</italic>, <italic>B</italic>²) for EE% all having <italic>p-</italic>values less than 0.05 are significant model terms. Also, a low coefficient of variation of 1.56, 10.33, and 0.3838 for PS, PDI, and EE%, respectively, was obtained, indicating the good reliability of the experimental values. The coefficients of determination <italic>R</italic>² values which were 0.9609, 0.988, and 0.9642 suggested that 96.09%, 98.83%, and 96.42% of variability in PS, PDI, and EE% responses, respectively. The predicted <italic>R</italic>² of 0.9275, 0.9324, and 0.9413 were in agreement with the adjusted <italic>R</italic>² of 0.9502, 0.9765, and 0.9564. Finally, the signal-to-noise ratio(s), or adequate precision, were equal to 29.352, 29.391, and 40.816 for PS, PDI, and EE%, respectively.</p>", "<p id=\"Par49\">Figure ##FIG##0##1## shows the three-dimensional response surface plots (3D plots) which revealed that the optimum conditions for minimum particle size, minimum PDI, and maximum EE% were polymer linker molar ratio of 1:3, homogenization time 14 min, homogenization speed 12,460 rpm, and PVA% 0.5.</p>", "<p id=\"Par50\">The normal probability plots of residuals for PS, PDI, and EE% (Fig. ##SUPPL##0##S2## a, b, and c, respectively) suggested that the residuals follow a normal plot as showed by the linear pattern.</p>", "<p id=\"Par51\">The Box Cox plots are useful tools that determine the utmost applicable power transformation. As shown by our results, the current lambda (<italic>λ</italic> = 1) was adequate for PS and EE% models (Fig. ##SUPPL##0##S3## a and c, respectively). Polydispersity index model was transformed to the power 2 as suggested by the software (Fig. ##SUPPL##0##S3##b).</p>", "<p id=\"Par52\">The predicted versus actual values plot of PS, PDI, and EE% displayed an acceptable agreement between the projected and the actual data (Fig. ##SUPPL##0##S4## a, b, and c, respectively).</p>", "<p id=\"Par53\">The residuals versus run number plot of PS, PDI, and EE% showed that the points were arbitrarily scattered around zero (Fig. ##SUPPL##0##S5## a, b and c, respectively) which point out that the model fits the data.</p>", "<title>Characterization of the prepared ODHP-NS</title>", "<p id=\"Par54\">The mean %yield of ODHP-NS was found to be 84.4% ± 0.42. The PS of optimized ODHP-NS was 332 ± 1.35 nm, while PDI was 0.233 ± 0.02 Fig. ##FIG##1##2##a. The zeta potential was − 13.8 ± 0.56 mV. Particle size spreading by intensity for optimized ODHP-NS and zeta potential distribution are represented in Fig. ##FIG##1##2##b. Entrapment efficiency of optimized ODHP-NS was found to be 90.14 ± 0.65%, and drug loading % (DL%) was found to be 87.5 ± 0.77%. The SEM image of the optimized ODHP-NS is shown in Fig. ##FIG##1##2##c, which revealed a spongy nanosized spherical NS with a porous surface. The texture of the nanosponge makes it easier for the drug to penetrate its interpenetrating network.</p>", "<title>Results of FTIR spectroscopy analysis</title>", "<p id=\"Par55\">Figure ##SUPPL##0##S6##a shows the captured FTIR spectrum of the complex, which was very close to the FTIR spectrum of β-CD (Fig. ##SUPPL##0##S6##b). This is because the complex and the host molecule have comparable chemical bonding properties. Furthermore, a broad hydroxyl band of β-CD at 3370.72 cm⁻¹ was found to be narrowed in the inclusion complex FTIR spectrum. The frequencies for β-CD were found at 1157.84 cm⁻¹, 1029.24 cm⁻¹, and 2928.53 cm⁻¹, respectively, which correspond to the symmetric and non-symmetric stretching of [CH2], [C–C], and bending vibration of [O–H]. The characteristic peaks of ODHP (Fig.##SUPPL##0##S6##c) disappeared in inclusion complex which suggests that these groups of the drug are included in the cavity.</p>", "<title>Differential scanning calorimetry</title>", "<p id=\"Par56\">DSC thermograms of pure ODHP and optimized nanosponge formulation are presented in Fig. ##SUPPL##0##S7## a and b, respectively. The endothermic DSC curve of a ODHP was reflected as a sharp peak at 247.45 °C, corresponding to its melting temperature. DSC curve of optimized ODHP-NS exhibits a broad endothermic peak, formed by coalescence of β-CD and ODHP as a result of successful drug encapsulation in porous cavities of NS. The disappearance of sharp drug peak and upward line higher than the baseline (exothermic) curve represents fusion of drug with homogenous drug distribution in the polymer, signifying stable optimized ODHP-loaded NS.</p>", "<title>Formulation and evaluation of topical hydrogel containing optimized ODHP-NS formula</title>", "<p id=\"Par57\">Carbopol 940 was the best gelling agent chosen for the ODHP-NS-HG preparation (Table ##SUPPL##0##S1##). Different gel formulae were prepared using carbopol 940 with compositions ranging from 0.2 to 1.5% w/w (Table ##SUPPL##0##S2##). However, the compositions of other constituents remained constant at a fixed concentration. The formula HG-5 was the best preparation and hence was selected for further studies. Table ##SUPPL##0##S3## demonstrates the results obtained for homogeneity and physical appearance of different carbopol 940-HG preparations.</p>", "<p id=\"Par58\">The characterization parameters (spreadability, extrudability, equilibrium swelling study, pH, and viscosity measurement) for the selected hydrogel were determined, and the results were recorded. HG-5 exhibited a translucent appearance with a smooth and uniform consistency, showing the most optimal measured parameters. The spreadability was 5.74 ± 0.032 cm, while pH was 6.75 ± 0.13 confirming skin compatibility. The swelling index was denoted as 350.6 ± 0. 66%, while the extrudability was recorded as 0.97 ± 0.11 (g/s). Moreover, the viscosity was estimated to be 1092 ± 4 cps. The percentage of drug content for the selected HG-5 was 90.96 ± 0.32%, suggesting the drug was equivalently scattered throughout the gel.</p>", "<title>In vitro drug release studies</title>", "<p id=\"Par59\">The release was best fitted into Higuchi diffusion kinetic model (coefficient of correlation <italic>R</italic>² value = 0.9976). To study the mechanism of release of ODHP from the prepared formula, Korsmeyer-Peppas model was employed. A diffusion exponent (<italic>n</italic> values 0.563) indicated a non-Fickian model (anomalous transport) indicating that the drug release is monitored by the diffusion and polymer chain relaxation. The various kinetic models of the in vitro release data are represented in Fig. ##SUPPL##0##S8## a, b, c, d and e, respectively. A comparison between the correlation coefficient of the different used kinetic models is shown in Table ##SUPPL##0##S4##.</p>", "<title>Photodegradation and stability studies</title>", "<p id=\"Par60\">The drug content of the irradiated sample was 89.04 ± 0.51% with non-significant difference (<italic>p</italic> &gt; 0.05) compared to non-exposed samples. After 3 months of storage in room temperature and in a refrigerator, no significant change could be noticed in the physical look, viscosity, pH, and drug content (<italic>p</italic> &gt; 0.05) (Table ##SUPPL##0##S5##).</p>", "<title>In vitro antifungal activity</title>", "<p id=\"Par61\">ODHP-NS-HG showed enhanced in vitro antifungal activity against <italic>C. albicans</italic> ATCC10231 by 1.5-fold (35.6 ± 0.5 mm) compared to the positive control fluconazole which showed an inhibition zone of 24.4 ± 0.2 mm (Fig. ##SUPPL##0##S9##).</p>", "<title>Cytotoxicity assay</title>", "<p id=\"Par62\">IC₅₀ values, corresponding to 50% inhibition of the cell growth in vitro of the optimized ODHP-NS and fluconazole (as reference standard), were 325.6 µg/mL and 287.8 µg/mL, respectively.</p>", "<title>In vivo studies</title>", "<title>Survival rate study</title>", "<p id=\"Par63\">The survival rates of the tested rats for each of the studied groups showed their maximum levels in positive control groups F and G and H and treated groups A and E with 100% survival rates, while they showed the same records for control groups B and D (40%) and were relatively higher in control group C (60%).</p>", "<title>Wound size measurement</title>", "<p id=\"Par64\">The wound size contraction on day 14 for group E was found to be 80%, which was 1.5-fold higher compared to positive control group F which showed only 54% contraction and 2.4-fold greater than positive control group G that showed 34% contraction. On the contrary, control groups B, C, and D showed impaired wound contraction as the wound size continued to enlarge. The mean wound diameters of group E were significantly different from those of groups B, C, D, and G (<italic>p</italic> &lt; 0.05) and not significantly different from group F (<italic>p</italic> &gt; 0.05). Wound photographs and data are presented as mean ± SD as shown in Fig. ##FIG##2##3##.</p>", "<title>Skin irritation study</title>", "<p id=\"Par65\">The applied ODHP-NS-HG formulation showed to be non-irritant and non-edematous on the rat intact skin. The final observations for erythema and edema scored zero.</p>", "<title>Histopathological examination</title>", "<p id=\"Par66\">Photomicrographs demonstrating the histopathological features (hematoxylin and eosin (H&amp;E)) of skin layers and wound healing process in different groups are shown (Figs. ##FIG##3##4## and ##FIG##4##5##). Group (A): The typical histological structures of the various skin layers were visible in a skin photomicrograph, including an apparent intact dermal layer, integral epithelium covering an intact epidermal layer (Fig. ##FIG##3##4##a). Also, it demonstrated significant normally distributed collagen deposition, as seen in Masson’s trichrome–stained tissue segments of all the samples (MTC) (Fig. ##FIG##4##5##a), up to 38.6% of the mean area percentage of the dermal content (Fig. ##FIG##5##6##). Group (B) showed significant dermal collagen necrosis and an accumulation of necrotic tissue debris, highly inflamed granulation tissue fills the wound gap (arrows). Some localized dermal hemorrhagic patches and inflammatory cell infiltrates can be seen as well (Fig. ##FIG##3##4##b). Moreover, this group displayed less developed collagen fibers (Fig. ##FIG##4##5##b), up to 11.21% of the mean dermal layer content area (Fig. ##FIG##5##6##). Group (C) demonstrated moderate inflamed granulation tissues occupying the wound gap with necrotic crust covering and epidermal hyperplasia at the wound edge (arrows) (Fig. ##FIG##3##4##c). This group also displayed insignificant records of mature collagen (Fig. ##FIG##4##5##c) up to 17.31% of the mean area percentage of the dermal layer content ensuing lower collagen deposition in the wound gap (MTC) (Fig. ##FIG##5##6##). Group (D) exhibited similar findings of group B. Photomicrograph of skin showing intense inflamed granulation tissue filling the wound gap with severe necrosis of dermal collagen and accumulation of necrotic tissue debris (arrows) (Fig. ##FIG##3##4##d). Also, photomicrograph of skin showing limited collagen deposition in the wound gap (MTC) (Fig. ##FIG##4##5##d) up to 10.37% of the mean area percentage of the dermal layer content (Fig. ##FIG##5##6##). Group (E): Photomicrograph of skin showing higher and accelerated wound gap healing degree with full re-epithelization indicating hyperplastic epidermal remodeling and collagen rich filling granulation tissue. Also, Fig. ##FIG##3##4##e showed a higher fibroblastic activity and an expressive decrease in inflammatory cells (arrows) and displayed a higher records of dermal collagen fibers (Fig. ##FIG##4##5##e) up to 33.14% (almost threefold more when compared to group (B) (Fig. ##FIG##5##6##). Group (F): photomicrographs showed less inflamed granulation tissue and persistent records of a narrow ulcerated wound gap covered a necrotic tissue debris (Fig. ##FIG##3##4##f) with a moderate maturation in dermal collagen fibers (Fig. ##FIG##4##5##f) up to 21.65% (Fig. ##FIG##5##6##). Group (G) demonstrated moderate inflamed granulation tissue occupying the wound gap with epidermal remodeling under necrotic crust at the wound edge (Fig. ##FIG##3##4##g) as well as an intermediate maturation in the collagen fibers (Fig. ##FIG##4##5##f) up to 22.64% (Fig. ##FIG##5##6##). Group (H) demonstrated the same records as group A samples with an intact covering epithelium and an intact dermal layer (Fig. ##FIG##3##4##h) and significant normally distributed collagen deposition (Fig. ##FIG##4##5##h) up to 39.3% (Fig. ##FIG##5##6##).</p>", "<title>In vitro skin permeation studies (ex vivo analysis)</title>", "<p id=\"Par67\">The permeation analysis indicate that the amounts of drug permeated from ODHP-NS-HG and isoconazole 1% (Candicure®) were 94.47 ± 2 and 60.041 ± 3 µg/cm², respectively, which indicates that the amount permeated from ODHP-NS-HG was significantly different (<italic>p</italic> &lt; 0.05) and 1.6-fold greater than that of isoconazole 1% (Candicure®).</p>", "<title>Angiogenesis, inflammatory markers, and pro-inflammatory cytokine measurements</title>", "<p id=\"Par68\">The mean levels of COX-2, TNF-α, NF-κB-p105, IL-6, and IL-1β for group E were 3.95 ± 0.3 ng/mL, 58.608 ± 1 pg/mL, 15.776 ± 3 ng/mL, 58.765 ± 3 pg/mL, and 157.748 ± 15 pg/mL, respectively, which were significantly lower than those of groups C, B, and D (<italic>p</italic> &lt; 0.001), positive control groups (G, F) (<italic>p</italic> &lt; 0.05), and not significantly different than values of groups A and H (<italic>p</italic> &gt; 0.05). The level of vascularization stated by VEGF levels assay was significantly higher in group E (359.178 ± 5 pg/mL) compared to groups C, B, and D (<italic>p</italic> &lt; 0.001), 98-folds higher than group B, 2-folds greater than positive control F (86.528 ± 6 pg/mL), 2.5-folds greater than positive control G (69.356 ± 5) (<italic>p</italic> &lt; 0.05), and not significantly different than those of groups A and H (<italic>p</italic> &gt; 0.05). Figure ##FIG##6##7## graphically demonstrates the levels of the respective biomarkers corresponding to the levels of inflammation and angiogenesis as mentioned.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par69\">This study was aimed to create a formulation containing the antifungal compound ODHP with the highest quality that would provide the best criteria required for topical application. ODHP is a potent antifungal agent that was previously extracted from <italic>Alcaligenes faecalis</italic> MT332429 culture broth, purified and production optimized using RSM in our previous study (El-Sayed et al. ##REF##33090249##2020a##). Secondary bacterial metabolites are stable and resistant to modification by microorganisms that produce them (El-Sayed et al. ##REF##35011429##2021##). The increasing demand for natural products and bulk chemicals demands sustainable fermentation technologies has identified beneficial soil bacteria as bio-factories that can boost yield while minimizing environmental risks (Bentzon-Tilia et al. ##REF##27452663##2016##). Antimicrobial misuse and resistance are increasing, necessitating the replacement of chemically synthesized antimicrobials with naturally produced ones (Årdal et al. ##REF##31745330##2020##). As a result, industrial microbiology offers environmentally friendly alternatives to fossil fuels, non-biodegradable plastics, and polluting chemical processes, making soil bacteria like <italic>Alcaligenes faecalis</italic> more attractive for sustainable production (Harwood et al. ##UREF##26##2018##).</p>", "<p id=\"Par70\">Researchers are moving towards nanocarriers with distinctive properties, optimal effectiveness, specificity, and less side effects. One effective solution is nanosponge particles, which are water soluble, can enclose the hydrophobic drug within the nanosponge, provide drug delivery at a targeted site, have less harmful side effects, are stable over a pH range from 1 to 11, are thermostable up to 130 °C, can be used to mask unpleasant flavors, are biodegradable, and transform liquid substances to solids (Potdar et al. ##UREF##40##2022##). Moreover, particles can be made smaller or bigger by varying the proportion of cross-linker to polymer and have predictable drug release (Pandey ##UREF##38##2019##). Nanosponges are also self-sterilizable because their typical pore size is 0.25 micron, which bacteria cannot penetrate (Potdar et al. ##UREF##40##2022##). In order to restrict COVID-19 fungi co-infections, nanosponges have been employed against SARS-CoV-2 and have demonstrated potential inhibitory effects for biological neutralization and antiviral medication delivery applications (Mostafavi et al. ##REF##35908684##2022##). Furthermore, such cellular nanosponges may be useful for biological neutralization of chemical toxic agents, inflammatory cytokines, bacterial toxins, virus fragments, and pathological antibodies (Wang et al. ##UREF##51##2022##). Other benefits of using NSs include a greater degree of entrapment, which aids NSs to serve as a reservoir for different pharmaceutical substances. They also aid in the protection of compounds from degradation (Tiwari and Bhattacharya ##REF##35244808##2022##). Hence, NSs were used for the delivery of ODHP and were prepared with the emulsion-solvent diffusion method. This method has two advantages: it does not require emulsifiers, and it has a straightforward and simple preparation yielding significant results (ARABI et al. ##UREF##7##2023##). We used the Box-Behnken design to optimize the process parameters to achieve an effective and economical result (Ahmed et al. ##UREF##2##2022##). This model of design was successfully employed in previous studies to optimize production of rhamnolipids (El-Housseiny et al. ##UREF##19##2016##), antibiotics (Ibrahim et al. ##REF##30616583##2019##; El-Housseiny et al. ##REF##33485318##2021##), and antifungal metabolites by their producing isolates (El-Sayed et al. ##REF##38137979##2023##, ##UREF##20##2020b##). Measurement of entrapment efficiency can be performed indirectly where the amount of free unentrapped drug is measured spectrophotometrically at the corresponding wavelength (i.e., <italic>λ</italic>_max), and thus the entrapped amount of drug can be calculated according to Fahmy et al. (##REF##37595853##2023##) by subtracting the drug content in the supernatant (after the first and second centrifugations) from the initial amount of drug added to the nano-system and dividing it by the total drug content. Alternatively, entrapment efficiency can be directly calculated via disrupting the membranes of the developed nanoparticles to allow for the release of the entrapped drug (for spectrophotometric detection) utilizing organic solvents (e.g., methanol) or Triton™ X-100 and measured as mentioned previously (Penjuri et al. ##UREF##39##2016##). However, the direct method does not take into consideration the amount of non-entrapped drug to allow more clear comparison, while the indirect methods could only be used during preparation process and could not be applied after lyophilization (Amini et al. ##REF##29171972##2017##). The entrapment efficiency was previously reported to increase along with the homogenization period and speed to a considerable extent (Rossi et al. ##UREF##44##2014##). In correlation with previous reports, the decreased cross-linker concentration resulted in reduced entrapment efficiency, suggesting that at low concentrations, there may have been fewer sites for drug complexation available due to insufficient meshwork inside the polymer (Srivastava et al. ##REF##34293406##2021##). However diphenyl carbonate may have destroyed the intermolecular hydrogen bond network of discrete units of β-CD at greater concentrations as previously reported by Mavila et al. (##REF##26270435##2016##). Hence, it was deemed necessary to optimize the process parameters to compromise and get the suitable ratio between β-CD and diphenyl carbonate. Particle size (PS), polydispersity index (PDI), and entrapment efficiency % (EE%) were considered the dependent process variables and influenced the formation of ODHP-NS in agreement with previous studies (Ghose et al. ##REF##33287406##2020##; Rehman et al. ##REF##33144070##2021##; Srivastava et al. ##REF##34293406##2021##). Upon characterization, the optimized ODHP-NS has a particle size of 332 ± 0.35 nm. It was found to be homogenous and had a porous surface and spherical morphology with the drug entrapped in the polymer matrix according to the SEM image. SEM is a robust technique for displaying the sample’s morphology, providing information on the sample’s pore structure and an indication of homogeneity (Datye and DeLaRiva ##UREF##15##2023##).</p>", "<p id=\"Par71\">The primary indicator for the stability of the colloidal dispersion is zeta potential. The zeta potential can be determined by adding an additional electrode to particle size analysis equipment or a zeta seizer. ODHP-NS has a mean ZP of − 13.8 ± 0.56 mV, indicating a relatively good stability and dispersion quality (Ahmed et al. ##REF##34135673##2021##; Penjuri et al. ##UREF##39##2016##). This is in agreement with studies which reported nanosponges with comparable negative zeta potential values and which produced stable water suspensions that do not undergo aggregation over time (Kumar et al. ##REF##33321649##2021##; Trotta et al. ##REF##23243470##2012##). The more stable a colloidal dispersion is, the higher its zeta potential value, positive or negative (Bhowmik et al. ##UREF##9##2018##). The “polydispersity index” (PDI) is a measure used to specify the size range of the NS systems regarding particle size distribution characterization. The degree of non-uniformity in a particle size distribution is referred to as “polydispersity” (Bera ##UREF##8##2015##; Kumar et al. ##REF##33321649##2021##). Because of the dimensionlessness and scale of this measure, values lower than 0.05 are often observed only with extremely monodisperse standards (Bera ##UREF##8##2015##). ODHP-NS has a PDI of 0.233 ± 0.02 showing reasonable and acceptable monodisperse system. A sample with a very wide particle size distribution and a PDI value greater than 0.7 is most likely not appropriate for analysis using the dynamic light scattering (DLS) method (Danaei et al. ##REF##29783687##2018##). The entrapment efficiency was found to be in an acceptable range of 90.14 ± 0.65% which was further corroborated from earlier study (Amer et al. ##REF##32154153##2020##). The drug loading was found to be 87.5%. The manner of drug loading into the nanosponges can influence the drug-nanosponge complexation. Although the efficacy of an approach is mostly determined by the nature or features of the drug and polymer, freeze-drying has been reported to alter drug and nanosponge complexation in some situations (Bhowmik et al. ##UREF##9##2018##). ODHP-NS formulation has attained high drug loading capacity; this is in accordance with many studies stated that cyclodextrin-based nanoparticles can maintain a high loading capacity of various small molecules for drug delivery (Deng et al. ##UREF##16##2021##). Nanosponges have a higher drug loading capacity than other nanocarriers, making them ideal for overcoming issues such as active drug stability, solubility, and delayed release (Tejashri et al. ##REF##24152895##2013##). Differential scanning calorimetry (DSC) measures the heat which is being absorbed or released during the process of heating or cooling. It is used to measure the heat of reaction, melting point, heat capacity, and glass transition (Akash et al. ##UREF##4##2020##). DSC of optimized ODHP-loaded NS ensured its development which leads to the reduction in crystallinity of the drug. The change in the structure from crystalline to amorphous established the fact that NS has been developed (Abdellatif et al. ##REF##28522423##2017##). The molecularly dispersed phase of ODHP within the NS structure leads to the broadening of the peak. The amorphous structure of the ODHP-NS established by the result obtained is desirable for enhanced drug entrapment within the NS structure (Fatima et al. ##UREF##22##2019##).</p>", "<p id=\"Par72\">Several gel formers have been preliminarily tested for the preparation of hydrogel of which carbopol 940 was selected. Carbopol 940 is a hydrophilic polyacrylic acid polymer with carboxyl functional groups that are ionized after interaction with triethanolamine. This results in the formation of a gel-like structure due to electrostatic repulsion between charged polymer strands. This stage increases the pH of the HG developed, making it suitable for skin application. Additionally, because carbopol is non-toxic and non-irritating, it can be used in gel preparations (Safitri et al. ##UREF##45##2020##). Unlike hydroxypropyl methylcellulose, which must be produced in hot water, carbopol gelling agents have the advantage of being able to be developed in room temperature water. Furthermore, the wide viscosity range of 40,000–60,000 cps of carbopol 940 led to its selection for hydrogel preparations (Daryab et al. ##UREF##14##2022##). The concentration of carbopol 940 gelling agent directly influences the viscosity of the preparation, which also influences its physical characteristics (Daood et al. ##UREF##13##2019##). Good spreadability is crucial for acceptable gel formulation. HG’s spreadability was found to be 5.74 ± 0. 32 cm, and pH was 6.75 ± 0.13. The HG’s pH, which was nearly neutral, indicated an absence of skin irritation potential, thus verifying its compatibility with the skin (Blaak and Staib ##UREF##10##2018##). The swelling data can be employed to determine the mechanical and viscoelastic properties, degradation rate, cross-linking degree, and refractive index (Sievers et al. ##UREF##47##2021##). The gel exhibited a favorable swelling index of 350.6 ± 0.66%, indicating good swelling characteristics that align with previous findings (Ambala and Vemula ##UREF##6##2015##). While the extrudability was recorded as 0.97 ± 0.11 (g/s), the viscosity of hydrogel was found to be 1092 ± 4cps which indicates good consistency and texture of the prepared hydrogel. The viscosity of hydrogel compositions reflects their consistency in general (Dejeu et al. ##REF##35215288##2022##).</p>", "<p id=\"Par73\">The percentage of drug content for the selected HG-5 was 90.96 ± 0.32% denoting high retention of the drug by the nanosponge system. Based on the coefficient of correlation (<italic>R</italic>² value = 0.9976), the release was best fitted into the Higuchi diffusion kinetic model. This model is based on several hypotheses, including that initial drug concentration in the matrix is substantially higher than drug solubility, matrix swelling and dissolution are minimal or non-existent, and drug diffusivity is constant (Wang et al. ##REF##36776789##2023##). The Korsmeyer-Peppas model was used to investigate the mechanism of ODHP release from the produced formula. A diffusion exponent (<italic>n</italic> = 0.563) reflected a non-Fickian model (anomalous transport) in which release is governed by a combination of diffusion and polymer chain relaxation (Yammine et al. ##UREF##53##2023##). The drug content was reassessed following exposure to UV light, as well as after conducting stability studies under the specified conditions. The results indicated that there was no significant difference (<italic>p</italic> &gt; 0.05) compared to the initial conditions, indicating the formulation’s exceptional stability properties. In vitro antifungal study demonstrated superior antifungal activity of ODHP-NS-HG against <italic>C. albicans</italic> ATCC10231 over the positive control fluconazole.</p>", "<p id=\"Par74\">Since its introduction by Mosmann in the 1980s, the MTT assay has become the gold standard for determining cell cytotoxicity (Hoogstraten et al. ##UREF##28##2021##). IC₅₀ values of the optimized ODHP-NS and fluconazole (as reference standard) were 325.6 µg/mL and 287.8 µg/mL, respectively. Cell viability was reduced by both of these samples in a dose-dependent manner (Van Tonder et al. ##REF##25645429##2015##). Finally, a thermal injury model in male Wistar albino rats infected with <italic>C. albicans</italic> was developed to assess the capability of the ODHP-NS designed as hydrogels to suppress the pathogenicity of this strain in rats. Many studies using <italic>C. albicans</italic> superficial skin infection in mice/rats have been described earlier (El-Sakhawy et al. ##REF##36647849##2023##; Macherla et al. ##REF##22701111##2012##). Our results revealed that the tested formulation of ODHP-NS-HG increased the survival rate, as well as increasing the deposition of dermal collagen fibers in the skin of treated groups compared to the other control groups. This is in agreement with the previous study investigating the level of collagen deposition and the healing of <italic>C. albicans</italic>–infected wound (Nejati et al. ##UREF##36##2015##). According to another study, it was proposed that the effectiveness of antifungal agents in the form of nanosponges could be enhanced by β-CD. This is because when β-CD interacts with <italic>C. albicans</italic>, it induces modifications in the cell wall and disrupts its protective function (Finger et al. ##UREF##23##2013##). Additionally, since <italic>C. albicans</italic> contains glucosylceramides in its cell wall, which activate an internal signaling pathway leading to the apoptosis of the fungal pathogen, it may have a greater tolerance to higher concentrations of β-CD compared to other microbes. This allows first-line therapies for virulent and highly resistant fungal infections to use antifungal agents formulated as β-CD-NS without the side effects of synthetic and semi-synthetic drugs (Desai and Shende ##UREF##17##2021##). The wound healing process necessitates integrated and sequential stages to repair cells and tissues and return them to their pre-injury state (Behere and Ingavle ##REF##34390324##2022##), and fungal contamination can delay the process of wound healing. The wound area and percentage of wound contraction were observed to assess the ODHP-NS-HG ability to cure wounds. In the current research, wound areas and wound contraction (%) were measured at days 1, 7, and 14 after the wound was created.</p>", "<p id=\"Par75\">According to the study’s results, ODHP-NS-HG can help treat wounds infected with <italic>C. albicans</italic> and speed up the healing process. It is worth noting that the proportion of wound contraction in ODHP-NS-HG–treated group was found to be 80% which was 1.5-fold higher compared to positive control group (F) and 2.4-fold greater than positive control group (G). Our study appears to be the first to investigate the efficacy of ODHP-NS-HG for the treatment of candidiasis in a rat thermal injury model. The histopathological inspection of various injured groups revealed varying degrees of tissue damage and healing mechanisms. Isoconazole 1% along with collagenase were used as positive controls in our research for the treatment of rat skin wounds, as described in a couple of studies (Durmus et al. ##UREF##18##2009##; Veraldi ##REF##23574019##2013##) owing to their wound healing properties. In comparison to the control group B (burned, infected, untreated), topical application of ODHP-NS-HG in group (E) showed a significant difference (<italic>p</italic> &lt; 0.05) in minimizing local wound infection and promoting rejuvenation of the skin, as well as higher records and a remarkable acceleration of dermal mature collagen fiber development. Thus, our findings support a previous report by Srivastava et al. that nanosponges of antifungal therapies could be promising in preventing wound-associated <italic>C. albicans</italic> infections (Srivastava et al. ##REF##34293406##2021##). The efficient dermal delivery of ODHP-NS through skin in topical gel formulation was confirmed via high drug amount in the in vitro permeation study.</p>", "<p id=\"Par76\">Dermatomycoses, or superficial fungal skin diseases, are caused by a variety of pathogens, including dermatophytes, yeasts, and molds (Costa-Orlandi et al. ##UREF##12##2023##; Jaishi et al. ##UREF##30##2022##). Because of exo-enzymes secreted by the fungal pathogen at the site of infection, such as keratinase (Veraldi ##REF##23574019##2013##), inflammatory symptoms and indications, such as pruritus and erythema, are very common (AbouSamra et al. ##UREF##1##2020##). Hence, it was deemed necessary to estimate the levels of angiogenesis (VEGF), inflammatory markers like cyclooxygenase (COX-2) and pro-inflammatory cytokines (TNF-α), NF-κB-p105, IL-6, and IL-1β based on ELISA technique. Angiogenesis, or the creation of new blood vessels, is critical in wound healing (Ahmad and Nawaz ##REF##36288574##2022##). The most significant and well-investigated angiogenic factor is vascular endothelial growth factor (VEGF) (Honnegowda et al. ##UREF##27##2015##). Many researchers believe that VEGF promotes wound epithelialization and collagen deposition so that high levels of VEGF are produced during the normal wound repair (Chereddy et al. ##REF##26238081##2015##). ODHP-NS-HG–treated group (E) exhibited significantly (<italic>p</italic> &lt; 0.05) higher level of VEGF compared to the infected untreated group (B) denoting increased level of re-epithelization and collagen deposition in accordance with previous studies (Abdel-Motaal et al. ##UREF##0##2022##). Cyclooxygenases are essential enzymes in the production of prostaglandins (PGs) from arachidonic acid. While COX-1 is constitutively expressed, COX-2 is activated in injured tissues, resulting in inflammatory processes (Carvalho et al. ##REF##35840810##2022##). COX-2 inhibition may result in anti-inflammatory effects (Ju et al. ##REF##35755295##2022##). Our ODHP-NS-HG formulation has significantly decreased the levels of COX-2 compared to the infected untreated group (B) implying its additional anti-inflammatory effect along with its antifungal one (Das et al. ##REF##20888359##2011##; López et al. ##REF##21237261##2011##). In the injured region, tumor necrosis factor (TNF)-α is rapidly produced, causing inflammation in wound tissues (Jaishi et al. ##UREF##30##2022##). Hence, TNF-α was elevated in infected untreated groups while it was neutralized significantly in ODHP-NS-HG–treated group E indicating good healing of the injured area. During wound healing, the classical NF-κB pathway is activated, resulting in the production of numerous cytokines, and other secondary inflammatory mediators, and apoptosis inhibitors (Hellweg ##REF##25688671##2015##).</p>", "<p id=\"Par77\">On the other hand, over expression of NF-κB can lead to reduced wound healing as previously confirmed (Jin et al. ##REF##34077834##2021##). Based on these facts, our ODHP-NS-HG formulation showed decreased levels (<italic>p</italic> &lt; 0.05) of NF-κB denoting healing of the wound compared to other untreated groups that showed higher levels denoting that the wound was still in the healing process. IL-6 has potential roles in the wound healing process as previously reported (Johnson et al. ##REF##32365896##2020##). Decreased levels of IL-6 in group E compared to untreated groups (<italic>p</italic> &lt; 0.05) indicate a normal wound repair. This comes in accordance with the observations from other reports (Johnson et al. ##REF##32365896##2020##). IL-1β induces fibroblast growth, promotes the production of collagenase, and inhibits endothelial cell development, making it an antagonist of extracellular matrix metabolism (Carvalho et al. ##REF##35840810##2022##). Furthermore, IL-1β has been shown to promote the proliferation of smooth muscle cells and to serve as a chemoattractant for neutrophils and macrophages (Paramel et al. ##REF##35792171##2022##). According to our study’s ELISA findings, IL-1β levels were higher in the untreated groups than in the treated ones. This indicates that ODHP-NS-HG application is effective at inhibiting inflammation via IL-1β, which is consistent with the findings of Aneesha et al. (##REF##35595596##2022##) and Gürgen et al. (##REF##24357416##2014##). The substantial reductions in COX-2 and pro-inflammatory cytokines found in group E indicate that ODHP-NS-HG speeds up the healing process by inhibiting the inflammation phase. In conclusion, this research demonstrates the effective optimized preparation of nanosponges from the antifungal ODHP. The developed NS was characterized for particle size, PDI, zeta potential, and FTIR, and based on the findings, a topical hydrogel formulation was prepared. Upon evaluation, the hydrogel had excellent spreadability, extrudability, and swelling properties. The hydrogel pH confirmed its skin compatibility, and it showed high drug content with potent in vitro antimycotic activity. The in vitro release studies were best fitted to Higuchi’s model. Furthermore, the stability studies denoted the high stability of this formulation. Further in vitro, ex vivo, and in vivo testing revealed that the prepared hydrogel inhibited fungal growth both and showed enhanced permeability following its topical application. The prepared ODHP-NS-HG reverted the inflammatory effect and suppressed the infection by compromising the levels of COX-2, TNF-α, NF-κB-p105, IL-6, and IL-1β in treated group E comparing to untreated groups. Moreover, VEGF levels were significantly higher in treated group E indicating higher level of vascularization than untreated groups.</p>" ]

[]

[ "<title>Abstract</title>", "<p id=\"Par1\">Octadecyl 3-(3,5-di-tert-butyl-4-hydroxyphenyl) propanoate (ODHP) was extracted in a previous study from the culture broth of soil isolate <italic>Alcaligenes faecalis</italic> MT332429 and showed a promising antimycotic activity. This study was aimed to formulate ODHP loaded β-cyclodextrins (CD) nanosponge (NS) hydrogel (HG) to control skin fungal ailments since nanosponges augment the retention of tested agents in the skin. Box-Behnken design was used to produce the optimized NS formulation, where entrapment efficiency percent (EE%), polydispersity index (PDI), and particle size (PS) were assigned as dependent parameters, while the independent process parameters were polyvinyl alcohol % (w/v %), polymer-linker ratio, homogenization time, and speed. The carbopol 940 hydrogel was then created by incorporating the nanosponges. The hydrogel fit Higuchi’s kinetic release model the best, according to in vitro drug release. Stability and photodegradation studies revealed that the NS-HG remained stable under tested conditions. The formulation also showed higher in vitro antifungal activity against <italic>Candida albicans</italic> compared to the control fluconazole. In vivo study showed that ODHP-NS-HG increased survival rates, wound contraction, and healing of wound gap and inhibited the inflammation process compared to the other control groups. The histopathological examinations and Masson’s trichrome staining showed improved healing and higher records of collagen deposition. Moreover, the permeability of ODHP-NS-HG was higher through rats’ skin by 1.5-folds compared to the control isoconazole 1%. Therefore, based on these results, NS-HG formulation is a potential carrier for enhanced and improved topical delivery of ODHP. Our study is a pioneering research on the development of a formulation for ODHP produced naturally from soil bacteria.</p>", "<title>Key points</title>", "<p id=\"Par2\">• <italic>Octadecyl 3-(3,5-di-tert-butyl-4-hydroxyphenyl) propanoate was successfully formulated as a nanosponge hydrogel and statistically optimized</italic>.</p>", "<p id=\"Par3\">• <italic>The new formula exhibited in vitro good stability, drug release, and higher antifungal activity against C. albicans as compared to the fluconazole</italic>.</p>", "<p id=\"Par4\">• <italic>Ex vivo showed enhanced skin permeability, and in vivo analysis showed high antifungal activity as evidenced by measurement of various biochemical parameters and histopathological examination</italic>.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00253-023-12819-3.</p>", "<title>Keywords</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).</p>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Acknowledgements</title>", "<p>We hereby acknowledge Dr. Fady Adel Malak and Dr. Shaymaa El-Hady, assistant lecturers, Pharmaceutics Department, Faculty of Pharmacy, Ahram Canadian University, for their help in the preparation of the hydrogel formulation and performing the required measurements.</p>", "<title>Author contribution</title>", "<p>Conceived and designed the study: KMA, GSE, NAA, and SEE; performed the experiments: SEE; statistical analysis and figure preparation: SEE; drafted the manuscript: KMA, GSE, NAA, and SEE; wrote the paper in its final format: KMA, GSE, NAA, and SEE. All authors read and approved the final manuscript.</p>", "<title>Funding</title>", "<p>Open access funding provided by The Science, Technology &amp; Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).</p>", "<title>Data availability</title>", "<p>The authors declare that the data supporting the findings of this study are available within the article and its supplementary information file. The 16S ribosomal RNA of <italic>Alcaligenes faecalis</italic> MT332429 deposited into the NCBI GenBank under the accession number MT332429 (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.ncbi.nlm.nih.gov/nuccore/MT332429\">https://www.ncbi.nlm.nih.gov/nuccore/MT332429</ext-link>) (accessed on 23 July 2023).</p>", "<title>Declarations</title>", "<title>Ethical approval</title>", "<p id=\"Par78\">The study was approved by the research ethical committee of the Faculty of Pharmacy, Ain Shams University, Egypt (Protocol approval number: ACUC-FP-ASU-RHDIRB2020110301-REC#39).</p>", "<title>Consent to participate</title>", "<p id=\"Par79\">Not applicable.</p>", "<title>Consent for publication</title>", "<p id=\"Par80\">Not applicable.</p>", "<title>Competing interests</title>", "<p id=\"Par81\">The authors declare no competing interests.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Three-dimensional response surfaces representing the effect of the four significant parameters on nanosponges’ dependent variables. <bold>a</bold> Particle size plot. <bold>b</bold> Polydispersity index plot. <bold>c</bold> Entrapment efficiency plot</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Particle size distribution by intensity (<bold>a</bold>), zeta potential distribution (<bold>b</bold>), and SEM image of the optimized ODHP-NS (<bold>c</bold>)</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>The photographs of the wounds of injured skin at 14th day of injury of a representative rat from each group with mean wound size (cm)</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Photomicrographs of different skin layers and wound healing process stained with Hematoxylin and Eosin (H&amp;E) of the different tested groups as follows: (<bold>a</bold>) unburned, uninfected, treated with ODHP -NS-HG (skin irritation test; (<bold>b</bold>) Control, burned, infected, untreated; (<bold>c</bold>) control, burned, uninfected, untreated; (<bold>d</bold>) control, burned, infected, treated with vehicle (negative control hydrogel); (<bold>e</bold>) burned, infected, treated with ODHP -NS-HG; (<bold>f</bold>) positive control-1, burned, infected, treated with Collagenase 0.6 IU (Iruxol®, Abbott Co., Wiesbaden, Germany); (<bold>g</bold>) positive control-2, burned, infected,  treated with Isoconazole hydrogel (ISN) 1% (Candicure®, Al-Esraa Pharmaceutical Optima Co., EGYPT); (<bold>h</bold>) normal control group (intact, unburned, uninfected, untreated). Arrows indicate significant and specific histopathological changes in the tissues of each group as indicated in the text</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Photomicrographs of skin layers, wound healing, and collagen formation stained with for Masson’s trichrome staining (MTC) of the different tested groups as follows: (<bold>a</bold>) unburned, uninfected, treated with ODHP -NS-HG (skin irritation test; (<bold>b</bold>) Control, burned, infected, untreated; (<bold>c</bold>) control, burned, uninfected, untreated; (<bold>d</bold>) control, burned, infected, treated with vehicle (negative control hydrogel); (<bold>e</bold>) burned, infected, treated with ODHP -NS-HG; (<bold>f</bold>) positive control-1, burned, infected, treated with Collagenase 0.6 IU (Iruxol®, Abbott Co., Wiesbaden, Germany); (<bold>g</bold>) positive control-2, burned, infected,  treated with Isoconazole hydrogel (ISN) 1% (Candicure®, Al-Esraa Pharmaceutical Optima Co., EGYPT); (<bold>h</bold>) normal control group (intact, unburned, uninfected, untreated)</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Bar chart showings area percentage of bluish stained sections in MTC staining for different groups. Data expressed as means ± SD. A significant difference is considered at <italic>p</italic> &lt; 0.05</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><p>The levels of the respective biomarkers for each group corresponding to the levels of the inflammation recovery. The biomarkers are displayed as follows: (<bold>a</bold>) COX-2, (<bold>b</bold>) TNF-α, (<bold>c</bold>) VEGF, (<bold>d</bold>) NF-kB-p105, (<bold>e</bold>) IL-6, and (<bold>f</bold>) IL-1β</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Independent and dependent variables of Box-Behnken design with their respective levels and goals</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\">Independent variables</th><th align=\"left\" colspan=\"3\">Levels of variables</th></tr><tr><th align=\"left\"> − 1</th><th align=\"left\">0</th><th align=\"left\">1</th></tr></thead><tbody><tr><td align=\"left\">A: polymer (β-CD)-cross-linker (diphenyl carbonate) molar ratio</td><td align=\"left\">1:2</td><td align=\"left\">1:4</td><td align=\"left\">1:10</td></tr><tr><td align=\"left\">B: homogenization speed (rpm)</td><td align=\"left\">10,000</td><td align=\"left\">12,500</td><td align=\"left\">15,000</td></tr><tr><td align=\"left\">C: homogenization time (min)</td><td align=\"left\">10</td><td align=\"left\">12</td><td align=\"left\">14</td></tr><tr><td align=\"left\">D: polyvinyl alcohol (%w/v)</td><td align=\"left\">0.3</td><td align=\"left\">0.4</td><td align=\"left\">0.5</td></tr><tr><td align=\"left\">Dependent variables</td><td align=\"left\" colspan=\"3\">Target goal</td></tr><tr><td align=\"left\">Particle size (nm)</td><td align=\"left\" colspan=\"3\">Minimize</td></tr><tr><td align=\"left\">Polydispersity index (PDI)</td><td align=\"left\" colspan=\"3\">Minimize</td></tr><tr><td align=\"left\">Entrapment efficiency %</td><td align=\"left\" colspan=\"3\">Maximize</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Box-Behnken design runs for the four different factors tested showing the observed and predicted responses</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Run</th><th align=\"left\">A: polymer-linker ratio</th><th align=\"left\">B: homogenization speed</th><th align=\"left\">C: homogenization time</th><th align=\"left\">D: PVA%</th><th align=\"left\">Particle size</th><th align=\"left\">Predicted particle size</th><th align=\"left\">PDI</th><th align=\"left\">Predicted PDI</th><th align=\"left\">EE</th><th align=\"left\">Predicted EE</th></tr></thead><tbody><tr><td align=\"left\">1</td><td align=\"left\">1:10</td><td align=\"left\">12,500</td><td align=\"left\">14</td><td align=\"left\">0.4</td><td align=\"left\">363</td><td align=\"left\">359.79</td><td align=\"left\">0.5</td><td align=\"left\">0.46</td><td align=\"left\">86.96</td><td align=\"left\">87.37</td></tr><tr><td align=\"left\">2</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">320</td><td align=\"left\">324.41</td><td align=\"left\">0.21</td><td align=\"left\">0.14</td><td align=\"left\">89.67</td><td align=\"left\">89.38</td></tr><tr><td align=\"left\">3</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">10</td><td align=\"left\">0.5</td><td align=\"left\">326</td><td align=\"left\">326.24</td><td align=\"left\">0.27</td><td align=\"left\">0.28</td><td align=\"left\">89.86</td><td align=\"left\">89.57</td></tr><tr><td align=\"left\">4</td><td align=\"left\">1:4</td><td align=\"left\">10,000</td><td align=\"left\">10</td><td align=\"left\">0.4</td><td align=\"left\">333</td><td align=\"left\">335.46</td><td align=\"left\">0.31</td><td align=\"left\">0.31</td><td align=\"left\">87.21</td><td align=\"left\">87.62</td></tr><tr><td align=\"left\">5</td><td align=\"left\">1:4</td><td align=\"left\">15,000</td><td align=\"left\">12</td><td align=\"left\">0.3</td><td align=\"left\">355</td><td align=\"left\">346.46</td><td align=\"left\">0.44</td><td align=\"left\">0.40</td><td align=\"left\">88</td><td align=\"left\">88.08</td></tr><tr><td align=\"left\">6</td><td align=\"left\">1:4</td><td align=\"left\">10,000</td><td align=\"left\">12</td><td align=\"left\">0.5</td><td align=\"left\">342</td><td align=\"left\">336.12</td><td align=\"left\">0.33</td><td align=\"left\">0.34</td><td align=\"left\">87.85</td><td align=\"left\">88.16</td></tr><tr><td align=\"left\">7</td><td align=\"left\">1:10</td><td align=\"left\">12,500</td><td align=\"left\">10</td><td align=\"left\">0.4</td><td align=\"left\">359</td><td align=\"left\">360.96</td><td align=\"left\">0.48</td><td align=\"left\">0.47</td><td align=\"left\">86.84</td><td align=\"left\">87.02</td></tr><tr><td align=\"left\">8</td><td align=\"left\">1:2</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.3</td><td align=\"left\">382</td><td align=\"left\">376.96</td><td align=\"left\">0.58</td><td align=\"left\">0.58</td><td align=\"left\">90.87</td><td align=\"left\">91.21</td></tr><tr><td align=\"left\">9</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">14</td><td align=\"left\">0.3</td><td align=\"left\">323</td><td align=\"left\">322.58</td><td align=\"left\">0.22</td><td align=\"left\">0.25</td><td align=\"left\">89.15</td><td align=\"left\">89.2</td></tr><tr><td align=\"left\">10</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">320</td><td align=\"left\">324.41</td><td align=\"left\">0.21</td><td align=\"left\">0.14</td><td align=\"left\">89.67</td><td align=\"left\">89.38</td></tr><tr><td align=\"left\">11</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">320</td><td align=\"left\">324.41</td><td align=\"left\">0.21</td><td align=\"left\">0.14</td><td align=\"left\">89.67</td><td align=\"left\">89.38</td></tr><tr><td align=\"left\">12</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">320</td><td align=\"left\">324.41</td><td align=\"left\">0.21</td><td align=\"left\">0.14</td><td align=\"left\">89.67</td><td align=\"left\">89.38</td></tr><tr><td align=\"left\">13</td><td align=\"left\">1:10</td><td align=\"left\">15,000</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">373</td><td align=\"left\">383.67</td><td align=\"left\">0.54</td><td align=\"left\">0.61</td><td align=\"left\">86.61</td><td align=\"left\">86.25</td></tr><tr><td align=\"left\">14</td><td align=\"left\">1:10</td><td align=\"left\">10,000</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">370</td><td align=\"left\">370.84</td><td align=\"left\">0.54</td><td align=\"left\">0.54</td><td align=\"left\">86.32</td><td align=\"left\">85.61</td></tr><tr><td align=\"left\">15</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">320</td><td align=\"left\">324.41</td><td align=\"left\">0.21</td><td align=\"left\">0.14</td><td align=\"left\">89.67</td><td align=\"left\">89.38</td></tr><tr><td align=\"left\">16</td><td align=\"left\">1:2</td><td align=\"left\">12,500</td><td align=\"left\">10</td><td align=\"left\">0.4</td><td align=\"left\">379</td><td align=\"left\">378.79</td><td align=\"left\">0.56</td><td align=\"left\">0.56</td><td align=\"left\">91.12</td><td align=\"left\">91.4</td></tr><tr><td align=\"left\">17</td><td align=\"left\">1:4</td><td align=\"left\">10,000</td><td align=\"left\">14</td><td align=\"left\">0.4</td><td align=\"left\">330</td><td align=\"left\">334.29</td><td align=\"left\">0.29</td><td align=\"left\">0.29</td><td align=\"left\">87.61</td><td align=\"left\">87.97</td></tr><tr><td align=\"left\">18</td><td align=\"left\">0.5</td><td align=\"left\">15,000</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">391</td><td align=\"left\">401.5</td><td align=\"left\">0.66</td><td align=\"left\">0.70</td><td align=\"left\">90.45</td><td align=\"left\">90.63</td></tr><tr><td align=\"left\">19</td><td align=\"left\">1:4</td><td align=\"left\">15,000</td><td align=\"left\">10</td><td align=\"left\">0.4</td><td align=\"left\">351</td><td align=\"left\">348.29</td><td align=\"left\">0.41</td><td align=\"left\">0.38</td><td align=\"left\">88.14</td><td align=\"left\">88.26</td></tr><tr><td align=\"left\">20</td><td align=\"left\">1:4</td><td align=\"left\">15,000</td><td align=\"left\">14</td><td align=\"left\">0.4</td><td align=\"left\">349</td><td align=\"left\">347.12</td><td align=\"left\">0.38</td><td align=\"left\">0.37</td><td align=\"left\">88.88</td><td align=\"left\">88.62</td></tr><tr><td align=\"left\">21</td><td align=\"left\">1:2</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.5</td><td align=\"left\">385</td><td align=\"left\">379.46</td><td align=\"left\">0.61</td><td align=\"left\">0.60</td><td align=\"left\">92.1</td><td align=\"left\">91.94</td></tr><tr><td align=\"left\">22</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">14</td><td align=\"left\">0.5</td><td align=\"left\">324</td><td align=\"left\">325.08</td><td align=\"left\">0.24</td><td align=\"left\">0.27</td><td align=\"left\">90.02</td><td align=\"left\">89.93</td></tr><tr><td align=\"left\">23</td><td align=\"left\">1:2</td><td align=\"left\">10,000</td><td align=\"left\">12</td><td align=\"left\">0.4</td><td align=\"left\">389</td><td align=\"left\">388.67</td><td align=\"left\">0.63</td><td align=\"left\">0.62</td><td align=\"left\">90.34</td><td align=\"left\">89.99</td></tr><tr><td align=\"left\">24</td><td align=\"left\">1:4</td><td align=\"left\">10,000</td><td align=\"left\">12</td><td align=\"left\">0.3</td><td align=\"left\">335</td><td align=\"left\">333.62</td><td align=\"left\">0.35</td><td align=\"left\">0.34</td><td align=\"left\">87.44</td><td align=\"left\">87.43</td></tr><tr><td align=\"left\">25</td><td align=\"left\">1:4</td><td align=\"left\">15,000</td><td align=\"left\">12</td><td align=\"left\">0.5</td><td align=\"left\">357</td><td align=\"left\">348.96</td><td align=\"left\">0.46</td><td align=\"left\">0.43</td><td align=\"left\">88.55</td><td align=\"left\">88.8</td></tr><tr><td align=\"left\">26</td><td align=\"left\">1:2</td><td align=\"left\">12,500</td><td align=\"left\">14</td><td align=\"left\">0.4</td><td align=\"left\">377</td><td align=\"left\">377.62</td><td align=\"left\">0.55</td><td align=\"left\">0.54</td><td align=\"left\">91.7</td><td align=\"left\">91.75</td></tr><tr><td align=\"left\">27</td><td align=\"left\">1:10</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.3</td><td align=\"left\">365</td><td align=\"left\">359.12</td><td align=\"left\">0.51</td><td align=\"left\">0.50</td><td align=\"left\">86.57</td><td align=\"left\">86.83</td></tr><tr><td align=\"left\">28</td><td align=\"left\">1:4</td><td align=\"left\">12,500</td><td align=\"left\">10</td><td align=\"left\">0.3</td><td align=\"left\">325</td><td align=\"left\">323.74</td><td align=\"left\">0.24</td><td align=\"left\">0.27</td><td align=\"left\">89</td><td align=\"left\">88.84</td></tr><tr><td align=\"left\">29</td><td align=\"left\">1:10</td><td align=\"left\">12,500</td><td align=\"left\">12</td><td align=\"left\">0.5</td><td align=\"left\">366</td><td align=\"left\">361.62</td><td align=\"left\">0.52</td><td align=\"left\">0.51</td><td align=\"left\">87</td><td align=\"left\">87.56</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>ANOVA table for particle size (PS) model, polydispersity index (PDI) model, and entrapment efficiency (EE%)</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Source</th><th align=\"left\">Sum of squares</th><th align=\"left\">df</th><th align=\"left\">Mean square</th><th align=\"left\"><italic>F</italic>-value</th><th align=\"left\"><italic>p</italic>-value</th></tr></thead><tbody><tr><td align=\"left\">Particle size</td><td align=\"left\">16,181.93</td><td align=\"left\">6</td><td align=\"left\">2696.99</td><td align=\"left\">90.03</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">A-polymer-linker ratio</td><td align=\"left\">954.08</td><td align=\"left\">1</td><td align=\"left\">954.08</td><td align=\"left\">31.85</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">B-homogenization speed</td><td align=\"left\">494.08</td><td align=\"left\">1</td><td align=\"left\">494.08</td><td align=\"left\">16.49</td><td align=\"left\">0.0005</td></tr><tr><td align=\"left\">C-homogenization time</td><td align=\"left\">4.08</td><td align=\"left\">1</td><td align=\"left\">4.08</td><td align=\"left\">0.1363</td><td align=\"left\">0.7155</td></tr><tr><td align=\"left\">D-PVA%</td><td align=\"left\">18.75</td><td align=\"left\">1</td><td align=\"left\">18.75</td><td align=\"left\">0.6259</td><td align=\"left\">0.4373</td></tr><tr><td align=\"left\"><italic>A</italic>²</td><td align=\"left\">13,902.45</td><td align=\"left\">1</td><td align=\"left\">13,902.45</td><td align=\"left\">464.09</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\"><italic>B</italic>²</td><td align=\"left\">1966.76</td><td align=\"left\">1</td><td align=\"left\">1966.76</td><td align=\"left\">65.65</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">Residual</td><td align=\"left\">659.03</td><td align=\"left\">22</td><td align=\"left\">29.96</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Lack of fit</td><td align=\"left\">659.03</td><td align=\"left\">18</td><td align=\"left\">36.61</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Pure error</td><td align=\"left\">0</td><td align=\"left\">4</td><td align=\"left\">0</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Cor total</td><td align=\"left\">16,840.97</td><td align=\"left\">28</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Polydispersity index</td><td align=\"left\">0.4263</td><td align=\"left\">14</td><td align=\"left\">0.0304</td><td align=\"left\">84.26</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">A-polymer-linker ratio</td><td align=\"left\">0.0264</td><td align=\"left\">1</td><td align=\"left\">0.0264</td><td align=\"left\">73.09</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">B-homogenization speed</td><td align=\"left\">0.0099</td><td align=\"left\">1</td><td align=\"left\">0.0099</td><td align=\"left\">27.42</td><td align=\"left\">0.0001</td></tr><tr><td align=\"left\">C-homogenization time</td><td align=\"left\">0.0002</td><td align=\"left\">1</td><td align=\"left\">0.0002</td><td align=\"left\">0.6164</td><td align=\"left\">0.4455</td></tr><tr><td align=\"left\">D-PVA%</td><td align=\"left\">0.0005</td><td align=\"left\">1</td><td align=\"left\">0.0005</td><td align=\"left\">1.29</td><td align=\"left\">0.2745</td></tr><tr><td align=\"left\">AB</td><td align=\"left\">0.0004</td><td align=\"left\">1</td><td align=\"left\">0.0004</td><td align=\"left\">1.04</td><td align=\"left\">0.326</td></tr><tr><td align=\"left\">AC</td><td align=\"left\">0.0002</td><td align=\"left\">1</td><td align=\"left\">0.0002</td><td align=\"left\">0.652</td><td align=\"left\">0.4329</td></tr><tr><td align=\"left\">AD</td><td align=\"left\">0.0002</td><td align=\"left\">1</td><td align=\"left\">0.0002</td><td align=\"left\">0.4463</td><td align=\"left\">0.515</td></tr><tr><td align=\"left\">BC</td><td align=\"left\">0</td><td align=\"left\">1</td><td align=\"left\">0</td><td align=\"left\">0.0947</td><td align=\"left\">0.7628</td></tr><tr><td align=\"left\">BD</td><td align=\"left\">0.0002</td><td align=\"left\">1</td><td align=\"left\">0.0002</td><td align=\"left\">0.6908</td><td align=\"left\">0.4198</td></tr><tr><td align=\"left\">CD</td><td align=\"left\">9.30E − 06</td><td align=\"left\">1</td><td align=\"left\">9.30E − 06</td><td align=\"left\">0.0257</td><td align=\"left\">0.8748</td></tr><tr><td align=\"left\"><italic>A</italic>²</td><td align=\"left\">0.3541</td><td align=\"left\">1</td><td align=\"left\">0.3541</td><td align=\"left\">979.82</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\"><italic>B</italic>²</td><td align=\"left\">0.0445</td><td align=\"left\">1</td><td align=\"left\">0.0445</td><td align=\"left\">123.26</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\"><italic>C</italic>²</td><td align=\"left\">0.0003</td><td align=\"left\">1</td><td align=\"left\">0.0003</td><td align=\"left\">0.8911</td><td align=\"left\">0.3612</td></tr><tr><td align=\"left\"><italic>D</italic>²</td><td align=\"left\">0.0054</td><td align=\"left\">1</td><td align=\"left\">0.0054</td><td align=\"left\">14.84</td><td align=\"left\">0.0018</td></tr><tr><td align=\"left\">Residual</td><td align=\"left\">0.0051</td><td align=\"left\">14</td><td align=\"left\">0.0004</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Lack of fit</td><td align=\"left\">0.0051</td><td align=\"left\">10</td><td align=\"left\">0.0005</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Pure error</td><td align=\"left\">0</td><td align=\"left\">4</td><td align=\"left\">0</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Cor total</td><td align=\"left\">0.4313</td><td align=\"left\">28</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Entrapment efficiency</td><td align=\"left\">72.07</td><td align=\"left\">5</td><td align=\"left\">14.41</td><td align=\"left\">123.9</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">A-polymer-linker ratio</td><td align=\"left\">57.55</td><td align=\"left\">1</td><td align=\"left\">57.55</td><td align=\"left\">494.74</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">B-homogenization speed</td><td align=\"left\">1.24</td><td align=\"left\">1</td><td align=\"left\">1.24</td><td align=\"left\">10.67</td><td align=\"left\">0.0034</td></tr><tr><td align=\"left\">C-homogenization time</td><td align=\"left\">0.3852</td><td align=\"left\">1</td><td align=\"left\">0.3852</td><td align=\"left\">3.31</td><td align=\"left\">0.0818</td></tr><tr><td align=\"left\">D-PVA%</td><td align=\"left\">1.58</td><td align=\"left\">1</td><td align=\"left\">1.58</td><td align=\"left\">13.56</td><td align=\"left\">0.0012</td></tr><tr><td align=\"left\"><italic>B</italic>²</td><td align=\"left\">11.31</td><td align=\"left\">1</td><td align=\"left\">11.31</td><td align=\"left\">97.23</td><td align=\"left\"> &lt; 0.0001</td></tr><tr><td align=\"left\">Residual</td><td align=\"left\">2.68</td><td align=\"left\">23</td><td align=\"left\">0.1163</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Lack of fit</td><td align=\"left\">2.68</td><td align=\"left\">19</td><td align=\"left\">0.1408</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Pure error</td><td align=\"left\">0</td><td align=\"left\">4</td><td align=\"left\">0</td><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Cor total</td><td align=\"left\">74.74</td><td align=\"left\">28</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr></tbody></table></table-wrap>" ]

[ "<disp-formula id=\"Equ1\"><label>1</label><alternatives><tex-math id=\"M1\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\%yield=\\frac{\\mathrm p\\mathrm r\\mathrm a\\mathrm c\\mathrm t\\mathrm i\\mathrm c\\mathrm a\\mathrm l\\;\\mathrm w\\mathrm t.\\mathrm o\\mathrm f\\;\\mathrm N\\mathrm S}{\\left(\\mathrm{wt}.\\mathrm o\\mathrm f\\;\\mathrm d\\mathrm r\\mathrm u\\mathrm g)+(\\mathrm{wt}.\\mathrm o\\mathrm f\\;\\mathrm\\beta-\\mathrm{CD}\\right)+(\\mathrm{wt}\\;\\mathrm{of}\\;\\mathrm{DPC})}\\times100$$\\end{document}</tex-math><mml:math id=\"M2\" display=\"block\"><mml:mrow><mml:mo>%</mml:mo><mml:mi>y</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>l</mml:mi><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">p</mml:mi><mml:mi mathvariant=\"normal\">r</mml:mi><mml:mi mathvariant=\"normal\">a</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi><mml:mi mathvariant=\"normal\">t</mml:mi><mml:mi mathvariant=\"normal\">i</mml:mi><mml:mi mathvariant=\"normal\">c</mml:mi><mml:mi mathvariant=\"normal\">a</mml:mi><mml:mi mathvariant=\"normal\">l</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">w</mml:mi><mml:mi mathvariant=\"normal\">t</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant=\"normal\">o</mml:mi><mml:mi mathvariant=\"normal\">f</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">N</mml:mi><mml:mi mathvariant=\"normal\">S</mml:mi></mml:mrow><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mi mathvariant=\"normal\">wt</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant=\"normal\">o</mml:mi><mml:mi mathvariant=\"normal\">f</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">d</mml:mi><mml:mi mathvariant=\"normal\">r</mml:mi><mml:mi mathvariant=\"normal\">u</mml:mi><mml:mi mathvariant=\"normal\">g</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>+</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"normal\">wt</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant=\"normal\">o</mml:mi><mml:mi mathvariant=\"normal\">f</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi>β</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant=\"normal\">CD</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi mathvariant=\"normal\">wt</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">of</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">DPC</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ2\"><label>2</label><alternatives><tex-math id=\"M3\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{\\%EE}=\\frac{\\mathrm{Actual\\;drug\\;content\\;in\\;NS\\;}}{\\mathrm{Theoretical\\;content }(\\mathrm{content\\;of\\;ODHP\\;initially\\;added})}\\times 100$$\\end{document}</tex-math><mml:math id=\"M4\" display=\"block\"><mml:mrow><mml:mrow><mml:mo>%</mml:mo><mml:mi mathvariant=\"normal\">EE</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">Actual</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">drug</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">content</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">in</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">NS</mml:mi><mml:mspace width=\"0.277778em\"/></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">Theoretical</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">content</mml:mi></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mi mathvariant=\"normal\">content</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">of</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">ODHP</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">initially</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">added</mml:mi></mml:mrow><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:mfrac><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ3\"><label>3</label><alternatives><tex-math id=\"M5\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{\\%DL}=\\frac{\\mathrm{Weight\\;of\\;ODHP\\;in\\;NS\\;}}{\\mathrm{weight\\;of\\;NS}}\\times 100$$\\end{document}</tex-math><mml:math id=\"M6\" display=\"block\"><mml:mrow><mml:mrow><mml:mo>%</mml:mo><mml:mi mathvariant=\"normal\">DL</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">Weight</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">of</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">ODHP</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">in</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">NS</mml:mi><mml:mspace width=\"0.277778em\"/></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">weight</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">of</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">NS</mml:mi></mml:mrow></mml:mfrac><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ4\"><label>4</label><alternatives><tex-math id=\"M7\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Swelling\\;index\\;}\\left({\\text{SW}}\\right)\\mathrm{\\%}=\\frac{\\mathrm{Wt }-{\\text{Wo}}}{{\\text{Wo}}} \\times 100$$\\end{document}</tex-math><mml:math id=\"M8\" display=\"block\"><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">Swelling</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">index</mml:mi><mml:mspace width=\"0.277778em\"/></mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mtext>SW</mml:mtext></mml:mfenced><mml:mo>%</mml:mo><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">Wt</mml:mi><mml:mo>-</mml:mo><mml:mtext>Wo</mml:mtext></mml:mrow><mml:mtext>Wo</mml:mtext></mml:mfrac><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equ5\"><label>5</label><alternatives><tex-math id=\"M9\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Wound\\;contraction\\;\\%}=\\frac{\\mathrm{Wt }-{\\text{Wo}}}{{\\text{Wo}}} \\times 100$$\\end{document}</tex-math><mml:math id=\"M10\" display=\"block\"><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">Wound</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">contraction</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mo>%</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi mathvariant=\"normal\">Wt</mml:mi><mml:mo>-</mml:mo><mml:mtext>Wo</mml:mtext></mml:mrow><mml:mtext>Wo</mml:mtext></mml:mfrac><mml:mo>×</mml:mo><mml:mn>100</mml:mn></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equa\"><alternatives><tex-math id=\"M11\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathrm{Particle\\;size}=800.44934-628.6289\\times A-0.064956\\times B-0.291667\\times C+12.50000\\times D+1122.01705\\times {A}^{2}+2.70091{\\text{E}}-06\\times {B}^{2}$$\\end{document}</tex-math><mml:math id=\"M12\" display=\"block\"><mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">Particle</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi mathvariant=\"normal\">size</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>800.44934</mml:mn><mml:mo>-</mml:mo><mml:mn>628.6289</mml:mn><mml:mo>×</mml:mo><mml:mi>A</mml:mi><mml:mo>-</mml:mo><mml:mn>0.064956</mml:mn><mml:mo>×</mml:mo><mml:mi>B</mml:mi><mml:mo>-</mml:mo><mml:mn>0.291667</mml:mn><mml:mo>×</mml:mo><mml:mi>C</mml:mi><mml:mo>+</mml:mo><mml:mn>12.50000</mml:mn><mml:mo>×</mml:mo><mml:mi>D</mml:mi><mml:mo>+</mml:mo><mml:mn>1122.01705</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mn>2.70091</mml:mn><mml:mtext>E</mml:mtext><mml:mo>-</mml:mo><mml:mn>06</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></alternatives></disp-formula>", "<disp-formula id=\"Equb\"><alternatives><tex-math id=\"M13\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\left(\\mathrm{Polydispersity\\;index}\\right)}^{2}=2.70996-3.40867\\times A-0.000331\\times B+0.056240\\times C-2.63667\\times D+0.000019\\times A\\times B-0.019188\\times A\\times C+0.317500\\times A\\times D-5.85000E-07\\times B\\times C+0.000032\\times B\\times D-0.007625\\times C\\times D+5.84104\\times {A}^{2}+1.32587{\\text{E}}-08\\times {B}^{2}-0.001761\\times {C}^{2}+2.87542\\times {D}^{2}$$\\end{document}</tex-math><mml:math id=\"M14\" display=\"block\"><mml:mrow><mml:msup><mml:mrow><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"normal\">Polydispersity</mml:mi><mml:mspace width=\"0.277778em\"/><mml:mi 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[ "<title>Introduction</title>", "<p id=\"Par2\">Histopathological analysis of skeletal muscle remains the diagnostic benchmark for detecting and distinguishing neuromuscular disorders, even though genetic and biochemical techniques have a well-established place in the diagnostic work-up. Historically, visual analysis of disease pathophysiology evolved from early studies employing light microscopy in the nineteenth century to examination on the subcellular level by contemporary methods such as electron microscopy [##REF##25924631##99##]. Histological analysis was augmented by staining of paraffin-embedded tissue prior to microscopy. Early staining strategies involved visualization by hematoxylin and eosin (HE) or modified Gömöri trichrome, while the emergence of immunohistochemistry (IHC) in the 1980s, as pioneered by the late Kiichi Arahata, Andrew Engel and many others [##REF##3288082##8##], allowed for the targeted analysis of specific proteins and cellular interplays. Together with clinical and laboratory parameters including antibody testing, histopathological analysis provides the framework for the contemporary classification of idiopathic inflammatory myopathies (IIM) [##REF##29651121##43##]. Currently, we recognize dermatomyositis (DM), immune-mediated necrotizing myopathy (IMNM), antisynthetase syndrome-associated myositis (ASyS), and inclusion body myositis (IBM) as prototypical entities across the IIM spectrum [##REF##29079590##42##]. However, this classification is challenged by a substantial clinical and histopathological overlap between different disorders as well as divergent disease outcomes even in individual subgroups of IIM. We and others have previously suggested that combining clinical, serological and morphological parameters in a clinico-seropathological model could enhance the classification of IIMs [##REF##31214105##10##, ##REF##27538058##11##, ##REF##29651121##43##, ##REF##32852298##87##]. Still, exact classification of disease is crucial for determining the individual treatment success, long-term outcomes, and clinical manifestations. Standardization of analytical workflows for muscle pathologies remains challenging as highlighted by a recent survey across 61 neuromuscular centers reporting highly variable diagnostic algorithms [##REF##31101462##91##]. To improve standardization, the EURO-neuromuscular diseases (NMD) pathology working group suggested a harmonized workflow aiming to standardize the classification of muscle diseases, including IIMs [##REF##31101462##91##]. While comprehensive, substantial resources and expertise are required for diagnostic algorithms directed at muscle pathologies often only available in highly specialized neuromuscular centers. However, a considerable number of affected patients are likely to live in low- and middle-income countries [##REF##33843773##28##, ##REF##25065005##48##]. The limitations imposed by these health care systems make it difficult to provide comprehensive, in-depth histopathological analysis as routine diagnostic approaches.</p>", "<p id=\"Par3\">To address this unmet need and to improve the diagnostic acuity of histopathology in a resource-limited setting, we here propose to distinguish IIM according to the current myopathological classification based on interpretation of major histocompatibility complexes classes I and II (MHC cl. I and -II) and complement patterns. This approach centers on visualizing MHC and complement, reflecting current knowledge of immunological concepts of disease. We also extend this framework to the analysis of skeletal muscle tissues of certain hereditary myopathies and the neuromuscular synapse, highlighting recent advances in those fields. In the following section, we will discuss the immunological background of MHC and complement in neuromuscular autoimmunity.</p>" ]

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[ "<p id=\"Par1\">Histopathological analysis stands as the gold standard for the identification and differentiation of inflammatory neuromuscular diseases. These disorders continue to constitute a diagnostic challenge due to their clinical heterogeneity, rarity and overlapping features. To establish standardized protocols for the diagnosis of inflammatory neuromuscular diseases, the development of cost-effective and widely applicable tools is crucial, especially in settings constrained by limited resources. The focus of this review is to emphasize the diagnostic value of major histocompatibility complex (MHC) and complement patterns in the immunohistochemical analysis of these diseases. We explore the immunological background of MHC and complement signatures that characterize inflammatory features, with a specific focus on idiopathic inflammatory myopathies. With this approach, we aim to provide a diagnostic algorithm that may improve and simplify the diagnostic workup based on a limited panel of stainings. Our approach acknowledges the current limitations in the field of inflammatory neuromuscular diseases, particularly the scarcity of large-scale, prospective studies that validate the diagnostic potential of these markers. Further efforts are needed to establish a consensus on the diagnostic protocol to effectively distinguish these diseases.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00401-023-02669-8.</p>", "<title>Keywords</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>" ]

[ "<title>Immunological background</title>", "<p id=\"Par4\">The MHC system is responsible for presentation of antigens. MHC class (cl.) I is present on all nucleated cells and presents immunogenic peptides salvaged from intracellular proteasomes to immune cells. Concurrently, MHC cl. II is employed by antigen-presenting cells (APC) to interact with CD4 T cells, eventually orchestrating the development of specific effector cells. Variations and functions including complexity of antigen presentation by MHC molecules have been extensively studied given their association with autoimmune, infectious and metabolic diseases among others [##REF##31627481##39##, ##REF##22076556##54##].</p>", "<p id=\"Par5\">In the context of muscle pathology, MHC positivity emerged as a histopathological feature shared across the IIM spectrum. In our experience and that of others, the majority of muscle samples derived from IIM patients stain positive for MHC cl. I [##REF##14707323##62##]. Although sarcolemmal MHC cl. I expression is highly characteristic for IIM, MHC cl. I can be observed in other muscle pathologies such as muscular dystrophy (~ 11% of cases) and others [##REF##14707323##62##]. The close association of MHC cl. I expression in IIM has fostered the view that MHC cl. I participates in the pathogenesis of the latter. The degree of MHC cl. I expression may coincide with the degree of muscle inflammation, but may also occur at distance from cellular infiltrates [##REF##35612662##68##, ##REF##32852298##87##]. Importantly, while MHC cl. I is usually not detected in healthy muscle tissue, regenerating myofibers may demonstrate sarcoplasmic MHC cl. I positivity. Further, the pattern and distribution of MHC cl. I varies considerably within different regions of fascicles and between different entities. Mechanistically, stimulation of human muscle cells by pro-inflammatory cytokines induces MHC cl. I and MHC cl. II expression allowing for antigen presentation to T cells [##REF##1352532##31##]. In a recent mouse model, muscle-specific upregulation of MHC cl. I resulted in development of myositis—partly reminiscent of disease patterns in humans [##REF##10922072##52##]. Intriguingly, autoantibodies directed against the histidyl-tRNA synthetase were detected in this model suggesting that the apparently non-specific upregulation of MHC cl. I may induce a highly specific autoimmune event as consequence. While convincing data on the association between MHC and muscle inflammation exists, our mechanistic understanding of how MHC complexes might instigate and sustain IIM is limited. MHC cl. I and MHC cl. II overlap in many characteristics such as a high level of polymorphism, a similar structural composition, a genetic location in one locus and similar functions as antigen-presenting molecules [##REF##22076556##54##]. Notably, MHC cl. II alleles emerged as convincing genetic markers for the development and severity of autoimmune diseases, including IIMs [##REF##23983088##49##, ##REF##31138531##74##]. MHC cl. II molecules are primarily expressed by APCs such as dendritic cells, macrophages and B cells. However, MHC cl. II and its upstream regulator CIITA can be induced by interferon-γ promoting the development of immune-mediated diseases [##REF##22076556##54##].</p>", "<p id=\"Par6\">Recently, sarcolemmal and capillary complement deposits were described as histopathological features of IIM with complement as a varying feature across the spectrum of IIM with ASyS, DM and IMNM as notable examples [##REF##29330311##2##]. Traditionally, complement has been regarded as a serum-effective response against microbes supporting the innate and adaptive immune responses. Over the past decade, this view has changed profoundly. It became clear that the complement system regulates immunological and metabolic functions beyond the elimination of microbial threats [##REF##37227781##56##, ##REF##31048789##69##]. While historically regarded as a linear system cumulating in the formation of the membrane attack complex (MAC) and target cell lysis, the contemporary view assumes that branches of the complement system act concurrently, thereby fine-tuning the immune response in relation to the offending threat [##REF##31048789##69##]. Extending the current knowledge of complement to IIM, its activation is thought to respond to myofiber destruction with necrotic muscle fibers often displaying deposits of terminal complement compounds [##REF##35323101##19##]. Exemplified in certain subtypes of DM, capillary endothelium is targeted by the MAC resulting in the release of proinflammatory cytokines [##REF##27190020##40##]. Inflammation is amplified by a cellular response further promoting a proinflammatory micromilieu. The release of cytokines also links complement activation to the upregulation of MHC cl. I as myofibers respond to soluble factors such as tumor necrosis factor α (TNFα) by expression of MHC cl. I [##REF##35323101##19##, ##REF##26646698##75##]. While the association of complement and muscle inflammation is convincing, it is challenging to pinpoint the pathophysiological role of complement in mediating IIMs. One theory, although controversial, suggests that autoantibodies may trigger the complement cascade via the classical complement pathway resulting in complement-mediated myofiber injury [##REF##29330311##2##]. However, this line of argumentation is challenged by a number of arguments: (1) Complement deposition is also observed in hereditary muscle disease such as muscular dystrophy (e.g., LGMDR2) [##REF##9443455##81##], thereby acting independently of any known autoantibodies. (2) Antibodies directed against structures such as the signal recognition particle (SRP) or the HMG-CoA reductase (HMGCR), as seen in IMNM, are non-specific as these antigens are ubiquitous cytoplasmic proteins expressed in several tissues. Selective muscle fiber damage would require a specific immune mechanism that directs complement specifically to muscle or capillaries in muscles, but not to all the other tissues [##REF##29582188##64##]. (3) Complement activation is also observed, albeit more rarely, in seronegative IIM such as IBM patients without detectable antibodies [##REF##35659120##55##], or seronegative IMNM [##REF##35659120##55##]. Conversely, it is conceivable that the respective autoantibodies have not yet been identified. Although complement plays a prominent role in immune mechanisms in IMNM [##REF##33093664##3##], complement inhibition did not prove effective in a recent phase 2 trial [##REF##36923454##46##].</p>", "<p id=\"Par7\">Taken together, the pathophysiological role of MHC and complement including their specific interactions in IIM requires further research efforts. Interestingly, the patterns formed by MHC and complement are consistently distinct across different IIM entities suggesting that pathophysiological characteristics might be reflected in these morphological differences.</p>", "<p id=\"Par8\">In this review, we will focus on the diagnostic value of MHC and complement patterns and how their signatures may be employed to distinguish inflammatory muscle diseases from each other and from potential differential diagnoses.</p>", "<title>MHC and complement patterns in idiopathic inflammatory myopathies</title>", "<p id=\"Par9\">The various subtypes of IIM are characterized by distinct pathomorphological presentations, which were extensively described in the past decades [##REF##31214105##10##, ##REF##32852298##87##]. Here, we will first aim to provide an overview of MHC cl. I, -II and complement patterns across IIM subtypes (Table ##TAB##0##1##). This simplified algorithm might improve diagnostic strategies in non-specialized centers or in resource-limited settings.</p>", "<title>Immune-mediated necrotizing myopathy</title>", "<p id=\"Par10\">Recently, we characterized complement activation in anti-signal recognition particle (SRP)- and anti-HMG-CoA reductase (HMGCR)-antibody positive IMNM [##REF##29330311##2##]. Focusing on complement patterns, it is noteworthy that biopsies from IMNM patients display a diffuse distribution of myofiber necrosis and regeneration with numerous fibers showing features of myophagocytosis [##REF##29330311##2##]. The sarcolemma stains positive for scattered MHC cl. I, while MHC cl. II is usually not detected on the sarcolemma. Here, complement deposits may be detected on the sarcolemma of non-necrotic myofibers with a punctuated pattern, likely derived from the classical complement pathway (Fig. ##FIG##0##1##a–i). Additionally complement is detectable sarcoplasmically in association with muscle fiber necrosis, but this is non-specific and may occur in myofiber necrosis irrespective of the underlying etiology. Conversely, a suspected case of IMNM that demonstrates MHC cl. II positivity on myofibers might hint toward an overlap myositis (see below). Interestingly, we observed a positive correlation between sarcolemmal complement deposits and muscle fiber necrosis in IMNM [##REF##29330311##2##]. This association might implicate complement in mediating muscle fiber destruction. Of note, the current morphological IMNM classification requires the regular presence of sarcolemmal complement deposits, while myofiber necrosis is excessively variable and hence unlikely to constitute a dominant histological feature [##REF##29330311##2##]. Based on our finding of considerable variation of muscle fiber necrosis, regeneration and inflammation, we suggest including the entire histopathological features of IMNM to capture the full range of disease presentation, particularly in those patients without detectable autoantibodies [##REF##33093664##3##, ##REF##29221629##5##, ##REF##29582188##64##]. These criteria were recently employed for a phase 2 study of IMNM investigating the C5 inhibitor zilucoplan [##REF##36923454##46##].</p>", "<title>Inclusion body myositis</title>", "<p id=\"Par11\">Sarcolemmal MHC cl. I, and -cl. II are consistently detected in IBM, and conversely the absence of MHC staining on sarcolemma is a strong argument against the diagnosis of IBM. MHC patterns are distinct from the above-mentioned patterns in IBM as they are not restricted to the perifascicular regions. Instead, both MHC cl. I and MHC cl. II are found in close proximity to areas of endomysial inflammation with intensities increased where lymphomonocytic cell infiltrates are particularly prominent (Fig. ##FIG##0##1##j, k) [##REF##30837708##33##, ##REF##35659120##55##]. In contrast, complement deposition is non-specific and may be restricted to areas of endomysial fibrosis, while sarcolemma or capillaries do not consistently stain positive for complement (Fig. ##FIG##0##1##l) [##REF##35659120##55##].</p>", "<title>Dermatomyositis</title>", "<p id=\"Par12\">While certain histopathological features are conserved across DM subtypes, the specific presentation of each subtype is highly characteristic for the associated autoantibodies. This concept might be best exemplified by DM mediated by antibodies against transcription intermediary factor 1 gamma (TIF1γ). Here, on a background of perifascicular fiber atrophy, MHC cl. I is strongly detected on the sarcolemma and the sarcoplasm as well, exhibiting a gradient toward the centrofascicular region in many fascicles [##REF##3288082##8##, ##REF##25644398##23##] (Fig. ##FIG##1##2##a). In contrast, MHC cl. II is negative on the sarcolemma, but positive on the many macrophages in the peri- and the endomysium and also positive physiologically on capillaries (Fig. ##FIG##1##2##b). Terminal complement is prevailing on capillaries rather than on the sarcolemma of myofibers, especially in severely affected muscle regions associated with capillary loss (Fig. ##FIG##1##2##c), and prominent vascular endothelial growth factor (VEGF) signaling [##REF##34043263##66##]. Together, these features create a highly specific pattern, characteristic of anti-TIF1γ-antibody mediated DM. These characteristics are associated with the presence of coincident cancer in 40–50% of adult cases [##REF##27343066##34##, ##REF##31791867##45##, ##REF##31101462##91##], whereas juvenile anti-TIF1γ-antibody DM is unlikely to coincide with cancer.</p>", "<p id=\"Par13\">A different pattern is observed in DM mediated by anti-Mi-2-antibodies. Here, the pathological perifascicular pattern consists of atrophic fibers in perifascicular regions, interleaved with myofiber necrosis. The latter may also occur in the centrofascicular regions and is not strictly confined to the perifascicular area. MHC cl. I is strongly positive on the sarcolemma of perifascicular myofibers with a gradient toward the centrofascicular region (Fig. ##FIG##1##2##d), while MHC cl. II is only weakly detected on the sarcolemma on sparse perifascicular muscle fibers while physiologically positive on capillaries. C5b-9 may be observed on the sarcolemma predominantly on atrophic muscle fibers of the perifascicular area but not significantly on capillaries. As such, the sarcoplasm of necrotic myofibers often stains positive for complement in anti-Mi2-antibody DM (Fig. ##FIG##1##2##e) [##REF##31214105##10##, ##REF##35942671##85##].</p>", "<p id=\"Par14\">In anti-nuclear matrix protein 2 (NXP2)-antibody positive DM, MHC cl. I is characteristically detected with perifascicular positivity on sarcolemmal membranes and occasionally on entire fascicles, while MHC cl. II is absent from the sarcolemma (Fig. ##FIG##1##2##g, h). C5b-9 may be detected on capillaries as well as on the sarcolemma of myofibers (Fig. ##FIG##1##2##i). A rare but unique feature is the presence of regional muscle fiber necrosis affecting parts of an entire fascicle encountered in some cases of anti-NXP2-antibody DM (not shown here) [##REF##31214105##10##, ##REF##35942671##85##].</p>", "<p id=\"Par15\">Anti-melanoma differentiation-associated gene 5 (MDA5)-antibody-mediated DM displays milder affection of skeletal muscle tissues, and the perifascicular pattern is usually only found in some areas of the specimen. MHC cl. I may be detected on the sarcolemma of some but not all fibers (Fig. ##FIG##1##2##j), while sarcolemmal MHC cl. II is usually not observed (Fig. ##FIG##1##2##k). Complement deposits either on scarce sarcolemmal membranes or on capillaries are only rarely encountered (Fig. ##FIG##1##2##l) [##REF##26806087##4##, ##REF##31214105##10##, ##REF##35942671##85##].</p>", "<p id=\"Par16\">Finally, the pattern of anti-small ubiquitin-like modifier activating enzyme (SAE)-antibody DM has not been systematically characterized and is subject of current research [##REF##37010495##22##, ##REF##32852298##87##]. Our own unpublished data point toward a pattern that is similar to the one described in anti-MDA5-antibody DM with mild MHC cl. I (Fig. ##FIG##1##2##m), absence of MHC cl. II on the sarcolemma of perifascicular myofibers (Fig. ##FIG##1##2##n), and relatively scarce complement deposits on sarcolemma and on capillaries (Fig. ##FIG##1##2##o).</p>", "<p id=\"Par17\">Broadly, complement is more frequently observed on capillaries than on the sarcolemma of myofibers in DM. The complement deposits on capillaries correlate with muscle damage characteristic of DM and capillary damage can be substantiated by ultrastructural visualization of tubuloreticular inclusions in vascular endothelium [##REF##25339355##6##, ##REF##31214105##10##].</p>", "<p id=\"Par18\">Finally, while this review is focused on patterns of complement and MHC, it should be highlighted that the interferon 1 response has emerged as a driver of DM pathogenesis, likely contributing to the characteristic muscle damage and capillary involvement seen in this disease [##REF##20425524##32##]. The binding of the type 1 interferons to their target receptors induces the transcription and translation of a gene signature consisting of type 1 interferon-inducible genes, such as myxovirus resistance protein A (MxA) (Supplemental Fig. 1). Following this line of argumentation, recent studies highlighted the diagnostic value of MxA staining by immunohistochemistry reflecting the underlying type 1 interferon response in DM [##REF##30267437##92##, ##REF##28039312##93##]. Indeed, two comparative studies recently demonstrated that the sensitivity and specificity of MxA to distinguish between DM and other forms of IIM range between 71% and 77%, and 98 and 100%, respectively [##REF##30267437##92##, ##REF##28039312##93##]. This renders MxA staining particularly valuable for improving the diagnostic confidence when differentiating between anti-Mi2-antibody mediated DM and cases of ASyS as these entities may closely resemble each other.</p>", "<title>Antisynthetase syndrome myositis</title>", "<p id=\"Par19\">Conversely, the pathomorphology of ASyS is largely consistent across the currently recognized antibody-subtypes (Fig. ##FIG##2##3##) [##REF##35612662##68##, ##REF##36882048##83##]. Recent research suggested two additional ASyS-associated antibodies (anti-lys, anti-val) directed against transfer-RNA [##REF##36193992##77##, ##REF##36572507##97##]. This observation is in line with recent data from our laboratory reporting only relatively subtle differences of inflammatory molecules on the molecular level across ASyS antibody groups [##REF##35612662##68##]. ASyS is identified by a perifascicular pathology characterized by myofiber necrosis aligned with both atrophic and hypertrophic muscle fibers differing from perifascicular atrophy patterns in DM. Here, MHC cl. I and MHC cl. II are both detected on the sarcolemma of myofibers with a decreasing gradient of intensity toward the centrofascicular regions (Fig. ##FIG##2##3##a, d, g). Specifically, MHC cl. II might more characteristically highlight this pattern as compared to MHC cl. I (Fig. ##FIG##2##3##b, e, h). In respect to complement, C5b-9 is frequently detected on the sarcolemma of perifascicular fibers, but only rarely on capillaries, and the pattern of perifascicular necrosis visualized by sarcoplasmic C5b-9 is variably intense from mild (Fig. ##FIG##2##3##c), intermediate (Fig. ##FIG##2##3##f) to strong (Fig. ##FIG##2##3##i) across ASyS samples [##REF##25746564##82##, ##REF##36882048##83##].</p>", "<title>Eosinophilic myofasciitis</title>", "<p id=\"Par20\">Eosinophilic myofasciitis (EF), also called Shulman syndrome, is an entity that affects the muscle fascia interface morphologically, and clinically follows a highly characteristic appearance that differentiates this disease from DM and ASyS. EF is not associated with known autoantibodies. MHC cl. I and cl. II are typically positive on the sarcolemma of perifacicular myofibres adjacent to the epimysial fascia (Fig. ##FIG##3##4##a, b), while the deeper layers of the muscle tissue show much less or even absence of any sarcolemmal staining [##REF##36130069##63##]. Complement is largely absent on the sarcolemma or capillaries of diseased muscle (Fig. ##FIG##3##4##c). The detection of eosinophils in the fascia may help distinguishing EF from other immune-mediated fasciitis with associated inflammatory myopathy.</p>", "<title>Immune checkpoint inhibitor-related myositis</title>", "<p id=\"Par21\">In immune checkpoint inhibitor-related (ir) myositis, the currently recognized pattern is muscle fiber necrosis with varying degrees of endomysial macrophage infiltrates and myophagocytosis [##REF##36815259##76##]. Here, lymphocytes, particularly CD8 T cells, are abundantly found in the endomysium. MHC cl. I and cl. II are frequently detected with different patterns and distribution reported (Fig. ##FIG##3##4##d, e). Systematic studies of complement are currently lacking. Still, necrotic myofibers are frequently encountered in ir-myositis and are highlighted by sarcoplasmic C5b-9 (which is useful but not disease-specific) (Fig. ##FIG##3##4##f) [##REF##30089619##90##]. The recent detection of three distinct subtypes of ir-myositis (ICI-DM with DM-like features; ICI-MYO1 with abundant inflammation and myocarditis; ICI-MYO2 with necrosis but with little inflammatory features and without myocarditis), revealed that ICI-MYO1 presenting with myocarditis and excessive inflammation had the worst prognosis [##REF##36801811##65##]. It should be noted that ir-myositis associated with myocarditis should be treated aggressively given its high mortality [##REF##36815259##76##].</p>", "<title>Overlap myositis</title>", "<p id=\"Par22\">This heterogeneous group of diseases is clinically characterized by overlap of rheumatological diseases with inflammation of skeletal muscles. Myositis-associated antibodies include anti-Ku, anti-PM/Scl, anti-U1-RNP-antibodies among others. Although heterogeneous, in our experience, these entities often display MHC cl. I and often cl. II on the sarcolemma, pronounced around endomysial infiltrates of immune cells, and sometimes even with a perifascicular distribution, but in contrast to the above-mentioned entities (DM and ASyS) complement deposits are only detected on the sarcolemma of single myofibers without any specific pattern. Although recent focus has been on the morphological description of the IIM sensu<italic> strictu</italic>, overlap myositis presenting with myositis-associated antibodies regularly demonstrate MHC cl. I and cl. II positivity on the sarcolemma, while the quantity and distribution of invading immune cell vary substantially and so does the capillary pathology [##REF##33864496##80##].</p>", "<p id=\"Par23\">Recently, two groups independently described the histopathological features of myositis in patients with systemic sclerosis, thereby raising the concepts of scleromyositis and minimal myositis with capillary pathology (MMCP) [##REF##35894636##25##, ##REF##34115197##26##, ##REF##33864496##80##]. Here, MHC cl. I is detected in a focal pattern linked to areas of endomysial inflammation (Fig. ##FIG##3##4##g), while MHC cl. II is only rarely found on individual myofibers or absent (Fig. ##FIG##3##4##h). While capillaries are enlarged and often positive for MHC cl. I and cl. II in many areas of the specimen, complement deposition is non-specifically found on myofibers and capillaries (Fig. ##FIG##3##4##i).</p>", "<p id=\"Par24\">Additionally, myopathy may also develop in patients with systemic lupus erythematosus (SLE) [##REF##32281474##13##, ##REF##35351810##88##]. About 6% of patients may encounter myopathy during the course of their disease. Histopathologically, SLE myopathy may present with areas of myofiber necrosis and regeneration. Perimysial or endomysial inflammation is found in approximately a third of patients [##REF##32281474##13##, ##REF##35351810##88##]. Importantly, SLE myopathy may mimic the clinical and histopathological manifestation of DM and IMNM constituting a diagnostic challenge (Fig. ##FIG##3##4##j, k, l). The overlap between SLE myopathy or DM might be due to a shared interferon type 1 response as pathophysiological driver [##REF##21859344##24##]. As such, integration of clinical characteristics, including the antibody status and SLE-specific symptoms, with the histopathological profile is important to effectively distinguish between SLE myopathy and DM.</p>", "<title>Hereditary myopathies</title>", "<p id=\"Par25\">To provide a broader picture of MHC and complement in muscle pathologies, we will also describe patterns in certain hereditary myopathies, aiming to cover relevant entities, since this endeavor has not been undertaken systematically in many of them. Limb-girdle muscular dystrophies (LGMD) are hereditary myopathies, which variably display inflammatory features. As such, sarcolemmal complement deposition is a striking finding on numerous myofibers in dysferlin-related limb-girdle muscular dystrophy R2 (LGMDR2) [##REF##35135626##9##, ##REF##27490667##95##]. Intriguingly, the amount of sarcolemmal complement detected in LGMDR2 may even exceed that in certain entities of IIM. Conversely, MHC cl. I and MHC cl. II staining is only mild or absent on occasional myofibers surrounding lymphocytic infiltrates [##REF##35135626##9##]. In biopsies from patients with limb-girdle muscular dystrophy R12 (LGMDR12) due to <italic>ANO5</italic> gene mutations, muscle inflammation may also be observed as evidenced by myophagocytosis and focal but not diffusely distributed muscle fiber necrosis and regeneration accompanied by scarce lymphocytes. Sarcolemmal MHC cl. I positivity is very mild, while sarcolemmal complement is sparsely detected on single myofibers [##REF##36157496##14##]. In contrast, in muscle biopsies obtained from patients with LGMDR9 related to <italic>FKRP</italic> mutations, we described a focal accumulation of sarcolemmal MHC cl. I, and MHC cl. II on specific myofibers associated with myofiber regeneration. Complement deposits were not found in these biopsies [##REF##33973272##37##]. Sparse sarcolemmal deposits of complement and focal MHC cl. I were also reported in LGMDR1 related to <italic>CAPN3</italic> mutations [##REF##35135626##9##]. In children diagnosed with inflammatory myopathy mor than half of them showed mutations in <italic>LMNA,</italic> highlighting that diagnosis of both hereditary and acquired myopathy with inflammation may be challenging [##REF##21632249##38##].</p>", "<p id=\"Par26\">In respect to Duchenne muscular dystrophy (DMD), specific inflammatory features emerged as characteristic alterations on muscle biopsy tissues [##REF##2857418##7##]. As such, DMD muscle fibers may contain epitopes targeted by autoreactive T cells with sarcolemmal MHC cl. I detected on myofibers [##REF##20925545##47##]. Following this line of argumentation, there is an ongoing discussion regarding the diagnostic significance of MHC cl. I detection. Currently, a systematic study of muscular dystrophies with focus on MHC and complement remains an unmet need. Notwithstanding, the observed inflammatory features provide an intriguing link between genetic muscle disorders and associated immunopathologies.</p>", "<title>Sporadic late onset myopathy</title>", "<p id=\"Par27\">Muscle biopsies from sporadic late onset nemaline myopathy (SLONM) patients are characterized by the presence of nemaline rods in the sarcoplasm of myofibers. Here, sarcolemmal MHC cl. I is observed in ~ 66% of cases, while only a marginal percentage of patients demonstrate MHC cl. II [##REF##34043258##86##]. Complement deposits were found on both capillaries and the sarcolemma at varying quantities, irrespective of an association with monoclonal gammopathies [##REF##34043258##86##].</p>", "<title>Autophagic vacuolar myopathies</title>", "<p id=\"Par28\">Autophagic vacuolar myopathies (AVM) are a heterogeneous group of muscle disorders that share autophagic vacuoles as pathomorphological hallmark [##REF##33393119##53##]. They share defective autophagy as common feature and include hereditary diseases, such as Pompe disease, Danon disease or X-linked myopathy with excessive autophagy and very rare disorders such as valosin-containing protein (VCP)-associated myopathy or matrin-3-related distal myopathy. Concurrently, acquired myopathies such as chloroquine/hydroxychloroquine toxicity may also present with autophagic vascular features [##REF##25644398##23##, ##REF##32419263##44##, ##REF##25154462##50##]. The interplay between disrupted autophagy mechanisms and the consequent buildup of cellular debris constitutes a central aspect of the pathophysiology of these disorders. Despite their rarity, AVMs constitute a diagnostic challenge as they may exhibit deposition of C5b-9 along the sarcolemma and within vacuoles, as well as sarcolemmal MHC cl. I staining on myofibers [##REF##24488655##18##, ##REF##25644398##23##]. Currently, there is a knowledge gap regarding the distribution of MHC class II in AVMs. Although the identification of sarcolemmal C5b-9 and MHC cl. I suggest an inflammatory muscle pathology, the diagnosis should be approached with caution if cytoplasmic autophagic vacuoles are also present, particularly when coupled with clinical manifestations like cardiomyopathy and a gradually progressive disease trajectories.</p>", "<title>Search strategy and study identification</title>", "<p id=\"Par29\">For the algorithm proposed in this manuscript, we aimed to systematically assess the available literature. Our aim was to mitigate bias and consolidate the available research to underpin a strategy employing MHC and complement staining patterns. The study's inclusion and exclusion criteria adhered to the guidelines outlined in the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) [##REF##33782057##61##], as depicted in Fig. ##FIG##4##5##.</p>", "<title>Eligibility criteria</title>", "<p id=\"Par30\">We considered all types of primary research including peer-reviewed publications, reports and posters. Preprints, commentaries, editorials, letters and book chapters were excluded. Only papers in English language were considered.</p>", "<title>Context</title>", "<p id=\"Par31\">Study inclusion required that the population consists of at least of one subtype of IIM and diseased or non-diseased controls. As outcome measure, we assessed histopathological descriptions of major histocompatibility complex (MHC) or terminal complement (C5b-9).</p>", "<title>Search strategy</title>", "<p id=\"Par32\">We identified relevant studies by searching the medical databases MEDLINE (PubMed), Web of Science and Google Scholar. The following strings were used as query: (1) (myositis OR idiopathic inflammatory myopathy) AND (major histocompatibility complex OR MHC) NOT review NOT animal study; (2) (myositis OR idiopathic inflammatory myopathy) AND complement NOT review NOT animal study. Our search was conducted on 10 October 2023. We used no publication date restrictions.</p>", "<title>Study extraction</title>", "<p id=\"Par33\">Records identified after applying our search strategy were uploaded into reference manager Zotero (v6.0.27) and duplicates were removed. Titles and abstracts were screened by CN and CBS. Full text articles were obtained for abstracts that needed to be included or that appeared unclear. Studies without controls were excluded.</p>", "<p id=\"Par34\">With this approach, we identified a total of 29 studies that provided data on the histomorphological appearance of MHC cl. I and II as well as terminal complement in IIMs. A shared limitation to the majority of studies was a lack of controls as well as comparative statistical approaches to determine diagnostic specificity and sensitivity. It is crucial to acknowledge these limitations when interpreting the proposed algorithm. Furthermore, these constraints underscore the pressing need for systematic, prospective assessments in the search for effective diagnostic markers for IIMs.</p>", "<title>A diagnostic algorithm based on MHC and complement patterns for IIM</title>", "<p id=\"Par35\">MHC cl. I and -II and complement patterns differ across IIM entities. Here, we propose that MHC cl. I and -II in combination with complement may be employed to define muscle pathologies following a simplified algorithm (Fig. ##FIG##5##6##), allowing for a broad but sufficient subclassification that is required for current therapeutic approaches [##REF##37158055##16##].</p>", "<p id=\"Par36\">It is important to highlight that the proposed approach is founded on the limited scope of existing research. The rarity and heterogeneity of IIMs constitute a challenge for the conduction of prospective, large-scale investigations aimed at interrogating the specificity and sensitivity of diagnostic markers. The algorithm outlined in this manuscript is intended to provide a framework for future studies and to provide muscle pathologists with clues that can enhance diagnostic confidence, even when operating with limited data or resources. Further studies are imperative to provide the necessary evidence for a conclusive diagnostic algorithm and with this review we hope to stimulate such research.</p>", "<p id=\"Par37\">Here, we propose to include MHC cl. I staining in the diagnostic work-up of IIMs as early step in order to distinguish established subtypes of this disease spectrum. A diffuse or patchy pattern of MHC cl. I suggests IBM or IMNM as underlying pathology, while a perifascicular pattern is observed in cases of ASyS or DM.</p>", "<p id=\"Par38\">Subsequently, MHC cl. II staining enables further differentiation. MHC cl. II appears diffuse and strong in IBM, while IMNM is usually negative for MHC cl. II. Concurrently, ASyS features a strong perifascicular MHC cl. II pattern, while MHC cl. II typically appears negative or weakly positive, such as in cases of anti-Mi2-antibodies, in DM.</p>", "<p id=\"Par39\">To improve diagnostic confidence, staining for C5b-9 may be employed. Here, IBM presents a negative or non-specific staining for C5b-9. IMNM, in contrast, features a sarcolemmal C5b-9 pattern with fine punctuation of a variable number of non-necrotic myofibers. ASyS demonstrates a perifascicular pattern of C5b-9 staining of myofibers. A similar pattern might be observed in anti-Mi2-antibody positive DM, constituting a diagnostic challenge. To resolve this challenge, additional staining for MxA is advised, given the high sensitivity and specificity of this marker in DM. Conversely, ASyS usually does not feature MxA positivity. Other serological groups of DM feature a capillary and to a lesser degree sarcolemmal pattern of C5b-9 in anti-NXP2-antibody and even more specifically anti-TIF1γ-antibody positive DM. In anti-MDA5-antibody and anti-SAE-antibody positive DM, C5b-9 staining on myofibers or capillaries is only rarely observed. Taken together, MHC cl. I, cl. II and complement (C5b-9) patterns may suggest an IIM subtype based on histopathological analysis. This assumption should be interpreted in the context of clinical and serological information.</p>", "<p id=\"Par40\">For further analysis, p62 may be useful to highlight autophagy in muscle pathology. This staining may be particularly useful to differentiate between the fine granular and homogenous p62 pattern seen in IMNM linked to defective chaperone-mediated autophagy [##REF##31376301##29##], and the pattern seen in IBM characterized by coarse, vacuolar staining of p62 in subsarcolemmal or perinuclear regions [##REF##25579751##12##] (Supplemental Fig. 2a, b). In DM and ASyS, p62 is detected in a non-specific pattern.</p>", "<title>Complement in myasthenia gravis</title>", "<p id=\"Par41\">Beyond the study of IIM, our current knowledge of complement also extends to other inflammatory neuromuscular disorders, such as myasthenia gravis (MG). Complement deposition was first described by Andrew Engel and the late Kiichi Arahata at the neuromuscular junction (NMJ) [##REF##3318619##27##]. Since then, complement emerged as a pathophysiological hallmark in MG driving antibody-mediated destruction of the NMJ. The pathogenic role of complement is underlined by the clinical efficacy of complement inhibitors as demonstrated in recent phase 3 trials studying MG patients [##REF##29066163##36##, ##UREF##1##96##]. Beyond serving as target for therapeutic strategies, complement might also serve as important diagnostic marker in MG. To understand how complement might serve diagnostic purposes, we shall first discuss the antibody patterns present in MG. Anti-acetylcholine receptor (AChR)-antibodies constitute the major serogroup of MG accounting for approximately 85% of cases [##REF##35246490##57##, ##REF##35413850##58##]. Anti-AChR-antibodies are primarily composed of immunoglobulin G1 (IgG1) and a minor proportion of IgG3 [##REF##29089519##78##]. Anti-muscle specific kinase (MuSK)-antibodies account for approximately 5% of patients and are predominantly of the IgG4 subtype [##REF##32793097##72##]. Less than 3% of MG patients harbor anti-low‐density lipoprotein receptor-related protein 4 (LRP4)-antibodies. Most anti-LRP4-antibodies belong to the IgG1 subclass [##REF##32483837##71##]. The remaining (10–18%) of MG patients are considered (triple) seronegative (3SN). Although not without contestation, IgG4 antibodies are suggested to not induce complement activation, while IgG1 antibodies (and IgG2 and IgG3 to a lesser extent) trigger the classical complement cascade [##REF##35323101##19##, ##REF##25368619##94##]. Following this line of thought, it seems intuitive that antibodies belonging to the IgG1 subclass trigger complement activation and damage to the NMJ. Exemplified by anti-AChR-antibody MG, this concept has been validated on the histopathological level [##REF##32157386##35##] and by the clinical efficacy of complement inhibitors [##UREF##1##96##]. In contrast, complement deposition can only be detected in a minority of anti-MuSK-antibody MG patients on a histopathological level [##REF##15668981##79##]. Assessing the effect of complement inhibition on the course of anti-MuSK-antibody MG is difficult as conclusive data from clinical trials are currently lacking [##REF##30767274##51##].</p>", "<p id=\"Par42\">From a diagnostic viewpoint, the detection of pathogenic antibodies in conjunction with characteristic clinical presentation often enables accurate diagnosis in seropositive patients. However, seronegative MG patients can constitute a diagnostic and therapeutic challenge, particularly if the clinical phenotype is inconclusive or if patients are therapy-refractory to basic therapy, [##UREF##0##17##, ##REF##32157386##35##]. To improve our understanding of seronegative MG, we recently studied external intercostal muscle biopsies from 13 3SN MG patients [##REF##32157386##35##]. We identified CD56⁺ endplates and detected the presence of C5b-9 with variable intensity on all analyzed muscle specimens. Intriguingly, C5b-9 colocalized with IgG1 as well as C1q [##REF##32157386##35##]. Together, these findings indicate that the currently unknown antibodies in 3SN MG might be of the IgG1 subclass mediating postsynaptic damage of the NMJ by inducing the classical complement pathway. Further studies are needed to provide the groundwork for therapeutic targeting of complement in seronegative MG. Still, as the presence of complement at the endplate is a highly specific finding for MG, histopathological analysis of (intercostal) muscle biopsies is a valuable approach to combat diagnostic uncertainty in seronegative MG. However, as muscle biopsies are invasive and therefore not a routine approach in MG, the additional diagnostic value must be assessed individually.</p>", "<title>Concluding remarks and future directions</title>", "<p id=\"Par43\">Histopathological analysis remains the gold standard for diagnosis in many inflammatory neuromuscular disorders. To improve the availability of accurate histopathology, standardized and cost-effective workflows are required. These workflows should incorporate a straightforward algorithm that can be applied broadly.</p>", "<p id=\"Par44\">The aim of this review was to highlight the diagnostic value of interpreting MHC and complement patterns in inflammatory muscle pathologies and relevant differential diagnoses. We suggest that MHC and complement can serve as a readily available set of IHC stains that can be used as biomarkers for disease classification. Minimizing the amount of required staining steps could be valuable in resource-limited settings and for design of diagnostic algorithms. It is important to highlight that clinical and laboratory information as well as conventional histology are needed to draw accurate conclusions from IHC. Concurrently, we also emphasize that while a biomarker might hold diagnostic significance, it does not necessarily imply direct pathophysiological importance—a point exemplified in the context of complement activation in IMNM. While complement deposition is a frequent feature of IMNM [##REF##29330311##2##, ##REF##35524238##100##], treatment with a C5 inhibitor did not appear effective [##REF##36923454##46##], suggesting that complement activation may be a secondary feature to muscle fiber necrosis. This concept is reinforced by hereditary myopathies, such as LGMDR2 myopathy [##REF##14512171##15##, ##REF##33973272##37##], where complement activation accompanies muscle fiber necrosis and regeneration. This association hints at complement involvement potentially being a nonspecific feature following muscle injury. Thus, while complement markers can serve as diagnostic indicators, interpreting their pathophysiological significance requires careful consideration. To test the sensitivity and specificity of MHC and complement patterns in a diagnostic algorithm, prospective and adequately powered studies are required. We believe this approach to be useful to determine the necessary IHC steps required for accurate diagnosis when moving toward a standardized workflow for muscle pathologies.</p>", "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>MHC class I, -II, and complement patterns in immune-mediated necrotizing myopathy and inclusion body myositis. In immune-mediated necrotizing myopathy (IMNM), the sarcolemma of myofibers is frequently positive for MHC class I in a diffuse distribution pattern (<bold>a, d, g</bold>). MHC class II is consistently negative on the myofiber sarcolemma (<bold>b, e, h</bold>). Macrophages consistently demonstrate diffuse MHC class II positivity in the endomysium. Capillaries are physiologically positive for MHC class I and MHC class II. In response to inflammation, MHC levels are typically upregulated. This phenomenon is non-specific across IIMs and applies to all figures shown in this manuscript. Terminal complement (C5b-9) is often positive on the sarcolemma of non-necrotic fibers in IMNM with a fine punctuated pattern (<bold>c, f, i</bold>). In inclusion body myositis (IBM), MHC class I and II are positive in a strong and diffuse pattern on the sarcolemma (and the sarcoplasm) without perifascicular staining pattern (<bold>j, k</bold>). C5b-9 may be detected non-specifically on fibroblasts, but not on the capillaries or the sarcolemma of myofibers in the majority of IBM cases (<bold>l</bold>). (<bold>c</bold>, <bold>f</bold>, <bold>i</bold>, <bold>l</bold>) are 600× magnification to exemplify the punctuated pattern in IMNM; all other images are 200 × magnification. <italic>IIM</italic> idiopathic inflammatory myopathy; <italic>MHC</italic> major histocompatibility complex</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>MHC class I, -II, and complement patterns in dermatomyositis subtypes. In dermatomyositis (DM), the sarcolemma of myofibers is positive for MHC class I in a strong perifascicular to a weak centrofascicular distribution (<bold>a, d, g, j, m</bold>). MHC class II is consistently negative on the sarcolemma of myofibers (<bold>b, h, k, n</bold>) with the exception of anti-Mi2-antibody DM (<bold>e</bold>). Here, myofibers in the perifascicular region are infrequently and relatively weakly positive for MHC class II. Terminal complement (C5b-9) is positive on the capillaries in perifascicular regions in anti-TIF1γ-antibody and anti-NXP2-antibody DM (<bold>c, i</bold>). C5b-9 is also found on the sarcolemma of non-necrotic myofibers in perifascicular regions in anti-Mi2-antibody DM (<bold>f</bold>). In anti-MDA5-antibody and anti-SAE-antibody DM, C5b-9 may be positive on individual capillaries or the sarcolemma of few myofibers without a specific pattern (<bold>l, o</bold>). (Original magnification × 200). <italic>MDA5</italic> melanoma differentiation-associated protein 5; <italic>MHC</italic> major histocompatibility complex; <italic>NXP2</italic> nuclear matrix protein 2; <italic>SAE</italic> small ubiquitin-like modifier-1 activating enzyme; <italic>TIF1γ</italic> transcriptional intermediary factor 1 gamma</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>MHC class I, -II, and complement patterns in subtypes of anti-synthetase syndrome. In anti-synthetase syndrome (ASyS), the sarcolemma of myofibers is often positive for MHC class I (<bold>a, d, g</bold>) and class II (<bold>b, e, h</bold>) in a strong perifascicular to weak centrofascicular pattern. Terminal complement (C5b-9) is positive on the sarcolemma of non-necrotic myofibers predominantly in the perifascicular region (<bold>c, f, i</bold>). A variable number of myofibers shown sarcoplasmic staining for C5b-9 highlighting the perifascicular necrotizing pattern of ASyS. (Original magnification × 200). <italic>MHC</italic> major histocompatibility complex</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>MHC class I, -II, and complement patterns in eosinophilic fasciitis, immune checkpoint inhibitor-related myositis, scleromyositis and systemic lupus erythematosus. In eosinophilic fasciitis, myofibers are positive for MHC class I on the sarcolemma, while MHC class II is observed with a perifascicular (strong) and centrofascicular (weak) pattern (<bold>a, b</bold>). Terminal complement (C5b-9) is negative on the sarcolemma and on capillaries, even in proximity to areas of inflammation (<bold>c</bold>). Immune checkpoint inhibitor-related myositis (ir-myositis) is characterized by strong positivity of MHC class I and II in areas of inflammation, hence with a focal pattern on the sarcolemma (<bold>d, e</bold>). C5b-9 is observed on necrotic myofibers in a non-specific pattern, but not on capillaries (<bold>f</bold>). In scleromyositis, MHC class I is positive on myofibers around inflammation (<bold>g</bold>). MHC class II is often negative and only observed in few cases sarcolemmaly (<bold>h</bold>). C5b-9 is detected on individual thickened capillary walls with a focally distributed pattern (<bold>i</bold>). In systemic lupus erythematosus (SLE), MHC class I positive myofibers are detectable with a characteristic (“chessboard”) pattern across entire fascicles (<bold>j</bold>) and MHC class II is highlighting myofibres adjacent to the perimysium (<bold>k</bold>). C5b-9-positive complement deposits are detected throughout fascicles and do not accumulate in perifascicular areas. Of note, (<bold>l</bold>) dense lymphomonocytic infiltrates may accumulate in the endomysium but invasion of myofibers is not visible. (Original magnification × 200 for all photomicrographs). <italic>MHC</italic> major histocompatibility complex</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Preferred reporting items for systematic reviews and meta-analyses (PRISMA) flowchart describing the study search and inclusion process for this review. We conducted two separate searches for major histocompatibility complex and for complement patterns. Duplicate studies across these two searches were only included in the upper flowchart</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Proposed algorithm for distinguishing inflammatory idiopathic myopathies. To distinguish inclusion body myositis (IBM), immune-mediated necrotizing myopathy (IMNM), anti-synthetase syndrome (ASyS) and dermatomyositis (DM), we propose to stain for MHC class I, MHC class II and terminal complement (C5b-9). By observing these patterns, a panel of only three stainings may suggest a diagnosis. For further analysis, one may use p62 as marker of autophagy and MxA as a marker for a type I interferon response indicating DM as likely diagnosis. <italic>MDA5</italic> melanoma differentiation-associated protein 5; <italic>MHC</italic> major histocompatibility complex; <italic>MxA</italic> myxovirus resistance protein A; <italic>NXP2</italic> nuclear matrix protein 2; <italic>SAE</italic> small ubiquitin-like modifier-1 activating enzyme; <italic>TIF1γ</italic> transcriptional intermediary factor 1 gamma</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Overview of MHC class I, MHC class II, and complement in inflammatory muscle diseases</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Disease</th><th align=\"left\">MHC class I</th><th align=\"left\">MHC class II</th><th align=\"left\">Complement (C5b-9)</th><th align=\"left\">Ref</th></tr></thead><tbody><tr><td align=\"left\" colspan=\"5\">Idiopathic inflammatory myopathies</td></tr><tr><td align=\"left\"> Immune-mediated necrotizing myopathy (SRP and HMGCR)</td><td align=\"left\"> + /++ </td><td align=\"left\">−</td><td align=\"left\"> + (sarc)</td><td align=\"left\">[##REF##29330311##2##, ##REF##33093664##3##, ##REF##23058368##67##, ##REF##27147697##98##, ##REF##35524238##100##]</td></tr><tr><td align=\"left\"> TIF1γ dermatomyositis</td><td align=\"left\"> +++ (pf)</td><td align=\"left\">−</td><td align=\"left\"> ++ (cap)</td><td align=\"left\">[##REF##31791867##45##, ##REF##34873015##84##]</td></tr><tr><td align=\"left\"> Mi2 dermatomyositis</td><td align=\"left\"> ++ (pf)</td><td align=\"left\"> + </td><td align=\"left\"> + (sarc)</td><td align=\"left\">[##REF##31791867##45##, ##REF##32758284##59##, ##REF##34873015##84##]</td></tr><tr><td align=\"left\"> NXP2 dermatomyositis</td><td align=\"left\"> +++ (pf)</td><td align=\"left\"> +/− </td><td align=\"left\"> ++ (cap)</td><td align=\"left\">[##REF##31791867##45##, ##REF##34873015##84##]</td></tr><tr><td align=\"left\"> MDA5 dermatomyositis</td><td align=\"left\"> + </td><td align=\"left\">−</td><td align=\"left\"> + (cap)</td><td align=\"left\">[##REF##31791867##45##, ##REF##34873015##84##]</td></tr><tr><td align=\"left\"> SAE dermatomyositis</td><td align=\"left\"> + </td><td align=\"left\"> +/− </td><td align=\"left\"> +/− (cap)</td><td align=\"left\">[##REF##31791867##45##, ##REF##34873015##84##, ##REF##35942671##85##]</td></tr><tr><td align=\"left\"> Anti-synthetase syndrome</td><td align=\"left\"> ++ (pf)</td><td align=\"left\"> ++ (pf)</td><td align=\"left\"> + (sarc)</td><td align=\"left\">[##REF##25339355##6##, ##REF##28586844##60##, ##REF##35612662##68##, ##REF##36882048##83##]</td></tr><tr><td align=\"left\"> Inclusion body myositis</td><td align=\"left\"> +++ </td><td align=\"left\"> +++ </td><td align=\"left\">−</td><td align=\"left\">[##REF##23343957##20##, ##REF##29780824##21##, ##REF##30837708##33##, ##REF##14707323##62##, ##REF##31143183##73##]</td></tr><tr><td align=\"left\"> Overlap myositis*</td><td align=\"left\"> + </td><td align=\"left\"> + </td><td align=\"left\">−</td><td align=\"left\">[##REF##31214105##10##, ##REF##29728522##41##, ##REF##22391471##70##]</td></tr><tr><td align=\"left\" colspan=\"5\">Other immune-mediated muscle diseases</td></tr><tr><td align=\"left\"> Eosinophilic fasciitis</td><td align=\"left\"> + </td><td align=\"left\"> + </td><td align=\"left\">−</td><td align=\"left\">[##REF##36130069##63##, ##REF##12913939##89##]</td></tr><tr><td align=\"left\"> Immune checkpoint inhibitor-related myositis</td><td align=\"left\"> + </td><td align=\"left\"> ++ </td><td align=\"left\">−</td><td align=\"left\">[##REF##32535094##1##, ##REF##36815259##76##]</td></tr><tr><td align=\"left\"> Scleromyositis and MMCP</td><td align=\"left\"> ++ </td><td align=\"left\"> +/− </td><td align=\"left\"> +/− (sarc)</td><td align=\"left\">[##REF##36776390##30##, ##REF##33864496##80##]</td></tr><tr><td align=\"left\" colspan=\"5\">Hereditary myopathies</td></tr><tr><td align=\"left\"> LGMDR1</td><td align=\"left\">−</td><td align=\"left\"> + </td><td align=\"left\"> +/− </td><td align=\"left\">[##REF##35135626##9##]</td></tr><tr><td align=\"left\"> LGMDR2</td><td align=\"left\"> + </td><td align=\"left\">−</td><td align=\"left\"> ++ + </td><td align=\"left\">[##REF##14512171##15##, ##REF##33973272##37##]</td></tr><tr><td align=\"left\"> LGMDR9</td><td align=\"left\"> + </td><td align=\"left\"> + </td><td align=\"left\">−</td><td align=\"left\">[##REF##14512171##15##, ##REF##33973272##37##]</td></tr><tr><td align=\"left\"> LGMDR12</td><td align=\"left\"> + </td><td align=\"left\">−</td><td align=\"left\"> +/− </td><td align=\"left\">[##REF##36157496##14##]</td></tr><tr><td align=\"left\"> Duchenne muscular dystrophy</td><td align=\"left\"> + </td><td align=\"left\"> + </td><td align=\"left\"> +/− </td><td align=\"left\">[##REF##2857418##7##, ##REF##20925545##47##]</td></tr><tr><td align=\"left\"> Autophagic vacuolar myopathies</td><td align=\"left\"> ++ (sarc)</td><td align=\"left\">?</td><td align=\"left\"> ++ (sarc)</td><td align=\"left\">[##REF##24488655##18##, ##REF##25644398##23##, ##REF##32419263##44##, ##REF##33393119##53##]</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>" ]

[ "<table-wrap-foot><p>Overview of MHC class I, MHC class II and complement in inflammatory muscle diseases. The intensities of the corresponding marker are indicated by + and – with +++ indicating very strong expression,  ++  strong expression, + mild/infrequent expression, − absence of the corresponding marker and  +/− indicating varying degrees of expression. ? indicates a marker with inconclusive data regarding its diagnostic value</p><p><italic>cap</italic> on the capillary; <italic>LGMD</italic> limb girdle muscular dystrophies; <italic>MDA5</italic> melanoma differentiation-associated protein 5; <italic>MMCP</italic> minimal myositis with capillary pathology; <italic>NXP2</italic> nuclear matrix protein 2; <italic>pf</italic> perifascicular; <italic>SAE</italic> small ubiquitin-like modifier-1 activating enzyme; <italic>sarc</italic> sarcolemmal; <italic>TIF1γ</italic> transcriptional intermediary factor 1 gamma</p><p>*The histopathological features of overlap myositis are highly heterogeneous and dependent on the clinical context and autoantibody status</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Influenza A virus (IAV) presents a continuous threat to human health, killing approximately half a million people annually [##REF##28807608##1##, ##REF##12206966##2##]. Influenza severity largely depends on the immune and health status of the individual [##REF##14643124##3##, ##REF##30349811##4##]. Notably, underlying health conditions, such as diabetes mellitus are associated with severe influenza outcomes [##REF##28197127##5##].</p>", "<p id=\"Par3\">The global prevalence of diabetes has been steadily rising for several decades [##REF##30961501##6##]. The continuous rise is driven primarily by type 2 diabetes, which is associated with urbanization and lifestyle factors [##REF##30961501##6##]. While the underlying cause differs, diabetes subtypes are characterized by chronically high concentrations of blood glucose (hyperglycemia) [##UREF##0##7##]. Analysis of glycated hemoglobin in blood via a HbA1c test provides an indicator of glycaemic control over the preceding 3-month period [##REF##27398023##8##]. Hyperglycemia especially has been identified as a risk factor for developing non-communicable complications associated with diabetes, including cardiovascular disease, nephropathy, and retinopathy [##REF##21299400##9##]. In addition to its role as a risk factor for non-communicable disease, there is rising evidence that hyperglycemia is associated with increased susceptibility to infectious disease and severe outcomes [##REF##28197127##5##, ##REF##34216102##10##, ##UREF##1##11##]. Specifically, there is evidence to suggest that hyperglycemia has a profound effect on the cellular adaptive immune response, such as that of CD8⁺ T cells [##UREF##2##12##–##REF##2789342##18##].</p>", "<p id=\"Par4\">The largest body of work suggests that hyperglycemia has detrimental effects on T cells. Specifically, outside the context of influenza virus infection, it has been suggested that hyperglycemia impairs T cell responses, increases the frequency of senescent cells, and impairs their proliferation [##UREF##2##12##–##REF##31251396##14##]. In vitro, high glucose concentrations reduce the CD8⁺ T cell production of TNF-α, IFN-γ, and IL-12 [##REF##35044446##15##, ##UREF##3##16##], and reduce cell viability [##UREF##4##17##]. Consistent with these experimental data, clinically, CD8⁺ T cells from donors with diabetes have a reduced target cell lysis ability compared to control donors without diabetes following influenza vaccination [##REF##2789342##18##]. Furthermore, genome-wide expression analysis of peripheral blood mononuclear cells (PBMCs) from donors with and without diabetes showed a significant reduction in activity of cytotoxic genes associated with diabetes [##REF##25582225##19##]. While there is a clear relationship between diabetes and altered CD8⁺ T cell function in a non-infectious context, these results cannot be directly extrapolated and applied to infectious pathogens. Furthermore, no study to date has investigated the effect of hyperglycemia on CD8⁺ T cell function in the context of influenza.</p>", "<p id=\"Par5\">Currently, there are two subtypes of IAV that circulate in the community, H1N1 and H3N2, and influenza pandemics often (although not always) are associated with the introduction of a new IAV subtype into the human population [##REF##29955068##20##]. While each virus is antigenically different, CD8⁺ T cells typically recognize conserved epitopes between influenza strains and provide heterosubtypic immunity [##REF##24257602##21##], where exposure to one influenza serotype can afford protection to another [##REF##24971078##22##]. Heterosubtypic immunity plays a crucial role in protection against both seasonal infection, and pandemic scenarios [##REF##26974887##23##, ##UREF##5##24##]. Thus, any reduction in the function of CD8⁺ T cells in response to high concentrations of glucose could possibly impair this heterosubtypic immunity to influenza virus. Together this suggests that, in the context of IAV infection, hyperglycemia may impair the development of poly-functional heterosubtypic immunity to influenza virus by reducing CD8⁺ T cell response to stimulation. By identifying the relationship between glucose concentrations and anti-viral immunity, this study sheds light on one of the mechanisms contributing to increased risk for severe influenza virus infection in individuals with diabetes.</p>" ]

[ "<title>Materials and methods</title>", "<title>Patient and control recruitment</title>", "<p id=\"Par6\">A cohort of 88 individuals were recruited for the study. The cohort consisted of 64 individuals with type 1 diabetes, 8 individuals with type 2 diabetes, and 16 healthy individuals without diabetes or other health conditions. Inclusion criteria for the donors with diabetes comprised 18–60 years of age, not pregnant at the time of study, non-smokers of nicotine cigarettes, no known immune disease requiring immuno-suppressants, and a minimum of 2-year duration of diabetes mellitus. Inclusion criteria for the donors without diabetes comprised 18–60 years of age, not pregnant at the time of study, non-smokers of nicotine cigarettes, and no underlying health conditions. Non-fasting blood and clinical data from these participants were collected at the point of recruitment. Informed consent was obtained from all subjects, and the study was approved by Mater Misericordiae Ltd Human Research Ethics Committee (Approval No. HREC/17/MHS/78) and the University of Queensland Humans Research Ethics Committee (Approval No. 2019/HE002522).</p>", "<title>PBMC isolation</title>", "<p id=\"Par7\">10 mL of non-fasting blood was collected from donors in BD Vacutainer EDTA tubes (BD Biosciences). PBMCs were isolated from donors with and without diabetes whole blood by Ficoll-Paque (GE Healthcare, Illinois, USA) gradient centrifugation. Cells were cryopreserved in fetal bovine serum (FBS) (Sigma-Aldrich) containing 10% dimethyl sulfoxide and stored below − 135°C until tested.</p>", "<title>Ex vivo T cell characterization</title>", "<p id=\"Par8\">Characterization of the T cell populations was performed as previously described [##REF##34006841##25##]. In short, PBMCs were washed and stained for lymphocyte (anti-human CD3-BV480, anti-human CD4-BV650, and anti-human CD8-PerCPCy5.5), and differentiation (anti-human CD27-APC, anti-human CD45RA-FITC, and anti-human CD95-BV421). Cells were subsequently washed and fixed using a cytofix kit (BD Biosciences). All samples were analyzed by flow cytometry on LSRFortessa (BD Biosciences). The gating for T cell characterization is outlined in Fig. ##FIG##0##1##a.</p>", "<title>T cell stimulation and intracellular cytokine staining (ICS)</title>", "<p id=\"Par9\">PBMCs from donors with and without diabetes were stimulated with either (i) A/H3N2 (HKx31) at a MOI of 10, (ii) PMA (1 µg/mL) and ionomycin (1 µg/mL), (iii) influenza virus peptide pool (4 µg/mL) (Table ##TAB##0##1##) (AnaSpec), (iv) CD3/CD28 magnetic beads (Thermo Fisher), or (v) left unstimulated for 18 h in the presence of anti-human CD107a-FITC (Biolegend), GolgiStop (BD Biosciences) and GoliPlug (BD Biosciences). Cells were then washed, fixed, and stained with anti-human CD8-PerCPCy5.5 (BD Biosciences) anti-human CD4-PE (BD Biosciences), CD3-PE-Cy7 (BD Biosciences), and NIR live/dead (Invitrogen). Following surface staining, cells were washed and permeabilized using the Cytofix/Cytoperm Fixation/Permeabilization kit (BD Biosciences) and stained with anti-human MIP-1β-APC (BD Biosciences), anti-human IFN-γ-V450 (BD Biosciences) and anti-human TNF-α-AF700 (BD Biosciences). Cells were then analyzed by flow cytometry on LSRFortessa (BD Biosciences) at the flow cytometry facility at the Translational Research Institute (TRI) (Brisbane, Australia). To assess the functionality of T cells, the number of MIP1-β⁺, IFN-γ⁺, TNF-α⁺, and CD107a⁺ cells was assessed using the gating strategy outlined in Fig. ##FIG##1##2##a.</p>", "<title>Statistical analysis</title>", "<p id=\"Par10\">Statistical analyses were performed using Graph Pad Prism software (version 9.3.1) for Windows (GraphPad Software, La Jolla, CA, USA). Statistical significance of categorical patient data was determined using a Fisher’s exact test. The normality of numerical patient data was determined to be not normally distributed, and subsequently Mann–Whitney test was used to determine statistical significance. Simple linear regression was used to determine the relationship between one independent variable and one dependent variable. Multiple linear regression was used to determine the relationship between multiple independent variables (including HbA1c, age, sex, BMI, and ethnicity) and one dependent variable. Independent variables were selected based on prior studies implicating their role in diabetes.</p>" ]

[ "<title>Results</title>", "<title>Study participant characteristics</title>", "<p id=\"Par11\">The clinical characteristics of donors are summarized in Table ##TAB##1##2##. Age, sex, and ethnicity were comparable between groups. As expected, both BMI and HbA1c were significantly higher in the cohort of donors with diabetes compared to donors without diabetes.</p>", "<title>Increasing HbA1c associated with changes in ex vivo T cell populations</title>", "<p id=\"Par12\">To assess if hyperglycemia was associated with changes to both CD4⁺ and CD8⁺ T cell populations, PBMCs were stained for lymphocyte and phenotypic markers.</p>", "<p id=\"Par13\">Increasing HbA1c correlated with an increased frequency of CD8⁺ T cells (defined as frequency of parent population). However, this increase was not enough to affect the overall CD4:CD8 ratio (Fig. ##FIG##0##1##b). This increase in proportion of CD8⁺ T cell population is characteristic of type 1 diabetes [##REF##8306503##28##]. There was no correlation between HbA1c and distribution of central memory, naïve, effector memory, and terminally differentiated effector memory subsets of the CD8⁺ T cell population (Fig. ##FIG##0##1##b). These data suggest that the hyperglycemia increased the overall proportion of CD8⁺ T cells but not their phenotypes.</p>", "<p id=\"Par14\">In contrast, increasing HbA1c was associated with an increasing proportion of effector memory and decreasing proportion of naïve CD4⁺ T cell populations (Fig. ##FIG##0##1##c). Alterations CD4⁺ T cell populations such as these are commonly observed in patients with diabetes [##REF##28842400##29##, ##REF##30574794##30##].</p>", "<p id=\"Par15\">Together these data suggest that HbA1c is associated with changes to T cell populations that are typically observed in individuals with diabetes.</p>", "<title>Expression of TNF-α from CD8⁺ T cells following IAV infection correlated to HbA1c</title>", "<p id=\"Par16\">To assess the effect of HbA1c on influenza virus-specific CD8⁺ T cell function and recall ability, PBMCs were infected with IAV for 18 h. Influenza virus-induced CD8⁺ T cell functionality was defined by expression of IFN-γ, TNF-α, MIP1-β, and CD107a (Fig. ##FIG##1##2##a). Using simple linear regression analysis, there was no correlation between HbA1c and CD8⁺ T cell expression of IFN-γ, MIP1-β, or CD107a (Fig. ##FIG##1##2##b). However, increasing HbA1c correlated with reduced proportion of TNF-α producing CD8⁺ T cells (Fig. ##FIG##1##2##b). In addition to the assessment of single activation markers, polyfunctionality of CD8⁺ T cells was also assessed. However, there was no significant effect of HbA1c (data not shown).</p>", "<title>Decreased TNF-α expression is specific to the activation of the TCR complex</title>", "<p id=\"Par17\">Having established that increased HbA1c is associated with decreased TNF-α expression following influenza virus infection, we next sought to replicate these findings under more controlled conditions and to determine if this effect was specific to influenza virus stimulation.</p>", "<p id=\"Par18\">The magnitude of peptide-specific cells is known to vary greatly between HLA-matched individuals and may be influenced by infection or vaccination history, and other HLA molecules present [##REF##24395804##31##–##REF##31811120##33##]. As such, it would be difficult to determine whether hyperglycemia has an effect on peptide-specific CD8⁺ T cells event in individuals that are HLA-matched for that peptide's restricting HLA molecule.</p>", "<p id=\"Par19\">Therefore, rather than stimulation with HLA-matched peptides, we chose to expose the PBMCs to either an influenza viral peptide pool containing 12 influenza viral peptides spanning 10 HLA subtypes (Table ##TAB##0##1##) or beads coated with anti-CD3/anti-CD28. Both the peptide pool and the beads stimulate CD8⁺ T cells via the TCR complex. Stimulation with PMA/I is known to bypass the required binding to the TCR complex on the cell surface [##REF##23985769##34##]. Instead, ionomycin (a calcium ionophore) facilitates the transport of calcium across the plasma membrane and directly increases the intracellular Ca²⁺, while PMA activates protein kinase C, leading to the activation of MAPK pathways.</p>", "<p id=\"Par20\">Successful activation by a peptide pool stimulation relies on both successful antigen presentation of the peptide, and on donors having a requisite HLA subtype that correspond to a peptide present in the pool (Table ##TAB##0##1##). The peptide pool used in this study has a 97% coverage of Caucasian population [##UREF##6##27##]. Therefore, only Caucasian donors were included for peptide pool analysis. When cells were stimulated with the influenza virus peptide pool, there was an inverse correlation between HbA1c and TNF-α expression by CD8⁺ T cells (Fig. ##FIG##2##3##a).</p>", "<p id=\"Par21\">While IAV infection, and stimulation with a peptide pool relies on successful antigen presentation by cells, anti-CD3/anti-CD28-coated beads partially mimic the binding of antigen presenting cells to T cells and thus induces TCR stimulation. When cells were stimulated with anti-CD3 and anti-CD8 coated beads, increasing HbA1c correlated with significantly reduced TNF-α expression from responding cells (Fig. ##FIG##2##3##b). This significant association remains when donors with type 2 diabetes are removed from the analysis (data not shown). Importantly, as this stimulation does not require antigen presentation by target cells, the reduced response can solely be attributed to the effector cells.</p>", "<p id=\"Par22\">In contrast to both the peptide pool and the bead stimulation, when cells were stimulated with PMA/I for 18 h, there was no correlation between the HbA1c and the resulting TNF-α expression (Fig. ##FIG##2##3##c), indicating that HbA1c specifically affects TCR-induced activation.</p>", "<p id=\"Par23\">Further analysis of the peptide pool stimulation determined that this reduced percentage of TNF-α expressing cells was not due to select confounding factors (specifically, age, sex, or BMI) (Fig. ##FIG##2##3##a). The response from age- and sex-matched donors was also compared (Fig. ##FIG##2##3##a). While there was a trend toward decreased response in donors with diabetes, these results did not reach significance, potentially due to the low numbers (11 donors per group).</p>", "<p id=\"Par24\">Similar to the peptide pool stimulations, further analysis of the anti-CD3/anti-CD28-coated beads stimulation also determined that this reduced TNF-α expression was not due to confounding factors (specifically, age, sex, BMI, or ethnicity) (Fig. ##FIG##2##3##b). When donors were matched for age and sex, the HbA1c-dependent decrease in TNF-α expression following stimulation with beads remained significantly different between the groups (Fig. ##FIG##2##3##b). When assessing poly-functionality, multiple TNF-α expressing CD8⁺ T cell populations were affected by increasing levels of HbA1c (Supplementary Fig. ##SUPPL##0##S1##a-d).</p>", "<p id=\"Par25\">Reduced TNF-α expression was also observed in CD4⁺ T cells and significantly associated with both HbA1c and ethnicity of the donor (Supplementary Fig. ##SUPPL##1##S2##a). When ethnicity was controlled for (i.e., only assessing Caucasian donors), the relationship between increasing HbA1c and reducing TNF-α expression remained (Supplementary Fig. ##SUPPL##1##S2##b).</p>", "<p id=\"Par26\">Taken together, as both peptide pool and anti-CD3/anti-CD28-coated bead responses were affected, these results suggest that increasing glucose concentrations have a detrimental effect on both CD8⁺ CD4⁺ T cell function upstream of where PMA and ionomycin act, i.e., the initial steps of the TCR signaling cascade.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par27\">Hyperglycemia plays an important role in the susceptibility of patients with diabetes to severe influenza [##REF##28197127##5##]. We have previously demonstrated in vitro that high glucose conditions prior to IAV infection increased virus-induced barrier damage [##REF##32697191##35##]. However, it is important to note that our previous work demonstrated the effect of hyperglycemia with no previous exposure to IAV and focused on the innate immune response, rather than adaptive. Most individuals have been exposed to at least one influenza virus by the age of six, and thus will possess a level of adaptive immunity to IAV [##REF##21209157##36##]. Furthermore, it is the adaptive immune response, and more specifically the CD8⁺ T cell response, that offers protection in the form of heterosubtypic immunity, to not only seasonally circulating IAV strains, but also to novel IAV strains with pandemic potential [##REF##24971078##22##, ##UREF##5##24##, ##REF##20616031##37##]. Given the critical role of CD8⁺ T cells in immune protection against severe influenza, it is imperative to investigate if this protection is altered in individuals with hyperglycemia.</p>", "<p id=\"Par28\">Hyperglycemia has previously been implicated in the redistribution of lymphocyte subsets [##REF##11441916##38##]. Analysis of whole blood lymphocyte count demonstrated a reduction of overall circulating lymphocyte populations in response to short term (2 h) hyperglycemia. This reduction included B cells, and CD4⁺ and CD8⁺ T cells, but subsets were not distinguished [##REF##11441916##38##]. While the results of our study do not report an effect of hyperglycemia on the percentage of CD8⁺ T cell phenotypes (such as naïve central memory, effector memory, and terminally differentiated effector memory), we did observe an increase in the overall proportion of CD8⁺ T cells, consistent with previous findings [##REF##8306503##28##]. Similarly, we report a redistribution of CD4⁺ T cell phenotypes. However, it is important to note that we did not investigate the abundance of influenza-specific CD8⁺ memory T cells, which is reduced in a similar metabolic condition often associated with type 2 diabetes, obesity [##REF##20173021##39##, ##REF##20592105##40##].</p>", "<p id=\"Par29\">Outside the context of influenza, in a non-infectious setting, hyperglycemia causes a five-fold decrease in proliferation of T cells in response to stimulation [##UREF##2##12##], and has been shown to have a detrimental impact on the survival and function of memory CD8⁺ T cells [##REF##35044446##15##]. As our results demonstrate a reduced ability to respond to TCR stimulation, it is likely that this would affect the downstream proliferation of antigen-specific CD8⁺ memory T cells. However, to confirm this further in vitro proliferation experiments from these donors would be required. Further in vitro experiments may also shed light on whether hyperglycemia has a direct effect on CD8⁺ T cells, or indirectly mediated by other cell populations.</p>", "<p id=\"Par30\">Of the measured markers of CD8⁺ T cell functionality in our cohort, the one significantly affected was TNF-α. TNF-α directly inhibits viral replication [##REF##11773383##41##] and acts as an effector molecule in CD8⁺ T cell-mediated cell lysis [##UREF##8##42##]. Therefore, any loss of the TNF-α response to influenza virus infection may be detrimental to the individual. Indeed, following influenza virus infection, TNF-α-deficient mice have a dysregulated inflammatory response and significantly increased lung immunopathology [##REF##22001698##43##].</p>", "<p id=\"Par31\">Our results demonstrate that hyperglycemia affects TCR-specific stimulation which hampers CD8⁺ T cell function by reducing the expression of TNF-α. However, hyperglycemia does not prevent their intrinsic ability to function, as demonstrated by the fact that PMA/I stimulation, which circumvents TCR stimulation, did not affect TNF-α expression. Indeed, our results are consistent with studies outside of the context of hyperglycemia, where oxidative stress has been implicated in T cell hypo-responsiveness [##REF##12884292##44##–##REF##17786224##47##]. Therefore, further investigation into hyperglycemia-induced oxidative stress in the context of T cell dysfunction is warranted. This research may hold clues for potential molecular pathways which could be targeted by medication to improve CD8⁺ T cell functionality in a hyperglycemic environment as observed in patients with diabetes mellitus. There are several limitations associated with this study. Firstly, the influenza vaccination status of the control cohort was not recorded. Despite this, it is well established that individuals are no longer immunologically naïve to influenza A viruses by the age of six, and thus possess some level of adaptive immune response to influenza [##REF##21209157##36##]. While the data suggests a role of hyperglycemia in reducing CD8⁺ T cell functionality, the possibility of other confounding factors not measured (e.g., cholesterol and triglyceride levels) need to be considered. For example, dyslipidemia is known to have a profound effect on the immune system, and specifically, can impact the activation and differentiation of T cells [##REF##34095011##48##]. Secondly, we were unable to assess the effect of exogenous insulin as all donors in this study with type 1 diabetes (&gt; 90% of our donors with diabetes) were receiving insulin treatment. While the present study was unable to assess the effect of insulin, Kavazović and colleagues recently demonstrated both in vitro and in vivo that hyperglycemia rather than hyperinsulinemia mediates memory CD8⁺ T cell dysfunction in a mouse model [##REF##35044446##15##].</p>", "<p id=\"Par32\">Originally, we set out to determine the effect of hyperglycemia on influenza specifically, however our conclusions are more far reaching. The results described herein are not limited to influenza virus-specific T cells, but instead to the function, or perhaps the expression, of the TCR complex. Thus, our results are potentially of importance in the context of other pathogens in which diabetes is a risk factor for severe infections, such as <italic>Mycobacterium tuberculosis</italic> (Mtb) and SARS-CoV-2. Our results are consistent with a previous study showing that Mtb antigen-specific CD8⁺ T cells from donors with type 2 diabetes have significantly diminished expression of cytotoxic marker compared to donors without diabetes [##REF##25363329##49##]. In the context of SARS-CoV-2 infection, there are indications that both increased senescence of CD4⁺ and CD8⁺ T cells, as well as the overall reduced proportions of these cell types in patients with diabetes may have contributed to the observed increase in severe COVID-19 [##REF##34216102##10##, ##UREF##9##50##]. There is also evidence that poorly controlled HbA1c (HbA1c 1-year mean &gt; 7%) following SARS-CoV-2 vaccination in a cohort of patients with type 2 diabetes is associated with a reduced cytokine response from CD4⁺ T cells and increased incidence of breakthrough infections [##REF##35484164##51##]. However, much like influenza, the mechanism underlying this impaired cellular function remains undefined. Therefore, the results of this study may shed some light on the mechanism at play in severe COVID-19 in patients with diabetes.</p>" ]

[]

[ "<p id=\"Par1\">Diabetes mellitus is on the rise globally and is a known susceptibility factor for severe influenza virus infections. However, the mechanisms by which diabetes increases the severity of an influenza virus infection are yet to be fully defined. Diabetes mellitus is hallmarked by high glucose concentrations in the blood. We hypothesized that these high glucose concentrations affect the functionality of CD8⁺ T cells, which play a key role eliminating virus-infected cells and have been shown to decrease influenza disease severity. To study the effect of hyperglycemia on CD8⁺ T cell function, we stimulated peripheral blood mononuclear cells (PBMCs) from donors with and without diabetes with influenza A virus, anti-CD3/anti-CD28-coated beads, PMA and ionomycin (PMA/I), or an influenza viral peptide pool. After stimulation, cells were assessed for functionality [as defined by expression of IFN-γ, TNF-α, macrophage inflammatory protein (MIP)-1β, and lysosomal-associated membrane protein-1 (CD107a)] using flow cytometry. Our results showed that increasing HbA1c correlated with a reduction in TNF-α production by CD8⁺ T cells in response to influenza stimulation in a TCR-specific manner. This was not associated with any changes to CD8⁺ T cell subsets. We conclude that hyperglycemia impairs CD8⁺ T cell function to influenza virus infection, which may be linked with the increased risk of severe influenza in patients with diabetes.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00018-023-05010-4.</p>", "<title>Keywords</title>", "<p> Open Access funding enabled and organized by CAUL and its Member Institutions</p>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Author contributions</title>", "<p>KDH: study conceptualization, methodology, data curation, data analysis, writing original draft, writing review and editing. ZWMT and ESD: Data curation. LCR and CEVDS: methodology, critical feedback on study, writing review and editing. KR, EJG, LAG, SG, KK and HLB: critical feedback on study, writing review and editing. KRS: study conceptualization, writing review and editing, resources, funding acquisition.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by CAUL and its Member Institutions. CEVDS was supported by ARC-DECRA Fellowship (#DE200100185) and University of Melbourne Establishment grant. KR was supported by the Mater Foundation. EJG was supported by an ARC-DECRA Fellowship (DE210101479) and an AINSE Early Career Research Grant. SG was supported by an NHMRC Senior Research Fellowship (#1159272). KK was supported by NHMRC Investigator Grant (#1173871) and a Dame Kate Campbell Fellowship from The University of Melbourne. HLB was supported by the Mater Foundation. KRS was supported by NHMRC Investigator Grant (#2007919). Study was supported by NHMRC APP1159959.</p>", "<title>Data availability</title>", "<p>The data sets generated during the current study are not publicly available due to nature of the ethical approvals. If you have a reasonable request, please contact the corresponding author.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par330\">KRS is a consultant for Sanofi, Roche and NovoNordisk.</p>", "<title>Ethics approval</title>", "<p id=\"Par33\">Informed consent was obtained from all subjects, and the study was approved by Mater Misericordiae Ltd Human Research Ethics Committee (Approval No. HREC/17/MHS/78) and the University of Queensland Humans Research Ethics Committee (Approval No. 2019/HE002522).</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Increasing HbA1c correlated with changes to CD4⁺ T cell subset populations. <bold>A</bold> Gating strategy employed to characterize CD8⁺ and CD4⁺ T cell populations. Fluorochrome-labeled antibodies were used to characterize the T cell populations. PBMCs were stained for lymphocyte and differentiation markers as outlined in the methods. <bold>B</bold> Correlation analysis between % HbA1c and CD8⁺ TCentral Memory (Tcm), TNaïve, TEffector Memory (T_EM) and T terminally differentiated effector memory (T_ERMA) subsets, overall CD8⁺ T cell population, and CD4:CD8 ratio. Data points represent individual donors (<italic>n</italic> = 88). Statistical significance was determined using simple linear regression, with significant <italic>P</italic> values displayed. <bold>C</bold> Correlation analysis between % HbA1c and CD4⁺ TCentral Memory, TNaïve, TEffector Memory and T terminally differentiated effector memory (TERMA), and overall CD4⁺ T cell population. Data points represent individual donors (<italic>n</italic> = 88). Statistical significance was determined using simple linear regression, with significant <italic>P</italic> values displayed.<bold> B</bold>, <bold>C</bold> Donors without diabetes are represented by green triangles. Donors with diabetes are represented by blue circles</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Percentage of CD8⁺ T cells expressing TNF-α following IAV infection inversely correlates to HbA1c. <bold>A</bold> Gating strategy employed to investigate CD8⁺ and CD4⁺ T cell response to stimulation. Fluorochrome-labeled antibodies were used to identify the CD4⁺ and CD8⁺ T cell populations expressing IFN-γ, TNF-α, MIP1-β and CD107a. <bold>B</bold> Correlation analysis between % HbA1c and frequency of cells expressing IFN-γ, TNF-α, CD107a and MIP-1β, with background staining subtracted. CD8⁺ T cells were infected with IAV (HKx31, H3N2) for 18 h. Results are relative to negative control condition (unstimulated cells). Data points represent individual donors (<italic>n</italic> = 88). Statistical significance was determined using simple linear regression, with significant <italic>P</italic> values displayed. <bold>A</bold>, <bold>B</bold> Donors without diabetes are represented by green triangles. Donors with diabetes are represented by blue circles</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>The association between HbA1c and TNF-α expression was observed following stimulation in a TCR-specific manner. CD8⁺ T cells were stimulated for 18 h using either, influenza virus peptide pool (<bold>A</bold>), anti-CD3/anti-CD28 coated beads (<bold>B</bold>), or PMA/I (<bold>C</bold>). Results are presented as the frequency of CD8⁺ T cells expressing TNF-α, with background staining subtracted. Data points represent individual donors (left &amp; middle: Beads and PMA/I <italic>n</italic> = 88, peptide pool <italic>n</italic> = 73 [Caucasian donors]) (right: age- and sex-matched donors [<italic>n</italic> = 11/group (<bold>A</bold>), <italic>n</italic> = 16/group (<bold>B</bold>)]. Statistical significance was determined using simple linear regression (left), multiple variable regression analysis, where input variables were age, sex, BMI, HbA1c and ethnicity (middle), or a Mann–Whitney test *<italic>P</italic> &lt; 0.05 (right). <bold>A</bold>–<bold>C</bold> Donors without diabetes are represented by green triangles. Donors with diabetes are represented by blue circles</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Influenza viral peptides included in the peptide pool, together covering 97% of the Caucasian population [##REF##30723466##26##, ##UREF##6##27##]</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">HLA Allele</th><th align=\"left\">Peptide Sequence</th><th align=\"left\">Virus Segment</th></tr></thead><tbody><tr><td align=\"left\">A1</td><td align=\"left\">VSDGGPNLY</td><td align=\"left\">Influenza A—PB1</td></tr><tr><td align=\"left\">A1</td><td align=\"left\">CTELKLSDY</td><td align=\"left\">Influenza A—NP</td></tr><tr><td align=\"left\">A2</td><td align=\"left\">GILGFVFTL</td><td align=\"left\">Influenza A—M</td></tr><tr><td align=\"left\">A2</td><td align=\"left\">FMYSDFHFI</td><td align=\"left\">Influenza A—PB2</td></tr><tr><td align=\"left\">A68</td><td align=\"left\">KTGGPIYKR</td><td align=\"left\">Influenza A—NP</td></tr><tr><td align=\"left\">A3</td><td align=\"left\">RVLSFIKGTK</td><td align=\"left\">Influenza A—NP</td></tr><tr><td align=\"left\">A3</td><td align=\"left\">ILRGSVAHK</td><td align=\"left\">Influenza A—NP</td></tr><tr><td align=\"left\">A3, A11, A60B1</td><td align=\"left\">SIIPSGPLK</td><td align=\"left\">Influenza A—M</td></tr><tr><td align=\"left\">B7</td><td align=\"left\">LPFDKTTVM</td><td align=\"left\">Influenza A—NP</td></tr><tr><td align=\"left\">B8</td><td align=\"left\">ELRSRYWAI</td><td align=\"left\">Influenza A—NP</td></tr><tr><td align=\"left\">B27</td><td align=\"left\">SRYWAIRTR</td><td align=\"left\">Influenza A—NP</td></tr><tr><td align=\"left\">B27</td><td align=\"left\">ASCMGLIY</td><td align=\"left\">Influenza A—M</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Clinical characteristics of donor cohort</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\">Donors without diabetes (<italic>n</italic> = 16)</th><th align=\"left\">Donors with diabetes (<italic>n</italic> = 72)</th><th align=\"left\"><italic>P</italic>-value</th></tr></thead><tbody><tr><td align=\"left\">Age, years</td><td align=\"left\">28.1 ± 5.4</td><td align=\"left\">30.6 ± 11.6</td><td align=\"left\">0.874</td></tr><tr><td align=\"left\">Female/male (% female)</td><td align=\"left\">11/5 (68.8%)</td><td align=\"left\">44/28 (60.3%)</td><td align=\"left\">0.776</td></tr><tr><td align=\"left\">BMI (kg/m²)</td><td align=\"left\">23 ± 4.6</td><td align=\"left\">27 ± 5.4</td><td align=\"left\">0.006 (*)</td></tr><tr><td align=\"left\">Ethnicity, % caucasian</td><td align=\"left\">68.8%</td><td align=\"left\">83.6%</td><td align=\"left\">0.157</td></tr><tr><td align=\"left\">HbA1c (%)</td><td align=\"left\">5.2 ± 0.3</td><td align=\"left\">8.4 ± 1.7</td><td align=\"left\"> &lt; 0.0001 (*)</td></tr><tr><td align=\"left\">T1DM/T2DM (% T1DM)</td><td align=\"left\">N/A</td><td align=\"left\">66/6 (90.4%)</td><td align=\"left\">N/A</td></tr><tr><td align=\"left\">Insulin treatment</td><td align=\"left\">N/A</td><td align=\"left\">66/6 (90.4%)</td><td align=\"left\">NA</td></tr><tr><td align=\"left\">Duration of diabetes (years)</td><td align=\"left\">N/A</td><td align=\"left\">14.8 ± 7.2</td><td align=\"left\">N/A</td></tr><tr><td align=\"left\">Non-steroidal anti-inflammatory drug (NSAID) use (% use)</td><td align=\"left\">0/16 (0%)</td><td align=\"left\">4/68 (5.5%)</td><td align=\"left\"> &gt; 0.999</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>", "<supplementary-material content-type=\"local-data\" id=\"MOESM2\"></supplementary-material>" ]

[ "<table-wrap-foot><p>Values are mean ± SD unless otherwise indicated</p><p>T1DM, Type 1 Diabetes mellitus; T2DM, Type 2 Diabetes mellitus; BMI, Body mass index</p><p>Significant <italic>P</italic> values indicated by an asterisk (*)</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"18_2023_5010_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"18_2023_5010_Fig2_HTML\" id=\"MO2\"/>", "<graphic xlink:href=\"18_2023_5010_Fig3_HTML\" id=\"MO3\"/>" ]

[ "<media xlink:href=\"18_2023_5010_MOESM1_ESM.docx\"><caption><p>Supplementary file 1 (DOCX 526 KB)</p></caption></media>", "<media xlink:href=\"18_2023_5010_MOESM2_ESM.pdf\"><caption><p>Supplementary file 2 (PDF 640 KB)</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par9\">Undescended testis (UDT) is one of the most common congenital malformations in male infants, with an incidence rate of 1% at 1 year of age [##UREF##0##1##, ##REF##17488243##2##]. Among UDT cases, palpable testes are the most common. Conventional laparoscopic orchiopexy (LO) has been shown to be effective in treating palpable testis [##REF##35509258##3##–##REF##33595353##5##]. However, a notable drawback is the presence of visible incision scars on the abdomen.</p>", "<p id=\"Par10\">In recent years, laparoendoscopic single-site surgery (LESS) has been increasingly used in the field of urology [##REF##18836465##6##]. In 2011, single-site LO was introduced in the pediatric population, offering the advantage of a concealed incision, which was well-received by parents [##REF##21292103##7##]. However, existing reports are limited and primarily focus on non-palpable testes [##REF##26568797##8##, ##REF##23750538##9##].</p>", "<p id=\"Par11\">There were few reports on the efficacy of single-site LO for palpable testes and many of these works included a small number of participants [##REF##25577840##10##]. Herein, we conducted a prospective cohort study with a large sample size, to investigate whether single-site LO can achieve favorable success rates and better cosmetic results than conventional LO for palpable UDT.</p>" ]

[ "<title>Materials and methods</title>", "<title>Patients</title>", "<p id=\"Par12\">We prospectively studied patients with UDT between July 2021 and June 2022. Patients with palpable UDT and those with affected testes located in the inguinal canal were included. The exclusion criteria were as follows: (1) presence of disorders of sex development (DSD) or chromosomal anomalies; (2) history of inguinal surgery; (3) history of hormonal therapy.</p>", "<p id=\"Par13\">Between July 2021 and June 2022, 261 patients with UDT were admitted to our ward. Twenty-nine patients with non-palpable testes and three patients with a history of inguinal surgery were excluded. Six patients with DSD or chromosomal anomalies were also excluded. In total, 223 patients were included in our study, and the surgical procedure was performed at the parents’ request. There were 105 patients in the single-site LO group (single site group) and 118 patients in the conventional LO group (conventional group). Patients were followed up at the outpatient clinic after discharge. Follow-up visits were performed up to 12 months after surgery to assess the testicular position and umbilical wound by physical examination and ultrasonography.</p>", "<p id=\"Par14\">The variables included age, operating time, complications (classified by the Clavien-Dindo system), hospital stay, postoperative testicular location, testicular volume (confirmed by ultrasonography), testicular atrophy, success rate, and cosmetic appearance. Testicular atrophy was defined as the presence of a nubbin or impalpable testis at the follow-up visit, confirmed by Doppler ultrasonography. The success rate was defined as a proper testicular position without testicular atrophy or ascent. The 12-month period was divided into the early stage (first 6 months) and late stage (last 6 months). Testicular hypotrophy was defined as a reduction &gt; 50% of the testicular volume compared to the contralateral, normally descended testis [##REF##27845220##11##].</p>", "<title>Surgical procedure</title>", "<p id=\"Par15\">During single-site LO, the patients were positioned supine with a 30° elevation on the affected side. Three small incisions were made along the border of the umbilicus (Fig. ##FIG##0##1##A). A 5-mm port was inserted for the camera through the central incision. Two 3-mm ports for the instruments were placed on either side of the first port within the umbilicus (Fig. ##FIG##0##1##B, C). The port on the affected side was positioned relatively higher, while that on the contralateral side was placed lower, resulting in a triangular configuration within the umbilicus (Fig. ##FIG##0##1##A). The peritoneum covering the testicular vessel and vas deferens was incised and dissected at the internal inguinal ring level (Fig. ##FIG##1##2##A, B). Releasing the testicular vessels from the peritoneum and retroperitoneum increased the length of the testicular vessels. The testis was brought into the abdominal cavity, and the gubernaculum was transsectioned (Fig. ##FIG##1##2##C). An ipsilateral scrotal incision was made at the bottom of the scrotum, creating a subdartos pouch. Forceps were passed through the scrotal incision into the abdomen. The testis was grasped at the gubernaculum and delivered into the subdartos pouch (Fig. ##FIG##1##2##D). Additional dissection was performed if tension was present in the vessel. Typically, the testis was brought down through the medial side of the inferior epigastric vessels to the scrotum, thus, shortening its distance.</p>", "<p id=\"Par16\">\n\n</p>", "<p id=\"Par17\">\n\n</p>", "<p id=\"Par18\">In conventional LO, the first port of the laparoscope was placed in the umbilicus. Two 5-mm ports were introduced on either side of the abdomen at the umbilicus level along the midclavicular line (Fig. ##FIG##0##1##D). The surgical procedure in the abdominal cavity was the same as that in single site LO.</p>", "<title>Institutional review board approval</title>", "<p id=\"Par19\">This study was approved by the ethics committee of our hospital, and informed consent was obtained from the guardians of all patients.</p>", "<title>Statistical analysis</title>", "<p id=\"Par20\">Continuous data were compared using a t-test or covariance analysis. Categorical variables were compared using the chi-squared test. All statistical analyses were performed with a two-sided significance level of 0.05, using SPSS software (version 26.0; IBM Corp., Armonk, NY, USA).</p>" ]

[ "<title>Results</title>", "<p id=\"Par21\">In the single-site group, 105 patients underwent single-site LO, including 89 with unilateral UDT and 16 with bilateral UDT. Their mean age was 2.42 years (range, 6 months–12 years). In the conventional group, 118 patients underwent conventional LO, including 98 unilateral UDT and 20 bilateral UDT cases. The mean age was 2.21 years (range, 7 months to 13 years) (Table ##TAB##0##1##).</p>", "<p id=\"Par22\">\n\n</p>", "<p id=\"Par23\">There were no significant differences between the groups in terms of age, laterality, operating time, or hospital stay. In the early stages, the operating time was longer in the single-site group than in the conventional group for the unilateral procedure (55.31 ± 12.04 min vs. 48.14 ± 14.39 min, <italic>P</italic> = 0.007). Nevertheless, in the later stages, the operating time in the single site group was similar to that of the conventional group (48.82 ± 13.49 min vs. 48.14 ± 14.39 min, <italic>P</italic> = 0.78). In the single site group, there was one case that required conversion to conventional LO in a 7-month-old boy who was underweight due to manipulation difficulty in the limited volume of the abdominal cavity.</p>", "<p id=\"Par24\">After the 1-year follow-up, there was one patient in each group with testicular ascent which required reoperations. The remaining testes were located in the scrotum without testicular atrophy. There was no significant difference in the success rate between the single-site group and the conventional group (99.0% vs. 99.2%, <italic>P</italic> = 0.93). Ultrasonography revealed a testicular volume growth of 0.12 mL in the single-site group and 0.11 mL in the conventional group (<italic>P</italic> = 0.2). In the single-site group, there was no visible scar on the abdomen, and the umbilical scars were hidden (Fig. ##FIG##2##3##A). Their parents were satisfied with the cosmetic appearance. In the conventional group, there were two noticeable scars on the abdomen (Fig. ##FIG##2##3##B).</p>", "<p id=\"Par25\">\n\n</p>", "<p id=\"Par26\">There were 3 complications in the single-site group (2.9%), including 2 hematomas (Grade I, Clavien-Dindo Classification), and 1 testicular ascent (Grade III). Similarly, there were 4 complications in the conventional group (3.4%), including 3 hematomas (Grade I), and 1 testicular ascent (Grade III). There was no significant difference in the complication rates between the two groups (<italic>P</italic> = 0.82).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par27\">To the best of our knowledge, this is the largest study evaluating single-site LO in comparison to conventional LO for palpable UDT in the pediatric population.</p>", "<p id=\"Par28\">Our study revealed that single-site LO is a favorable technique for palpable UDT. It has a superior cosmetic appearance and a success rate comparable to that of conventional LO. Single-site LO is a safe, effective, and convenient technique that offers satisfactory cosmetic results. This method can be used extensively in children with palpable UDT.</p>", "<p id=\"Par29\">Single-site LO has been increasingly used recently and offers several advantages. First, it provides favorable cosmetic outcomes. The small incision is hidden in the umbilicus, which results in no visible scar on the abdomen. The top and bottom of the umbilical ring are typically used as landmarks for the cranial and caudal ends of the skin incision to hide the incision in the umbilicus [##REF##24993421##12##]. All parents were extremely satisfied with the cosmetic results. Other studies have also shown similar results [##REF##23750538##9##, ##REF##25577840##10##]. Wang et al. illustrated that a transumbilical single-site multiport procedure resulted in a smaller scar and less pain [##REF##32410833##13##]. The incision is smaller than that used for the single-port procedure. Sultan et al. reported that single-port orchiopexy needs a 2.5-cm incision to accommodate a Triport (Advanced Surgical Concepts, Wicklow, Ireland) [##REF##21292103##7##]. However, the 2.5-cm incision was longer than the 5-mm camera trocar and two 3-mm instrument ports. In our procedure, the incision was &lt; 1.5 cm (Fig. ##FIG##2##3##A). Thus, the advantages of single-site surgery include superior esthetics with a smaller scar and less pain, and it is considered a less burdensome surgery for pediatric patients [##REF##26411287##14##].</p>", "<p id=\"Par30\">Second, single-site LO has a high success rate. In our study, only one patient had testicular ascent, and the procedure had a success rate of 99%. It can completely release the spermatic cord and simultaneously complete the diagnostic exploration and treatment. Thus, most patients have a scrotal testicular location without testicular atrophy. Both groups showed testicular volume growth after surgery, indicating that most testes grew well. The surgical results of single-site LO were comparable to those of conventional LO. Previous reports have also revealed that single-site LO had favorable results [##REF##23750538##9##, ##REF##25577840##10##]. A previous study revealed that laparoscopic single-site orchiopexy also has the potential to accomplish diagnosis and treatment with good cosmetic outcomes and less injury. Thus, single-site LO is a feasible and effective technique for the treatment of palpable inguinal UDT in children [##REF##25577840##10##].</p>", "<p id=\"Par31\">Third, single-site LO is convenient and easy to master. This technique uses common trocars and instruments without the need for special instruments. The use of adjacent puncture sites for instrumentation eliminates the need for commercial multichannel ports [##REF##27256182##15##]. In selected patients, laparoendoscopic single-site surgery (LESS) for urological indications using conventional laparoscopic instruments has been shown to be safe and feasible, with no additional cost [##REF##23914819##16##]. Although instrument crashing remains a concern in single-site surgery, our technique involved placing the two instrument ports 1 cm apart, effectively reducing the occurrence of crashing. As a result, the learning curve for this procedure is not extensive. In our experience, the initial operating time was 55 min in the single site group; however, it decreased to 48 min after 6 months, similar to that in the conventional group. This indicates that surgeons can quickly acquire proficiency in performing this procedure.</p>", "<p id=\"Par32\">Limitations of single-site procedures include restricted motion and instrument crossings. Therefore, it is difficult to perform this procedure in a small abdominal cavity. LESS is accompanied by a lengthy learning curve and technical limitations associated with existing instrumentation. There is less range of motion, instrument crossing, and more instrument clashing during single-port surgery [##REF##21292103##7##]. In our study, we encountered a situation where a trocar had to be added to the abdomen to complete orchiopexy for a 7-month-old underweight infant. In thin infants, this procedure should be performed with caution. Surgeons require training and experience in regular orchiopexy to perform single-site surgery proficiently. Therefore, further investigation is warranted to explore methods that can reduce the associated difficulties.</p>", "<p id=\"Par33\">There are guidelines for single-site procedures. First, as single-site LO is known to be more challenging than standard LO, the locations of the three incisions need to be prospectively designed. The affected-side incision should be located higher than the contralateral instrument port, with the three incisions forming a triangle. This provides an acceptable distance between the two instruments (Fig. ##FIG##0##1##A, B). Second, for thin infants, preparation should be done for conversion to regular orchiopexy and the parents should be informed about the possible need for conversion before surgery.</p>", "<p id=\"Par34\">There were differences between the results of our study and those of previous reports. Specifically, in previous works, patients had almost non-palpable testes [##REF##21292103##7##–##REF##23750538##9##]. However, our patients had palpable testes located in the inguinal canal; thus, surgeons needed to pull the testes back to the abdomen and transect the gubernaculum. Spermatic cords and testes were carefully pulled, as excessively strong traction would cause injury to the spermatic vessels. Therefore, we should be aware of the anatomical structure of the spermatic cord, dissect the peritoneum on the spermatic vessel, softly pull the cord, dilate the internal ring, and return the testes to the abdomen.</p>", "<p id=\"Par35\">This was a prospective study that included a large number of cases, which was a strength of this study. Moreover, all testes were measured using ultrasonography before and after surgery, which provided objective and reliable data.</p>", "<p id=\"Par36\">This study had some limitations. First, this was not a randomized, double-blind study. Second, long-term follow-up is required to confirm the superiority of this technique.</p>", "<p id=\"Par37\">In conclusion, single-site LO offers superior cosmetic results and comparable success rates to conventional LO for palpable UDT. It seems to be an effective, safe, and convenient technique that achieves satisfactory cosmetic results. It can be used extensively for palpable UDT in the pediatric population.</p>" ]

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[ "<title>Purpose</title>", "<p id=\"Par1\">To evaluate the feasibility of single-site laparoscopic orchiopexy for palpable undescended testes in children.</p>", "<title>Methods</title>", "<p id=\"Par2\">We prospectively studied patients with undescended testes between July 2021 and June 2022. In total, 223 patients were included in our study: 105 underwent single-site laparoscopic orchiopexy and 118 underwent conventional laparoscopic orchiopexy. During single-site laparoscopic orchiopexy, 3 ports were inserted within the umbilicus.</p>", "<title>Results</title>", "<p id=\"Par3\">No differences were observed between the groups in terms of age and laterality. For unilateral undescended testes, the operating time was longer in the single site group than in the conventional group at the early stages (55.31 ± 12.04 min vs. 48.14 ± 14.39 min, <italic>P</italic> = 0.007), but it was similar to the conventional group at the later stages (48.82 ± 13.49 min vs. 48.14 ± 14.39 min, <italic>P</italic> = 0.78). Testicular ascent occurred in one patient from each group. There was no significant difference in the success rate between the single-site group and the conventional group (99.0% vs. 99.2%, <italic>P</italic> = 0.93). In the single-site group, no visible abdominal scarring was observed, while in the conventional group, there were two noticeable scars on the abdomen.</p>", "<title>Conclusion</title>", "<p id=\"Par4\">Single-site laparoscopic orchiopexy offers superior cosmetic results and comparable success rates compared to conventional laparoscopic orchiopexy for palpable undescended testes.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00383-023-05630-8.</p>", "<title>Keywords</title>" ]

[ "<title>Electronic supplementary material</title>", "<p>Below is the link to the electronic supplementary material.</p>", "<p>\n\n</p>" ]

[ "<title>Acknowledgements</title>", "<p>The authors would like to acknowledge Pan Zhao, Jianchunn Yin, and Jiaqiang Li for refining this article.</p>", "<title>Author contributions</title>", "<p>Zhilin Yang and Yingying He planned the study. Pengyu Chen and Tiejun Zhang collected data. Zhicong Ke, Fenghao Sun Guanglun Zhou, and Weiguang Zhao performed statistical analyses. Shoulin Li and Zhilin Yang wrote the main manuscript text. All authors reviewed the manuscript.</p>", "<title>Funding</title>", "<p>This work was supported by the Guangdong High-level Hospital Construction Fund, and Shenzhen Fund for Guangdong Provincial High-level Clinical Key Specialties (SZXK035).</p>", "<title>Declarations</title>", "<title>Competing interests</title>", "<p id=\"Par7234\">The authors have no conficts of interest to declare.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p><bold>A.</bold> Location of the three incisions in the umbilicus for left undescended testis in single-site laparoscopic orchiopexy <bold>B.</bold> A 5-mm port for the camera was placed in the middle of umbilicus, and two 3-mm ports for instruments were located on each side <bold>C. </bold>Cosmetic appearance after accomplishment of single-site laparoscopic orchiopexy <bold>D.</bold> Location of three ports in conventional laparoscopic orchiopexy</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Surgical procedure of single-site laparoscopic orchiopexy for left undescended testis <bold>A.</bold> Preoperative findings <bold>B.</bold> Peritoneum over the testicular vessel and vas deferens was incised and dissected <bold>C.</bold> The testis was taken to the abdominal cavity and the gubernaculum was transsectioned <bold>D.</bold> The testis was delivered into the subdartos pouch from the abdominal cavity</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Cosmetic appearance after laparoscopic orchiopexy <bold>A.</bold> Cosmetic appearance after single-site laparoscopic orchiopexy. The incision scars were hidden in the umbilical fold <bold>B.</bold> Cosmetic result after conventional laparoscopic orchiopexy. Two noticeable incision scars were observed on the abdomen</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Demography and surgical outcomes of single-site laparoscopic orchiopexy versus conventional laparoscopic orchiopexy</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Variable</th><th align=\"left\">Single-site group</th><th align=\"left\">Conventional group</th><th align=\"left\">P</th></tr></thead><tbody><tr><td align=\"left\">Number of patients(testes)</td><td align=\"left\">105 (121 testes)</td><td align=\"left\">118 (138 testes)</td><td align=\"left\"/></tr><tr><td align=\"left\">Age (range)</td><td align=\"left\">2.42 ± 2.82</td><td align=\"left\">2.21 ± 2.36</td><td char=\".\" align=\"char\">0.54</td></tr><tr><td align=\"left\">Unilateral/bilateral</td><td align=\"left\">89/16</td><td align=\"left\">98/20</td><td char=\".\" align=\"char\">0.73</td></tr><tr><td align=\"left\">Operating time (min)</td><td align=\"left\">55.84 ± 16.02</td><td align=\"left\">52.82 ± 17.69</td><td char=\".\" align=\"char\">0.19</td></tr><tr><td align=\"left\"><p>Early stage operating time (min)</p><p>unilateral</p></td><td align=\"left\">55.31 ± 12.04</td><td align=\"left\">48.14 ± 14.39</td><td char=\".\" align=\"char\">0.007</td></tr><tr><td align=\"left\"><p>Late stage operating time (min)</p><p>unilateral</p></td><td align=\"left\">48.82 ± 13.49</td><td align=\"left\">48.14 ± 14.39</td><td char=\".\" align=\"char\">0.78</td></tr><tr><td align=\"left\">Pre-operative testicular hypotrophy</td><td align=\"left\">26 (24.8%)</td><td align=\"left\">29 (24.6%)</td><td char=\".\" align=\"char\">0.97</td></tr><tr><td align=\"left\">Post-operative testicular hypotrophy</td><td align=\"left\">18 (17.1)</td><td align=\"left\">22 (18.6%)</td><td char=\".\" align=\"char\">0.77</td></tr><tr><td align=\"left\">Testicular volume growth (ml)</td><td align=\"left\">0.07 ± 0.11</td><td align=\"left\">0.06 ± 0.12</td><td char=\".\" align=\"char\">0.33</td></tr><tr><td align=\"left\">Complications</td><td align=\"left\">3 (2.9%)</td><td align=\"left\">4 (3.4%)</td><td char=\".\" align=\"char\">0.82</td></tr><tr><td align=\"left\">Hospital stay(days)</td><td align=\"left\">3.43 ± 0.97</td><td align=\"left\">3.31 ± 1.04</td><td char=\".\" align=\"char\">0.36</td></tr><tr><td align=\"left\">Testicular atrophy</td><td align=\"left\">0</td><td align=\"left\">0</td><td char=\".\" align=\"char\">&gt; 0.05</td></tr><tr><td align=\"left\">Testicular ascent</td><td align=\"left\">1</td><td align=\"left\">1</td><td char=\".\" align=\"char\">0.93</td></tr><tr><td align=\"left\">Redo-orchiopexy</td><td align=\"left\">1</td><td align=\"left\">1</td><td char=\".\" align=\"char\">0.93</td></tr><tr><td align=\"left\">Success rate</td><td align=\"left\">99.0%</td><td align=\"left\">99.2%</td><td char=\".\" align=\"char\">0.93</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<fn-group><fn><p><bold>Publisher’s Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"383_2023_5630_Fig1_HTML\" id=\"d32e331\"/>", "<graphic xlink:href=\"383_2023_5630_Fig2_HTML\" id=\"d32e354\"/>", "<graphic xlink:href=\"383_2023_5630_Fig3_HTML\" id=\"d32e574\"/>" ]

[ "<media xlink:href=\"383_2023_5630_MOESM1_ESM.mp4\"><caption><p>Supplementary Material 1</p></caption></media>" ]

{ "acronym": [ "UDT", "LO", "LESS", "DSD" ], "definition": [ "undescended testis", "laparoscopic orchiopexy", "laparoendoscopic single-site surgery", "disorders of sex development" ] }

[ "<title>Introduction</title>", "<p id=\"Par5\">Ozone is a principal component of photochemical air pollution endogenous to numerous metropolitan areas and is a potent oxidant gas. Ozone exposure is known to induce irritant effects on the respiratory tract impairing lung function, resulting in subjective symptoms of respiratory discomfort and detriments in exercise capacity and performance in susceptible and healthy individuals (Adams ##REF##3324257##1987##; Bosson et al. ##REF##18321939##2008##).</p>", "<p id=\"Par6\">Athletes often have greater exposure to air pollutants when training outdoors and may be more susceptible to its negative effects (Carlisle and Sharp ##REF##11477012##2001##). During exercise there is an increase in minute ventilation, and at higher-exercise intensities, a larger fraction of air is inhaled which will proportionately increase the quantity of pollutants. The air flow velocity of this higher respiration also carries the pollutants deeper into the respiratory tract (Carlisle and Sharp ##REF##11477012##2001##; Kubesch et al. ##REF##25475111##2015##). Research examining the relationship between ozone exposure, athletic performance and lung function reports that both aerobic capacity and lung function are negatively affected by poor air quality and ozone exposure (Foxcroft and Adams ##REF##3759781##1986##; Reche et al. ##REF##32065890##2020##), and that continuous exercise produces a greater effect (Adams ##REF##3324257##1987##).</p>", "<p id=\"Par7\">Acute airway epithelial inflammatory response to ozone results in bronchial airway narrowing, reduced pulmonary gas diffusion and arterial oxygenation, impaired vasoregulation, and increased blood viscosity (Cakmak et al. ##REF##22000598##2011##). The pathways underlying these effects are complex and poorly understood; however, oxidative stress repeatedly emerges as a potential mechanism in all these detrimental cardiovascular and respiratory actions. Ozone inhalation induces the production of reactive oxygen species (ROS) within the airways by interacting with the epithelial lining fluid and unsaturated compounds present in the respiratory tract (Gomes et al. ##REF##22092484##2011##, Cho et al. 2006, Mudway ##REF##10445623##1999##), activating ROS-signalling pathways and initiating inflammatory responses (Cho and Kleeberger ##REF##19646463##2010##; Holz et al. ##REF##10051250##1999##; Mumby et al. ##REF##31354743##2019##).</p>", "<p id=\"Par8\">Large-scale epidemiological studies have found a negative correlation between polyphenol consumption and respiratory disease, respiratory decline and prevalence of respiratory symptoms (Nyanhanda et al. ##REF##24526266##2014##; Garcia-Larsen et al. ##REF##25884660##2015##, Garcia-Larsen et al. ##REF##29342980##2018##, Morton and Braakhuis ##REF##34959825##2021##). A sub-class of polyphenols, anthocyanins and proanthocyanins, have been found to attenuate lung inflammation (Nyanhanda et al. ##REF##24526266##2014##, Shaw et al. ##UREF##6##2020##). Blackcurrants (<italic>Ribes nigrum L</italic>.) are very high in antioxidant activity and are amongst the top dietary sources of anthocyanins. Blackcurrant (BC) supplementation has been shown to improve cycling performance under ambient air conditions (Cook et al. ##REF##26175097##2015##), but to our knowledge no one has examined the effects of polyphenol supplementation on exercise performance with trained athletes in high ozone conditions.</p>", "<p id=\"Par9\">Therefore, the purpose of this study was to investigate the efficacy of 7 days of polyphenol supplementation on cycling time trial performance and respiratory function in healthy male adults exercising in ozone. We hypothesise there will be no difference in exercise performance or respiratory function between the polyphenol supplemented or control trials.</p>" ]

[ "<title>Methods</title>", "<title>Participants</title>", "<p id=\"Par10\">Thirteen healthy male cyclists (mean ± SD: age, 43.8 ± 12.38 years; height, 177.8 ± 7.1 cm; weight, 76.03 ± 7.88 kg; O_2max 4.12 ± 0.72 L min⁻¹) volunteered to participate in this study. All subjects gave written informed consent after the experimental procedures, associated risks and potential benefits were explained and before the commencement of study participation. The study was approved by the Northern Health and Disability Ethics Committee (21/NTB/68), registered with the Australia New Zealand Clinical Trial Registry (ACTRN12622001198718) and conformed to the 2013 Declaration of Helsinki. An a priori analysis was conducted for sample size estimation using G*Power version 3.1.9.4 (Faul et al. ##UREF##3##2009##). The estimation was based on a meta-analysed effect of <italic>d</italic> = 0.45 for BC on exercise performance (Braakhuis, et al. ##REF##32460873##2020##). Based on a repeated-measures ANOVA and between and within groups, <italic>α</italic> = 0.05 and power (1− β) = 0.8, yielded a required sample size of 12. Two subjects withdrew from the study after the first ozone exposure due to the respiratory symptoms experienced in the ozone environment, and one participant withdrew due to work commitments. Three subjects became infected with Covid during the trial. All three chose to return following their infection, but were required to complete their isolation period, and complete a minimum of four weeks of normal training before being readmitted to the study. Once readmitted, subjects had to complete the familiarisation trial again. The final sample size was, therefore, 10. Participants attended all testing sessions at the same time of day (± 90 min) and were required to refrain from strenuous physical activity and replicate any light training in the 24 h preceding each trial. Participants recorded their nutrition intake in the 24 h preceding the first trial and replicated this intake for all subsequent trials. Participants refrained from eating and only drank plain water for the two hours before each testing session commenced.</p>", "<title>Experimental design</title>", "<p id=\"Par11\">The study was a randomised, double-blind, placebo-controlled crossover design. Participants visited the laboratory on three occasions. All subjects completed (i) an incremental test to exhaustion (O_2max) and familiarisation and (ii) two exercise testing trials in an ozone polluted environment following 7 days of supplementation of either placebo (PL) or blackcurrant (PB). During the initial visit to the laboratory, cyclists completed an incremental ramp test to determine their maximal oxygen consumption (O_2max) on a calibrated Velotron Dynafit Pro cycle ergometer (RacerMate Inc, WA, USA) using the company’s associated software package, followed by a 10-min rest and then a 4 km time trial (TT). The same cycle ergometer was used in all testing sessions. All components of the experimental procedure were included to familiarise participants with the test procedure and equipment. The incremental test and familiarisation were conducted in an environmentally controlled laboratory (temperature 19 ± 1º C: relative humidity 36 ± 6%) and ambient air conditions. The ozone trials were conducted in a sealed environmental chamber. Ozone was generated by silent discharge method (N50-C Ozone Generator) with a relay sensor (airQual, SM-70, Novozone, Auckland, NZ) to automatically maintain an ozone level of 0.25 ppm within ± 10%. There was a 14-d washout period between each supplement regime. All tests were supervised by the same researcher who was blinded to the experimental condition. A summary of the study design is shown in Fig. ##FIG##0##1##.</p>", "<title>Incremental test</title>", "<p id=\"Par12\">On the first laboratory visit participants performed an incremental ramp test to determine maximal oxygen uptake (O_2max) and calculation of work-rate outputs (watts) for the preload/steady state protocol for the intervention trials. The cycle ergometer was adjusted to a position that resembled the set-up of the participant’s own racing bicycle and participants performed a 10-min warm-up at a self-selected sub-maximal intensity. Power output was increased to 100 W and increased continuously at a rate of 25 W.min⁻¹ until the cyclist reached volitional exhaustion. Participants were required to remain seated throughout the test and maintain a cadence of 80 – 100 rpm. Indicators of achieving O_2max were volitional fatigue, a plateau in O₂, a drop in cadence below 80 rpm, and/or a RER ≥ 1.1. During the incremental test, respiratory gases and heart rate were measured continuously with a calibrated metabolic system (Metamax, Cortex, Leipzig, Germany) using breath by breath mode. Peak power output (PPO) was defined as the average power sustained during the final 30-s of the test; O_2max was defined as the highest O₂ measured over 30-s. Workloads for the preload protocol were calculated for each rider as 50%, 60% and 70% of the PPO achieved in the incremental test.</p>", "<title>Experimental trial</title>", "<p id=\"Par13\">All experimental arms were conducted in ozone (0.25 ppm). Subjects were randomly assigned in a crossover design to receive either PB or PL. Subjects consumed a commercially available product (Ᾱrepa™) containing freeze dried blackcurrant (PB) or PL for a period of 7 days prior to exercise testing. Subjects completed two separate intervention arms: PL + ozone cycling, and PB + ozone cycling. Each trial was separated by a 14-day washout period, after which subjects consumed their alternative treatment for 7 days before their final trial. Both the PB and PL were encapsulated into berry flavoured, purple gelatine capsules (The Capsule Guy, Adelaide, Australia) and dispensed into opaque unmarked bottles. The bottles were given to the researcher on the day of testing by an independent person for distribution to participants. The researcher remained blinded to the interventions throughout data collection. Supplement adherence was monitored by oversupplying participants with capsules and counting the returned capsules at each performance test.</p>", "<p id=\"Par14\">The polyphenol blend powder (PB) contained a combination of freeze-dried NZ blackcurrant (94%), L-theanine (3%) and Pinus Radiata extract (3%) which provided 200 mg anthocyanins per 5g serve. PB was provided as a dose to provide 4.3 mg anthocyanins/kg body weight. The placebo was a manufactured berry flavoured powder matched for all nutritional composition, colour, and taste (Sensient, Auckland, New Zealand), but contained no phenolics, active ingredients or Vitamin C. To maintain the bioactivity of the phenolics, the PB capsules were made in batches close to testing. Supplements were allocated by an individual independent of the study, and neither the researcher nor subjects were aware of the intervention allocation.</p>", "<p id=\"Par15\">Following 7 days of supplementation participants completed the experimental protocol. Participants were weighed when they arrived at the laboratory and fitted with measurement equipment. Participants then entered the environmental chamber and respiratory testing was performed and respiratory symptoms recorded. All cycling trials were performed on the ergometer described previously using the saddle and handlebar height recorded at the first visit. During all tests pulmonary gas exchange and ventilation were measured continuously using the metabolic system previously described. Participants performed a warm-up for 5 min, before completing a preload protocol consisting of 10 min at 50% PPO, 10 min at 60% PPO and 5 min at 70% PPO. Cycling load was automatically controlled by the ergometer. Ratings of perceived exertion (Borg RPE 6–20 scale) were obtained in the last 15 s of each stage during the preload. A 10 min rest followed the preload protocol and participants reported their respiratory symptoms. Participants were required to then complete a 4 km TT in the shortest time possible. Participants could only view their gearing and distance covered but were blinded to any other information to reduce potential pacing effects. Participants reported their RPE immediately after completion of the 4 km TT and then dismounted the ergometer. In a seated position within the chamber, participants completed a FeNO measure, and respiratory symptoms were assessed and another FeNo measurement completed (10-min post exercise). Maximal spirometry testing was then undertaken, once at 10 min post 4 km TT completion and another at 20 min post. Muscle oxygen saturation was measured from the onset of the preload until 15 min after the completion of the 4 km TT. All cycling data (time, distance, power, cadence, rpm, speed) was captured by the ergometer’s associated software package (RacerMate Inc, WA, USA). Participants were cooled with standing floor fans during the experimental trials and permitted to drink water ad libitum in the rest period and post the 4 km TT.</p>", "<title>Respiratory measurements</title>", "<p id=\"Par16\">Fraction expired Nitric Oxide (FeNO) measurements were obtained using a FeNO analyser (NObreath, Bedfont Scientific Ltd, England. Concentration range 5 – 300 ppb, accuracy ± 5 ppb/ ± 10% of measured value, repeatability ± 5 ppb/ ± 10% of measured value) using the guidelines of the American Thoracic Society (ATS) (Dweik et al. ##UREF##2##2011##). In brief, subjects inhaled to total lung capacity and exhaled at a constant expiratory flow rate of 50 mL/s for approximately 6 s. All FeNO measures were obtained prior to spirometry testing as results have been shown to be affected by preceding maximal spirometry testing (Hoyte et al. ##UREF##5##2018##). Participants performed spirometry testing for forced vital capacity (FVC), forced expiratory volume (FEV₁), forced expiratory flow (FEF _25–75%), peak expiratory flow (PEF) according to the guidelines of the American Thoracic Society (Graham et al. 2019), using a digital spirometer interfaced to a computer (Medikro Pro, Kuopio, Finland. Volume range 0–14 L, flow range ± 14L/sec, flow accuracy ± 2% or 0.020 L/s, volume accuracy ± 2% or 0.05 L/s). Spirometry measures were repeated until two tests were within 150 mL limits of each other (Dweik et al. ##UREF##2##2011##; Graham et al. ##UREF##4##2019##), and the mean of the two highest qualified data values for FVC and FEV₁ selected. Respiratory symptoms were assessed pre- and immediately post the preload protocol and post the 4 km TT using a visual analogue scale. Participants were asked to rate severity of cough (SOC), pain on deep inspiration (PDI), shortness of breath (SOB) and throat irritation (TI) on a five-point scale ranging from 0 (none) to 4 (most severe).</p>", "<title>Muscle oxygenation</title>", "<p id=\"Par17\">Skeletal muscle oxygenation (%SmO₂) of the vastus lateralis of the right leg was continuously measured using a near infrared spectroscopy (NIRS) sensor (Moxy monitor, Fortiori Design LLC, Minnesota, USA). The sensor was firmly attached at half the length of the vastus lateralis (greater trochanter to lateral knee joint space) in a black light blocking case to reduce light interference. The transmitted light was recorded at 0.5 Hz and received into proprietary software (PerfPro Software v 5.82.06, Hartware Technologies, Rockman, MI). Data were interpolated to 1-s intervals and averaged over every 60-s for the preload, and 15-s for the 4 km TT.</p>", "<title>Data analysis procedures and statistical analysis</title>", "<p id=\"Par18\">Breath-by-breath data for O₂, CO₂, RER, E, BF and V_T from each test were examined for errant breaths and outliers (&gt; 3 SDs from the mean) removed. The breath-by-breath data were averaged into 1-min intervals for each stage of the preload, and 2-min steady state data from each stage used for analysis of steady state cycling. The 4 km TT data (time, average power) was averaged by distance into 1 km distances. Breath-by-breath O₂, CO₂, RER data and mean power output (W) were averaged over the time for each km of the 4 km TT. Cycling efficiency could not be calculated at 70% PPO as RER values were &gt; 1.0, and values therefore include unknown energetic contributions from anaerobic metabolism. Gross cycling economy of steady state cycling in the preload was calculated instead as WR/O₂ (W), where O₂ of each stage was used as the measure of O₂ cost and mean power output over the distance as the power output (WR). Skeletal muscle oxygenation was averaged into 1-min intervals from start (pre-preload) to 5 min post 4 km TT completion. The mean of 2-min steady state SmO₂ was used as the value for each stage of the preload. Due to the inter-individual variability in FeNO measures, changes were expressed as percentage change from resting pre-exposure values.</p>", "<p id=\"Par19\">Statistical analyses were conducted using GraphPad Prism version 9.3.0 for Windows (GraphPad Software, San Diego, California USA). The normality of data residuals was confirmed using the Shapiro–Wilk test prior to all analyses. Differences between treatments were determined using a one-way repeated measures analysis of variance (ANOVA), or via a two-tailed, two-way repeated measures ANOVA (treatment x time). Where significance was detected, Šídák’s multiple comparisons test post-hoc analysis was used to compare differences between treatments. Paired samples <italic>t</italic>-tests were used to compare change from pre or baseline between treatments. Fischer’s exact test of 2 × 2 contingency table (symptoms vs. no symptoms) was used to determine the association between treatment and each respiratory symptom (SOC, PDI, SOB and TI). Statistical significance was defined as <italic>p</italic> ≤ 0.05. The magnitudes of the standardised effects for the test measures were also determined using the Cohen effect size (<italic>d</italic>). Thresholds of 0.2, 0.5, and 0.8 for small, moderate, and large effects, respectively, were used in accordance with the recommendations of Cohen (1988). ES values &lt; 0.2 were deemed trivial differences. Simple group statistics are shown as means ± SD, unless otherwise stated. Percentage (%) differences between treatments are reported as mean ± 95% confidence intervals (CI).</p>" ]

[ "<title>Results</title>", "<p id=\"Par20\">One participant was excluded from analysis as they were unable to complete the full preload protocol under the PL condition, therefore, nine subjects were included in the final analysis of all performance data.</p>", "<title>Steady state cycling</title>", "<p id=\"Par21\">A summary of measured variables during steady state cycling in the preload is shown in Table ##TAB##0##1##. Heart rate, O₂ (L min−1), CO₂ (L min−1), E (L/min), breathing frequency (BF) tidal volume (V_T), SmO₂ responses, and RPE were not significantly different between PB and PL across the three intensities of the preload protocol (Table ##TAB##1##2##). At 60% PPO V_T was 2.75 ± 0.45 in PL and 2.65 ± 0.47 in PB (<italic>p</italic> = 0.06)). RER was lower at 70% PPO in the PB condition (<italic>p</italic> = 0.03). Cycling economy (W.L min−1) at fixed workloads were not different between the two conditions (<italic>p</italic> = 0.31).</p>", "<title>4 km cycling TT performance</title>", "<p id=\"Par22\">Time to complete the 4 km TT with PB was 406.43 ± 50.29 s, and 426.20 ± 75.06 s with PL but were not significantly different (<italic>p</italic> = 0.09, 95% CI -43.47 to 3.92, <italic>d</italic> = 0.31, Fig. ##FIG##1##2##).</p>", "<p id=\"Par23\">Average power output in the 4 km TT was 258.95 ± 71.35 W following PB supplementation, compared to 242.52 ± 87.26 W with PL (16.43 ± 23.78 W, 95% CI 1.84 to 34.71, <italic>p</italic> = 0.07, <italic>d</italic> = 0.20). The average power output across the baseline 4 km TT was 274.56 ± 82.85 W. Analysis of mean power output between PB and PL in each km of the 4 km TT under ozone showed a significant main effect for distance (<italic>p</italic> &lt; 0.01), and a significantly higher power output was observed in the first km of the TT following PB supplementation (− 27.85 W, 95% CI − 50.95 to − 4.75, <italic>p</italic> = 0.01, <italic>d</italic> = 0.33. Fig. ##FIG##2##3##). A summary of measured variables per km of the 4 km TT is shown in Table ##TAB##1##2##.</p>", "<p id=\"Par24\">A significant treatment effect for O₂ was found in the PB condition (− 0.17, 95% CI − 0.29 to − 0.05, <italic>p</italic> = 0.01, <italic>d</italic> = 0.24), with a higher mean O₂ in the 4 km TT compared to PL (Fig. ##FIG##3##4##). No differences were observed in RPE, HR, CO₂ or RER between the two conditions during the TT.</p>", "<title>Respiratory function</title>", "<p id=\"Par25\">Ozone exposure resulted in significant decreases in FEV₁, FVC, FVC/FEV₁, FEF_25-75 and PEF compared ambient air. FVC was reduced by 12.00 ± 13.81% in PL (<italic>p</italic> = 0.001) and 11.04 ± 9.21% in PB (<italic>p</italic> = 0.02) after cycling in ozone compared to a 6.94 ± 13.24% increase after exercise in ambient air conditions. FVC continued to decrease 20 min post the 4 km TT in the PL condition but improved slightly in the PB condition (PB − 9.03 ± 10.86%, PL − 12.73 ± 13.13%, <italic>p</italic> = 0.28, <italic>d</italic> = 0.28). Similarly, FEV₁ decreased by 18.15 ± 13.49% with PL (<italic>p</italic> &lt; 0.01) and 15.45 ± 10.48% with PB (<italic>p</italic> &lt; 0.01) following exercise in ozone. FEV₁ increased 5.36 ± 6.63% following exercise in ambient air. FEV₁ measures improved in both PL (− 15.80 ± 16.50%) and PB (− 15.43 ± 12.33%, <italic>p</italic> = 0.99, <italic>d</italic> = 0.02) trials by 20 min post exercise. Lung function following ozone exposure was similar in PB and PL conditions. A significant time effect was found for FEF_25-75 following ozone exposure. FEF_25-75 decreased –22.03% ± 28.40% 15 min post cycling in ozone following PL supplementation and –36.56 ± 34.63% with PB supplementation (− 29.30, 95% CI − 4.72 to 33.79, <italic>p</italic> = 0.14, <italic>d</italic> = 0.46). At 20 min post exercise FEF25-75 decreased -34.77 ± 21.39% with PL treatment and − 29.19 ± 40.71% with PB (− 31.98, 95% CI − 24.83 to 13.68, <italic>p</italic> = 0.71, <italic>d</italic> = 0.17). The means of pre and post exercise spirometry measurements are summarised in Table ##TAB##2##3##. There was a decrease in FeNO (ppb) levels following exercise in ozone (<italic>p</italic> = 0.07, <italic>d</italic> = 0.49). Fisher’s exact test was used to determine if there was a significant association between supplementation and respiratory symptoms (SOC, PDI, SOB and TI). There was a statistically significant relationship between PB supplementation and severity of cough (<italic>p</italic> = 0.03, two tailed), with lower symptom scores compared to PL. No differences were observed for the other respiratory symptoms (Table ##TAB##3##4##).</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par26\">This study investigated the effects of 7 days of polyphenol blend supplementation at a standardised dose of 4.3 mg/kg anthocyanins on cycling performance in healthy males exercising under ozone conditions. We found no significant differences in measured variables across submaximal exercise intensities of 50%, 60% and 70% PPO in the preload. Furthermore, the 4 km TT time with PB supplementation (406 s) compared to PL (426 s) was not statistically different, but there was a small effect (<italic>d</italic> = 0.31). A significantly higher O₂ was observed in the 4 km TT following PB supplementation, along with higher mean power in the first km compared to PL.</p>", "<p id=\"Par27\">We did not statistically compare the 4 km TT times under ozone to the TT time in ambient air during familiarisation due to the differences in preload preceding the 4 km TT, but it is worth noting that the time in the PB treatment was only 1.86 ± 4.87% slower than ambient air performance compared to a decrease of − 6.18 ± 5.85% with PL. There were large individual changes in 4 km TT performance between the PB and PL conditions under ozone. Three subjects improved substantially, two subjects performed marginally worse, and four subjects had ~ equivalent 4 km TT times. Previous research has reported considerable individual variation in inflammation and lung function parameters as well as subjective symptomatic responses following ozone exposure (Hazucha et al. ##REF##12871968##2003##, Mudway et al. ##REF##11595381##2001##, Holz et al. ##REF##10051250##1999##, Passannante et al. ##REF##9804592##1998##). In the current study, supplementation with PB for 7 days resulted in a significant reduction in the severity of cough. We also observed lower scores in throat irritation, pain on deep inspiration and shortness of breath following PB treatment after both the preload protocol and the 4 km TT. The better performance in the subsequent 4 km TT in some subjects with PB could be related to a perceived lower stress due to reduced adverse respiratory symptoms.</p>", "<p id=\"Par28\">Despite cross-sectional studies showing respiratory and pulmonary benefits from anthocyanin intake (Garcia-Larsen et al. ##REF##25884660##2015##, Tan et al. ##REF##25451569##2014##, Morton and Braakhuis ##REF##34959825##2021##), the results from the present study failed to show any benefit from PB supplementation on lung function measures following acute ozone exposure. Significant decreases in FEV1, FVC, FEV/FEV1, and FEF_25-75 were observed in subjects after cycling in ozone 15 min post exercise, and continued to decline at 20 min post. The greatest respiratory decreases were observed in FEF_25-75 which decreased by as much as 30% in both PL and PB. FEF_25-75 measures describe the flow from medium-to-small airways, and reductions in FEF_25-75 reflects resistance and possible functional impairment of peripheral and small airways caused by inflammatory processes (Szefler et al. ##REF##32399899##2020##). FEF_25-75 is, however, non-specific, not uniformly reproducible and is dependent on FVC (Deepak et al. ##UREF##1##2017##). Measuring FeNO provides a non-invasive surrogate measure of airway inflammation and insight into inflammation in the distal airways. Nitric oxide (NO) in the lung promotes inflammation at higher concentrations as a result of the overactivity of oxidative pathways (Hoyte et al. ##UREF##5##2018##). The increase in FeNO levels with PL and PB in the present study at 10 min post exercise could indicate the onset of airway inflammation.</p>", "<p id=\"Par29\">The ozone dose is an important factor in exposure studies with a cumulative dose determined by ozone concentration [ppb] x duration of exposure (min) x V’E (L/min) (Adams et al. ##REF##7263448##1981##, Arjomandi et al. ##UREF##0##2018##). The inclusion of an incremental steady state protocol prior to a maximal effort 4 km TT was used to induce a fatiguing protocol relative to the rider’s individual ability and extend the ozone exposure to approximately 60 min. In addition to this, it allowed us to observe any perturbations to physiology and performance at fixed exercise intensities. Furthermore, the incremental increase in work rate would increase the inspiration of ozone. All measured variables were similar at work rates of 50% and 70% PPO. Breathing frequency increased, tidal volume decreased, and gross cycling economy were lower with PB treatment at 60% PPO. Collectively these shifts indicate a higher respiratory cost to produce the workload, and a higher BF and lower V_T a shallower breathing pattern, which typically indicates lower perfusion rates. A reduction in V_T has been observed in previous work with ozone exposure (Adams ##REF##3324257##1987##).</p>", "<p id=\"Par30\">The current study is novel in its attempt to use polyphenols supplementation to improve athletic performance in a polluted environment. The lack of other studies examining antioxidant supplementation, ozone and exercise performance makes comparisons difficult. In addition, the lack of clear underlying physiological mechanisms means that any reasons for improved performance are speculative and based on assumptions from studies in ambient air. To our knowledge one other controlled study has utilised an antioxidant intervention to determine the effects on exercise performance in ozone. Gomes et al. (##REF##22092484##2011##) performed a randomised, double-blind crossover to determine if supplementation of Vitamin C (500 mg/day) and vitamin E (100 IU/day) for two weeks would improve 8 km running performance in a hot (31°C), humid (70%), ozone polluted (0.10 ppm) environment. Despite changes to plasma and nasal lavage antioxidant status, no effect on running performance was found, despite positive correlations between antioxidant concentration and improvements in running time.</p>", "<p id=\"Par31\">A major limitation of the current study is the reduced sample size which was unfortunately caused by subject drop out beyond our control. The loss of participants compromised our final statistical analysis. A larger sample size would have aided clearer effects of PB supplementation, or lack thereof, more clearly on exercise performance under ozone. Another limitation is we did not control for subjects normal dietary polyphenol intake, choosing instead to supplement anthocyanins with the usual diet. This may have resulted in higher polyphenol and anthocyanin consumption in some subjects. However, previous work has estimated the mean consumption of anthocyanins from dietary sources to be only 43 – 67 mg/day (Copetti et al. ##REF##35204268##2022##). Finally, while we prescribed the polyphenol powder based on the anthocyanin content, we acknowledge the commercial powder also contained other extracts (L-theanine and pine bark) which may have affected the findings.</p>" ]

[ "<title>Conclusion</title>", "<p id=\"Par32\">Supplementation with a polyphenol blend at a dose of 4.3 mg/kg.bw anthocyanins for 7 days resulted in a small but non-significant increase in 4 km cycling performance. Oxygen consumption during the TT was also significantly greater with polyphenol treatment. Finally, the severity of cough experienced when exercising in ozone was significantly reduced with supplementation. Further studies with larger sample size are required to confirm the results of this study and to determine the underlying mechanisms responsible for any potential benefits.</p>" ]

[ "<title>Purpose</title>", "<p id=\"Par1\">Polluted environments can adversely affect lung function and exercise performance. Evidence suggests that some nutrient supplements may offset pollution’s detrimental effects. This study examined the effect of polyphenol supplementation on lung function and exercise performance in an ozone-polluted environment.</p>", "<title>Methods</title>", "<p id=\"Par2\">Ten male cyclists (mean ± SD: age, 43.8 ± 12.4 years; height, 177.8 ± 7.1 cm; weight, 76.03 ± 7.88 kg; VO_2max 4.12 ± 0.72 L min⁻¹) initially completed a baseline maximal incremental test and maximal effort 4 km time trial in ambient air. Thereafter cyclists completed two trials in an ozone-polluted environment (0.25 ppm) following seven days of supplementation with either polyphenol (PB) or placebo (PL). Experimental trials consisted of a three-stage submaximal test (50%, 60% and 70% incremental peak power) followed by a 4 km time trial. Lung function was measured pre- and post-exercise via spirometry and adverse respiratory symptoms with a Likert scale.</p>", "<title>Results</title>", "<p id=\"Par3\">Ozone exposure significantly reduced (<italic>p</italic> &lt; 0.05) lung function relative to ambient air. There were no significant differences (<italic>p</italic> &gt; 0.05) in measured variables across the three submaximal intensities. There was a small (<italic>d</italic> = 0.31) non-significant difference (<italic>p</italic> = 0.09) in 4 km performance in PB (406.43 ± 50.29 s) vs. PL (426.20 ± 75.06 s). Oxygen consumption during the time trial was greater in PB (3.49 ± 0.71 L min⁻¹) vs PL (3.32 ± 0.71 L min⁻¹, <italic>p</italic> = 0.01, <italic>d</italic> = 0.24). Cough severity (SOC) was lower (<italic>p</italic> = 0.03) with PB relative to PL.</p>", "<title>Conclusion</title>", "<p id=\"Par4\">PB supplementation may provide small benefits to performance and reduce cough symptoms during high-intensity exercise in ozone-polluted environments.</p>", "<title>Keywords</title>", "<p>Open Access funding enabled and organized by CAUL and its Member Institutions</p>" ]

[]

[ "<title>Acknowledgements</title>", "<p>We would like to thank the participants for their involvement in this study.</p>", "<title>Author contributions</title>", "<p>All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Lillian Morton. The first draft of the manuscript was written by Lillian Morton and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by CAUL and its Member Institutions. Funding for the present work was provided by High Value Nutrition (HVN) (HVN1913 3721400) Ko Ngā Kai Whai Painga National Science Challenge. Lillian Morton was supported by a Callaghan Institute Research Development grant.</p>", "<title>Data availability</title>", "<p>The data that support the findings of this study are available from the corresponding author, L. C. Morton, upon reasonable request.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par33\">The authors declare no conflicts of interest.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Study design and data collection points</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p><bold>A</bold>—Mean ± SD 4 km TT time (s) in ozone following PB or PL supplementation for 7 days. <bold>B</bold> – Change in performance (%) relative to baseline following supplementation with PB or PL</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p><bold>A</bold>—Mean ± SD power output (Watts) for the 4 km TT in ozone following PB or PL supplementation for 7 days. <bold>B</bold> – Average power output (Watts) per km of the 4 km TT. Power output in the first km was significantly higher following PB supplementation, * <italic>p</italic> = 0.01</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p><bold>A</bold> Mean pulmonary oxygen uptake (O₂ L min−1) during 4 km TT cycling performance in ozone following 7 days supplementation of PB or PL. A significant difference in O₂ during the 4 km TT observed with PB supplementation compared to PL, * <italic>p</italic> = 0.01. <bold>B</bold> – O₂ per km of the 4 km TT</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Metabolic responses, skeletal muscle oxygenation and cycling economy during the steady state preload cycling protocol (10-min at 50 PPO, 10-min at 60% PPO and 5-min at 70% PPO)</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" colspan=\"2\">50% PPO</th><th align=\"left\" colspan=\"2\">60% PPO</th><th align=\"left\" colspan=\"2\">70% PPO</th></tr><tr><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th></tr></thead><tbody><tr><td align=\"left\">O₂ (L min−1)</td><td char=\"±\" align=\"char\">2.79 ± 0.35</td><td char=\"±\" align=\"char\">2.80 ± 0.47</td><td char=\"±\" align=\"char\">3.27 ± 0.43</td><td char=\"±\" align=\"char\">3.31 ± 0.56</td><td char=\"±\" align=\"char\">3.72 ± 0.49</td><td char=\"±\" align=\"char\">3.73 ± 0.66</td></tr><tr><td align=\"left\">CO₂ (L min−1)</td><td char=\"±\" align=\"char\">2.59 ± 0.32</td><td char=\"±\" align=\"char\">2.59 ± 0.47</td><td char=\"±\" align=\"char\">3.11 ± 0.40</td><td char=\"±\" align=\"char\">3.13 ± 0.53</td><td char=\"±\" align=\"char\">3.76 ± 0.47</td><td char=\"±\" align=\"char\">3.73 ± 0.70</td></tr><tr><td align=\"left\">Heart rate (bpm)</td><td char=\"±\" align=\"char\">136 ± 11</td><td char=\"±\" align=\"char\">135 ± 10</td><td char=\"±\" align=\"char\">152 ± 12</td><td char=\"±\" align=\"char\">154 ± 12</td><td char=\"±\" align=\"char\">167 ± 12</td><td char=\"±\" align=\"char\">167 ± 13</td></tr><tr><td align=\"left\">RER</td><td char=\"±\" align=\"char\">0.93 ± 0.02</td><td char=\"±\" align=\"char\">0.92 ± 0.03</td><td char=\"±\" align=\"char\">0.95 ± 0.02</td><td char=\"±\" align=\"char\">0.94 ± 0.02</td><td char=\"±\" align=\"char\">1.01 ± 0.03</td><td char=\"±\" align=\"char\">0.99 ± 0.02*</td></tr><tr><td align=\"left\">E (L. min⁻¹)</td><td char=\"±\" align=\"char\">72.49 ± 7.81</td><td char=\"±\" align=\"char\">70.60 ± 9.64</td><td char=\"±\" align=\"char\">91.11 ± 12.26</td><td char=\"±\" align=\"char\">92.31 ± 12.10</td><td char=\"±\" align=\"char\">120.30 ± 14.51</td><td char=\"±\" align=\"char\">116.93 ± 18.27</td></tr><tr><td align=\"left\">BF (min)</td><td char=\"±\" align=\"char\">29.50 ± 6.12</td><td char=\"±\" align=\"char\">28.95 ± 5.38</td><td char=\"±\" align=\"char\">33.99 ± 6.91</td><td char=\"±\" align=\"char\">35.54 ± 5.96</td><td char=\"±\" align=\"char\">43.02 ± 8.36</td><td char=\"±\" align=\"char\">41.82 ± 7.35</td></tr><tr><td align=\"left\">V_T (L)</td><td char=\"±\" align=\"char\">2.53 ± 0.43</td><td char=\"±\" align=\"char\">2.52 ± 0.52</td><td char=\"±\" align=\"char\">2.75 ± 0.45</td><td char=\"±\" align=\"char\">2.65 ± 0.47</td><td char=\"±\" align=\"char\">2.86 ± 0.49</td><td char=\"±\" align=\"char\">2.85 ± 0.52</td></tr><tr><td align=\"left\">SmO₂ (%)</td><td char=\"±\" align=\"char\">30.22 ± 5.28</td><td char=\"±\" align=\"char\">31.07 ± 10.47</td><td char=\"±\" align=\"char\">21.91 ± 5.66</td><td char=\"±\" align=\"char\">21.87 ± 11.28</td><td char=\"±\" align=\"char\">17.07 ± 5.52</td><td char=\"±\" align=\"char\">17.46 ± 11.42</td></tr><tr><td align=\"left\">RPE</td><td char=\"±\" align=\"char\">12 ± 1</td><td char=\"±\" align=\"char\">12 ± 1</td><td char=\"±\" align=\"char\">15 ± 1</td><td char=\"±\" align=\"char\">15 ± 2</td><td char=\"±\" align=\"char\">18 ± 1</td><td char=\"±\" align=\"char\">18 ± 1</td></tr><tr><td align=\"left\"><p>Cycling Economy</p><p>(W.L min−1)</p></td><td char=\"±\" align=\"char\">68.07 ± 5.63</td><td char=\"±\" align=\"char\">69.91 ± 10.12</td><td char=\"±\" align=\"char\">69.84 ± 5.65</td><td char=\"±\" align=\"char\">66.93 ± 4.98</td><td char=\"±\" align=\"char\">71.14 ± 4.55</td><td char=\"±\" align=\"char\">70.84 ± 4.75</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Mean power, ventilatory and gas exchange dynamics during 4 km TT cycling performance under ozone following 7-day supplementation with PB and PL</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" colspan=\"2\">1 km</th><th align=\"left\" colspan=\"2\">2 km</th><th align=\"left\" colspan=\"2\">3 km</th><th align=\"left\" colspan=\"2\">4 km</th></tr><tr><th align=\"left\">PL</th><th align=\"left\">PB</th><th align=\"left\">PL</th><th align=\"left\">PB</th><th align=\"left\">PL</th><th align=\"left\">PB</th><th align=\"left\">PL</th><th align=\"left\">PB</th></tr></thead><tbody><tr><td align=\"left\">Power (watts)</td><td align=\"left\"><p>216.00</p><p> ± 95.89</p></td><td align=\"left\"><p>244.74</p><p> ± 71.43**</p></td><td align=\"left\"><p>232.75</p><p> ± 89.76</p></td><td align=\"left\"><p>248.39</p><p> ± 74.55</p></td><td align=\"left\"><p>242.99</p><p> ± 89.62</p></td><td align=\"left\"><p>256.06</p><p> ± 78.29</p></td><td align=\"left\"><p>277.43</p><p> ± 78.85</p></td><td align=\"left\"><p>286.59</p><p> ± 74.64</p></td></tr><tr><td align=\"left\"><p>O₂</p><p>(L min−1) ^*</p></td><td align=\"left\"><p>2.61</p><p> ± 0.67</p></td><td align=\"left\"><p>2.80</p><p> ± 0.53</p></td><td align=\"left\"><p>3.32</p><p> ± 0.80</p></td><td align=\"left\"><p>3.51</p><p> ± 0.81</p></td><td align=\"left\"><p>3.52</p><p> ± 0.69</p></td><td align=\"left\"><p>3.70</p><p> ± 0.79</p></td><td align=\"left\"><p>3.82</p><p> ± 0.69</p></td><td align=\"left\"><p>3.95</p><p> ± 0.76</p></td></tr><tr><td align=\"left\"><p>CO₂</p><p>(L min−1)</p></td><td align=\"left\"><p>2.04</p><p> ± 0.66</p></td><td align=\"left\"><p>2.15</p><p> ± 0.66</p></td><td align=\"left\"><p>3.16</p><p> ± 0.90</p></td><td align=\"left\"><p>3.24</p><p> ± 1.18</p></td><td align=\"left\"><p>3.46</p><p> ± 1.02</p></td><td align=\"left\"><p>3.49</p><p> ± 1.27</p></td><td align=\"left\"><p>3.91</p><p> ± 0.84</p></td><td align=\"left\"><p>3.81</p><p> ± 1.350</p></td></tr><tr><td align=\"left\">Heart rate (bpm)</td><td align=\"left\"><p>138.78</p><p> ± 11.26</p></td><td align=\"left\"><p>141.54</p><p> ± 13.96</p></td><td align=\"left\"><p>155.16</p><p> ± 13.82</p></td><td align=\"left\"><p>156.99</p><p> ± 13.46</p></td><td align=\"left\"><p>161.66</p><p> ± 15.82</p></td><td align=\"left\"><p>164.17</p><p> ± 13.51</p></td><td align=\"left\"><p>169.35</p><p> ± 15.88</p></td><td align=\"left\"><p>169.91</p><p> ± 12.96</p></td></tr><tr><td align=\"left\">RER</td><td align=\"left\"><p>0.81</p><p> ± 0.06</p></td><td align=\"left\"><p>0.80</p><p> ± 0.03</p></td><td align=\"left\"><p>0.95</p><p> ± 0.06</p></td><td align=\"left\"><p>0.96</p><p> ± 0.06</p></td><td align=\"left\"><p>0.98</p><p> ± 0.05</p></td><td align=\"left\"><p>0.98</p><p> ± 0.06</p></td><td align=\"left\"><p>1.04</p><p> ± 0.05</p></td><td align=\"left\"><p>1.02</p><p> ± 0.05</p></td></tr><tr><td align=\"left\"><p>E</p><p>(L. min⁻¹)</p></td><td align=\"left\"><p>72.12</p><p> ± 14.90</p></td><td align=\"left\"><p>75.66</p><p> ± 10.83</p></td><td align=\"left\"><p>106.16</p><p> ± 19.96</p></td><td align=\"left\"><p>106.80</p><p> ± 21.10</p></td><td align=\"left\"><p>119.97</p><p> ± 25.21</p></td><td align=\"left\"><p>121.01</p><p> ± 23.54</p></td><td align=\"left\"><p>143.47</p><p> ± 21.17</p></td><td align=\"left\"><p>140.63</p><p> ± 26.25</p></td></tr><tr><td align=\"left\"><p>BF</p><p>(min)</p></td><td align=\"left\"><p>37.13</p><p> ± 8.39</p></td><td align=\"left\"><p>38.62</p><p> ± 6.68</p></td><td align=\"left\"><p>41.87</p><p> ± 7.53</p></td><td align=\"left\"><p>42.42</p><p> ± 7.87</p></td><td align=\"left\"><p>45.93</p><p> ± 10.46</p></td><td align=\"left\"><p>47.14</p><p> ± 8.42</p></td><td align=\"left\"><p>52.78</p><p> ± 10.21</p></td><td align=\"left\"><p>54.27</p><p> ± 12.39</p></td></tr><tr><td align=\"left\"><p>V_T</p><p>(L)</p></td><td align=\"left\"><p>1.99</p><p> ± 0.47</p></td><td align=\"left\"><p>1.99</p><p> ± 0.38</p></td><td align=\"left\"><p>2.61</p><p> ± 0.54</p></td><td align=\"left\"><p>2.57</p><p> ± 0.53</p></td><td align=\"left\"><p>2.71</p><p> ± 0.68</p></td><td align=\"left\"><p>2.62</p><p> ± 0.57</p></td><td align=\"left\"><p>2.81</p><p> ± 0.62</p></td><td align=\"left\"><p>2.69</p><p> ± 0.62</p></td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Respiratory responses and symptoms after cycling exercise in ozone (0.25 ppm) following PL or PB supplementation</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" colspan=\"2\">PRE</th><th align=\"left\" colspan=\"2\">Post 1 (15 min)</th><th align=\"left\" colspan=\"2\">Post 2 (20 min)</th></tr><tr><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th></tr></thead><tbody><tr><td align=\"left\">FVC (L)</td><td char=\"±\" align=\"char\">4.87 ± 0.98</td><td char=\"±\" align=\"char\">4.82 ± 0.93</td><td char=\"±\" align=\"char\">4.25 ± 0.90</td><td char=\"±\" align=\"char\">4.28 ± 0.87</td><td char=\"±\" align=\"char\">4.19 ± 0.82</td><td char=\"±\" align=\"char\">4.37 ± 0.94</td></tr><tr><td align=\"left\">FEV₁</td><td char=\"±\" align=\"char\">3.75 ± 0.77</td><td char=\"±\" align=\"char\">3.64 ± 0.62</td><td char=\"±\" align=\"char\">3.01 ± 0.52</td><td char=\"±\" align=\"char\">3.06 ± 0.53</td><td char=\"±\" align=\"char\">3.10 ± 0.66</td><td char=\"±\" align=\"char\">3.06 ± 0.63</td></tr><tr><td align=\"left\">FVC/FEV₁</td><td char=\"±\" align=\"char\">76.28 ± 6.45</td><td char=\"±\" align=\"char\">76.42 ± 6.55</td><td char=\"±\" align=\"char\">71.76 ± 8.43</td><td char=\"±\" align=\"char\">72.35 ± 7.49</td><td char=\"±\" align=\"char\">73.04 ± 9.30</td><td char=\"±\" align=\"char\">71.48 ± 6.39</td></tr><tr><td align=\"left\">FEF_25-75</td><td char=\"±\" align=\"char\">3.20 ± 0.89</td><td char=\"±\" align=\"char\">3.06 ± 0.65</td><td char=\"±\" align=\"char\">2.43 ± 1.22</td><td char=\"±\" align=\"char\">1.92 ± 1.15</td><td char=\"±\" align=\"char\">1.91 ± 0.74</td><td char=\"±\" align=\"char\">1.95 ± 1.16</td></tr><tr><td align=\"left\">PEF</td><td char=\"±\" align=\"char\">8.04 ± 1.94</td><td char=\"±\" align=\"char\">7.54 ± 1.51</td><td char=\"±\" align=\"char\">6.70 ± 1.92</td><td char=\"±\" align=\"char\">6.38 ± 1.50</td><td char=\"±\" align=\"char\">6.49 ± 2.01</td><td char=\"±\" align=\"char\">6.16 ± 1.64</td></tr><tr><td align=\"left\">FeNO</td><td char=\"±\" align=\"char\">27.22 ± 20.90</td><td char=\"±\" align=\"char\">27.33 ± 19.07</td><td char=\"±\" align=\"char\">25.11 ± 21.24</td><td char=\"±\" align=\"char\">23.00 ± 16.83</td><td char=\"±\" align=\"char\">26.67 ± 21.03</td><td char=\"±\" align=\"char\">26.00 ± 19.61</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab4\"><label>Table 4</label><caption><p>Respiratory symptom scores after cycling exercise in ozone (0.25 ppm) following PL or PB supplementation</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\"/><th align=\"left\" colspan=\"2\">PRE</th><th align=\"left\" colspan=\"2\">Post (15 min)</th><th align=\"left\" colspan=\"2\">Post (20 min)</th></tr><tr><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th><th align=\"left\">Placebo</th><th align=\"left\">Polyphenol Blend</th></tr></thead><tbody><tr><td align=\"left\">SOC</td><td align=\"left\">2</td><td align=\"left\">0</td><td align=\"left\">10 *</td><td align=\"left\">7</td><td align=\"left\">12 *</td><td align=\"left\">6</td></tr><tr><td align=\"left\">PDI</td><td align=\"left\">2</td><td align=\"left\">1</td><td align=\"left\">19</td><td align=\"left\">20</td><td align=\"left\">19</td><td align=\"left\">14</td></tr><tr><td align=\"left\">SOB</td><td align=\"left\">0</td><td align=\"left\">5</td><td align=\"left\">22</td><td align=\"left\">20</td><td align=\"left\">21</td><td align=\"left\">16</td></tr><tr><td align=\"left\">TI</td><td align=\"left\">3</td><td align=\"left\">10</td><td align=\"left\">17</td><td align=\"left\">16</td><td align=\"left\">21</td><td align=\"left\">18</td></tr></tbody></table></table-wrap>" ]

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id=\"M67\">\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym} \n\t\t\t\t\\usepackage{amsfonts} \n\t\t\t\t\\usepackage{amssymb} \n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${\\dot{\\text{V}}}$$\\end{document}</tex-math><mml:math id=\"M68\"><mml:mover accent=\"true\"><mml:mtext>V</mml:mtext><mml:mo>˙</mml:mo></mml:mover></mml:math></alternatives></inline-formula>" ]

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[ "<table-wrap-foot><p>Data reported as mean ± SD from 9 subjects. <italic>PPO</italic> Peak power output, <italic>V</italic>_{<italic>T</italic>} Tidal volume, <italic>E</italic> ventilation, <italic>BF</italic> breathing frequency, <italic>RER</italic> respiratory exchange ratio, <italic>RPE</italic> rating of perceived exertion. * <italic>p</italic> &lt; 0.05</p></table-wrap-foot>", "<table-wrap-foot><p>Data reported as mean ± SD from 9 subjects. Significant main effect for treatment in O₂ with PB supplementation compared to PL, * <italic>p</italic> = 0.01. ** Higher mean power output over the first km in PB, <italic>p</italic> = 0.01, 95% CI – 50.95 to − 4.74, <italic>d</italic> = 0.34. <italic>RER</italic> respiratory exchange ratio, <italic>V</italic>_{<italic>T</italic>} Tidal volume, E ventilation, <italic>BF</italic> breathing frequency</p></table-wrap-foot>", "<table-wrap-foot><p>Data reported as mean ± SD. Pre testing was performed upon entry to the chamber containing ozone (&lt; 2 min exposure time). FeNO—Fraction expired nitric oxide, FVC—forced vital capacity, FEV₁—forced expiratory volume in 1 s, FEF_25-75—forced expiratory flow over the middle one half of the FVC</p></table-wrap-foot>", "<table-wrap-foot><p>Respiratory symptom scores are the Σ of scores for 10 subjects. Pre testing was performed upon entry to the chamber containing ozone (&lt; 2 min exposure time, <italic>SOC</italic>—severity of cough, <italic>PDI</italic>—pain on deep inspiration, <italic>SOB</italic>—shortness of breath, <italic>TI</italic>—throat irritation. <bold>*</bold>\n<italic>p</italic> = 0.03, two tailed</p></table-wrap-foot>", "<fn-group><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Traumatic brain injury (TBI) involves the functional disruption or pathological changes in the brain due to an external physical force. This could involve road traffic incidents, accidental falls, and other injuries. Therefore, TBI is a significant global health problem, becoming and a leading cause of death and disability in trauma patients (Gao et al. ##REF##32702336##2020##; Khellaf et al. ##REF##31563989##2019##). TBI can be characterized as mild, moderate, and severe depending on injury severity (Lee et al. ##REF##31314607##2019##). Unfortunately, effective treatments to combat TBI-related disorders are still lacking (Chytrova et al. ##REF##18093178##2008##).</p>", "<p id=\"Par3\">Since physical rehabilitation is one of the only established therapies for TBI, its efficacy requires better optimization. Exercise is beneficial to overall health and has been associated with cognitive function. Voluntary wheel running in mice is intermittent and resembles interval training among humans (Manzanares et al. ##REF##30539969##2018##). Effective pharmacotherapies can be facilitated through a more comprehensive understanding of mechanisms behind exercise-related cognitive improvement due to exercise post-TBI.</p>", "<p id=\"Par4\">Voltage-gated sodium channels (VGSCs) transmembrane protein complexes, including Nav1.1–1.9 plus Nax subtypes, propagate action potentials in excitable cells (Manzanares, Brito-da-Silva and Gandra ##REF##32114117##2020##). VGSCs are highly activated by TBI and are associated with TBI-induced pathological progress. For instance, Nav 1.3 and 1.6 messenger ribonucleic acid (mRNA) and protein expression were considerably up-regulated in the ipsilateral-injured cortex of rats during the very early stage post-TBI. Thus, it is linked with TBI severity and associated with diffuse axonal injury post event in mice (Huang et al. ##REF##22928478##2013##; Mao et al. ##REF##20421839##2010a##, ##UREF##3##b##; Wolf et al. ##REF##11245677##2001##). Mechanical trauma of axons leads to a Na + influx through VGSCs and subsequently triggers Ca²⁺ influx, causing neuronal death (Iwata et al. ##REF##15140932##2004##). Our previous study observed that exercise-induced cognitive improvement is related to sodium channel-mediated excitability (Tan ##REF##32256560##2020##). However, the correlation between voluntary RW exercise-induced cognitive recovery in the TBI model remains unknown. Therefore, whether voluntary RW exercise recovered cognitive function after TBI by correcting the VGSCs is unconfirmed.</p>", "<p id=\"Par5\">In the current study, mice were treated with voluntary RW before or after TBI or combined before and after injury. Subsequently, the behavioral changes, electroencephalography (EEG) electrophysiology recording, and VGSC expression levels in mice were evaluated. Primary cultured neurons helped establish an in vitro TBI model. Neuronal hyperexcitability, sodium current, and protein expression of VGSCs in TBI-injured neurons helped determine the impact of serum cell viability in exercising mice.</p>" ]

[ "<title>Materials and methods</title>", "<title>Animal grouping for in vivo experiments</title>", "<p id=\"Par6\">A total of 252 C57BL/6 J male mice aged 4–6 weeks, were randomly divided into exercise pre-training, post-injury exercise intervention, and pre-training combined with TBI post-injury exercise training groups. The PASS software helped determine the sample size. The calculation details and the number of mice in each group are demonstrated in Supplementary Tables 1, 2, 3. Each group involved sham-operated and TBI mice. Mice in the sham-operated group only received craniotomy without TBI injury. However, TBI mice suffered from a mild TBI operation. Moreover, the experimenters did not inform the treatment of experimental animal groupings.</p>", "<p id=\"Par7\">All the cages had a runner wheel (RW) (diameter = 12 cm, width = 5 cm; Nalge Nunc International, Rochester, NY, USA). It was used for voluntary exercise and free rotation. As previously reported, it was attached to a receiver to monitor the number of revolutions (Vital Viewer Data Acquisition System software, Mini Mitter, Sunriver, OR, USA) (Bao et al. ##REF##24920273##2014##; Hu et al. ##REF##26018937##2015##). The mice exercised ad libitum in individual cages with unlimited RW access. The mean revolutions were determined from 7 p.m. to 7 a.m. for the most active period every night. Mice from the sedentary (SED) or Non-runners (NR) control group were exposed to fixed and non-rotating RW.</p>", "<p id=\"Par8\">In the exercise pre-training group, the mice were housed with voluntary access to an RW or an immobilized RW for three weeks prior to the operation. In the post-injury exercise intervention group, the mice were housed with voluntary access to an RW (Runner, R) or an immobilized RW (Non-Runner, NR) for 3 weeks post-injury. In the mixture exercise training group, mice were treated with voluntary RW exercise before and after TBI for 3 weeks each (PreS + Non-Runner, PS NR; Pre + Runner, PR). The mice in the SED control group were exposed to fixed and non-rotating RW.</p>", "<p id=\"Par9\">The mice treated with preliminary voluntary RW exercise were anesthetized with isoflurane inhalation and decapitated at 2, 6, 12 or 24 h post-operation (hpo). The ipsilateral hippocampus in the exercise pre-training group was removed and prepared to depict the Nav1.1, 1.3, and 1.6 protein expression levels (<italic>n</italic> = 9).The mice were prepared for recording (EEG) or behavioral tests (open field, Morris water maze, and object recognition test) at 21 days post-operation (dpo). After behavioral evaluation, the mice were decapitated, and the ipsilateral hippocampus was removed to undergo Western blotting. Besides, excitatory postsynaptic potentials (fEPSPs) (long-term potential) were recorded in the CA1 of the hippocampal slice at 24 hpo and 21 dpo.</p>", "<p id=\"Par10\">Behavioral tests (open field, Morris water maze and novel object recognition test), EEG and fEPSPs recording in the CA1 of the hippocampal slice were performed at 21 dpo in mice treated with voluntary RW exercise for 3 weeks post-TBI. Then, the protein expression levels of Nav1.1, 1.3, and 1.6 in the ipsilateral frontal cortex and hippocampus were assessed post-behavioral evaluation.</p>", "<p id=\"Par11\">Moreover, behavioral tests, EEG tests, and fEPSPs recording in the CA1 of the hippocampal slice were undertaken in mice treated with voluntary RW exercise before and after TBI for 3 weeks each. Then, the mice were sacrificed to determine the Nav1.1, 1.3, and 1.6 protein expression levels in the ipsilateral frontal cortex and hippocampus. The experimenters or data processors were blinded to the animal grouping information to ensure unbiased results.</p>", "<title>Animal grouping for in vitro experiments</title>", "<p id=\"Par12\">We randomly chose 18 C57BL/6 J male mice aged 4–6 weeks as serum donors for cell culture. These mice were uniformly divided into free exercise pre-training (Runners, R) and sedentary control groups (Non-runners, NR) groups. Exercising mice possessed voluntary access to the RW, while the SED control ones were accessible to the same RW in the locked position. The mice could exercise ad libitum in the individual cages for three weeks with unlimited access to the RW. After training, the mice from each group were sacrificed to obtain exercise-conditioned (Runners, R) or non-exercise-conditioned (Non-runners, NR) serum.</p>", "<title>TBI operation</title>", "<p id=\"Par13\">The mild-TBI mouse model was performed following our previous study (Hu et al. ##REF##26018937##2015##). Surgical anesthesia was started by exposing mice to a mixture of 3% isoflurane in oxygen within an incubation chamber. Anesthesia was maintained with 1–2% isoflurane in oxygen during surgery using an isoflurane vaporizer (Riward R580S, Shenzhen, China). After anesthesia, the animals were fixed on a stereotactic platform (Riward 71,000, Shenzhen, China). Then, the skull was opened to expose the corticomotor area in the cerebral cortex. A mild-TBI mouse model was developed with a device to generate controlled cortical impact (CCI), allowing independent tissue deformation and impact velocity manipulation. Then, the left parietotemporal cortex was subjected to CCI [2 mm tissue deformation at a rate of 6.0 m/s (moderate)]. It possessed a depth of 1 mm and a contact time of 200 ms or Sham surgery (Fox et al. ##REF##9726259##1998##; Hu et al. ##REF##26018937##2015##). After the operation, the incision was closed with interrupted 6–0 silk sutures. The anesthesia was terminated, and the animal was placed inside a heated cage to maintain normal core temperature for 45 min post-operation. All the animals were carefully monitored everyday post awakening. The same modeler underwent preoperative anesthesia and CCI modeling over a short time (3 days) to decrease experimental practice differences.</p>" ]

[ "<title>Results</title>", "<title>Voluntary exercise before or post-injury improved TBI-induced impairment in exploratory locomotor activity and anxiety-like behavior</title>", "<p id=\"Par29\">Open field tests can depict exploratory and anxiety-like behavior and locomotor activity (Kraeuter et al. ##REF##30535688##2019##). The numbers of rearing up, fecal ball, and stationary behavior during the 10-min test are measured to determine anxiety-like behavior. The total number of rearing up indicated no significant difference between the pre-exercise and age-matched SED controls groups in the Sham or TBI groups (<italic>p</italic> &gt; 0.05). A similar result could be observed between the runner and non-runner controls (<italic>p</italic> &gt; 0.05). No significant difference was identified between PR and PS NR controls in the Sham or TBI groups (<italic>p</italic> &gt; 0.05) (Fig. ##FIG##0##1##a–c).</p>", "<p id=\"Par30\">TBI-injured mice defecated more during tests than the mice that underwent sham operation. The mice in the TBI group (TBI RW and TBI SED, TBI NR and TBI R, TBI PS NR) showed more fecal balls than the Sham group (Sham RW and Sham SED, Sham NR and Sham R, Sham PS NR) (TBI RW vs. Sham RW,<italic> p</italic> &lt; 0.05; TBI SED vs. Sham SED, <italic>p</italic> &lt; 0.001; TBI NR vs. Sham NR, <italic>p</italic> &lt; 0.001; TBI R vs. Sham R, <italic>p</italic> &lt; 0.001; TBI PS NR vs. Sham PS NR, <italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##d–f). Moreover, the mice in the TBI RW group had fewer fecal balls than the TBI SED group (<italic>p</italic> &lt; 0.05)(Fig. ##FIG##0##1##d). The TBI R group revealed a remarkably significantly declined trend with the fecal balls than the TBI NR group (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##e). Compared with the TBI PS NR group, the mice in the TBI PR group possessed significantly decreased fecal balls (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##f). In pre-training groups, the TBI SED group mice had more standing behavior than the Sham SED group (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##j). A significant difference could be seen in the stationary behavior between the TBI SED and TBI RW groups (<italic>p</italic> &lt; 0.01) (Fig. ##FIG##0##1##j). The mice in TBI NR group mice in post-injury exercise groups showed a higher stationary behavior frequency than the Sham NR group (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##k). The post-injury exercise intervention decreased stationary behavior in TBI mice. The TBI R group mice had a reduced trend in stationary behavior than the TBI NR group (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##k). The TBI PS NR groups showed increased stationary behavior than the in Sham PS NR (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##l). The TBI PR group mice exhibited less stationary behavior than the TBI PS NR group (<italic>p</italic> &lt; 0.001) (Fig. ##FIG##0##1##l).</p>", "<p id=\"Par31\">These fecal ball numbers and stationary behavior results indicated that the mild TBI operation led to anxiety in mice. Moreover, the voluntary exercise implemented before and/ or after injury effectively enhanced anxiety-like behavior.</p>", "<p id=\"Par32\">Specifically, TBI surgery significantly reduced general motor and exploratory activity in mice, however, this improved after exercise training (Fig. ##FIG##0##1##g–i). In groups that did exercise prior to operation, mice in the TBI groups (TBI SED and TBI RW) covered less compared to the sham group as measured by the total distance covered (Sham SED and Sham RW) (TBI SED vs. Sham SED, <italic>p</italic> &lt; 0.001; TBI RW vs. Sham RW, <italic>p</italic> &lt; 0.01) (Fig. ##FIG##0##1##g). However, the TBI SED and TBI RW exercise groups depicted nearly equal distances (<italic>p</italic> &gt; 0.05) (Fig. ##FIG##0##1##g). In post-injury exercise intervention mice, the TBI group mice (TBI NR and TBI R) traveled shorter distances than the Sham NR groups (TBI NR vs. Sham NR)(TBI NR vs. Sham NR, <italic>p</italic> &lt; 0.001; TBI R vs. Sham R, <italic>p</italic> &lt; 0.05) (Fig. ##FIG##0##1##h). The TBI Runner groups indicated an increasing trend in total distance to the TBI Non-Runner (<italic>p</italic> &lt; 0.05) (Fig. ##FIG##0##1##h). The TBI groups (TBI PS NR and TBI PR) revealed a more significant reduction in total distance than the Sham groups (Sham PS NR and Sham PR) (TBI PS NR vs. Sham PS NR, <italic>p</italic> &lt; 0.001; TBI PR vs. Sham PR,<italic> p</italic> &lt; 0.05) among the mixture exercise groups (Fig. ##FIG##0##1##i). TBI PR had a more elevating trend in total distance than the TBI PS NR group (<italic>p</italic> &gt; 0.05) (Fig. ##FIG##0##1##i).The open-filed test indicated that the TBI operation impaired the gross locomotor and exploratory activity in mice. Before or after TBI injury, voluntary exercise showed promising effects in reversing the damage. Furthermore, TBI mice treated with voluntary exercise before and after injury significantly enhanced gross locomotor and exploratory functions.</p>", "<title>Simultaneous voluntary exercise before and after injury ameliorated spatial memory and recognition deficiency induced by TBI</title>", "<p id=\"Par33\">The MWM and NOR tests helped assess whether voluntary exercise affected spatial and recognition memory deficiencies related to TBI in mice, depicted by analysis of variance. The first five days of the hidden platform test demonstrated that the escape latency of all the groups decreased gradually with time. The TBI group mice spent more time identifying the hidden underwater platform than the age-matched mice in the Sham groups. However, RW exercise training before or after the injury can decrease the difference and significantly improve the spatial memory ability of TBI mice (TBI RW vs. TBI SED, <italic>p</italic> &lt; 0.01; TBI R vs. TBI NR, <italic>p</italic> &lt; 0.05)(Fig. ##FIG##1##2##a, b). The escape latency of TBI mice on the fifth day of pre-training combined with the post-injury exercise training group (TBI PR) was lower than that the pre-training combined with the sitting group (TBI PR vs. TBI PS NR, <italic>p</italic> &lt; 0.01)(Fig. ##FIG##1##2##c).</p>", "<p id=\"Par34\">On the sixth day, the platform was removed for probe testing. In TBI groups, no significant differences were observed in the number of target crossing and mean swimming speed between RW exercise training groups and without training groups (<italic>p</italic> &gt; 0.05) (Fig. ##FIG##1##2##d–f, j–l). Compared with the TBI SED, TBI NR, and TBI PS NR groups, the RW training group mice had a shorter time to identify the target (TBI RW vs. TBI SED,<italic> p</italic> &lt; 0.001; TBI R vs. TBI NR, <italic>p</italic> &lt; 0.001; TBI PR vs. TBI PS NR,<italic> p</italic> &lt; 0.05) (Fig. ##FIG##1##2##g–i).</p>", "<p id=\"Par35\">One-way RM variance analysis indicated that the exercising Sham RW mice spent more time on the NOR task than those in the Sham SED (Sham RW vs. Sham SED, <italic>p</italic> &lt; 0.01)or TBI RW groups (Sham RW vs. TBI RW, <italic>p</italic> &lt; 0.01) (Fig. ##FIG##2##3##a). However, no difference could be seen in the time spent on novel object exploration among the groups treated with only three weeks of exercise training and those treated with three-week pre-training and three-week exercise training after TBI operation (TBI R vs. TBI NR, <italic>p</italic> &gt; 0.05; TBI PR vs. TBI PS NR, <italic>p</italic> &gt; 0.05) (Fig. ##FIG##2##3##b, c).</p>", "<title>Simultaneous treatment with exercise before and after injury redressed the abnormal Delta and Beta Frequency Band increases due to TBI</title>", "<p id=\"Par36\">The EEG recordings helped determine whether voluntary exercise impacted the functional integrity of neuronal networks among TBI mice. The results indicated that TBI SED ones had a significant increase in the delta and beta frequency band than the Sham SED group (TBI SED vs. Sham SED, <italic>p</italic> &lt; 0.01) (Fig. ##FIG##3##4##a, d). The TBI RW group showed a downtrend in the delta frequency band compared with the TBI SED group (Fig. ##FIG##3##4##a, <italic>p</italic> &lt; 0.05). No significant differences could be observed in theta and alpha frequency between the sedentary and RW exercise groups (Fig. ##FIG##3##4##b, c, <italic>p</italic> &gt; 0.05) (Fig. ##FIG##3##4##a–d). Similar results were observed in the post-injury exercise intervention and pre-training associated with TBI post-injury exercise training groups (Fig. ##FIG##3##4##e, Sham NR vs. TBI NR, <italic>p</italic> &lt; 0.01; Sham R vs. TBI R, <italic>p</italic> &lt; 0.05; h, Sham NR vs. TBI NR, <italic>p</italic> &lt; 0.01; i, Sham PS NR vs. TBI PS NR, <italic>p</italic> &lt; 0.05; l, Sham PS NR vs. TBI PS NR, <italic>p</italic> &lt; 0.01). In TBI groups, RW exercise intervention groups reduced the delta and beta frequency bands (Fig. ##FIG##3##4##a, TBI RW vs. TBI SED, <italic>p</italic> &lt; 0.05; e, h, TBI R vs. TBI NR, <italic>p</italic> &lt; 0.05; i, l, TBI PR vs. TBI PS NR, <italic>p</italic> &lt; 0.05). However, the means are not significantly different between the TBI SED group and TBI RW group in beta frequency (<italic>p</italic> &gt; 0.05) (Fig. ##FIG##3##4##d). Similarly, no evident changes could be seen in theta and alpha bands between the post-injury training intervention and the pre-training combined post-injury training intervention groups (Fig. ##FIG##3##4##f, g, and j, k, <italic>p</italic> &gt; 0.05). Therefore, the TBI operation elevated the delta and beta frequency bands. In contrast, voluntary exercise treatment before and after the operation redressal those EEG parameters adequately.</p>", "<title>Exercise simultaneously before and after injury improved the hippocampal synaptic plasticity damage due to TBI</title>", "<p id=\"Par37\">The electrophysiology recordings validated the injury impact on the hippocampus and determined whether exercise affects the synaptic plasticity post-TBI. The results depicted that the fEPSP slope in mice was indistinguishable at 24 hpo (Fig. ##FIG##4##5##a, b) and 21 dpo (Fig. ##FIG##4##5##c–h). However, a tetanic stimulation train (100 Hz, 1 s) for 60 min post-treatment, having a high-frequency outcome and robust fEPSP slope was induced in mice. The slope magnitude varies among groups (Fig. ##FIG##4##5##b, d, f, h). The TBI mice showed a lower normalized fEPSP slope than Sham SED (TBI SED vs. Sham SED, <italic>p</italic> &lt; 0.001) or Sham RW groups (TBI RW vs. Sham RW, <italic>p</italic> &lt; 0.001)(Fig. ##FIG##4##5##b) in preliminary voluntary RW exercise-treated groups after 24 h of operation. In contrast, the RW exercise-treated mice possessed a higher normalized fEPSP than the sedentary groups (Fig. ##FIG##4##5##b, Sham RW vs. Sham SED, <italic>p</italic> &lt; 0.001; TBI RW vs. TBI SED, <italic>p</italic> &lt; 0.001). Similarly, the TBI mice indicated a decline in normalized fEPSP than in Sham SED (TBI SED vs. Sham SED, <italic>p</italic> &lt; 0.001) and Sham RW groups (TBI RW vs. Sham RW, <italic>p</italic> &lt; 0.001). The reason is that the mice were treated with preliminary voluntary RW exercise 21 days post-operation (Fig. ##FIG##4##5##d). In contrast, the TBI RW group had a higher fEPSP slope than the TBI SED group (Fig. ##FIG##4##5##d, <italic>p</italic> &lt; 0. 01). There were lower normalized fEPSP slopes in the TBI mice than among the sham-operated mice in post-injury exercise intervention groups (Fig. ##FIG##4##5##f, TBI NR vs. Sham NR, <italic>p</italic> &lt; 0.001; TBI R vs. Sham R, <italic>p</italic> &lt; 0.001). In contrast, the exercise-trained TBI R mice showed a higher fEPSP slope than the TBI NR group (Fig. ##FIG##4##5##f, <italic>p</italic> &lt; 0.001). The fEPSP of TBI PS NR groups was more reduced than in Sham PS NR (Fig. ##FIG##4##5##h, <italic>p</italic> &lt; 0.001) or TBI PR groups (Fig. ##FIG##4##5##h, <italic>p</italic> &lt; 0.001) mice who had received pre-training combined with the post-injury exercise intervention group.</p>", "<p id=\"Par38\">Thus, TBI impaired synaptic plasticity, which was countered through exercising before or after injury. Furthermore, the synaptic plasticity was restored to the pre-injury level through simultaneous exercising simultaneously before and after the TBI operation.</p>", "<title>Exercise before and after injury corrected the aberrant expression increase of Nav1.1, Nav1.3, and Nav1.6 proteins due to TBI</title>", "<p id=\"Par39\">In the preliminary voluntary RW group, the Nav1.1 protein expression in the hippocampus was significantly up-regulated at 6 hpo in the TBI mice than in Sham SED or RW groups (Fig. ##FIG##5##6##b, Sham SED vs. TBI SED, <italic>p</italic> &lt; 0.001; Sham RW vs. TBI RW, <italic>p</italic> &lt; 0.001). Nav1.1 protein expression was decreased in the TBI RW group from 12 hpo to 21 dpo when compared with the TBI SED group (Fig. ##FIG##5##6##c, <italic>p</italic> &lt; 0.05; d, <italic>p</italic> &lt; 0.01; e, <italic>p</italic> &lt; 0.001). The TBI RW group possessed a lower Nav 1.3 expression than the TBI SED group at 12 hpo (Fig. 0.6 h, <italic>p</italic> &lt; 0.001). The Nav1.3 protein expression consistently trended at 24 hpo with 12 hpo (Fig. ##FIG##5##6##h, i, <italic>p</italic> &lt; 0.001). The Nav1.6 protein expression was lower in the TBI RW group than in the TBI SED group at 24 hpo (Fig. ##FIG##5##6##n, <italic>p</italic> &lt; 0.001).</p>", "<p id=\"Par40\">Nav1.1, 1.3 and 1.6 proteins expressions in the hippocampus were up-regulated within TBI NR at 21 dpo in the post-injury exercise intervention group than the Sham NR group (Fig. ##FIG##6##7##a–c, <italic>p</italic> &lt; 0.001). Nav 1.1, 1.3 and 1.6 protein levels were down-regulated in the hippocampus after exercise treatment in TBI mice (Fig. ##FIG##6##7##b, <italic>p</italic> &lt; 0.01; a, c, <italic>p</italic> &lt; 0.05;).</p>", "<p id=\"Par41\">Moreover, the hippocampal expression of Nav1.1, 1.3 and 1.6 proteins was significantly enhanced in TBI PS NR at 21 dpo. Simultaneously, the above indicators were considerably down-regulated in the TBI PR group (Fig. ##FIG##6##7##d–f, <italic>p</italic> &lt; 0.001). Additionally, there were no significant differences in Nav1.1, 1.3, and 1.6 protein expressions between Sham PR and Sham PS NR (Fig. ##FIG##6##7##d–f).</p>", "<p id=\"Par42\">These results indicated that TBI up-regulated Nav1.1, Nav1.3 and Nav1.6 protein expressions. In contrast, exercise treatment before and after injury reversed these changes. Furthermore, the protein expression was restored to the Sham level when exercising simultaneously before and after injury.</p>", "<title>The cell viability is improved in injured cortical cells cultivated inside an exercise-conditioned medium</title>", "<p id=\"Par43\">The cell viability of TBI-injured cultured cortical neurons was evaluated using the MTT assay. The injured neurons cultivated in a non-exercise-conditioned medium at 2, 6, and 24 hpo decreased cell viability compared to the uninjured ones (Fig. ##FIG##7##8##b, <italic>p</italic> &lt; 0.01; c, d, <italic>p</italic> &lt; 0.001). However, the cell viability of injured neurons in exercise-conditioned medium was higher than those in non-exercise-conditioned medium (Fig. ##FIG##7##8##b, <italic>p</italic> &lt; 0.05; c, d, <italic>p</italic> &lt; 0.001).</p>", "<p id=\"Par44\">These results indicated that TBI impairs cortical neuron viability. Moreover, culturing cortical cells inside an exercise-conditioned medium significantly repairs the injured cortical cell viability.</p>", "<title>The neuronal hyperexcitability and sodium current overload caused by TBI were reversed with exercise-conditioned serum in injured cortical cell treatment</title>", "<p id=\"Par46\">Whole-cell patch-clamp recordings were conducted on cultured cortical cells after different treatments to identify whether exercise mice serum repressed the neuronal hyperexcitability caused by injury. The action potential frequency of impaired cortical cells inside the non-exercise-conditioned medium at 2, 6, and 24 hpo was significantly improved compared to uninjured cortical cells (Fig. ##FIG##8##9##g–i, <italic>p</italic> &lt; 0.001). A significant decrease could be observed in the threshold current at 24 hpo post-injury (Fig. ##FIG##8##9##l, <italic>p</italic> &lt; 0.001).The AP frequency of injured cortical cells treated using the exercise-conditioned medium at 2, 6 and 24 hpo was significantly decreased compared to those treated with the non-exercise-conditioned medium(Fig. ##FIG##8##9##g,<italic> p</italic> &lt; 0.05; h, <italic>p</italic> &lt; 0.05; i, <italic>p</italic> &lt; 0.001). Therefore, the medium injury treatment induced neuronal hyperexcitability across injured cortical neurons, which the serum from exercise mice reduced.</p>", "<p id=\"Par47\">Electrophysiological patch clamp recording validated whether neuronal excitability was related to the elevated sodium current. The sodium current density curves and current density in non-exercise-conditioned medium-treated ones (NEX-TBI) were significantly reduced compared to the uninjured ones at 2, 6 and 24 hpo (Fig. ##FIG##8##9##a–c). The Na⁺ and peak current densities of injured cortical cells cultivated in the exercise-conditioned medium (EX-TBI group) at 2, 6 and 24 hpo post-injury were significantly enhanced compared to those in non-exercise-conditioned medium-treated cells (NEX-TBI) (Fig. ##FIG##8##9##d–f, <italic>p</italic> &lt; 0.001). Therefore, the serum from exercise mice helped restore the neuronal aberrant sodium current induced by TBI.</p>", "<title>Effects of exercise-conditioned serum on the aberrant status of sodium-channel proteins caused by TBI</title>", "<p id=\"Par48\">In uninjured and injured cultured cortical cells, the expression levels of sodium-channel proteins, such as Nav1.1, Nav1.3 and Nav1.6, were investigated to determine the underlying mechanism by which exercise mice serum redressed neuronal hyperexcitability and sodium-channel overload induced by TBI. The expression of Nav1.1, Nav1.3 and Nav1.6 in impaired cortical cells grown in the non-exercise-conditioned medium (NEX-TBI group) was significantly elevated at 6 and 24 hpo post-injury compared to those in the uninjured group (Fig. ##FIG##9##10##b, c, e, f, h, <italic>p</italic> &lt; 0.001). After 24 hpo, the Nav1.1, Nav1.3, and Nav1.6 expression levels were decreased in cortical cells grown in an exercise-conditioned medium (EX-TBI group) compared to those in the non-exercise-conditioned medium (NEX-TBI group) (Fig. ##FIG##9##10##c, <italic>p</italic> &lt; 0.001; f, <italic>p</italic> &lt; 0.01). The differences were insignificant compared to those in the uninjured group (Fig. ##FIG##9##10##, <italic>p</italic> &gt; 0.05). Moreover, the Nav1.3 expression in the EX-TBI group at 6 hpo was significantly reduced (Fig. ##FIG##9##10##e, <italic>p</italic> &lt; 0.01). It was not substantially different from the uninjured cells (Fig. ##FIG##9##10##e, <italic>p</italic> &gt; 0.05). In the NEX-TBI group, the Nav1.6 expression was decreased declined at 2 hpo post-injury compared to the uninjured ones (Fig. ##FIG##9##10##g, <italic>p</italic> &lt; 0.001). However, Nav1.6 levels were significantly reduced after treatment with the exercise-conditioned medium at 2 hpo post-injury compared to those treated with non-exercise-conditioned medium groups (Fig. ##FIG##9##10##g, <italic>p</italic> &lt; 0.01). The results from the uninjured groups showed no significant difference (Fig. ##FIG##9##10##g, <italic>p</italic> &gt; 0.05).</p>", "<p id=\"Par49\">These results depicted that the exercise-conditioned serum alleviated neuronal excitability, which could be linked with the decreasing Nav1.1, 1.3, and 1.6 expressions.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par50\">The present study describes the promising therapeutic effects of voluntary RW exercise in the TBI mice model and mechanically injured cortical cells in vitro. TBI mice treated with voluntary RW training before and/or after TBI improves locomotor function, emotion and cognition ability while restoring the aberrant neuronal excitability. Simultaneously, the voluntary RW exercise alters the increased VGSCs, such as Nav1.1, Nav1.3, and Nav1.6, in the ipsilateral frontal cortex and hippocampus of TBI mice. Moreover, exercise-conditioned medium treatment rescued cells through viability recovery and redressing sodium current. Moreover, up-regulated Nav1.1, Nav1.3 and Nav1.6 are resumed in injured cortical neurons after treatment with exercise-conditioned medium.</p>", "<p id=\"Par51\">TBI is a severe global public health, with traffic accidents and accidental falls being the most common cause in younger and older adults. TBI is associated with varying consciousness degrees and cognitive impairment (Corrigan et al. ##REF##24495919##2014##). Applying combinatorial biomarkers and electrophysiological techniques could highlight the brain injury mechanism, facilitating neurological function recovery. Thus, it provides a helpful reference to the rehabilitate patients.</p>", "<p id=\"Par52\">Secondary brain injury due to the primary outcome of TBI, including ischemia and hypoxia, ion channel dysfunction, brain edema, and neuroinflammatory response, involves a complex physiological and biochemical cascade (Iaccarino et al. ##REF##25702231##2015##). Previous studies have indicated that TBI can elevate the cascade reactions of different cytokines, enhance the sodium current (Na⁺) intensity and excitability of neurons, and control BDNF to suppress elevated VGSC expressions (W. Chen et al. ##UREF##0##2017##). mRNA and protein expressions of Nav1.1, Nav1.2, Nav1.3, and Nav1.6 in the nervous system of mammals were altered in the epilepsy model (Huang et al. ##REF##22928478##2013##; Mao et al. ##REF##20421839##2010a##, ##UREF##3##b##). Therefore, sodium influx and depolarization regulated by VGSCs is an early event in a series of cellular abnormalities caused by TBI. Consequently, it is well positioned as an upstream target for pharmacological modulation of different pathological responses against TBI. Studies have established that improving neuronal plasticity and activity is essential to in the recovery post-TBI injury (Batulu et al. ##REF##30988787##2019##; Trompoukis and Papatheodoropoulos ##REF##32625076##2020##). Researchers have observed that physical exercise lasting more than 4 weeks could be a safe and noninvasive rehabilitation method to alleviate cognitive impairment in brain injury patients. However, the underlying mechanisms still need to be explored.</p>", "<p id=\"Par53\">Our study depicted that exercise training treated in TBI models repaired fEPSP. Thus, it improves synaptic plasticity in the hippocampus and enhances neuronal activity, consistent with previous studies (Radahmadi et al. ##REF##27693393##2016##). Thus, RW exercise training leads to recovery from TBI. The treatment improves autonomous movement and anxiety-like behaviors and enhances learning and memory.</p>", "<p id=\"Par54\">EEG data depict that the Delta and Beta rhythms enhance after TBI. In contrast, three-week RW training treatment before and after TBI repressed abnormal EEG rhythms and restored athletic ability, spatial learning, and memory. Delta oscillations are correlated with many cognitive processes, including working memory (Harmony ##REF##24367301##2013##). Elevated synchrony in the beta and delta frequency bands after TBI is associated with different alterations in deeper brain structures and dysfunctional cortical action (Atlan and Margulies ##REF##30909806##2019##; Shah et al. ##REF##28462682##2017##). Thus, the EEG recordings obtained in this study partially indicated the behavioral changes in TBI mice after RW exercise treatment.</p>", "<p id=\"Par55\">TBI also reduced fEPSP slops and elevated neuronal sodium current, neuronal excitability, and Nav1.1, Nav1.3, and Nav1.6 protein expressions in the hippocampus and cortex. Similar results could be observed in primary cortical neurons cultured from the cortical and hippocampal regions of mice. RW exercise treatment for TBI redressed the abnormal EEG synchrony, Nav protein expression, and neuronal hyperexcitability. The free exercise with RW for four weeks before TBI improved the emotion-loss motor and cognitive functions of TBI mice. It suppressed neuronal loss and cortical microglia activation by inhibiting cytochrome C and Bcl-2 up-regulation and mitochondrial membrane permeability down-regulation. Thus, RW exercise training before an injury could restore neuronal activity and spatial memory ability induced by TBI in mice (Zhao et al. ##REF##25419789##2015##).</p>", "<p id=\"Par56\">Voluntary RW exercise can enhance memory ability, hippocampal neuronal excitability, and long-term potentiation (Ivy et al. ##REF##32513972##2020##; Sakalem et al. ##REF##27701786##2017##). Previous studies have demonstrated that the cognitive functional recovery of TBI through exercise is achieved by improving the expression of cytochrome C oxidase and BDNF in mitochondria and enhancing neuronal number and density. The cognitive improvement-related molecules and proteins remain unknown (Gu et al. ##REF##24746931##2014##). Fortunately, our results identified that 3-week pre-training or post-injury training in TBI mice rectifies neuronal hyperexcitability due to Na current overload post-TBI. Moreover, improving neuronal plasticity and activity is vital in TBI injury recovery (Batulu et al. ##REF##30988787##2019##; Dobryakova et al. ##UREF##1##2020##). Neuronal protections are linked with redressing neuronal hyperexcitability by VGSCs to investigate the neuronal protections produced by RW exercise, such as improvement of learning and memory. We examined the peak current density, firing frequency and threshold of AP neuronal potential in injured neurons treated with exercise-conditioned medium. Exercise-conditioned medium treatment redressed peak current density, decreased firing frequency, and enhanced the threshold current of sodium current, restoring neuronal excitability. The study demonstrates that RW exercise training enhances fEPSP slopes, elevates hippocampal synaptic plasticity, decreases AP frequency, and improves the threshold of neuronal excitability correction.</p>", "<p id=\"Par57\">Moderate aerobic exercise inhibits TBI injury through several mechanisms. Reports depict that aerobic exercise over 2 weeks can regulate neurotrophic factor BDNF gene expressions in rats. Moreover, neuronal plasticity, spatial learning, and memory ability are also improved. Therefore, BDNF is crucial in recovering neural and cognitive function enhanced by exercise (Zafonte et al. ##REF##30482373##2018##). The present study established that RW exercise training protects neuronal excitability, facilitating cognitive behavior neuroprotection. Therefore, it could be correlated with the expressional current regulation from the neuronal sodium channel proteins.</p>", "<p id=\"Par58\">The current work indicated a novel molecular pathological training-mediated exercise mechanism to enable cognitive improvement in TBI mice, consistent with previous research (Zafonte et al. ##REF##30482373##2018##). Moreover, high expression of Nav1.1α was associated with cognitive deficits in AD mouse models (Martinez-Losa et al. ##REF##29551491##2018##). Nav1.3 upregulation in the damaged cortex was significantly identified 2 h post-TBI acute phase exposure in rats (Chen et al. ##REF##25300818##2014##). Others revealed that inhibiting Nav1.6 channel expressions was a determinant of the Aβ_1-42 oligomer. Moreover, there was induced membrane depolarization, elevated peak frequency, and hippocampal neuron hyperexcitability (Ciccone et al. ##REF##31537873##2019##). These results indicated that blocking the Nav1.1, Nav1.3 and Nav1.6 expression partially restored cognitive dysfunction and brain disorders due to TBI. TBI mice or cortical neurons treated using voluntary RW training or exercise-conditioned medium lead to improved action function, learning and memory ability, neuronal activity recovery, or neuronal activity regulation. The abnormal increase in Nav1.1, Nav1.3, and Nav1.6 levels corrected the neuronal excitability and Na current. Therefore, exercise training for TBI mice could be a promising strategy for TBI treatment and counter the cognitive deficits and neuronal hyperexcitation.</p>" ]

[]

[ "<p>Communicated by Sreedharan Sajikumar.</p>", "<p id=\"Par1\">Traumatic brain injury (TBI) leads to disturbed brain discharge rhythm, elevated excitability, anxiety-like behaviors, and decreased learning and memory capabilities. Cognitive dysfunctions severely affect the quality of life and prognosis of TBI patients, requiring effective rehabilitation treatment. Evidence indicates that moderate exercise after brain injury decreases TBI-induced cognitive decline. However, the underlying mechanism remains unelucidated. Our results demonstrate that TBI causes cognitive impairment behavior abnormalities and overexpression of Nav1.1, Nav1.3 and Nav1.6 proteins inside the hippocampus of mice models. Three weeks of voluntary running wheel (RW) exercise treatments before or/and post-injury effectively redressed the aberrant changes caused by TBI. Additionally, a 10% exercise-conditioned medium helped recover cell viability, neuronal sodium current and expressions of Nav1.1, Nav1.3 and Nav1.6 proteins across cultured neurons after injury. Therefore, the results validate the neuroprotection induced by voluntary RW exercise treatment before or/and post-TBI. The RW exercise-induced improvement in cognitive behaviors and neuronal excitability could be associated with correcting the Nav1.1, Nav1.3, and Nav1.6 expression levels. The current study proves that voluntary exercise is an effective treatment strategy against TBI. The study also highlights novel potential targets for rehabilitating TBI, including the Navs proteins.</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00221-023-06734-2.</p>", "<title>Keywords</title>" ]

[ "<title>Behavioral tests</title>", "<title>Open field assessment</title>", "<p id=\"Par14\">As previously described, the open-field assessment tested anxiety-like behavior and locomotor activity (Hazra et al. ##REF##24964253##2014##). The mice were placed inside a brightly lit circular arena (40 × 40 × 40 cm³) to evaluate their general activity levels while assessing their gross locomotor and exploratory activity in each group. The horizontal (entire distance traveled) and vertical (the number of rearing up movements) activities were deciphered and quantified using the TOPSCAN tracking system (Clever Sys Inc., USA) over a 10-min trial period. The number of fecal balls was evaluated during the 10-min trial period. The stationary behavior is a transient state during which animals are immobile and do not engage in defined behavior. This behavior was also evaluated (Hazra et al. ##REF##24964253##2014##).</p>", "<title>Morris water maze (MWM) test</title>", "<p id=\"Par15\">The MWM possesses a circular pool (100 cm in diameter, 50 cm deep) filled with white water at 24 ± 1 °C at 20 cm depth (XR-XM101-Z; Shanghai XinRuan Information Technology Co., Ltd., China). The MWM test was run as previously demonstrated (XiYang et al. ##REF##25575679##2016##). All the mice underwent a preliminary experiment for water adaptation. This helped them to step on a white platform (hidden below the water surface) and escape a day before the regular testing. For this investigation, a mouse was allowed to swim in the water for 10 s. Then, they were placed on a white platform submerged under water for 1 to 2 s. The hidden platform was placed in a different location for regular testing. The time during which the mice discovered the submerged white platform was recorded as escape latency, recorded for 5 days. On testing day 6, the platform was removed for the probe trial. Each mouse was allowed to swim for 60 s to evaluate its platform location memory. Percentages of time spent in the target quadrant, path, number of target platform crossings, and the swim speed (mm/s) were documented. The time spent and distances traveled in the four quadrants were also noted. The animals were tracked using an overhead video camera, and an Animal behavior video analysis system helped analyze the data (Shanghai XinRuan Information Technology Co., Ltd., China).</p>", "<title>Novel object recognition (NOR) task</title>", "<p id=\"Par16\">As previously described, NOR tasks were performed within the same arena (40 × 40 × 40 cm³) for the open-field assessment (Figueiredo et al. ##REF##23739959##2013##; Lourenco et al. ##REF##24315369##2013##). Test objects (4 or 5 cm in height) were glass or plastic with different shapes, textures, colors and sizes. The mice were placed at the arena center with two identical objects during the initial training period of 5 min. Trained researchers independently determined the time required to explore each object. At 1 h post-training, the mice were reinserted into the arena for a 10 min test session. One of the objects was replaced by a novel one in this session. It had a different shape and color but was consistent in height. Object exploration was characterized as the direct contact of the nose or front paws with the object. During the formal testing phase, the exploration time of mice toward novel or familiar objects was measured to determine the Discrimination Index (DI). The specific calculation formula is DI = (NT–FT) / (NT + FT), where NT indicates the time spent by mice exploring the new object and FT indicates the time spent exploring the familiar object. The obtained DI helps in comprehending understand the cognitive ability of mice.</p>", "<title>Electrophysiological recordings for mice</title>", "<title>EEG recordings</title>", "<p id=\"Par17\">Mice underwent EEG implantation surgery seven days prior to their final time point, 14 dpo. A three-channel two twisted bipolar stainless-steel electrode used with a diameter of 0.010 in (P Technologies) was used in all the EEG implantations. The protocols of electrode implantation and EEG recordings protocols followed the literature with certain modifications (Hu et al. ##REF##29245901##2017##; Lee et al. ##UREF##2##2011##; Szu et al. ##UREF##4##2020a##, ##REF##32484924##b##; Tan et al. ##REF##32256560##2020##). The 2-mm twisted bipolar wires were implanted in the ipsilateral dorsal hippocampus. The 0.5-mm untwisted wire was utilized to ground within the cortex. Approximately, 0.5 mm of the insulating coat was removed from the distal wire tip to achieve reliable EEG recordings (Szu et al. ##UREF##4##2020a##, ##REF##32484924##b##). Before EEG recordings, the mouse was fixed on the stereotaxic instrument for electrode fixation after being anesthetized. First, the middle scalp was incised about 2 cm to expose the skull. The bregma and lambda points (electrode position on the surface of the mouse brain) were identified on the skull based on the mouse brain atlas (Paxinos and Franklin’s The Mouse Brain in Stereotaxic Coordinates). Then, the mice were implanted with an electrode pedestal into the hippocampus (AP-2.1 mm, ML-1.5, DV-1.5 mm) until it rested on the skull. Next, two micro screws, used as ground and reference, were fixed on the occipital bone above the cerebellum region.</p>", "<p id=\"Par18\">The mouse with the microelectrode implant recovered for 6 days post operation. The connector was linked with a multi-channel EEG amplifier system to gather, and the neural electrical signals. EEG acquisition began after recovery, and the signal was collected in freely moving mice lasting 24 h.</p>", "<p id=\"Par19\">The original recording signal obtained by the recording electrode is amplified 5000 × with the amplifier. The analog signals were digitized at a sampling frequency rate of 1 kHz using a CED Micro1401 data acquisition system and an A/D sampling rate of 128 Hz. Moreover, the signal became a band-passed filter between 0.1 and 35 Hz, digitized at 625 samples/s.</p>", "<p id=\"Par20\">The power spectral density (PSD) analyses were performed blind. The resting EEG data acquired during the 24 h was extracted using the AcqKnowledge software (Biopac), and PSD was analyzed with BrainVision Analyzer 2.1 (Brain Products). The artifacts were removed using a semiautomatic procedure based on maximum-minimum, low activity, and amplitude criteria. The EEG signals were divided into 10-s segments, and a fast Fourier transform was applied to each segment at 1-Hz resolution from 1 to 35 Hz to generate the frequency values. The EEG frequency bands were delta (1–3 Hz), theta (4–7 Hz), alpha (8–14 Hz), and beta (15–35 Hz). The fast Fourier transform results were extracted using the BrainVision Analyzer 2.1 and averaged using specialized MATLAB scripts (MathWorks).</p>", "<title>Hippocampal field excitatory postsynaptic potential (fEPSP) recording</title>", "<p id=\"Par21\">The synaptic functions were systematically analyzed in the hippocampus to identify whether hippocampal synaptic plasticity was affected by voluntary RW exercise in TBI mice (XiYang et al. ##REF##25575679##2016##). The fEPSP was recorded at CA1 Schaeffer collateral synapses within hippocampal slices collected from mice at 24 h and 21 d after undergoing the operation. Hippocampal slices (350 μm) were cut using a vibrating microtome in an ice-cold slicing buffer bubbled with 95% O₂ and 5% CO₂. Then, the slices were transferred to a holding chamber possessing oxygenated artificial cerebrospinal fluid for 45 min at 34 °C and another 45 min at 22 °C for recovery. Later, it was transferred to a submersion recording chamber while continually perfusing with 32 °C oxygenated ACSF. The slices were equilibrated before each recording for at least 15 min. ACSF-filled glass electrodes (resistance &lt; 1 MΩ) were positioned inside the stratum radiatum of the CA1 area for extracellular recording. The synaptic responses were evoked by stimulating the Schaeffer collateral with 0.2 ms pulses using a bipolar tungsten electrode (WPI Inc., Sarasota, FL) once every 15 s. The stimulation intensity was systematically enhanced to identify the maximal fEPSP slope and adjusted to provide 50% of the maximal fEPSP slope. The experiments with maximal fEPSPs &lt; 0.5 mVor using substantial changes in the fiber volley were rejected. Long-term potential (LTP) was provoked using one 1 s/100 Hz stimulus train for 60 min after a stable baseline recording for 20 min.</p>", "<title>Primary neurons culture in <italic>vitro</italic></title>", "<p id=\"Par22\">The cortical or hippocampal tissues were retrieved from postnatal day 0 (P0) C57BL/6 J mice (Kim and Magrané, ##REF##21913093##2011##). The crushed cortical and hippocampal tissues were digested using 1.25% pancreatin (Gibco, ThermoFisher Scientific) inside an incubator at 37 °C for 10 min before being resuspended with fetal bovine serum (Gibco). The resulting tissue suspension was filtered using a 70 μm cell strainer to gather the cortical or hippocampal cells. These cells were incubated inside six-well culture plates pre-coated with poly-D-lysine (Sigma-Aldrich). They were soaked with neuronal medium (Gibco) possessing 2% B27 supplement (Gibco), 0.5% penicillin/streptomycin, and 0.25% GlutaMax (Gibco). Half of the culture medium was replaced every three days. Then, the cultured cells underwent a mechanical injury (trauma) after 10–12 days to mimic TBI in vitro (Katano et al. ##REF##10574349##1999##; Mori et al. ##REF##11919515##2002##). A sterile 21-gauge needle was used to from parallel scratches across circular wells of culture plates (9 × 9 scratches in six-well and 6 × 6 scratches in 12-well plates). The control wells were left uninjured, and the medium was replaced using serum-free DMEM/F12 and incubated at 37 °C.</p>", "<title>Effects of the exercise-conditioned medium on primary cortical cultures</title>", "<p id=\"Par23\">The mice from the Runners or Non-Runners group were sacrificed to obtain exercise- (R) or non-exercise-conditioned (NRs) serum (<italic>n</italic> = 9) (Hojman et al. ##REF##21653222##2011##). Blood was collected by decapitation, followed by quick excision, dry ice freezing and sorting in 100% alcohol. The serum from the exercising mice was pooled in the groups. It was followed by heat inactivation at 56 °C for 30 min and sterile filtration. At 2, 6 or 24 h after mechanical injury, the primarily injured cortical neurons were treated with using 1 ml medium having 10% exercise-conditioned or non-exercise- serum instead of the neurobasal medium (Chen et al. ##UREF##0##2017##; Hojman et al. ##REF##21653222##2011##). The cells were implanted in 12-well plates with 1 × 10⁵ cells per well.</p>", "<p id=\"Par24\">Uninjured (intact) neurons were spread across 12-well plates (1 × 10⁵ cells per well), incubated for 24 h, and washed thrice with the prewarmed neurobasal medium. The intact cultures were exposed for 2, 6 or 24 h in 1 ml of a mixed medium containing 10% exercise- or non-exercise-conditioned serum. The control cells were incubated in 1 ml of the fresh neurobasal medium. The cells were incubated for 2, 6 or 24 h within the medium for 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay, electrophysiological recording and Western blotting assay.</p>", "<title>3-(4,5-Dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay</title>", "<p id=\"Par25\">The cell viability was determined using the MTT assay kit (Sigma-Aldrich) based on the manufacturer’s guidelines. The primary neuronal cells were seeded in 96-well plates at 2 × 10⁴ cells per well and treated with various exogenous substances depending on the following protocol. The MTT reagent was added to the cells at 37 °C post-incubation. The culture medium was replaced with 100 μL DMSO to dissolve the formazan crystals after incubating for 4 h. The absorbance of each well was determined at 570 nm using a microplate reader (Microplate reader, Bio-Rad, 3550).</p>", "<title>Electrophysiological recording in vitro</title>", "<p id=\"Par26\">Electrophysiological assessments could detect action potentials or sodium currents in the primary cortex or hippocampal neurons at room temperature. As described previously, the electrophysiological patch clamp recording was performed (Hu et al. ##REF##33088260##2020##; Shan et al. ##REF##31422151##2019##). Briefly, the cells were patched in voltage-clamp mode and regulated at − 70 mV. The membrane capacitance (Cm), input resistance (Rm), and time constant (tau) were measured by applying the depolarization step voltage command (mV) and using the pClamp10 software integration membrane test function. Next, the recordings were switched to the current clamp mode. The resting film potential was adjusted to  – 80 mV by introducing a positive current (50–100 pA). The, a series of depolarizing current pulses were used. The intrinsic excitation was determined by developing the input–output (i–o) function.</p>", "<title>Western blotting</title>", "<p id=\"Par27\">After the EEG recording, the 4–6-week-old C57BL/6 J mice were sacrificed by cervical dislocation and decapitation. The brains were rapidly kept in ice-cold phosphate-buffered saline (PBS) inside a sterile dish for western blotting. The injured or intact neurons treated with or without an exercise-conditioned medium were harvested for western blotting. The manufacturer helped to determine the specificity of the primary antibodies, and previous reports depicted by amino acid and/or mass spectrometry analysis (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.alomone.com/p/anti-nav1-1-2/\">https://www.alomone.com/p/anti-nav1-1-2/</ext-link> ASC-001?b = 390) The tissues or cells were homogenized separately on ice in lysis buffer possessing 10% sodium dodecyl sulfate (SDS), 10 mM Tris–HCl buffer (pH 7.4), 30% Triton-1000, 10 mM ethylenediaminetetraacetic acid (EDTA), protease inhibitor cocktail (Roche, Switzerland), and NaCl, using a homogenizer. The homogenates were centrifuged at 5000 g for 10 min at 4 °C. The protein was quantified using the bicinchoninic acid reagent (Sigma-Aldrich; Merck KGaA, Darmstadt, Germany) method. The equal protein amounts were resolved using SDS–polyacrylamide gel electrophoresis (PAGE) on 4–12% gels and transferred to nitrocellulose membranes. Then, they were incubated against Nav1.1 (1:800; cat. no. ASC-001; Alomone), Nav1.3 (1:500; cat. no. ASC-004; Alomone), or Nav1.6 (1:600; cat. no. ASC-009; Alomone) using antibodies. GAPDH (mouse monoclonal anti-GAPDH; 1:800; no. sc-47724, Santa Cruz, Delaware, CA, USA) was used as a reference. The membranes were incubated with matched secondary antibodies for 2 h at 20–25 ˚C. Horseradish peroxidase-conjugated anti-rabbit antibodies used to detect Nav1.1, Nav1.3, and Nav1.6 (1:2,500; cat. no. PI-1000; Vector Laboratories, Inc.). A peroxidase-conjugated anti-mouse secondary antibody (1:3,000; cat. no. PI-2000; Vector Laboratories, Inc.) was used for β-actin detection. Elevated chemiluminescence luminol reagent (Beyotime Institute of Biotechnology, Shanghai, China) helped quantify protein. A Bio-Rad Gel Imaging System (ChemiDoc™ XRS + ; Bio-Rad Laboratories, Inc., Hercules, CA, USA) was used for densitometric analysis of the target protein bands. The Quantity One software v4.6.6 (Bio-Rad Laboratories, Inc.) was used to quantify the protein expression levels of each group.</p>", "<title>Statistics</title>", "<p id=\"Par28\">SPSS software (version 22.0 IBM, Armonk, NY, USA) helped in statistical analysis. The data were expressed as means ± standard division (SD). Normality and variance homogeneity tests were assessed using SPSS. The data from two or more groups were statistically analyzed using one-way and bidirectional variance assessments, followed by post hoc adjustments using an LSD correction. MWM test and electrophysiological analysis were executed with two-way repeated measures (RM) ANOVA, followed by an LSD post hoc test. <italic>P</italic> &lt; 0.05 indicated statistically significant results. The Tamhane test was used for data analyzing. Graphs were made using the software Prism (version 9.3.1).</p>", "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Acknowledgements</title>", "<p>The authors would like to thank Jia Liu and Lu-Lu Xue for their guidance on experimental techniques.</p>", "<title>Author contributions</title>", "<p>All authors contributed to the study conception and design. Conceptualization: DW, H-RZ, H-XZ, G-JY, YBXY. Data curation: DW, H-RZ. Formal analysis and investigation: DW, RM. Methodology: X-HD, Y-XT, SL. Project administration: YBXY. Resources: X-YW, RM. Supervision: YBXY, M-NL. Validation and visualization: DW, G-JY, YBXY. Writing—original draft: DW, H-XZ. Writing—review &amp; editing: H-RZ, L-NL. Funding acquisition: YBXY.</p>", "<title>Funding</title>", "<p>This work was supported by the National Natural Science Foundation of China (grant number 81960210 and 81560238), Special Fund of the Applied Basic Research Programs of Yunnan Province associated with Kunming Medical University in China (grant no. 202101AY070001-005), Yunnan Revitalization Talent Support (grant no. YNWR-QNBJ-2019-008), and Foundation of Science and Technology Innovative Team Building of Kunming Medical University (grant no. CXTD201807).</p>", "<title>Data availability</title>", "<p>The data used to support the findings of this study are available from the corresponding author upon reasonable request.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par59\">The authors have no relevant financial or non-financial interests to disclose. The authors have no financial or proprietary interests in any material discussed in this article.</p>", "<title>Ethics approval</title>", "<p id=\"Par60\">Animal use and care protocols were conformed to the Principles of Laboratory Animal Care formulated by the National Committee of Medical Research, and the Guide for the Use of Laboratory Animals issued by the Institute of Laboratory Animal Resources of China, which were also approved by the Administrative Committee of Experimental Animal Care and Use of Kunming Medical University, China (Number of licence: kmmu20200240). All personnel engaged in industrial animal operation have the qualification certificates; the current research in research department has a relatively perfect animal experiment facility that can provide.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Voluntary RW exercise improved the performances of TBI mice in open field assessment. <bold>a</bold>–<bold>c</bold>, number of rearing up; <bold>d–f</bold>, number of fetal balls; <bold>g</bold>–<bold>i</bold>, distance traveled (<bold>m</bold>); (<bold>j</bold>–<bold>l</bold>), the number of stationary behaviors during the 10 min trial period. Data are expressed as Mean ± SD. Sham SED (Sham SED, mice were treated with sedentary treatment before sham surgery), Sham RW (Sham Running Wheel exercise, mice were treated with 3 weeks free running wheel exercise before sham surgery), Sham NR (Sham Non-Runner, mice were treated no running wheel training for 3 weeks after sham surgery), Sham R (Sham-Runner, mice were treated with 3 weeks of running wheel exercise training after sham surgery), Sham PS NR (Sham PreS + Non-runner, mice were treated no running wheel pre-training and post-injury training after sham surgery), Sham PR (Sham + Pre-Runner, mice were treated with 3 weeks of running wheel pre-training combined with 3 weeks of running wheel post-injury training after sham surgery); TBI SED (TBI sedentary, mice were treated with sedentary treatment before TBI surgery), TBI RW (TBI Running Wheel, mice were treated with 3 weeks free running wheel exercise before TBI surgery), TBI NR (TBI Non-Runner, mice were treated with no running wheel training for 3 weeks after TBI surgery), TBI R (TBI-Runner, mice were treated with 3 weeks of running wheel exercise training after TBI surgery), TBI PS NR (TBI PreS + Non-runner, mice were treated with no running wheel pre-training and post-injury training after TBI surgery), TBI PR (TBI + Pre-Runner, mice were treated with 3 weeks of running wheel pre-training combined with 3 weeks of running wheel post-injury training after TBI surgery)</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Voluntary RW exercise partially alleviated TBI-induced spatial learning and memory impairments indicated by MWM test. Two-way RM ANOVA followed by Bonferroni post hoc test were employed for the MWM test. <bold>a–c</bold>: the escape latency of mice in the training period from 1 to 5 days. <bold>a</bold>:*<italic>p</italic> &lt; 0.05, the Sham RW group vs. the TBI RW group; ^###<italic>p</italic> &lt; 0.001, the Sham SED group vs. the TBI SED group; ^$<italic>p</italic> &lt; 0.05, the Sham SED group vs. the TBI RW group. <bold>b</bold>: *<italic>p</italic> &lt; 0.05, ***<italic>p</italic> &lt; 0.001, the Sham R group vs. the TBI NR group; ^###<italic>p</italic> &lt; 0.001, the Sham NR group vs. the TBI NR group; <bold>c</bold>: *<italic>p</italic> &lt; 0.05, ***<italic>p</italic> &lt; 0.001, the Sham PS NR group vs. the TBI PS NR group; ^###<italic>p</italic> &lt; 0.001, the Sham PR group vs. the TBI PS NR group. <bold>d</bold>–<bold>f</bold> The number of target platform crossings in the target platform during the probe test. <bold>g</bold>–<bold>i</bold> Target of quadrant time of mice in probe testing. <bold>j</bold>–<bold>l</bold> Mean swimming speed (cm/sec) of mice during probe test. Data are expressed as Mean ± SD (<italic>n</italic> = 9)</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Voluntary RW exercise treated following injury restored the retrieval of object recognition memory of TBI mice. <bold>a</bold>–<bold>c</bold>: The Discrimination Index in different groups. Data are expressed as Mean ± SD (<italic>n</italic> = 9)</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Voluntary RW exercise partially redressed the abnormal EEG recording indicated by spectral power in Sham and TBI groups on 21 dpo. <bold>a</bold>–<bold>d</bold>: delta(1–3 Hz), theta(4–7 Hz), alpha(8–14 Hz) and delta(15–35 Hz) frequency range bands during the free exercise pre-training group mice. <bold>e</bold>–<bold>h</bold>: delta theta, alpha and delta frequency range bands during the post-injury exercise intervention group mice. <bold>i</bold>–<bold>l</bold>: delta, theta, alpha and delta frequency range bands during the pre-training combined with TBI post-injury exercise training group mice. Data are expressed as Mean ± SD (<italic>n</italic> = 5)</p></caption></fig>", "<fig id=\"Fig5\"><label>Fig. 5</label><caption><p>Voluntary RW exercise restored synaptic LTP of hippocampus in TBI mice. After treatment with a high-frequency, tetanic stimulation train (100 Hz, 1 s), a robust fEPSP slope was induced in mice both from Sham and TBI groups. Effect of exercise pre-training 24 h (<bold>a</bold>–<bold>b</bold>) or 21 days (<bold>c</bold>–<bold>d</bold>) after operation on LTP changes of mice. <bold>e</bold>–<bold>f</bold> Effect of post-injury exercise intervention 21 days after operation on LTP changes of mice. <bold>g</bold>–<bold>h</bold> Effect of pre-training combined with TBI post-injury exercise training 21 days after operation on LTP changes of mice. Data are expressed as Mean ± SD (<italic>n</italic> = 5). Two-way (RM) ANOVA followed by Bonferroni post hoc test was employed for analysis of the LTP of each group</p></caption></fig>", "<fig id=\"Fig6\"><label>Fig. 6</label><caption><p>Preliminary RW exercise redressed abnormal VGSCs protein expression of TBI mice. The expression of Nav1.1 (<bold>a</bold>–<bold>e</bold>), Nav1.3 (<bold>f</bold>–<bold>j</bold>) and Nav1.6 (<bold>k</bold>–<bold>o</bold>) proteins in each group was treated with exercise pre-training at different periods, which indicated by western blotting assay. Data are expressed as Mean ± SD (<italic>n</italic> = 9)</p></caption></fig>", "<fig id=\"Fig7\"><label>Fig. 7</label><caption><p>Either voluntary RW before TBI or prior-injury combined with post-injury exercise training redressed abnormal VGSCs protein expression of TBI mice. <bold>a</bold>–<bold>c</bold> The expression of Nav1.1, Nav1.3, Nav1.6 transmembrane protein in preliminary voluntary RW group. <bold>d</bold>–<bold>f</bold> The expression of Nav1.1, Nav1.3, Nav1.6 transmembrane protein in pre-training combined with TBI post-injury exercise training group. Data are expressed as Means ± SD (<italic>n</italic> = 9)</p></caption></fig>", "<fig id=\"Fig8\"><label>Fig. 8</label><caption><p>Treat with exercise-conditioned serum induced primary cortical neurons recovery following mechanical injury indicated by MTT assay. NEX-TBI: at 2, 6 or 24 h after mechanical injury, primary injured cortical neurons were treated with 1 ml of medium containing 10% non-exercise-conditioned serum instead of neurobasal medium. EX-TBI: At 2, 6 or 24 h after mechanical injury, primary injured cortical neurons were treated with 1 ml of medium containing 10% exercise-conditioned serum instead of neurobasal medium. Data are expressed as Mean ± SD (<italic>n</italic> = 7)</p></caption></fig>", "<fig id=\"Fig9\"><label>Fig. 9</label><caption><p>Exercise conditioned medium treatment redressed the neuronal sodium current after mechanical injury recorded using electrophysiological patch clamp. <bold>a</bold>–<bold>c</bold> Current–voltage relationships of sodium current density in cells with different treatments. <bold>d</bold>–<bold>f</bold> Peak current density. Effects of exercise training on changes in action potentials of damaged neurons provoked by TBI. <bold>g</bold>–<bold>i</bold> AP firing frequencies <bold>j</bold>–<bold>l</bold> Threshold current (PA) Data are expressed as Mean ± SD (<italic>n</italic> = 7)</p></caption></fig>", "<fig id=\"Fig10\"><label>Fig. 10</label><caption><p>Exercise-conditioned serum treatment redressed the abnormal expressions of Nav1.1, Nav1.3, Nav1.6 proteins in cortical neurons. The Nav1.1 protein expression showed in (<bold>a</bold>–<bold>c</bold>), the Nav1.3 protein expression showed in (d-f), while the Nav1.6 protein expression showed in (<bold>g</bold>–<bold>i</bold>). Data are expressed as Mean ± SD (<italic>n</italic> = 7)</p></caption></fig>" ]

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[ "<fn-group><fn><p><bold>Publisher's Note</bold></p><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></fn><fn><p>Dan Wang and Hui-Xiang Zhang authors contributed equally to this work.</p></fn></fn-group>" ]

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[ "<title>Introduction</title>", "<p id=\"Par2\">Attention-deficit/hyperactivity disorder (ADHD) is a common neurodevelopmental disorder, affecting 5–7% of children/adolescents worldwide [##REF##17541055##1##, ##UREF##0##2##]. It is characterized by an age-inappropriate, persistent pattern of inattention, and/or hyperactivity and impulsive behaviors that interferes with functioning and development [##UREF##1##3##]. ADHD is a multifactorial disorder, with both genetic and environmental factors, as well as their interaction, contributing to its etiology [##UREF##2##4##–##REF##29361339##6##].</p>", "<p id=\"Par3\">One of the most prominent neurocognitive biomarkers of ADHD is impaired response inhibition, which refers to the ability to voluntarily stop or suppress behaviors that are inappropriate for the context and/or individual goals [##UREF##4##7##, ##REF##14979754##8##]. Functional magnetic resonance imaging (fMRI) studies on response inhibition have shown that individuals with ADHD exhibit decreased activation during action cancellation and restraint compared with controls in specific brain areas: the fronto-parietal network, consisting of the prefrontal and superior parietal regions, and the fronto-striatal network, involving the prefrontal cortex and basal ganglia [##REF##28551777##9##–##UREF##8##15##]. By focusing on action cancellation assessed by the stop-signal task [##REF##23315233##16##], previous research has also reported that impairments in behavioral performance [##REF##25615565##14##–##REF##6232345##17##] and aberrant neural activity associated with response inhibition [##REF##25615565##14##] are not only present in children and adolescents with ADHD but also in their unaffected first-degree relatives. This led researchers to propose impaired inhibitory control as a possible endophenotype or candidate neurocognitive biomarker of ADHD that shares familial loading with the phenotype [##UREF##9##18##].</p>", "<p id=\"Par4\">Family-based studies have indeed shown that both behavioral performance of response inhibition and response inhibition-related brain activity are heritable, up to 60%. Two twin studies reported significant contribution of additive genetic variance to action cancellation during the stop-signal task [##REF##18473654##19##, ##REF##21205410##20##]. There has only been one genome-wide association study (GWAS) regarding behavioral response inhibition performance as assessed by the stop-signal task, but no significant loci were detected, probably due to the small sample size of 4,611 participants from a general population cohort [##REF##31598132##21##]. As for the neural correlates, there is no functional magnetic resonance imaging (fMRI) study directly investigating the heritability of response inhibition-related brain activation, but two twin studies addressing action restraint using a Go/NoGo task also reported that 50 to 60% of the variance in amplitudes of response inhibition-related-event-related potential components in adolescents and adults are attributable to genetic factors [##REF##15364418##22##, ##REF##28300615##23##].</p>", "<p id=\"Par5\">ADHD is a heritable disorder with a highly polygenic nature involving the combined effect of many genetic variants with small individual effects on the overall disease risk. The largest published GWAS of ADHD to date (comprising 20,183 cases and 35,191 controls) reported a SNP heritability of 22% and identified twelve genome-wide significant loci across the genome [##REF##31086353##24##]. This GWAS of ADHD not only confirms the polygenic architecture of ADHD [##REF##31086353##24##], but also enables the construction of polygenic risk scores (PRS) for ADHD to investigate a potentially shared genetic etiology between ADHD and cognitive and neural measures [##UREF##10##25##]. A systematic review of the existing literature on PRS-ADHD revealed that PRS-ADHD has also been linked with ADHD traits, other externalizing behaviors, impaired working memory, and reduced brain volume [##UREF##11##26##]. The relation between PRS-ADHD and hyperactivity-impulsivity symptoms may be partially mediated by neuroanatomical variation [##REF##33173195##27##]. Moreover, inhibitory control (as assessed by the Stroop task) has been linked with PRS-ADHD and was found to partially mediate the link between PRS-ADHD and symptoms of ADHD [##REF##33139708##28##]. A recent study investigating whether PRS-ADHD influenced attention regulation and response inhibition in ADHD reported significant associations of PRS-ADHD with reaction time variability but not with the number of commission errors during the Go/No-Go task [##REF##33531098##29##]. The aforementioned studies point to genetic sharing between ADHD and different cognitive traits and neuroimaging-derived variables and also suggest that certain (response inhibition-related) cognitive and neural processes mediate the link between genetic liability to ADHD as reflected in PRS-ADHD and ADHD symptomatology. However, to date, a possible shared genetic background between ADHD and brain activation during response inhibition has not been investigated yet.</p>", "<p id=\"Par6\">Therefore, in the present study, we investigated whether genetic liability to ADHD (PRS-ADHD) was associated with neural activity related to response inhibition (i.e., as measured during a stop-signal task), and whether such response inhibition-related neural activity would mediate the link between PRS-ADHD and ADHD symptoms. Moreover, we aimed to expand previous evidence pointing to genetic sharing between ADHD and inhibitory control [##REF##33531098##29##] by investigating whether PRS-ADHD would be related to behavioral performance measures during a stop-signal task, as well as investigating a possible mediating role of these behavioral correlates in the relation between PRS-ADHD and ADHD symptoms, in a relatively modest sample of individuals with ADHD, their unaffected siblings, and controls (NeuroIMAGE).</p>" ]

[ "<title>Methods</title>", "<title>Participants</title>", "<p id=\"Par7\">All subjects participated in the NeuroIMAGE project, which is a Dutch follow-up of the International Multicenter ADHD Genetics (IMAGE) project, a multi-site international cohort study [##UREF##12##30##]. Participants were included as ADHD probands if they met criteria for ADHD diagnosis on the Kiddie Schedule for Affective Disorders and Schizophrenia Present and Lifetime Version [##REF##9394946##31##] and/or Conners’ ADHD questionnaires, as obtained briefly prior to scanning [##UREF##13##32##, ##UREF##14##33##]. Inclusion criteria for unaffected siblings and controls (without an ADHD diagnosis) were having fewer than three symptoms on both inattention and hyperactivity-impulsivity subscales [##UREF##12##30##]. Details regarding the NeuroIMAGE project and exclusion criteria are provided in Supplementary Information. Participants with ADHD who used ADHD medication discontinued their medication for 24 h prior to scanning. Written informed consent was obtained from parents and from participants who were older than 12 years, in accordance with national legislation. The study had been approved by the respective local ethics committees.</p>", "<p id=\"Par8\">Genetic data and data regarding symptoms of ADHD were available from 952 participants, but 44 participants were excluded from further analysis because of being outliers in their genetic background (see below, Genotyping). Of the remaining 908 participants (43% female, mean age = 16.9 years, see Supplementary Table 1), stop-signal task fMRI data were available from 454 participants.</p>", "<title>ADHD symptoms</title>", "<p id=\"Par9\">For each participant, the severity of ADHD symptoms on the ‘cognitive problems/inattention’ (12 items) and ‘hyperactivity’ (9 items) subdomains were assessed using a parent questionnaire (Conners’ Parent Rating Scales-Revised:Long version, CPRS-R:L) [##UREF##13##32##] rated on a 4-point Likert scale from 0 (not at all) to 3 (severely). The CPRS-R:L has been shown to have high internal consistency (Cronbach’s α ranging from 0.75 to 0.94) and construct validity to discriminate individuals with ADHD from a non-clinical group; sensitivity 92.3%, specificity 94.5%, positive predictive power 94.4%, negative predictive power 92.5%) [##UREF##13##32##]. The total ADHD symptom severity score was calculated as the sum of severity scores for inattention and hyperactivity-impulsivity.</p>", "<title>Genotyping</title>", "<p id=\"Par10\">Genotyping was done using the Infinium PsychArray-24 BeadChip v1.1, Illumina, comprising ~ 593 K markers. Quality control and imputation were performed using the Ricopili (Rapid Imputation for COnsortias PIpeLIne for GWAS) pipeline [##REF##32758139##34##] and 1 KG phase 3 European reference samples [##UREF##15##35##]. Details regarding preprocessing and quality control of genotype data can be found in Supplementary Information. Only SNPs passing quality control filters regarding imputation quality (&gt; 0.8), minor allele frequency (≥ 0.05), Hardy–Weinberg equilibrium test (<italic>p</italic>-value cut-off 1 × 10^–6), and SNP-call rate (&gt; 0.98) were retained. After imputation, genome-wide genotype data were available for 2,840,886 SNPs.</p>", "<p id=\"Par11\">Four principal components were used as covariates to correct for ancestry. A scatterplot of the first and second principal components showed that the individuals from the NeuroIMAGE clustered closely with the European British and CEPH populations of the 1000 Genomes Project [##UREF##15##35##] (Supplementary Fig. 1). Individuals with values &gt;  ± 2 SD from the mean on the first four principal components were removed (N = 44), leaving 908 subjects for the polygenic risk score analysis.</p>", "<title>Polygenic risk scoring</title>", "<p id=\"Par12\">The 2019 GWAS meta-analysis for ADHD conducted by the Psychiatric Genomics Consortium (PGC) [##REF##31086353##24##] was used as ‘base dataset’ to calculate individual-level PRS in NeuroIMAGE as the ‘target sample’. To avoid overlap between base and target samples, we used GWAS results in which the individuals from NeuroIMAGE were excluded. A total of 2,175,131SNPs overlapped between the base and target datasets and were available for computing PRS. PRS-ADHD were calculated using the PRSice-2 software (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.prsice.info\">https://www.prsice.info</ext-link>) [##REF##31765472##36##]. The SNPs were clumped based on linkage disequilibrium with a cutoff of <italic>r</italic>² = 0.1 in a 250-kb bidirectional window to keep a set of independent SNPs (resulting in a total of 66,978 clumped SNPs). PRS-ADHD were initially computed for a few increasingly inclusive SNP <italic>p</italic>-value thresholds (<italic>p</italic> &lt; 1 × 10^–6, 1 × 10^–4, 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 1). From these, only the PRS-ADHD showing the strongest association with ADHD symptom scores were used in relation to the subsequent neuroimaging analyses.</p>", "<title>Stop-signal task</title>", "<p id=\"Par13\">A visual version of the stop-signal task was used to probe the behavioral and neural mechanisms of response inhibition [##REF##6232345##17##]. Details regarding the task are provided in the Supplementary Information. Response inhibition performance was measured by the stop-signal reaction time (SSRT), which was calculated by subtracting the mean stop-signal delay from the mean reaction time. Other task outcomes of interest were the mean reaction time to go-stimuli (MRT), and the intra-individual coefficient of variation of reaction time to go stimuli (IRT). Since MRT and IRT are related to attentional processing, these are also important (complementary) components of response inhibition, in particular when considering ADHD patients who are suffering from inattention symptomatology.</p>", "<title>fMRI acquisition and preprocessing</title>", "<p id=\"Par14\">Information on imaging parameters and fMRI acquisition, and preprocessing following ICA-AROMA [##REF##25770991##37##] were previously described in detail [##REF##25615565##14##, ##REF##31546048##38##] and can be found in the Supplementary Information.</p>", "<title>fMRI data analyses</title>", "<title>First-level fMRI data analysis</title>", "<p id=\"Par15\">The initial within-subject analysis was conducted across all participants using a general linear model in FSL-FEAT (FMRIB’s Software Library, <ext-link ext-link-type=\"uri\" xlink:href=\"http://www.fmrib.ox.ac.uk/fsl\">www.fmrib.ox.ac.uk/fsl</ext-link>; fMRI Expert Analysis Tool, version 6.0) [##REF##21979382##39##, ##REF##11707093##40##]. Factors of interest were successful go- and successful and failed stop-trials. Failed go-trials, movement trials (trials within an 8-s interval before movements exceeding 1 mm), signal from cerebral spinal fluid and white matter, and 24 realignment parameters (six motion parameters plus their six temporal derivatives, and quadratic terms of these twelve regressors) were added as covariates. Activation maps of contrasts of interests [successful inhibition—go (using successful stop- versus successful go-trials to isolate the activation of successful inhibition and to identify brain regions that are specifically involved in response inhibition processes), failed inhibition—go (using unsuccessful stop- versus successful go-trials to identify regions that are activated when the participant fails to inhibit a prepotent response), and failed—successful inhibition (using unsuccessful versus successful stop-trials to model activation unique to the error processing and adjustment of behavior after an error)] were calculated and spatially normalized to 2-mm MNI152 template, and subsequently combined over all the runs within each subject using a fixed effects model.</p>", "<title>Between-subjects fMRI data analysis</title>", "<p id=\"Par16\">In the between-subjects analysis, mixed-effects analyses using the FSL-FLAME1 [##REF##15501092##41##] procedure were conducted to generate t-contrasts with the contrasts mentioned above. As one of the main aims of the study was to identify the regions exhibiting PRS-ADHD-related activation during the stop-signal task and, according to the best of our knowledge, there has been no previous research on this, the regions of interest (ROIs) were not chosen a priori, but rather determined by hypothesis-free voxel-based analysis. We used PRS-ADHD as the regressor of interest while controlling for the above-mentioned covariates to identify the ROIs showing PRS-ADHD-related activation in three different contrasts, namely successful inhibition—go, failed inhibition—go, and failed—successful inhibition. We used the FSL default cluster-forming threshold of <italic>Z</italic> &gt; 2.3 for Z-statistic images [##REF##15501092##41##]—which is commonly used and should provide a sufficiently stringent cut-off to distinguish random noise from signal [##REF##25615565##14##, ##REF##16510720##42##–##REF##24405185##44##], while a family-wise error rate (FWER)-corrected cluster significance threshold of p = 0.05 across the whole brain was applied. After the voxel-based analyses, the mean parameter estimates for all clusters found to be associated with PRS-ADHD (i.e., the identified ROIs) were extracted for each participant for further analyses outside FSL. It was not feasible to correct for sibling relatedness in FSL, but for all subsequent analyses using the mean neural activity from clusters that mapped significantly onto PRS-ADHD, we applied this correction in the regression and mediation models (see Statistical data analysis).</p>", "<title>Statistical data analysis</title>", "<p id=\"Par17\">We performed a series of regression analysis based on the Baron and Kenny [##UREF##17##45##] analysis strategy to test our mediation hypotheses. A detailed explanation of the analysis strategy can be found in the Supplementary Information. All statistical analyses were performed using <italic>R</italic> 4.0.2 (<ext-link ext-link-type=\"uri\" xlink:href=\"https://www.r-project.org/\">https://www.r-project.org/</ext-link>) [##UREF##18##46##]. A false discovery rate (FDR) [##UREF##19##47##] correction was applied to correct for multiple testing (see Supplementary Information).</p>", "<title>Regression models</title>", "<p id=\"Par18\">Mixed model regression analyses (using R package lme4 [##UREF##20##48##]) were performed to test for separate associations between PRS-ADHD, ADHD symptom severity, and behavioral and neural correlates of response inhibition. To explore the direct effect of PRS-ADHD (predictor) on ADHD symptoms (outcome) (c’ path on Baron and Kenny’s mediation model [##UREF##17##45##]), we first investigated associations of PRS-ADHD with ADHD symptom severity (inattention, hyperactivity-impulsivity, and total ADHD severity). The <italic>p-value</italic> threshold at which the PRS-ADHD showed the strongest association with ADHD symptom severity was selected for the subsequent analyses. Second, to evaluate the effect of PRS-ADHD (predictor) on response inhibition-related behavioral measures and brain activation (mediator) (a path on Baron and Kenny’s mediation model [##UREF##17##45##]), we investigated association of PRS-ADHD with the Stop-Signal performance parameters (MRT, IRT, and SSRT) and the mean SSRT-associated brain activation (extracted from the clusters during successful inhibition—go, failed inhibition—go, and failed—successful inhibition fMRI contrasts); those significant after FDR-correction were selected for the next analyses. Third, to investigate the effect of response inhibition-related behavioral measures and brain activation (mediator) on ADHD symptoms (outcome) (b path on Baron and Kenny’s mediation model [##UREF##17##45##]), we explored the associations of behavioral and neural correlates of response inhibition with ADHD symptom severity, controlling for PRS-ADHD; those significant after FDR-correction were selected for mediation analyses (see section below). Mediation (indirect effect) can be estimated by the product of the a × b path coefficients. Before establishing the mediation model, this regression analysis was run to find out which mediators were associated with ADHD symptoms. Age and sex were included as fixed covariates in all analyses, and, where applicable, family identity was included as a random variable to adjust for sibling relatedness. In addition, genotyping batch and the first four genetic principal components were entered as covariates in the analyses involving PRS-ADHD, while fMRI scanning site was entered as a covariate in the analyses involving neural activity.</p>", "<title>Mediation analyses</title>", "<p id=\"Par19\">Mediation analyses (using R package mediation [##UREF##21##49##]) were performed to explore the potential mediation effect of behavioral outcomes and neural activity of the stop-signal task associated with PRS-ADHD on the relation between PRS-ADHD and ADHD symptoms. Behavioral and neural correlates of response inhibition that were found to be associated with ADHD symptoms after controlling for PRS-ADHD were selected as potential mediators. The mediation (indirect), direct, and total effects were estimated using mixed models involving family identity as a random factor and aforementioned covariates. The quasi-Bayesian Monte Carlo simulation was used with 10,000 iterations to generate 95% confidence intervals for estimates. To control Type I errors, we applied FDR correction for the behavioral and neural correlates of response inhibition separately because these are different experiments (see ‘<xref rid=\"Sec14\" ref-type=\"sec\">Mediation analyses</xref>’ in the Results section).</p>" ]

[ "<title>Results</title>", "<title>Participants</title>", "<p id=\"Par20\">The main sample consisted of 454 participants with both genetic and imaging data available, originating from 267 families. Overall, 178 (39.2%) met criteria for ADHD, 103 (22.7%) were unaffected siblings, and 173 (38.1%) were controls. Details regarding sample characteristics can be found in Table ##TAB##0##1##.</p>", "<title>PRS-ADHD and ADHD symptoms</title>", "<p id=\"Par21\">There were positive associations between PRS-ADHD and total ADHD, inattention, and hyperactivity-impulsivity symptom scores at all PRS <italic>p</italic>-value thresholds except for 1 × 10^–4 and 1 × 10^–6 in all participants with genetic data available (<italic>N</italic> = 908; Table ##TAB##1##2##). The results in the participants with both genetic and fMRI data available (<italic>N</italic> = 454) were similar (Supplementary Table 2). The strongest association was observed at a <italic>p</italic>-value threshold of 1 for total ADHD (<italic>R</italic>²-PRS = 0.044; p-FDR = 9.21 × 10^–9), inattention (<italic>R</italic>²-PRS = 0.039; p-FDR = 1.32 × 10^–8), and hyperactivity-impulsivity symptom scores (<italic>R</italic>²-PRS = 0.04; p-FDR = 1.65 × 10^–8). Therefore, the PRS-ADHD at a<italic> p</italic>-value threshold of 1 (66,978 SNPs), which also explained the most variance for all symptom scales, was selected for further analyses.</p>", "<title>PRS-ADHD and behavioral correlates of response inhibition</title>", "<p id=\"Par22\">PRS-ADHD showed significant positive associations with MRT (R²-PRS = 0.014; p-FDR = 0.015) and IRT (R²-PRS = 0.014; p-FDR = 0.015), but not with SSRT (Table ##TAB##2##3##). Therefore, MRT and IRT were selected as the behavioral correlates of interest for the subsequent analyses.</p>", "<title>PRS-ADHD and neural correlates of response inhibition</title>", "<title>Successful inhibition—go</title>", "<p id=\"Par23\">For successful inhibition—go contrast, there was a significant negative association between PRS-ADHD and activation in the left fronto-insular regions and putamen (Z = 4.7, p-FWER = 6.25 × 10^–4, 855 voxels) (Supplementary Table 3, Fig. ##FIG##0##1##a). Post hoc analyses revealed that 4.1% of the variance in the cluster-average activity was explained by PRS-ADHD (Table ##TAB##2##3##).</p>", "<title>Failed inhibition—go</title>", "<p id=\"Par24\">For failed inhibition—go contrast, there was significant positive associations between PRS-ADHD and activation in the left temporal pole and anterior parahippocampal gyrus (PHG) (<italic>Z</italic> = 4.28, p-FWER = 0.027, 438 voxels) and in the right putamen (<italic>Z</italic> = 4.38, p-FWER = 0.03, 428 voxels) (Supplementary Table 3, Fig. ##FIG##0##1##b-c). Post hoc analyses showed that PRS-ADHD explained, respectively, 4.2% and 4.4% of the variance in the average activity in these clusters located on the left and right hemisphere (Table ##TAB##2##3##).</p>", "<title>Failed—successful inhibition</title>", "<p id=\"Par25\">For failed—successful inhibition contrast, there were significant positive associations between PRS-ADHD and activation in the left fronto-insular, putamen, anterior temporal regions, and anterior PHG (<italic>Z</italic> = 4.15, p-FWER = 1.79 × 10^–7, 2033 voxels) and in the right basal ganglia and thalamus (<italic>Z</italic> = 3.81, p-FWER = 0.01, 609 voxels) (Supplementary Table 3, Fig. ##FIG##0##1##d–e). Post hoc analyses revealed that PRS-ADHD explained, respectively, 7.1% and 5.6% of the variance in the average activity in these clusters located on the left and right hemisphere (Table ##TAB##2##3##).</p>", "<title>Behavioral correlates of response inhibition and ADHD symptoms, controlling for PRS-ADHD</title>", "<p id=\"Par26\">MRT was positively associated with total ADHD (p-FDR = 0.002), inattention (p-FDR = 0.01), and hyperactivity-impulsivity symptom scores (p-FDR = 0.003). Likewise, IRT was positively associated with total ADHD (p-FDR = 1.12 × 10^–7), inattention (p-FDR = 8.08 × 10^–6), and hyperactivity-impulsivity symptom scores (p-FDR = 2.05 × 10^–7), adjusting for PRS-ADHD. Details regarding the results are provided in Supplementary Information and Supplementary Table 4. For completeness, the results of the regression analyses between behavioral correlates and ADHD symptoms without controlling for PRS-ADHD are provided in the Supplementary Information and Supplementary Table 6.</p>", "<title>Neural correlates of response inhibition and ADHD symptoms, controlling for PRS-ADHD</title>", "<p id=\"Par27\">The activation in the left temporal pole and anterior PHG was negatively associated with hyperactivity-impulsivity symptom scores (p-FDR = 0.075). This result failed to survive FDR-correction, but was carried forward to the mediation analyses because it showed at least a nominal significant association (<italic>p</italic> = 0.04) with ADHD symptom scores, when adjusting for PRS-ADHD. The cluster-average activity and PRS-ADHD explained, respectively, 1% and 5.2% of the variance in hyperactivity-impulsivity symptom scores. More detailed results can be found in Supplementary Table 5. For completeness, the results of the regression analyses between neural correlates and ADHD symptoms without controlling for PRS-ADHD are provided in Supplementary Information and Supplementary Table 7.</p>", "<title>Mediation analyses</title>", "<p id=\"Par28\">MRT and IRT were the only behavioral correlates associated with both PRS-ADHD and all ADHD symptoms, and we applied FDR correction for a total of six tests [2 mediators (MRT and IRT) × 3 symptom scales (total, inattention and hyperactivity-impulsivity symptoms)]. Regarding neural correlates, only the left temporal pole and anterior parahippocampal gyrus activation during failed inhibition—go contrast was nominally significantly (<italic>p</italic> = 0.04) associated with symptoms of hyperactivity-impulsivity, so there was only one mediation model involving neural correlates and therefore no additional multiple testing correction could be applied here (see also under Methods).</p>", "<title>Behavioral mediators</title>", "<p id=\"Par29\">As MRT and IRT were associated with ADHD symptoms, controlling for PRS-ADHD (see above), they were selected as potential behavioral mediators. Mediation analyses showed that both MRT and IRT partially mediated the association between PRS-ADHD and ADHD symptoms. Specifically, the association between PRS-ADHD and the total ADHD symptom score was mediated by MRT (indirect effect β = 0.018, 95% CI = (0.003, 0.04); p-FDR = 0.014, accounting for 7.7% of the total effect) and IRT (indirect effect β = 0.034, 95% CI = (0.011, 0.07); p-FDR = 0.012, accounting for 15.7% of the total effect). Similar results were also obtained for the inattention and hyperactivity-impulsivity symptom scores (see Supplementary Information). Figure ##FIG##1##2## represents path diagrams of mediation analyses.</p>", "<title>Neural mediators</title>", "<p id=\"Par30\">As the cluster-average activity in the left anterior temporal pole and PHG during failed inhibition was (nominally significantly) associated with hyperactivity-impulsivity symptoms, controlling for PRS-ADHD (see above), it was selected as potential neural mediator. The association between PRS-ADHD and hyperactivity-impulsivity symptoms was partially mediated by activity in the left temporal pole and anterior PHG during failed inhibition—go [indirect effect β =  −0.02, 95% CI = (−0.046, −0.001); <italic>p</italic> = 0.04, accounting for 9.5% of the total effect). Figure ##FIG##1##2## represents path diagrams of mediation analyses.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par31\">This study investigated the relationships between genetic liability to ADHD (PRS-ADHD), its core symptoms, and behavioral and functional neural correlates of response inhibition in a sample of children, adolescents, and young adults with ADHD, their unaffected siblings, and healthy controls. A higher genetic liability to ADHD was associated with higher levels of symptom severity in both symptom domains of inattention and hyperactivity-impulsivity, as well as with total ADHD symptom severity. Further, PRS-ADHD were found to be associated with slower and more variable responses to go-stimuli in the stop-signal task and with altered neural activity in several regions of the bilateral fronto-striatal network during response inhibition. We identified behavioral performance in the stop-signal task (MRT and IRT) as partial mediators of the association between PRS-ADHD and ADHD symptoms in both symptom domains; activity in the left temporal pole and anterior parahippocampal gyrus (PHG) during failed inhibition was observed to be a mediator in the relationship of PRS-ADHD with hyperactivity-impulsivity symptoms.</p>", "<p id=\"Par32\">Our finding that PRS-ADHD were positively associated with not only total ADHD symptom scores, but also with inattention and hyperactivity-impulsivity symptom scores, is consistent with our hypothesis and previous studies [##UREF##11##26##, ##UREF##22##50##, ##REF##32033925##51##]. The explained variance by PRS-ADHD for both ADHD symptom domains was similar (3.9% for inattention and 4% for hyperactivity-impulsivity).</p>", "<p id=\"Par33\">The significant positive associations that we found between the PRS-ADHD and latency of go responses, as indexed by MRT, and intra-individual reaction time variability, as indexed by IRT, point to an overlap between genetic effects on ADHD and MRT and IRT; it also further supports the hypothesis of increased intra-individual response variability as an endophenotype of ADHD [##UREF##23##52##]. Elevated reaction time and greater reaction time variability in a cognitive task are among the most consistent findings in the literature of childhood ADHD [##REF##16979141##53##–##REF##21463041##55##] and have been repeatedly observed in stop-signal task studies [##REF##25615565##14##, ##REF##21463041##55##–##UREF##25##58##]. The unaffected siblings of individuals with ADHD have been shown to have levels of IRT intermediate between probands with ADHD and controls [##REF##25615565##14##]. Further to that, multivariate genetic analyses of ADHD cases and unaffected sibling pairs showed that cognitive impairment in ADHD related to response time (variability) during a Go/No-Go task [##REF##21041617##59##], and a link between PRS-ADHD and reaction time variability in response inhibition tasks have also been recently reported [##REF##33531098##29##, ##UREF##26##60##].</p>", "<p id=\"Par34\">There was no significant association of PRS-ADHD with SSRT, the core measure of inhibitory control during the stop-signal task. Impaired response inhibition, as indexed by greater SSRT values, is thought to be one of the primary deficits associated with ADHD [##UREF##25##58##, ##UREF##27##61##, ##UREF##28##62##]. Nevertheless, previous stop-signal task studies (sample sizes ranging from 45 to 170) indeed reported shorter, but also <italic>similar</italic> SSRT values in children with ADHD compared to healthy controls [##UREF##29##63##–##REF##15163457##66##]. Moreover, our results are in line with a recent study that reported no association between PRS-ADHD and inhibitory control, as indexed by commission errors during a Go/No-Go task [##REF##33531098##29##] and SSRT during stop-signal tasks [##UREF##26##60##, ##REF##29496126##67##]. However, a link between PRS-ADHD and cognitive interference, measured in the Stroop task, has also been reported [##REF##33139708##28##]. These somewhat inconsistent results in the current literature might result from different samples (the previous studies were limited to individuals with ADHD [##REF##33139708##28##, ##REF##33531098##29##], whereas we also included unaffected siblings and healthy controls) and/or different experimental tasks (since each inhibitory paradigm has its own measure of inhibitory control). As suggested earlier [##REF##33531098##29##, ##UREF##26##60##, ##REF##29496126##67##], the genetic variants captured by the PRS-ADHD might not be directly related to the core behavioral measures of response inhibition, but rather to other response inhibition-related components (MRT, IRT) and neural activity. It is also possible that shared genetic effects between ADHD and certain behavioral correlates of response inhibition (i.e., SSRT) are more subtle than what we can detect with our current ‘base’ and ‘target’ samples. Therefore, larger future studies are needed to more robustly confirm genetic sharing of ADHD with different behavioral performance measures of response inhibition across different experimental paradigms. All in all, our findings point to the influence of genetic liability to ADHD on attentional processing during response inhibition rather than inhibitory control as such.</p>", "<p id=\"Par35\">To our knowledge, this is the first study to investigate a possible shared genetic background between ADHD and brain activation in the response inhibition network by using individual-level PRS and fMRI data. PRS-ADHD was significantly related to activity of several regions in the bilateral fronto-striatal-thalamo-cortical network associated with response inhibition. We identified a cluster within the left fronto-insular regions and putamen, for which activity during successful inhibition was negatively associated with the PRS-ADHD. To further investigate the brain activation related to failed response inhibition, we used two separate contrasts, “<xref rid=\"Sec21\" ref-type=\"sec\">failed inhibition—go</xref>” and “<xref rid=\"Sec22\" ref-type=\"sec\">failed—successful inhibition</xref>”, which provide complementary information about the neural mechanisms underlying response inhibition (the first contrast is thought to reflect such as the engagement of the inhibitory control network and the detection of a stop signal, while the second contrast compares error processing and adjustment) [##REF##17274022##68##, ##REF##20600968##69##]. The failed inhibition—go contrast revealed two clusters positively associated with PRS-ADHD, located in the left temporal pole and anterior PHG, and in the right putamen. In failed—successful inhibition contrasts, positive associations of PRS-ADHD with neural activation were found within two clusters localized in the left fronto-insular, putamen, anterior temporal, and parahippocampal regions, and in the right thalamus and basal ganglia.</p>", "<p id=\"Par36\">Our findings regarding neural activity converge with a previous meta-analysis (607 participants; 287 ADHD cases and 320 healthy controls), which reported aberrant activation in individuals with ADHD during response inhibition for a large neural network encompassing these same areas [##UREF##7##12##]. Moreover, decreased activation in bilateral fronto-parietal and fronto-striatal regions during the stop-signal task has also been reported in unaffected siblings of individuals with ADHD when compared to healthy controls in a previous study that also used the NeuroIMAGE sample (420 participants; 185 ADHD cases, 111 of their unaffected siblings, and 124 healthy controls) [##REF##25615565##14##]. During failed inhibition, we also identified a cluster in the left anterior temporal pole and PHG, in addition to areas of inhibition in the basal ganglia whose activities were positively associated with PRS-ADHD. The PHG with its surrounding areas, such as the entorhinal cortex and hippocampus, has been associated with post-error processing and error-driven learning strategy [##REF##19494138##70##]. The positive association between PRS-ADHD and activity in the left PHG may therefore reflect different strategies adopted by the individuals with higher PRS-ADHD for performance-monitoring and error-processing during the stop-signal task. These results, combined with our findings regarding the significant associations of PRS-ADHD with the activity of key nodes in the response inhibition network such as the prefrontal areas, anterior cingulate cortex, basal ganglia, and thalamus, suggest that common risk variants for ADHD play a role in altered neural substrates of inhibitory control in ADHD.</p>", "<p id=\"Par37\">Our finding that MRT and IRT mediated the association between PRS-ADHD and the total ADHD, inattention, and hyperactivity-impulsivity symptom scores confirms disrupted attentional processing during response inhibition as a key cognitive variable in the context of ADHD. Individuals who had a greater polygenic risk for ADHD showed slower go responses with greater variability in response time, which in turn partially mediated the link between PRS-ADHD and ADHD symptom severity. MRT and IRT varied with regard to how much of the total effect they mediated. MRT mediated 7.7% of the total association of PRS-ADHD with total ADHD symptom severity, whereas the corresponding percentage for IRT was 15.7%. Similar patterns emerged for the inattention and hyperactivity-impulsivity symptom scores. A recent study also demonstrated that reaction time variability is associated with PRS-ADHD and also partially mediated the relationship between PRS-ADHD and ADHD traits [##UREF##26##60##]. Furthermore, increased reaction time variability has repeatedly been reported in children and adults with ADHD [##UREF##24##54##, ##UREF##31##71##–##REF##25479234##73##]. Moreover, reaction time variability in particular has been suggested to be a robust and reliable feature of ADHD across stop-signal and other cognitive tasks [##UREF##31##71##]. Thus, higher genetic liability to ADHD, as indexed by higher PRS-ADHD, might lead to the development of more ADHD symptoms somewhat more clearly through altered IRT than MRT as a possible intermediate phenotype.</p>", "<p id=\"Par38\">As for the neural correlates of response inhibition, the association of PRS-ADHD with the severity of hyperactivity-impulsivity symptoms was partially mediated by lower activity in the left temporal pole and anterior PHG during failed inhibition. As the indirect effect of the neural activation was negative while the total effect had a positive sign, the effect of neural activation as a mediator indirectly reduced the effect of PRS-ADHD on ADHD symptoms, which may suggest a ‘suppressive’ or inhibiting (neural mediation) effect. More specifically, a subset of the SNPs that drive the direct effect of PRS-ADHD on the severity of hyperactivity-impulsivity symptoms might also be involved in the above-mentioned indirect pathway involving activation in the left temporal pole and anterior PHG during failed inhibition. Given the association between the PHG with its surrounding areas and post-error processing [##REF##19494138##70##], the increased activation of the anterior temporal pole and PHG in participants with a high genetic liability to ADHD may represent a compensatory response to error processing. It can be speculated that these individuals leverage their errors during failed inhibition to help optimize future behavior in upcoming trials in the stop-signal task and might develop a strategy to develop better general behavioral control skills to self-regulate their non-optimal impulsive behavior. However, because the association between the neural activity in the left temporal pole and anterior PHG and the hyperactivity-impulsivity symptoms was only nominally significant, further research is warranted.</p>", "<p id=\"Par39\">Our results should be interpreted in light of the study’s potential strengths and limitations. As a unique feature, we consider the inclusion of individuals with ADHD, their unaffected siblings, and controls in our ‘target’ sample, which together may represent a more comprehensive and representative range of ADHD symptomatology and response inhibition correlates than a case-only study. Our PRS-ADHD—based on a well-powered GWAS of ADHD—showed a robust association with (both inattention and hyperactivity-impulsivity) ADHD symptoms in our ‘target’ sample. Nevertheless, a possible limitation of our current study could be the somewhat modest sample size of NeuroIMAGE. Future studies would benefit from larger ‘target’ sample sizes and probably even more powerful GWAS to allow for more definite conclusions about the shared genetic architecture between ADHD and behavioral and neural correlates of response inhibition. It is also worth keeping in mind that fMRI detects the hemodynamic changes in cerebral blood flow rather than direct neural activity, and our findings of fMRI analysis reflect altered brain activation related to cognitive processing during a stop-signal task. The clinical interpretation of altered brain activity (i.e., whether findings may reflect pathological or just altered physiological brain functioning) remains complicated. Although we used cross-sectional rather than longitudinal data to investigate mediation effects, the use of genetic risk scores together with the nature of brain functioning and (neurodevelopmental) behavioral symptomatology means that in this case inference of causality with regard to temporal precedence is not necessarily limited by the study design.</p>", "<p id=\"Par40\">To conclude, our findings provide evidence for and better understanding of a shared genetic etiology between ADHD and behavioral measures and neural activity related to response inhibition in youth with a diagnosis of ADHD, unaffected siblings, and controls, corroborating response inhibition as a potential endophenotype. Partial mediation effect of brain activation in the left temporal pole and anterior PHG during failed inhibition on the association of PRS-ADHD with severity of hyperactivity-impulsivity symptoms may point to a possible pathway from genetic liability for ADHD to the expression of hyperactivity-impulsivity symptoms through altered brain activation during response inhibition. Moreover, MRT and IRT partially mediated the relationships of PRS-ADHD and ADHD symptom severity, suggesting that genetic liability to ADHD influences attention regulation, which in turn may affect the severity of both inattention and hyperactivity-impulsivity symptoms. Overall, our findings lend support for the conceptualization of response inhibition as a neurobiological mechanism underlying the etiology of ADHD. Our findings also provide novel insights regarding the genetic sharing of ADHD symptomatology with cognitive and underlying neural processing related to response inhibition.</p>" ]

[]

[ "<p id=\"Par1\">Impaired response inhibition is commonly present in individuals with attention-deficit/hyperactivity disorder (ADHD) and their unaffected relatives, suggesting impaired response inhibition as a candidate endophenotype in ADHD. Therefore, we explored whether behavioral and neural correlates of response inhibition are related to polygenic risk scores for ADHD (PRS-ADHD). We obtained functional magnetic resonance imaging of neural activity and behavioral measures during a stop-signal task in the NeuroIMAGE cohort, where inattention and hyperactivity-impulsivity symptoms were assessed with the Conners Parent Rating Scales. Our sample consisted of 178 ADHD cases, 103 unaffected siblings, and 173 controls (total <italic>N</italic> = 454; 8–29 years), for whom genome-wide genotyping was available. PRS-ADHD was constructed using the PRSice-2 software. We found PRS-ADHD to be associated with ADHD symptom severity, a slower and more variable response to Go-stimuli, and altered brain activation during response inhibition in several regions of the bilateral fronto-striatal network. Mean reaction time and intra-individual reaction time variability mediated the association of PRS-ADHD with ADHD symptoms (total, inattention, hyperactivity-impulsivity), and activity in the left temporal pole and anterior parahippocampal gyrus during failed inhibition mediated the relationship of PRS-ADHD with hyperactivity-impulsivity. Our findings indicate that PRS-ADHD are related to ADHD severity on a spectrum of clinical, sub-threshold, and normal levels; more importantly, we show a shared genetic etiology of ADHD and behavioral and neural correlates of response inhibition. Given the modest sample size of our study, future studies with higher power are warranted to explore mediation effects, suggesting that genetic liability to ADHD may adversely affect attention regulation on the behavioral level and point to a possible response inhibition-related mechanistic pathway from PRS-ADHD to hyperactivity-impulsivity.</p>", "<title>Electronic supplementary material</title>", "<p>The online version of this article (10.1007/s00406-023-01632-8) contains supplementary material, which is available to authorized users.</p>", "<title>Keywords</title>" ]

[ "<title>Electronic supplementary material</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Acknowledgements</title>", "<p>We are very grateful to all families who participated in the NeuroIMAGE project, and the whole NeuroIMAGE-team, including interviewers, technicians, scientists, clinicians, volunteers, and managers of all involved organizations and facilities, for recruitment and collection, and preprocessing of the data used in this study. We are very grateful to the Donders Institute for Brain, Cognition and Behavior of the Radboud University Nijmegen for granting us access to the high-performance computing environment required to conduct this study.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par41\">This publication is the work of the authors, and this research is supported by the European Community’s Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 603016 (MATRICS) and no. 602805 (Aggressotype). The NeuroIMAGE-project was supported by NWO Large Investment Grant 1750102007010 and ZonMW Grant 60-60600-97-193 (to J.K.B.), and grants from Radboud University Nijmegen Medical Center, University Medical Center Groningen and Accare, and VU University Amsterdam. G.S., I.H.R., D.v.R., E.S., B.F., A.D. and P.J.H. reported no financial interests or potential conflicts of interest. J.K.B. has been a consultant to/advisory board member of/and/or a speaker for Janssen Cilag BV, Eli Lilly, Shire, Lundbeck, Roche, and Servier. He is not an employee of any of these companies and not a stock shareholder of any of these companies. He has no other financial or material support, including expert testimony, patents, or royalties.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Brain regions that were (<bold>a</bold>) negatively correlated with PRS-ADHD at <italic>x</italic> = −34, <italic>y</italic> = −10, <italic>z</italic> = −2 during successful inhibition—go, (b-c) positively correlated with PRS-ADHD at <italic>x</italic> = −36, <italic>y</italic> = 16, <italic>z</italic> = −28 (<bold>b</bold>) and at <italic>x</italic> = 22, <italic>y</italic> = 16, <italic>z</italic> = 2 (<bold>c</bold>) during failed inhibition—go, and (d-e) positively correlated with PRS-ADHD at <italic>x</italic> = −58, <italic>y</italic> = 8, <italic>z</italic> = 12 (<bold>d</bold>) and at <italic>x</italic> = 8, <italic>y</italic> = 2, <italic>z</italic> = 6 (<bold>e</bold>) during failed—successful inhibition, shown in radiologic view with the right brain shown on the left. The color bar represents Z-scores (2.3–4.7)</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Path diagrams (including standardized regression coefficients and 95% confidence intervals) of the mediation analyses demonstrating that the associations between polygenic risk score for ADHD at <italic>p</italic>-value threshold of 1 (PRS-ADHD) and total ADHD (<bold>a</bold>, <bold>d</bold>), inattention (<bold>b</bold>, <bold>e</bold>), and hyperactivity-impulsivity symptom scores (<bold>c</bold>, <bold>f</bold>, <bold>g</bold>) are mediated by mean reaction time (MRT) (<bold>a</bold>–<bold>c</bold>), intra-individual coefficient of variation of reaction time (IRT) (<bold>d</bold>–<bold>f</bold>), and cluster-average activity in the left temporal pole and anterior parahippocampal gyrus during failed inhibition (<bold>g</bold>). Path “a” represents the effect of PRS-ADHD on the mediator. Path “b” represents the impact of the mediator on ADHD symptom scores controlling for the PRS-ADHD effect. Together, Path “a” and Path “b” represent the indirect (mediated) effect of PRS-ADHD on ADHD symptom scores through the mediator. Path “c” represents the direct effect of PRS-ADHD on ADHD symptom scores and is calculated controlling for the indirect, mediated effect. Path “c” represents the total (mediated and direct) effect of PRS-ADHD on ADHD symptom scores. The asterisks indicate significance using FDR-correction († p-uncorrected &lt; 0.05, * p-FDR &lt; 0.05, ** p-FDR &lt; 0.01, *** p-FDR &lt; 0.001). See also Supplementary Tables 4–5. β, standardized regression coefficients; CI, 95% confidence intervals</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Demographic characteristics and stop-signal task outcome measures</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"5\">Demographic characteristics</th></tr><tr><th align=\"left\"/><th align=\"left\"><italic>N</italic></th><th align=\"left\" colspan=\"3\"/></tr></thead><tbody><tr><td align=\"left\">Sex (female/male)</td><td align=\"left\">454</td><td align=\"left\" colspan=\"3\">197 (43.4%)/ 257 (56.6%)</td></tr><tr><td align=\"left\">Medication use (yes/no)</td><td align=\"left\">453</td><td align=\"left\" colspan=\"3\">77 (17%)/ 376 (83%)</td></tr><tr><td align=\"left\">Handedness (right/left)</td><td align=\"left\">451</td><td align=\"left\" colspan=\"3\">49 (10.9%)/ 402 (89.1%)</td></tr><tr><td align=\"left\"/><td align=\"left\">N</td><td align=\"left\">Mean</td><td align=\"left\">SD</td><td align=\"left\">Range</td></tr><tr><td align=\"left\"> Age</td><td align=\"left\">454</td><td align=\"left\">17.1</td><td align=\"left\">3.5</td><td align=\"left\">[7.7–29.2]</td></tr><tr><td align=\"left\"> Estimated IQ^a</td><td align=\"left\">451</td><td align=\"left\">100.1</td><td align=\"left\">16.56</td><td align=\"left\">[55–144]</td></tr><tr><td align=\"left\"> Total ADHD symptom score^b</td><td align=\"left\">423</td><td align=\"left\">11.98</td><td align=\"left\">11.78</td><td align=\"left\">[0–52]</td></tr><tr><td align=\"left\"> Inattention symptom score^b</td><td align=\"left\">438</td><td align=\"left\">7.73</td><td align=\"left\">7.21</td><td align=\"left\">[0–27]</td></tr><tr><td align=\"left\"> Hyperactivity-impulsivity symptom score^b</td><td align=\"left\">431</td><td align=\"left\">4.57</td><td align=\"left\">5.43</td><td align=\"left\">[0–27]</td></tr><tr><td align=\"left\" colspan=\"5\"><italic>Stop-signal task outcomes</italic></td></tr><tr><td align=\"left\"> MRT (ms)</td><td align=\"left\">454</td><td align=\"left\">497.9</td><td align=\"left\" colspan=\"2\">91.61</td></tr><tr><td align=\"left\"> IRT(ms)</td><td align=\"left\">454</td><td align=\"left\">0.19</td><td align=\"left\" colspan=\"2\">0.05</td></tr><tr><td align=\"left\"> SSRT (ms)</td><td align=\"left\">454</td><td align=\"left\">259.2</td><td align=\"left\" colspan=\"2\">78.58</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Associations between polygenic risk score for ADHD (PRS-ADHD) at a range of p-value thresholds and total, inattention, and hyperactivity-impulsivity symptom scores for all participants with genetic data available</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" rowspan=\"2\" colspan=\"2\">Independent<break/>variable</th><th align=\"left\" colspan=\"12\">Dependent variable</th></tr><tr><th align=\"left\" colspan=\"4\">Total symptom score (<italic>N</italic> = 845)</th><th align=\"left\" colspan=\"4\">Inattention symptoms (<italic>N</italic> = 866)</th><th align=\"left\" colspan=\"4\">Hyperactivity-impulsivity symptoms (<italic>N</italic> = 859)</th></tr><tr><th align=\"left\">PRS PT</th><th align=\"left\"># of SNPs</th><th align=\"left\">β (SE)</th><th align=\"left\">p-uncor</th><th align=\"left\">p-FDR</th><th align=\"left\">R²-PRS</th><th align=\"left\">β (SE)</th><th align=\"left\">p-uncor</th><th align=\"left\">p-FDR</th><th align=\"left\">R²-PRS</th><th align=\"left\">β (SE)</th><th align=\"left\">p-uncor</th><th align=\"left\">p-FDR</th><th align=\"left\">R²-PRS</th></tr></thead><tbody><tr><td align=\"left\">1</td><td align=\"left\">66,978</td><td align=\"left\">0.215 (0.034)</td><td align=\"left\">3.07 × 10^–10</td><td align=\"left\">9.21 × 10^–9</td><td align=\"left\">0.044</td><td align=\"left\">0.202 (0.033)</td><td align=\"left\">1.58 × 10^–9</td><td align=\"left\">1.32 × 10^–8</td><td align=\"left\">0.039</td><td align=\"left\">0.204 (0.034)</td><td align=\"left\">3.14 × 10^–9</td><td align=\"left\">1.65 × 10^–8</td><td align=\"left\">0.04</td></tr><tr><td align=\"left\">0.5</td><td align=\"left\">49,274</td><td align=\"left\">0.209 (0.034)</td><td align=\"left\">1.04 × 10^–9</td><td align=\"left\">1.32 × 10^–8</td><td align=\"left\">0.042</td><td align=\"left\">0.194 (0.033)</td><td align=\"left\">7.53 × 10^–9</td><td align=\"left\">2.51 × 10^–8</td><td align=\"left\">0.036</td><td align=\"left\">0.199 (0.034)</td><td align=\"left\">8.37 × 10^–9</td><td align=\"left\">2.51 × 10^–8</td><td align=\"left\">0.038</td></tr><tr><td align=\"left\">0.4</td><td align=\"left\">43,169</td><td align=\"left\">0.206 (0.034)</td><td align=\"left\">1.76 × 10^–9</td><td align=\"left\">1.32 × 10^–8</td><td align=\"left\">0.041</td><td align=\"left\">0.188 (0.033)</td><td align=\"left\">2.31 × 10^–8</td><td align=\"left\">5.33 × 10^–8</td><td align=\"left\">0.033</td><td align=\"left\">0.199 (0.034)</td><td align=\"left\">8.29 × 10^–9</td><td align=\"left\">2.51 × 10^–8</td><td align=\"left\">0.038</td></tr><tr><td align=\"left\">0.3</td><td align=\"left\">35,937</td><td align=\"left\">0.202 (0.034)</td><td align=\"left\">3.85 × 10^–9</td><td align=\"left\">1.65 × 10^–8</td><td align=\"left\">0.039</td><td align=\"left\">0.184 (0.033)</td><td align=\"left\">4.66 × 10^–8</td><td align=\"left\">9.99 × 10^–8</td><td align=\"left\">0.032</td><td align=\"left\">0.195 (0.034)</td><td align=\"left\">1.84 × 10^–8</td><td align=\"left\">4.60 × 10^–8</td><td align=\"left\">0.037</td></tr><tr><td align=\"left\">0.2</td><td align=\"left\">27,386</td><td align=\"left\">0.204 (0.034)</td><td align=\"left\">3.35 × 10^–9</td><td align=\"left\">1.65 × 10^–8</td><td align=\"left\">0.04</td><td align=\"left\">0.18 (0.034)</td><td align=\"left\">1.03 × 10^–7</td><td align=\"left\">1.82 × 10^–7</td><td align=\"left\">0.031</td><td align=\"left\">0.197 (0.034)</td><td align=\"left\">1.31 × 10^–8</td><td align=\"left\">3.57 × 10^–8</td><td align=\"left\">0.038</td></tr><tr><td align=\"left\">0.1</td><td align=\"left\">16,756</td><td align=\"left\">0.185 (0.034)</td><td align=\"left\">8.50 × 10^–8</td><td align=\"left\">1.59 × 10^–7</td><td align=\"left\">0.033</td><td align=\"left\">0.165 (0.034)</td><td align=\"left\">1.12 × 10^–6</td><td align=\"left\">1.68 × 10^–6</td><td align=\"left\">0.026</td><td align=\"left\">0.176 (0.034)</td><td align=\"left\">3.92 × 10^–7</td><td align=\"left\">6.19 × 10^–7</td><td align=\"left\">0.03</td></tr><tr><td align=\"left\">0.05</td><td align=\"left\">10,133</td><td align=\"left\">0.185 (0.034)</td><td align=\"left\">8.48 × 10^–8</td><td align=\"left\">1.59 × 10^–7</td><td align=\"left\">0.033</td><td align=\"left\">0.163 (0.034)</td><td align=\"left\">1.56 × 10^–6</td><td align=\"left\">2.23 × 10^–6</td><td align=\"left\">0.025</td><td align=\"left\">0.183 (0.034)</td><td align=\"left\">1.55 × 10^–7</td><td align=\"left\">2.58 × 10^–7</td><td align=\"left\">0.033</td></tr><tr><td align=\"left\">0.01</td><td align=\"left\">2,898</td><td align=\"left\">0.125 (0.035)</td><td align=\"left\">3.4 × 10^–4</td><td align=\"left\">4.45 × 10^–4</td><td align=\"left\">0.015</td><td align=\"left\">0.107 (0.034)</td><td align=\"left\">0.002</td><td align=\"left\">0.003</td><td align=\"left\">0.011</td><td align=\"left\">0.126 (0.035)</td><td align=\"left\">3.1 × 10^–4</td><td align=\"left\">4.16 × 10^–4</td><td align=\"left\">0.016</td></tr><tr><td align=\"left\">1 × 10^–4</td><td align=\"left\">79</td><td align=\"left\">-0.006 (0.035)</td><td align=\"left\">0.871</td><td align=\"left\">0.871</td><td align=\"left\">1 × 10^–4</td><td align=\"left\">0.013 (0.034)</td><td align=\"left\">0.71</td><td align=\"left\">0.735</td><td align=\"left\">2 × 10^–4</td><td align=\"left\">-0.015 (0.035)</td><td align=\"left\">0.658</td><td align=\"left\">0.705</td><td align=\"left\">2 × 10^–4</td></tr><tr><td align=\"left\">1 × 10^–6</td><td align=\"left\">1</td><td align=\"left\">0.049 (0.034)</td><td align=\"left\">0.157</td><td align=\"left\">0.188</td><td align=\"left\">0.002</td><td align=\"left\">0.037 (0.034)</td><td align=\"left\">0.272</td><td align=\"left\">0.302</td><td align=\"left\">0.001</td><td align=\"left\">0.042 (0.035)</td><td align=\"left\">0.22</td><td align=\"left\">0.254</td><td align=\"left\">0.002</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab3\"><label>Table 3</label><caption><p>Associations of polygenic risk score for ADHD at the p-value threshold of 1 (PRS-ADHD) with stop-signal task outcomes and task-related neural activity</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\" colspan=\"2\">Dependent variable (<italic>N</italic> = 454)</th><th align=\"left\">β (SE)</th><th align=\"left\">p-uncor</th><th align=\"left\">p-FDR</th><th align=\"left\">R²-PRS</th></tr></thead><tbody><tr><td align=\"left\" rowspan=\"3\">Stop-signal task outcomes</td><td align=\"left\">MRT</td><td align=\"left\">0.123 (0.047)</td><td align=\"left\">0.01</td><td align=\"left\">0.015</td><td align=\"left\">0.014</td></tr><tr><td align=\"left\">IRT</td><td align=\"left\">0.122 (0.046)</td><td align=\"left\">0.008</td><td align=\"left\">0.015</td><td align=\"left\">0.014</td></tr><tr><td align=\"left\">SSRT</td><td align=\"left\">0.053 (0.049)</td><td align=\"left\">0.285</td><td align=\"left\">0.285</td><td align=\"left\">0.003</td></tr><tr><td align=\"left\" colspan=\"6\">Task-related neural activity</td></tr><tr><td align=\"left\"> Successful inhibition—go</td><td align=\"left\">Left fronto-insular regions and putamen</td><td align=\"left\">−0.208 (0.047)</td><td align=\"left\">1.09 × 10^–5</td><td align=\"left\">1.09 × 10^–5</td><td align=\"left\">0.041</td></tr><tr><td align=\"left\" rowspan=\"2\"> Failed inhibition—go</td><td align=\"left\">Left temporal pole and anterior PHG</td><td align=\"left\">0.212 (0.047)</td><td align=\"left\">7 × 10^–6</td><td align=\"left\">1.17 × 10^–5</td><td align=\"left\">0.042</td></tr><tr><td align=\"left\">Right putamen</td><td align=\"left\">0.213 (0.048)</td><td align=\"left\">1.06 × 10^–5</td><td align=\"left\">1.33 × 10^–5</td><td align=\"left\">0.044</td></tr><tr><td align=\"left\" rowspan=\"2\"> Failed—successful inhibition</td><td align=\"left\">Left fronto-insular, putamen, anterior temporal regions, and PHG</td><td align=\"left\">0.273 (0.047)</td><td align=\"left\">1.44 × 10^–8</td><td align=\"left\">7.2 × 10^–8</td><td align=\"left\">0.071</td></tr><tr><td align=\"left\">Right basal ganglia and thalamus</td><td align=\"left\">0.242 (0.048)</td><td align=\"left\">7.23 × 10^–7</td><td align=\"left\">1.81 × 10^–6</td><td align=\"left\">0.056</td></tr></tbody></table></table-wrap>" ]

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[ "<supplementary-material content-type=\"local-data\" id=\"MOESM1\"></supplementary-material>" ]

[ "<table-wrap-foot><p><italic>N</italic>, number of participants with data available; attention-deficit/hyperactivity disorder (ADHD); <italic>MRT</italic> mean reaction time to go-stimuli, <italic>IRT</italic> intra-individual coefficient of variation of reaction time to go stimuli, <italic>SSRT</italic> stop-signal reaction time</p><p>^aBased on the block-design and vocabulary subtests of the Wechsler Intelligence Scale for Children or Wechsler Adult Intelligence Scale[##REF##11483475##64##]</p><p>^bScores on the Conners’ Parent Rating Scale—Revised: Long version[##UREF##13##32##]</p></table-wrap-foot>", "<table-wrap-foot><p>Associations for the participants with both genetic and fMRI data available (<italic>N</italic> = 454) can be found in Supplementary Table 2</p><p><italic>PRS PT</italic> p-value threshold of PRS-ADHD, <italic># of SNPS</italic> number of SNPs used to calculate PRS-ADHD at corresponding p-value threshold, <italic>β</italic> standardized regression coefficients, <italic>SE</italic> standard error, <italic>p-uncor</italic> uncorrected p-value, <italic>p-FDR</italic> FDR-corrected p-value, <italic>R</italic>^{<italic>2</italic>}<italic>-PRS</italic> the proportion of variance explained by PRS-ADHD</p></table-wrap-foot>", "<table-wrap-foot><p><italic>MRT</italic> mean reaction time to go-stimuli, <italic>IRT</italic> intra-individual coefficient of variation of reaction time to go-stimuli, <italic>SSRT</italic> stop-signal reaction time, <italic>β</italic> standardized regression coefficients; SE, standard error, <italic>p-uncor</italic> uncorrected p-value, <italic>p-FDR</italic> FDR-corrected p-value, <italic>R</italic>^{<italic>2</italic>}<italic>-PRS</italic> the proportion of variance explained by PRS-ADHD, <italic>PHG</italic> parahippocampal gyrus</p></table-wrap-foot>" ]

[ "<graphic xlink:href=\"406_2023_1632_Fig1_HTML\" id=\"MO1\"/>", "<graphic xlink:href=\"406_2023_1632_Fig2_HTML\" id=\"MO2\"/>" ]

[ "<media xlink:href=\"406_2023_1632_MOESM1_ESM.docx\"><caption><p>Supplementary file1 (DOCX 198 kb)</p></caption></media>" ]

{ "acronym": [], "definition": [] }

[ "<title>Background</title>", "<p id=\"Par3\">Adult attention-deficit/hyperactivity disorder (ADHD) is a common neurodevelopmental disorder with a worldwide prevalence of at least 2.8% [##REF##27866355##1##]. It is a childhood-onset disorder and characterized by the three-core symptoms attention-deficit, impulsivity, and hyperactivity [##REF##27189265##2##]. In about 60% of pediatric patients, the symptoms persist into adulthood [##REF##22901345##3##] and result in detrimental impacts on social, financial, and professional functioning [##REF##19372500##4##]. The economic impact of adult ADHD places a significant burden on society. Despite the increasing awareness of ADHD, many affected adults are still underdiagnosed and untreated [##REF##27183901##5##]. The overlap of ADHD symptoms with several other psychiatric disorders, including mood disorders, substance abuse, and anxiety, as well as the high incidence of comorbid psychiatric conditions is likely the reason for the high number of missed ADHD diagnoses in adults [##REF##27866355##1##, ##REF##16977548##6##]. The exact etiology of ADHD remains unclear. A multifactorial genesis with high genetic underpinnings [##REF##15950004##7##] and imbalances in dopaminergic and noradrenergic systems is assumed [##REF##19587853##8##].</p>", "<p id=\"Par4\">Treatment guidelines for adult ADHD patients suggest multimodal therapy consisting of ADHD-specific medication and psychotherapy. Psychostimulants are recommended as the first-line medication for adults [##REF##30453134##9##], but 30% of adult patients with ADHD do not respond to medication and its use may be limited by side effects and concerns of abuse [##REF##17415287##10##, ##REF##25295651##11##]. Non-medication treatments, have shown limited efficacy [##REF##28700715##12##] and do not specifically target the underlying dysfunctional cortical activity [##REF##18061324##13##]. Due to these limitations, there is an urgent need to evaluate and establish further treatment methods.</p>", "<p id=\"Par5\">In addition to ADHD core Symptoms, ADHD patients also exhibit executive dysfunction in domains such as response inhibition or working memory [##REF##15950006##14##], which are linked to the prefrontal cortex and its associated regions such as dorsolateral prefrontal cortex (DLPFC) [##REF##33997292##15##]. Meta-analysis of functional Magnetic Resonance Imaging (fMRI) studies in ADHD showed consistent fronto-striato-parietal dysfunctions during tasks of inhibition and attention including the inferior frontal cortex, supplementary motor area, anterior cingulate cortex for inhibition, DLPFC, parietal, and cerebellar areas for attention [##UREF##0##16##]. Non-invasive brain stimulation treatments, such as transcranial direct current stimulation (tDCS), may be a suitable alternative treatment option, as they allow the targeted stimulation of functional altered key brain regions in ADHD, such as the prefrontal cortex and the fronto-subcortical system [##UREF##0##16##].tDCS applies a weak continuous electric current to the underlying brain via scalp electrodes with the electrical current passing between a positively charged anode and a negatively charged cathode. The transcranial application of weak direct currents to the human primary motor cortex is capable of eliciting intra-cortical excitability changes. The direction of these modulations depends on stimulation polarity: Anodal stimulation increases excitability, while cathodal stimulation decreases it. The respective changes evolve during the stimulation but remain for up to 1 h after the end of stimulation, given sufficiently long stimulation duration [##REF##10990547##17##].</p>", "<p id=\"Par6\">Until today, a small number of tDCS single-center studies have been conducted in adults with ADHD. A parallel, randomized, double blind, sham-controlled trial examined the efficacy of tDCS on the modulation of inhibitory control in adults with ADHD. Thirty patients were randomly allocated to each group and performed a go/no-go task before and after a single session of either anodal stimulation (1 mA) over the left DLPFC or sham stimulation. Data analysis showed no significant differences between the two groups regarding behavioral performance in the go/no-go tasks [##REF##26267861##18##]. Another study applied double anodal stimulation of 1.8 mA tDCS for 20 min over the left and right DLPFC in 20 adult ADHD patients, which, compared to sham, improved only hyperactivity measures for a sustained attention task [##REF##29681876##19##]. A double-blind crossover study applied three sessions of anodal 2 mA tDCS over the left DLPFC during working memory training in 37 adult ADHD patients. Compared to sham, anodal tDCS reduced commission errors in a sustained attention task immediately after treatment; however, the effect was gone three days after last stimulation [##REF##29885858##20##].</p>", "<p id=\"Par7\">A randomized, sham-controlled, double blind, crossover study showed that anodal tDCS over the left DLPFC modulated cognitive (reaction time) and physiological (P300 amplitude) measurements in the Eriksen flanker task in a state-dependent manner, but no effects were found in the stop signal reaction time of the stop signal task [##REF##33549516##21##].</p>", "<p id=\"Par8\">In a recent double-blind, randomized, sham-controlled crossover pilot study eleven pediatric ADHD patients underwent five consecutive sessions of cathodal 1.5 mA tDCS applied over the left DLPFC. Qualitative electroencephalography and participants behavioral responses were recorded. Compared to sham, immediately after the tDCS stimulation, alpha power increased in the right frontal area and delta power in the left frontal area while omission errors decreased, with no differences at follow-ups [##REF##35367657##22##]. Finally, a meta-analysis of 14 tDCS studies, including 10 pediatric and 4 adult studies, reported limited evidence that 1 to 5 sessions, mostly of the DLPFC, improved clinical or cognitive measures of ADHD. The author’s summarize, a conclusive evidence from this meta-analysis is hampered by heterogeneity in stimulation protocols, sample age, and cognitive measurements. Furthermore, the authors call for larger, double-blind, randomized, controlled trials with homogeneous protocols testing both clinical and cognitive outcomes [##REF##33009906##23##].</p>", "<p id=\"Par9\">It is still unknown how long any improvement of ADHD symptoms lasts after applying tDCS. A few studies support the hypothesis of a lasting effect of tDCS with improved clinical symptoms beyond the end of stimulation. In children and adolescents, 20–30 min anodal stimulation over the left DLPFC for five days yielded superior results in the stimulation group, as compared to sham as assessed by neuropsychological [##REF##26879095##24##, ##REF##27853926##25##] and clinical measurements [##REF##26879095##24##, ##REF##27853926##25##]. The latter study describes lasting clinical effects, which were most prominent 7 days after the stimulation. Notably, there is evidence that tDCS application over multiple days increases the duration of its beneficial effects to several weeks [##REF##17166593##26##–##REF##21343407##29##], although these studies were not conducted in patients with ADHD. Examining persisting effects of tDCS on ADHD symptoms in adult patients, Cachoeira et al. [##REF##27863315##30##] found strong effects (Cohen’s <italic>d</italic> &gt; 1) in a pilot study (<italic>N</italic> = 17) concerning inattention, and moderate ones concerning hyperactivity/impulsivity two weeks post-intervention (p.i.). Four weeks p.i. the effect size in regard to inattention was moderate compared to sham stimulation, supporting the hypothesis of a lasting effect of tDCS with improved clinical symptoms beyond the end of stimulation. In their randomized controlled pilot study, 20 min anodal stimulation of the right DLPFC over five consecutive days was applied, with similar placement and time regimen in the sham group. In data obtained in our own working group we found further justification for active electrode placement on the right side [##REF##31732713##31##]. In a [11C] MRB-PET/MRI study with adult ADHD patients, we found lower noradrenaline transporter availability in right than in left prefrontal-thalamic regions, which may indicate that prefrontal hypo-activation is more pronounced on the right side, justifying anodal tDCS stimulation on the right DLPFC.</p>", "<p id=\"Par10\">Given some evidence of clinical and cognitive improvements with anodal tDCS over the right DLPFC, the main objective of this clinical trial is to systematically test the efficiency of anodal tDCS over the right DLPFC in reducing ADHD symptoms when used as an alternative or add-on therapy to stable ongoing treatment compared to sham stimulation. We hypothesize that the benefits will persist for at least two weeks after the end of the stimulation. Our stimulation protocol is based on the pilot study by Cachoiera et al. [##REF##27863315##30##], which showed promising results in a small sample.</p>" ]

[ "<title>Design and methods</title>", "<p id=\"Par11\">This prospective study is designed as a multi-center, randomized, double blind, sham-controlled clinical trial and aims to demonstrate the superiority of anodal tDCS over the right DLPFC compared to sham stimulation in adult ADHD. Altogether, 250 patients will be randomly assigned (1:1 ratio) to the two parallel treatment arms. Patients will receive either experimental or control intervention. The experimental intervention consists of five 21-min sessions of bifrontal tDCS with the anode over right DLPFC (F4) and the cathode over the left DLPFC (F3) for five consecutive days over the course of one week. The control intervention consists of sham stimulation with identical electrode placement and identical timely regimen as in experimental intervention. Both interventions will be applied as alternative or add-on treatment to stable ongoing standard therapy. Study assessment with observer and self-ratings will be conducted for screening and baseline, every day during the treatment period and during the follow-up period at day 7, 14, 28, 56, and 90 p.i.</p>", "<title>Study population</title>", "<p id=\"Par12\">The clinical trial will include in- and outpatients aged from 18 to 65 years with a primary diagnosis of adult ADHD according the DSM-5 criteria. Experienced study investigators will perform a clinical interview based on the Diagnostic and Statistical Manual of Mental Disorders 5th Edition (DSM-5 [##UREF##1##32##]). Table ##TAB##0##1## contains all inclusion and exclusion criteria for the present study.</p>", "<title>Study centers and recruitment</title>", "<p id=\"Par13\">Besides the Department of Psychiatry and Psychotherapy of the University of Leipzig (coordinating center), six additional psychiatric departments in Germany will participate in the trial. These centers must have the appropriate technical equipment and experienced staff regarding diagnosis and treatment of adult ADHD patients and in applying of tDCS in psychiatric conditions. During the pre-screening period, a trained study investigator will give comprehensive verbal and written information about trial-related objectives, procedures, and possible risks to each patient. All patients will have the opportunity to ask questions and will have enough time to consider whether they want to participate in the study. Before any study-specific measures are administered, an informed consent form must be signed. The consent to participate in the trial can be withdrawn at any given time during the study and without the necessity to provide a reason for withdrawal.</p>", "<p id=\"Par14\">Continuous site monitoring will ensure the early identification of recruitment or performance problems. In case of relevant delays, site-specific measures will be taken, e.g., additional dedicated staff, alternative organizational structures, intensified social media activity, and further involvement of local patient groups. However, in case of persistent and substantial recruitment delays, the study center will be closed and a suitable new center will be identified and initiated.</p>", "<title>Patient involvement</title>", "<p id=\"Par15\">To empower affected individuals and give patients a voice concerning their key concerns and symptoms to be included to evaluate subjective improvement in addition to clinical improvement, we closely cooperate with patients’ organizations (e.g., “Selbsthilfegruppe ADHS im Erwachsenenalter Leipzig”). In addition, we cooperated with our current outpatients affected by adult ADHD and their relatives during various stages of the preparation of the trial. As part of the trial-planning phase, we organized a meeting at the ADHD outpatient center of Leipzig University with members of local self-help groups and current outpatients to ensure that the overall goal and outcome of research is relevant to them. Further, we informed them about the planned study design and asked for their opinion about the selected methods, the frequency of visits and the acceptance of the tDCS devices. Additionally, we asked the participants about their opinions regarding the relevance of selected outcome variables for patients. Based on their feedback, we chose outcomes in accordance with patients’ experiences and revised the list of questionnaires to be included. Patient involvement throughout the whole duration of trial is planned. We will organize further meetings, in Leipzig, and if possible at the other centers, to ensure that the recruitment process is practical and feasible.</p>", "<title>Study timeline</title>", "<p id=\"Par16\">The trial comprises a pre-treatment phase, a treatment phase of 1-week duration, and a follow-up phase of 3 months. The flow chart (Fig. ##FIG##0##1##) gives an overview of the study timeline. In the context of a pre-screening, the most important inclusion and exclusion criteria are informally checked. If pre-screening examination confirms a suspected adult ADHD diagnosis, an appointment for screening will be offered to the patient concerned. Patients will receive the study information and consent in advance, allowing sufficient time for the consent form to be studied before it is being signed after a final discussion with the investigator. After informed consent, the screening takes place within 10 days prior to randomization and start of the intervention. It includes verification of the ADHD diagnosis as part of the review of the inclusion/exclusion criteria. Furthermore, severe psychiatric, somatic and neurological concomitant diseases will be excluded. Patients who meet the inclusion and exclusion criteria will complete all pre-treatment assessments comprising the baseline visit and will then be randomized to active or sham tDCS following the randomization procedure. During the treatment phase, each patient will receive one active/sham tDCS session per day on five consecutive days over the course of one week. At each tDCS session, possible adverse events will be checked. Major protocol violations such as missing one (or more) intended stimulations or an overall duration of treatment longer than 8 days will result in exclusion from per-protocol analysis.</p>", "<p id=\"Par17\">During the follow-up phase, five visits are scheduled at day 7, 14, 28, 56, and 90 after the end of treatment. Patients’ participation in the trial will end with the last follow-up visit.</p>" ]

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[ "<title>Discussion</title>", "<p id=\"Par55\">Here, we report on the design and rationale of a clinical trial conceived to investigate the efficacy of anodal tDCS over the right DLPFC in reducing ADHD symptoms as an alternative or add-on therapy to stable ongoing treatment compared to sham stimulation. There is a lot of evidence that tDCS can lead to an improvement in ADHD symptoms; however, it is still unclear how it can be used in routine clinical practice. To our knowledge, this study represents the first attempt to investigate the effect of tDCS on ADHD symptoms in adults systematically in a multi-center study design.</p>", "<p id=\"Par56\">Over last years, several small tDCS studies with heterogeneous study designs have been conducted in patients with ADHD. The majority of these studies have been conducted in pediatric ADHD patients, presumably due to the high tolerability and relatively low side effect profile of tDCS [##REF##34440925##50##]. Based on the dysfunction findings in fMRI studies conducted in ADHD over the last two decades [##UREF##0##16##], most of them used tDCS in either one or five sessions targeting mostly DLPFC. Meta-analyses of tDCS effects, mostly over DLPFC, show small effect sizes for improved cognition [##REF##33009906##23##, ##REF##30978259##51##]. However, only a small number of studies have measured clinical improvement in ADHD patients using tDCS, with inconsistent findings [##REF##34440925##50##]. The authors of a meta-analysis of 10 pediatric and 4 adult tDCS studies summarize that a conclusive result is hampered by heterogeneity in stimulation protocols, sample age, and cognitive measures. Therefore, the authors call for larger, double-blind, randomized, controlled trials with homogeneous protocols testing both clinical and cognitive outcomes in ADHD [##REF##33009906##23##]. Almost all authors of reviews and meta-analyses on the use of tDCS in ADHD also conclude that the efficacy of tDCS, and especially its clinical benefit on ADHD symptoms, cannot yet be conclusively assessed and further studies with optimized designs are warranted (see as example [##REF##32418073##52##]). With our study, we aim to contribute to gathering more robust data on this.</p>", "<p id=\"Par57\">The intention of this clinical trial is to include both medicated and unmedicated ADHD patients, to investigate the effects of tDCS as an add-on therapy to the treatment adhering to standard ADHD guidelines as well. Thus, the design is primarily intended to reflect clinical reality, because in our opinion the investigation of tDCS as a stand-alone therapy would only be applicable to a small group of clinical patients. Another important point in the preparation of our study was the choice of primary and secondary endpoints. In order to choose measures that are also relevant from a patient perspective, we involved patients and their relatives in this decision. Previous studies mostly investigated either the effects of tDCS on neuropsychological symptoms or clinical symptoms [##REF##32418073##52##], however we decided to survey both aspects, including quality of life parameters in our study, which was also supported by the patients.</p>", "<p id=\"Par58\">Concerning electrode placement, stimulation intensity, and frequency, the methodological decision was based on the above mentioned evidence. The lateralization of the excitatory electrode over right DLPFC was supported by neuroimaging study of our own working group, which indicated that prefrontal hypo-activation is more pronounced on the right side [##REF##31732713##31##]. The selection of the stimulation parameters was based on the previous pilot study by Cachoiera et al. [##REF##27863315##30##], which showed significant lower self-reported ADHD symptoms after active tDCS in comparison with sham stimulation. In order to measure short-term and also possible mid-term effects, we significantly extended the follow-up period with visits up to day 90 after the intervention. Potentially observed long-lasting effects would be instrumental in clinical implementation of tDCS in ADHD.</p>", "<p id=\"Par59\">In summary, positive results of this parallel, randomized, double-blinded, sham-controlled, multi-center trial would expand the treatment options for adult ADHD patients with an alternative or add-on therapy to psychostimulants with a low risk for side effects. Detailed reporting of study protocols is intended to increase transparency in clinical research.</p>", "<title>Trial status</title>", "<p id=\"Par60\">Enrollment for the study began in September 2022. At the time of submission, we have enrolled 28 participants at two study sites (Leipzig, Wurzburg).</p>" ]

[]

[ "<p id=\"Par1\">Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation treatment used as an alternative or complementary treatment for various neuropsychiatric disorders, and could be an alternative or add-on therapy to psychostimulants in attention-deficit hyperactivity disorder (ADHD). Previous studies provided some evidence for improvements in cognition and clinical symptoms in pediatric and adult ADHD patients. However, data from multi-center randomized controlled trials (RCTs) for this condition are lacking. Thus, our aim is to evaluate short- and mid-term effects of tDCS in this multi-center, randomized, double blind, and sham-controlled, parallel group clinical trial with a 1:1 randomization ratio. Primary endpoint is the total score of DSM-IV scale of the internationally established Conners’ Adult ADHD Rating Scales (German self-report screening version, CAARS-S-SR), at day 14 post-intervention (p.i.) to detect short-term lasting effects analyzed via analyses of covariance (ANCOVAs). In case of significant between-groups differences at day 14 p.i., hierarchically ordered hypotheses on mid-term lasting effects will be investigated by linear mixed models with visit (5 time points), treatment, treatment by visit interaction, and covariates as fixed categorical effects plus a patient-specific visit random effect, using an unstructured covariance structure to model the residual within-patient errors. Positive results of this clinical trial will expand the treatment options for adult ADHD patients with tDCS and provide an alternative or add-on therapy to psychostimulants with a low risk for side effects.</p>", "<p id=\"Par2\"><italic>Trial Registration</italic> The trial was registered on July 29, 2022 in the German Clinical Trials Register (DRKS00028148).</p>", "<title>Keywords</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>" ]

[ "<title>Assessment</title>", "<title>Clinical measures</title>", "<p id=\"Par18\">The assessments and the procedures performed during the pre-screening, screening, baseline, treatment period and follow-up visits are summarized in Table ##TAB##1##2##.</p>", "<p id=\"Par19\">In the context of the pre-screening, the German Adult ADHD self-report scale (ASRS-vI.I [##REF##15841682##33##]) symptom checklist, for evaluation of current symptoms, and the short form of German Wender Utah Rating Scale (WURS-K [##REF##12215873##34##]), for retrospective assessment of symptoms in a participant’s childhood, is filled out online by those interested in participating.</p>", "<p id=\"Par20\">The screening visit includes the registration of the sociodemographic characteristics, the collection of the medical and psychiatric history, a physical–neurological examination, the documentation of treatment status and the tDCS safety screening. In addition, a detailed psychopathological examination is carried out with the clinician version of the Structured Clinical Interview for DSM-5® Disorders-Clinical Version (SCID-5-CV [##UREF##2##35##]), the Screening Personality Questionnaire (SCID-5-SPQ [##UREF##3##36##]) and the Section for Bipolar Personality Disorder (BPD) for Personality Disorders (SCID-5-PD [##UREF##3##36##]). In addition, the participants fill out the following questionnaires: Conners' Adult ADHD Rating Scales self-report screening form (CAARS-S-SR [##UREF##4##37##]), WURS-K, Beck Depression Inventory-II (BDI-II [##UREF##5##38##]), Alcohol Use Disorders Identification Test (AUDIT [##UREF##6##39##]), Drug Use Disorders Identification Test (DUDIT [##UREF##7##40##]), Wortschatztest (vocabulary-based IQ screening, WST [##UREF##8##41##]), and a functional level rating scale.</p>", "<p id=\"Par21\">At the baseline visit and before the first active/sham tDCS, the following procedures and questionnaires will be performed: urine drug test, and if applicable, a urine pregnancy test, documentation of the concomitant medication, Adult ADHD Quality of Life Questionnaire (AAQoL [##UREF##9##42##]), CAARS-S-SR, BDI-II, Clinical Global Impression of Severity (CGI-S [##UREF##10##43##]), Continuous Performance Test (CPT [##UREF##11##44##]), Symptom Checklist‐90‐Standard (SCL-90-S [##UREF##12##45##]), and the Pittsburgh Sleep Quality Index (PSQI [##REF##2748771##46##]).</p>", "<p id=\"Par22\">At each active/sham tDCS session, every participant will be asked about adverse events and the Comfort Rating Questionnaire (CRQ [##UREF##13##47##]) will be performed. Additionally, all participants will be asked whether they believe they received active or sham stimulation after the first and last treatment session at visits 1 and 5 (“blinding check”).</p>", "<p id=\"Par23\">The following procedures and questionnaires will be performed immediately after the last active/sham tDCS: documentation of any changes of the concomitant treatment, AAQoL, BDI-II, CAARS-S-SR, CPT, CGI-S, Clinical Global Impression of Improvement (CGI-I [##UREF##10##43##]), SCL-90-S, and PSQI.</p>", "<p id=\"Par24\">Finally, during the follow-up period, the following assessments will be repeated on day 7 ± 2, 14 ± 2, 28 ± 4, 56 ± 4, and 90 ± 7 after end of intervention: documentation of any changes of the concomitant medication, AAQoL, BDI-II, CAARS-S-SR, CGI-S, CGI-I, SCL-90-S, and PSQI. CPT will be repeated at 14 and 90 days after the end of intervention.</p>", "<title>Randomization and blinding</title>", "<p id=\"Par25\">All study participants will be randomized by the trial site using a secure online procedure provided by the ZKS Leipzig, which results in an automatic e-mail confirmation on successful randomization to the site itself and the ZKS Leipzig. Stratification by ADHD subtypes (combined, inattentive or hyperactive/ impulsive) and regular ADHD-specific medication/s at baseline (yes/no) was applied.</p>", "<p id=\"Par26\">Randomization will take place as follows: The neuroConn GmbH generated the intervention code lists for active/sham tDCS procedure. The technical data required for stimulation (active/sham procedure) are uploaded in a cloud (Microsoft Azure Cloud) by neuroConn GmbH. The ZKS Leipzig receives intervention code lists for active/sham tDCS procedure from the neuroConn GmbH. The ZKS Leipzig transferred these intervention code lists into the randomization tool. During randomization, the result of the randomization is assigned to the patient-ID in a blinded manner. The trial site will download the technical data required for stimulation from the cloud using the intervention code. After end of intervention, the associated technical data of the stimulation performed will be uploaded to the cloud using the intervention code. The neuroCare group AG is able to monitor the uploaded data of the stimulations, so that problems or possible technical faults can be detected. Only technical data are transmitted via cloud, patient data are gathered outside the cloud. Thus, all sites remain blinded for the entire duration of the trial.</p>", "<title>Intervention</title>", "<title>Stimulation</title>", "<p id=\"Par27\">Intervention will be conducted as five 21-min stimulation sessions on five consecutive days over the course of one week (5 sessions in total).</p>", "<p id=\"Par28\">The 21-min stimulation will be administered with a bipolar DC-STIMULATOR MOBILE (neuroConn GmbH), using two 5 × 7 cm electrodes (inserted in saline-soaked sponges) with the anode over the right DLPFC (F4), cathode over the left DLPFC (F3); electrodes will be placed based on the international 10–20 system and fixed with a headband.</p>", "<p id=\"Par29\">A constant current of 2 mA (current density = 0.0571 mA/cm²) will be applied in verum tDCS. Current will be ramped up/down for 30 s at the beginning/end of the session to avoid fast transients enabling subjects to distinguish between real and sham stimulations [##REF##24920029##48##]. Output current, output voltage, and impedance are monitored continuously. If threshold values are exceeded, the DC-STIMULATOR MOBILE is switched off for safety reasons. The current stimulation is stopped in Safe-Stop mode. The Save-Stop mode prevents an uncomfortable and sometimes even painful “current jump” by slowing down the present current to 0 mA when stimulation is manual or automatic stopped.</p>", "<title>Sham stimulation</title>", "<p id=\"Par30\">In contrast to the active tDCS condition, current for the sham intervention will be ramped up to 2 mA for 30 s followed by a 30 s fade out at the beginning and end of each session to mimic the experience of mild itching and tingling that is commonly reported during active stimulation [##REF##27863315##30##], but no effective stimulation will occur for the remaining duration of the intervention. The induced sensory impression of being stimulated serves to improve the blinding.</p>", "<title>Technical devices</title>", "<p id=\"Par31\">For active and sham tDCS, a neuroConn DC-STIMULATOR MOBILE with study mode is used (neuroConn GmbH, Ilmenau, Germany). This device is a microprocessor-controlled, battery-driven constant current source, complying with the Medical Device Directive of the European Union (CE-certified). The electrodes are separately inserted in 35 cm² saline-soaked sponges before placed over the scalp. An elastic strap made of non-conducting material will be used to fix the electrodes in place. Application time, current range, and frequencies are programmable, settings can be saved. Active or sham stimulation mode is chosen by entering of different number codes.</p>", "<title>Blinding</title>", "<p id=\"Par32\">The control arm receives sham stimulations that will be applied in a way that is indistinguishable from active stimulation, i.e., in the same time-schedule of intervention and at identical localizations.</p>", "<p id=\"Par33\">For all data transfers between the trial site and the cloud, the EDSM—Energy and Data Storage Module is used as an integral component of the neuroConn DC-STIMULATOR MOBILE. The data transmitted via cloud, e.g., the technical data required for stimulation, cannot be changed by trial site. Thus, the blinding is guaranteed.</p>", "<title>Concomitant treatment</title>", "<p id=\"Par34\">All medications that are approved according the guidelines for the treatment of adult ADHD in Germany are permitted as additional treatment during study participation. Other psychotropic medication is not allowed (i.e., benzodiazepines, z-hypnotics, antidepressants, neuroleptics). If present, the pharmacological therapy should be stable within the last 3 months before randomization and should be kept constant until assessment of the primary endpoint. Critical changes within the treatment period lead to exclusion from per-protocol analysis. Changes in medication and non-pharmacological treatments are continuously registered.</p>", "<title>Study endpoints</title>", "<title>Primary outcome measure</title>", "<p id=\"Par35\">Primary objective is to test the hypothesis whether or not tDCS is effective in reducing ADHD symptoms with a benefit for at least 2 weeks after the end of stimulation and superior to sham stimulation determined by DSM-IV ADHD symptoms total score (DSM-ADHS) of the CAARS-S-SR. Potential lasting effects of active and sham stimulation will be monitored for 90 days p.i.</p>", "<title>Secondary outcome measures</title>", "<p id=\"Par36\">As secondary endpoints, the following scores and safety assessments will be compared between active and sham stimulation:<list list-type=\"bullet\"><list-item><p id=\"Par37\">CAARS-S-SR DSM-IV scales: inattentive symptoms (DSM-IN) and hyperactive-impulsive symptoms (DSM-HY/I) on visit 1, 5, and all follow-up visits (6–10)</p></list-item><list-item><p id=\"Par38\">Assessment of Reaction time, variability, omission, and action errors by CPT on visit 1, 5, 7, and 10</p></list-item><list-item><p id=\"Par39\">ADHD-specific quality of life assessed by AAQoL on visit 1, 5, and all follow-up visits</p></list-item><list-item><p id=\"Par40\">Symptomatic distress assessed by SCL-90-S on visit 1, 5, and all follow-up visits</p></list-item><list-item><p id=\"Par41\">Sleep quality and disturbance assessed by PSQI on visit 1, 5, and all follow-up visits</p></list-item><list-item><p id=\"Par42\">BDI-II before first and after last tDCS application and on all follow-up visits CRQ after each tDCS application</p></list-item><list-item><p id=\"Par43\">Incidences of adverse clinically relevant findings</p></list-item></list></p>", "<title>Sample size calculation</title>", "<p id=\"Par44\">The estimation of the requested sample size in Stim-ADHD was based on various data from our own former, in parts unpublished, research activities and studies. According to our pre-/post-data, moderate to high correlations between baseline and post-treatment data of <italic>r</italic> ≈ 0.39… &gt; 0.7 were observed in previous populations, with lower values in pharmacotherapy, and <italic>r</italic> = 0.57 in the aggregated dataset. Because of the rather small samples and since no valid assumption can be made on the impact of the further stratification criteria on pre-/post-correlation, we conservatively chose <italic>r</italic> ≈ 0.5 for calculation of sample size.</p>", "<p id=\"Par45\">PASS sample size software (<ext-link ext-link-type=\"uri\" xlink:href=\"http://www.ncss.com/software/pass/pass-documentation\">http://www.ncss.com/software/pass/pass-documentation</ext-link>; version 14, 2016) was used, based on an ANCOVA design with baseline CAARS DSM-IV and the stratification criteria as covariates, means as reported and <italic>R</italic>² = 0.25.</p>", "<p id=\"Par46\">With a significance level of <italic>α</italic> = 5%, a randomization ratio 1:1, and 208 patients in total, a power of 81% will be reached to detect between-group differences of 3.5 points (assuming a small sham effect and/or regression to the mean in our control group as well as to be conservative in our assumptions).</p>", "<p id=\"Par47\">The effect size of this design is determined by <italic>f</italic> = SD_{group means}/SD SD_{CAARS DSM-IV ADHD total post} = 0.172. According to Cohen [##UREF##14##49##], <italic>f</italic> &lt; 0.1 is regarded as small, <italic>f </italic>≈ 0.25 as moderate. With less conservative (but reasoned) assumptions on higher <italic>R</italic>² (see observed pre–post-correlation) and lower SD_post (due to a rather homogeneous population and standardized intervention), and with possibly lower dropouts (because of the non-pharmacological intervention as seen in our patients), the power would increase and possibly smaller effect sizes may be detectable.</p>", "<title>Statistical analysis</title>", "<p id=\"Par48\">The full analysis set [FAS, based on the intention-to-treat (ITT) strategy] contains all randomized patients with informed consent and (at least) a single study intervention performed. The per-protocol (PPS) comprises all patients belonging to the FAS without major protocol violations. To identify between-groups differences for the primary endpoint, an ANCOVA with treatment (tDCS vs. sham stimulation) as main factor and CAARS DSM-IV ADHD total at randomization, ADHD sub-type and pre-medication (stratification criteria) as covariates within the FAS will be performed.</p>", "<p id=\"Par49\">If a significant between-groups difference is identified in the primary analysis, a linear mixed model (LMM) for repeated measurements will be applied to analyze the course of CAARS DSM-IV ADHD total, including 5 assessments per patient: at baseline, at days 14, 28, 56, and 90 post-intervention. For sensitivity analysis, multiple missing value (MV) imputations may be performed to support the results of the repeated measurements LMM and investigate the influence of MVs. No α adjustment for multiple testing is required. (Quasi-)metric secondary and safety endpoints will be analyzed analogously to the primary endpoint.</p>", "<title>Documentation, monitoring, and data management</title>", "<p id=\"Par50\">All clinical data entered by the site staff into eCRFs will be recorded in a pseudonymized form exclusively using the patient’s identification code.</p>", "<p id=\"Par51\">The Clinical Trial Centre Leipzig (ZKS Leipzig) will be responsible for trial monitoring. Pre-study, initiation, interim, and close-out visits will be performed in all centers. During the visits, the monitor will: (a) check informed consent forms of all patients enrolled, (b) perform targeted source data verification for patients with possible deviations, (c) perform source data verification of the key data in a random sample of at least 40% of the site’s patients (d) discuss open queries raised by data management or safety personnel check and update the investigator site file.</p>", "<p id=\"Par52\">For creation of the trial database, the EDC tool secuTrial®, developed and distributed by interActive Systems GmbH (iAS), will be used. The information entered into the eCRF by an authorized member of the trial team will be systematically checked for completeness, consistency, and plausibility. The site staff is responsible for data correction and can resolve queries directly in the eCRF-page. During the whole course of the trial, daily backups of the data are made. Unauthorized access to patient data is prevented by the access concept of the trial database, which is based on a strict hierarchy and role concept. Any change of data is recorded automatically via audit trail within the database. At the end of the trial, once the database has been declared complete and accurate, the database will be locked.</p>", "<title>Safety aspects and data safety monitoring board</title>", "<p id=\"Par53\">The exclusion criteria of this trial include all contraindications for the application of tDCS (e.g., metal plates or electronic implants in the brain or skull, skull defects, history of epileptic seizures, cardiac pacemaker). In addition, major depressive disorder (MDD) severity and suicide risk will be measured during treatment and follow-up visits with the BDI-II due to the theoretical risk of worsening or new development of depressive symptoms. This risk arises as the electrode placement in our study is opposite to the usual placement in depression treatment.</p>", "<p id=\"Par54\">Information on adverse events (AEs) and serious adverse events (SAEs) will be collected during treatment period and up to the first follow-up visit after treatment period. (S)AE will be followed up until complete recovery and/or patient’s status is stable. A Data Monitoring Committee (DMC), consisting of three independent experts without conflicts of interest, will meet periodically to perform a review of the accumulated study data regarding the safety of the trial intervention as well as the integrity and validity of the data.</p>" ]

[ "<title>Acknowledgements</title>", "<p>We thank Ms. Tina Stibbe for her English editing. We would also like to thank the Clinical Trial Centre Leipzig, i.e., Brigitte Höfler and Franziska Gottschald-Busch for material preparation, as well as Monika Rohwedder for the preparation of the initiation of the study centers. This study is funded by the German Research Foundation (DFG): Reference STR 1514/3-1.</p>", "<title>Author contributions</title>", "<p>Conceptualization: MS, CU, NM; Methodology: MS, CU, NM, AF; Formal analysis and investigation: AF, Funding acquisition: MS, CU, NM, AF; Project administration: MS, HB; Writing—original draft preparation: MS, NM, AF, CU; Writing—review and editing: TE, OG, TF, KH, GJ, SK-S, AM, AP, CP, AR, GCZ.</p>", "<title>Funding</title>", "<p>Open Access funding enabled and organized by Projekt DEAL.</p>", "<title>Declarations</title>", "<title>Conflict of interest</title>", "<p id=\"Par61\">AR has served on advisory boards and has received speaker’s honoraria from Medice and Shire/Takeda. SKS has received author’s and speaker’s honoraria from Takeda and Medice Arzneimittel Pütter GmbH&amp;Co.KG in the past 3 years. MS has received speaker’s fees from MEDICE Arzneimittel Pütter GmbH &amp; Co. KG and Takeda and was an advisory board member for Takeda in the past 3 years. AP has received research funding from the Federal Ministry of Research and Education, the EU (Horizon2020, ITEA), the NIHR, the German Research Foundation, the State North Rhine Westphalia and Medice and has been a consultant for Takeda, Medice, Boehringer, Janssen-Cilag and was a supervisor for Behavioral Therapy and DBT supervisor, articles/books on ADHD published by Elsevier, Hogrefe, Schattauer, Thieme, Oxford Press, Kohlhammer, Springer and Medizinisch Wissenschaftliche Verlagsgesellschaft. The other authors do not report any possible conflicts of interest.</p>", "<title>Ethical standards</title>", "<p id=\"Par62\">This trial will be conducted in accordance with the International Standard ISO 14155: 2021. All persons participating in the conduct of the study commit themselves to adhere to the Declaration of Helsinki of the World Medical Association (WMA), as well as all pertinent national laws and the ISO 14155: 2021 Good Clinical Practice for Medical Devices. The trial follows the medical device regulation (MDR) article 82 and MPDG § 47 (1–2). Thus, approval has to be obtained from the responsible ethics committee and a notification has to be filed to the competent authority, i.e., Bundesinstitut für Arzneimittel und Medizinprodukte (BfArM). The Ethics Committee of the Faculty of Medicine of the University of Leipzig (DE-22-00014008) and the responsible Ethics Committees of the participating centers have approved the protocol, patient information, and consent form of this clinical trial. All persons gave their written informed consent prior to their inclusion in the study.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Study timeline</p></caption></fig>" ]

[ "<table-wrap id=\"Tab1\"><label>Table 1</label><caption><p>Inclusion and exclusion criteria of the trial</p></caption><table frame=\"hsides\" rules=\"groups\"><tbody><tr><td align=\"left\">Inclusion criteria</td><td align=\"left\">Primary diagnosis of ADHD according to DSM-5 diagnostic criteria</td></tr><tr><td align=\"left\"/><td align=\"left\">Age between 18 and 65 years</td></tr><tr><td align=\"left\"/><td align=\"left\">German speaking participants with ability to understanding informed consent</td></tr><tr><td align=\"left\"/><td align=\"left\">Written informed consent</td></tr><tr><td align=\"left\"/><td align=\"left\">ADHD-specific medication must be stable for at least 3 month before randomization</td></tr><tr><td align=\"left\">Exclusion criteria</td><td align=\"left\">Acute suicidality (based on personal assessment of the investigator and/or SCID-5-CV, item 9 marked as above threshold and/or BDI-II, item 9 &gt; 2</td></tr><tr><td align=\"left\"/><td align=\"left\">Acute severe depression episode (defined as ≥ 7 symptoms of MDD with a minimum of 3 main criteria</td></tr><tr><td align=\"left\"/><td align=\"left\">Diagnosis of the following psychiatric disorders as primary clinical presentation:</td></tr><tr><td align=\"left\"/><td align=\"left\"> a. Persistent depressive disorder</td></tr><tr><td align=\"left\"/><td align=\"left\">b. Psychotic symptoms</td></tr><tr><td align=\"left\"/><td align=\"left\"> c. Bipolar disorder</td></tr><tr><td align=\"left\"/><td align=\"left\"> d. Schizoaffective disorder</td></tr><tr><td align=\"left\"/><td align=\"left\"> e. Schizophrenia</td></tr><tr><td align=\"left\"/><td align=\"left\"> f. Psychosis</td></tr><tr><td align=\"left\"/><td align=\"left\"> g. Borderline personality disorder</td></tr><tr><td align=\"left\"/><td align=\"left\">Diagnosis of current alcohol or substance use disorder (except for tobacco) as primary clinical presentation and/or a positive urine drug screening</td></tr><tr><td align=\"left\"/><td align=\"left\">Change in ADHD-specific medication/s planned before assessment of the primary endpoint</td></tr><tr><td align=\"left\"/><td align=\"left\">Current use/washing out of psychotropic medication (e.g., antidepressants, antipsychotics, anticonvulsants, lithium)</td></tr><tr><td align=\"left\"/><td align=\"left\">Severe somatic comorbidities</td></tr><tr><td align=\"left\"/><td align=\"left\">Severe neurological comorbidities (e.g., history of brain surgery, significant brain malformation or neoplasm, head injury, stroke, epilepsy, neurodegenerative disorder)</td></tr><tr><td align=\"left\"/><td align=\"left\">Contraindications for tDCS intervention (e.g., mental plates or electronic implants in the brain or skull, skull defects and skin lesions on the scalp, history of epileptic seizure, cardiac pacemaker or defibrillator)</td></tr><tr><td align=\"left\"/><td align=\"left\">Pregnant or nursing females</td></tr></tbody></table></table-wrap>", "<table-wrap id=\"Tab2\"><label>Table 2</label><caption><p>Schedule of assessments and procedures</p></caption><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\">Study period</th><th align=\"left\" colspan=\"2\">Pre-treatment</th><th align=\"left\" colspan=\"5\">Treatment</th><th align=\"left\" colspan=\"5\">Follow-up</th></tr><tr><th align=\"left\">Visit</th><th align=\"left\">PS</th><th align=\"left\">SV</th><th align=\"left\">1</th><th align=\"left\">2</th><th align=\"left\">3</th><th align=\"left\">4</th><th align=\"left\">5</th><th align=\"left\">6</th><th align=\"left\">7</th><th align=\"left\">8</th><th align=\"left\">9</th><th align=\"left\">10</th></tr><tr><th align=\"left\">Week</th><th align=\"left\" colspan=\"2\">−1</th><th align=\"left\" colspan=\"5\">1</th><th align=\"left\">2</th><th align=\"left\">3</th><th align=\"left\">5</th><th align=\"left\">9</th><th align=\"left\">14</th></tr><tr><th align=\"left\">Day^a</th><th align=\"left\"/><th align=\"left\">−10</th><th align=\"left\">1</th><th align=\"left\">2</th><th align=\"left\">3</th><th align=\"left\">4</th><th align=\"left\">5</th><th align=\"left\">12±2</th><th align=\"left\">19±2</th><th align=\"left\">33±4</th><th align=\"left\">61±4</th><th align=\"left\">95±7</th></tr><tr><th align=\"left\"><italic>Assessments</italic></th><th align=\"left\"/><th align=\"left\"/><th align=\"left\" colspan=\"10\"><italic>Screening and consent</italic></th></tr></thead><tbody><tr><td align=\"left\">Informed consent for pre-screening</td><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">ASRS-v1.1</td><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">WURS-K</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Informed consent for clinical trial</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">In-/exclusion criteria</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">SCID-5-CV</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">SCID-5-SPQ^b</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">SCID-5-PD^c</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">AUDIT</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">DUDIT</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">WST</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Functional level rating scale</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Physical and neurological exam</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Medical and psychiatric history</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Treatment status</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Concomitant medication</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Urine drug test</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Urine pregnancy test</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^f</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">Randomization</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\"/><th align=\"left\" colspan=\"10\"><italic>Intervention</italic></th></tr></thead><tbody><tr><td align=\"left\">Active/sham tDCS</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\"/><th align=\"left\" colspan=\"10\"><italic>Efficacy</italic></th></tr></thead><tbody><tr><td align=\"left\">CAARS-S-SR</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td></tr><tr><td align=\"left\">CPT</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\"/><th align=\"left\" colspan=\"10\"><italic>Safety</italic></th></tr></thead><tbody><tr><td align=\"left\">tDCS safety screening</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">BDI-II</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td></tr><tr><td align=\"left\">CRQ</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•^e</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">(S)AE (only during active/sham tDCS)</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\"/><th align=\"left\" colspan=\"10\"><italic>Social functioning and quality of life</italic></th></tr></thead><tbody><tr><td align=\"left\">AAQoL</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td></tr><tr><td align=\"left\">SCL-90-S</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td></tr><tr><td align=\"left\">PSQI</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td></tr></tbody></table><table frame=\"hsides\" rules=\"groups\"><thead><tr><th align=\"left\"/><th align=\"left\"/><th align=\"left\"/><th align=\"left\" colspan=\"10\"><italic>Other</italic></th></tr></thead><tbody><tr><td align=\"left\">Demographics</td><td align=\"left\"/><td align=\"left\">•</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr><tr><td align=\"left\">CGI-S</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^d</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td></tr><tr><td align=\"left\">CGI-I</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td><td align=\"left\">•</td></tr><tr><td align=\"left\">Blinding check</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\">•^e</td><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/><td align=\"left\"/></tr></tbody></table></table-wrap>" ]

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[ "<table-wrap-foot><p><italic>PS</italic> pre-screening, <italic>SV</italic> screening visit</p><p>^aRelated to randomization</p><p>^bScreening questions for BPD only</p><p>^cInquiring of the positively screened items from the BPD section only</p><p>^dBefore active/sham tDCS</p><p>^eAfter active/sham tDCS</p><p>^fFor females of child-bearing potential</p></table-wrap-foot>", "<fn-group><fn><p>Nicole Mauche and Christine Ulke are co-first authors and contributed equally.</p></fn></fn-group>" ]

[ "<graphic xlink:href=\"406_2023_1652_Fig1_HTML\" id=\"MO1\"/>" ]

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{ "acronym": [], "definition": [] }

[ "<title>Introduction</title>", "<p id=\"Par5\">The broad applicability of capsaicin (8-methyl-<italic>N</italic>-vanillyl-6-nonenamide) and capsaicin analogues in the food, pharmacy, and health industry has led to a renewed interest in these compounds (Abdel-Salam ##UREF##0##2014##; Basith et al. ##UREF##4##2016##; Santos et al. ##UREF##18##2023##). Among the spectrum of applications, perhaps the most promising one is the apoptotic effect of capsaicin in several human cancer cell lines such as KB (Lin et al. ##UREF##13##2013##), prostate cancer (Mori et al. ##REF##16540674##2006##), and glioblastoma cells (Lee et al. ##REF##11078921##2000##; Szoka and Palka ##REF##33038582##2020##). Glioblastomas account for 46% of primary malignant brain tumors, and the survival rate of patients diagnosed with this form of glioma is only 5% (Ostrom et al. ##UREF##15##2015##). Capsaicin induces apoptosis in several human glioblastoma cells, such as A172 (Lee et al. ##REF##11078921##2000##), LN-18 (Szoka and Palka ##REF##33038582##2020##), U87-MG (Jeon et al. ##UREF##9##2012##), and U373 (Amantini et al. ##REF##17442041##2007##), in a dose-dependent manner. The apoptotic induction of capsaicin is linked to an up-regulation of PPARɣ and an activation of caspases-9 and -3, and it is not related with a stimulatory effect on vanilloid receptors nor with an increase in intracellular calcium ions (Lee et al. ##REF##11078921##2000##; Jacobsson et al. ##REF##11714882##2001##; Szoka and Palka ##REF##33038582##2020##).</p>", "<p id=\"Par6\">Besides the natural capsaicinoids present in <italic>Capsicum</italic> plants, several capsaicin analogues have been synthetically obtained at laboratory scale (Kobata et al. ##UREF##12##1998##, ##REF##11999404##2002##; Reyes-Duarte et al. ##UREF##17##2002##; Castillo et al. ##UREF##6##2007##). The first non-pungent capsaicin analogue designed, olvanil, aimed to unveil the mechanism underlying TRPV1 activation (Dray et al. ##REF##2384136##1990##; Szallasi and Blumberg ##REF##10353985##1999##). However, further investigations revealed that olvanil exhibits greater apoptotic effect compared to capsaicin in C6 rat glioma cells (Jacobsson et al. ##REF##11714882##2001##) and superior anti-invasive activity on human small cell lung cancer cells, with a concentration 20 times lower than that required for capsaicin (Hurley et al. ##REF##27196129##2017##). Surprisingly, capsazepine, a potent capsaicin antagonist, did not block the cytotoxicity effect of olvanil when combined, suggesting a similar mechanism of action for olvanil as seen in capsaicin, where vanilloid receptors are not involved in the apoptosis of tumoral cells (Jacobsson et al. ##REF##11714882##2001##).</p>", "<p id=\"Par7\">To increase the biological activity of capsaicin analogues, the incorporation of unsaturated long chain fatty acids to the side chain is preferred (Hurley et al. ##REF##27196129##2017##; Friedman et al. ##REF##29246887##2018##). One group of fatty acids with attractive physiological properties are trienoic fatty acids (with three alternating double bonds) and omega-3 polyunsaturated fatty acids (n-3 PUFAs) (Aruna et al. ##REF##33371578##2016##; Saini and Keum ##REF##29715470##2018##). Research has shown that trienoic fatty acids are more potent than other dienoic fatty acids (with two alternating double bonds, also known as conjugated linoleic acid) (Aruna et al. ##REF##33371578##2016##), and n − 3 PUFAs (<italic>e.g.</italic> docosahexaenoic acid) protect against chronic and metabolic diseases such as diabetes, obesity, inflammation, and osteoporosis (Saini and Keum ##REF##29715470##2018##). Some trienoic fatty acids, such as α-eleostearic, jacarid acid, catalpic acid, and punicic acid, among others, are naturally found in plant seed oils (Yuan et al. ##REF##24760201##2014##). Punicic acid (PA), also called trichosanic acid, is an omega 5 long chain polyunsaturated fatty acid (18:3, n-5) which is accountable for the 70–80% of fatty acid content in pomegranate seed oil (<italic>Punica granatum</italic>) (Alfekaik and AL-Hilfi ##UREF##1##2016##). PA shows anti-cancer, anti-inflammatory, anti-obesity, anti-diabetic, and hypolipidemic properties (Yuan et al. ##REF##24760201##2014##; Alfekaik and AL-Hilfi ##UREF##1##2016##; Aruna et al. ##REF##33371578##2016##). Due to these properties, PA is a promising fatty acid for the synthesis of bioactive capsaicin analogues.</p>", "<p id=\"Par8\">Capsaicin analogues can be chemical or enzymatically synthetized. The latter technique exhibits additional advantages as enzymatic processes are usually performed in aqueous, environmental-friendly, and mild conditions (physiological pH, room temperature, and atmospheric pressure), with high specificities and selectivities (Andualema and Gessesse ##UREF##3##2012##; Sheldon and Van Pelt ##REF##23532151##2013##). Additionally, enzymes can be immobilized ensuring a reusable, stable, and cost-efficient process. Although the available literature concerning enzyme immobilization is vast, the existing methodologies can be defined as carrier-bound or carrier-free (Cao et al. ##REF##12943847##2003##). Among the carrier-free immobilization methods, crosslinked enzyme aggregates (CLEAs) is a simple and effective technique for the immobilization of many industrially relevant enzymes (Sheldon ##UREF##19##2011a##). Lipases, such as Lipase PS from <italic>Burkholderia cepacia</italic>, lipase B from <italic>Candida antarctica</italic> (CALB), and lipase from <italic>Pseudomonas cepacia</italic> are the preferred biocatalysts to obtain capsaicin analogues (Kobata et al. ##REF##11999404##2002##; Reyes-Duarte et al. ##UREF##17##2002##; Liu ##UREF##14##2009##). In a recent work developed by our research group, CLEAs of CALB were employed to efficiently synthetize olvanil, a capsaicin derivative of oleic acid (Diaz-Vidal et al. ##REF##30883025##2019##).</p>", "<p id=\"Par9\">In the present work, the synthesis of capsaicin analogues from linoleic acid, docosahexaenoic acid, and punicic acid was evaluated by a chemo-enzymatic process catalyzed by CLEAs from recombinant CALB, and the catalytic efficiency was compared to commercial immobilized CALB. The cytotoxicity of the capsaicin analogues obtained, in addition to olvanil and capsaicin, was studied on human glioblastoma cells.</p>" ]

[ "<title>Materials and methods</title>", "<title>Chemicals and reagents</title>", "<p id=\"Par10\"><italic>C. antarctica</italic> lipase B immobilized on Immobed 150 (CALB-150, ≥ 2000 U g⁻¹), <italic>Candida rugosa</italic> lipase (lyophilized powder, ≥ 40,000 U mg⁻¹), oleic acid (technical grade, 90%), linoleic acid (≥ 95%), docosahexaenoic acid (DHA, ≥ 98%), capsaicin natural (65% capsaicin, 35% dihydrocapsaicin), capsaicin ≥ 95% (from <italic>Capsicum</italic> sp.), temozolomide (≥ 98% HPLC), isooctane, 2-methyl-2-butanol (2M2B), silica TLC plates (20 cm × 20 cm, fluorescent indicator), N,N-diisopropylethylamine (DIPEA), syringe filters (Supelco, Iso-Disc syringe tip filter, PTFE membrane, 0.2 μm pore size, 4 mm diameter) and Vanillylamine hydrochloride were purchased from Sigma-Aldrich (Mexico). Flash chromatography column was from ChemGlass Life Sciences (Vineland, NJ). Dulbecco's Modified Eagle Medium (DMEM), fetal bovine serum, penicillin, streptomycin, and amphotericin B were from Gibco.</p>", "<p id=\"Par11\">Punicic acid was extracted from pomegranate seeds (<italic>Punica granatum</italic>) purchased at a local store (Mexico). Zeocin™ was obtained from Invitrogen (Carlsbad, CA). The restriction enzymes (DNA polymerase, and DNA ligase) and their buffers were obtained from New England Biolabs (Ipswich, MA). All other reagents and solvents were from Sigma-Aldrich (Mexico).</p>", "<title>Production of recombinant CALB lipases in <italic>P. pastoris</italic></title>", "<p id=\"Par12\">The sequence of CALB with its native signal peptide (GenBank: Z30645.1) was codon optimized and synthetized by Genscript® (Tucson, AZ, USA) for expression in <italic>Pichia pastoris</italic> (GenBank: OR227685 and Supplementary Material). <italic>Eco</italic>RI and <italic>Kpn</italic>I restriction sites were added by PCR and the resulting fragment was inserted into pGAPZB vector to generate the recombinant plasmid pGAPZB/CALB. The plasmid was linearized with <italic>Bsp</italic>HI and transformed into <italic>P. pastoris</italic> SMD1168H cells (Invitrogen™, Thermo Fisher Scientific, MA, USA) by electroporation. Transformed cells were cultured on yeast extract–peptone–dextrose (YPD) plates containing Zeocin™ (100 μg mL⁻¹) and incubated at 30 °C. Positive clones were transferred to YPD plates containing 1% (v/v) of emulsified tributyrin (TG (4:0)) and the best CALB-producing strain was chosen after observing a halo formation due to lipase activity.</p>", "<title>Protein estimation and enzymatic activity</title>", "<p id=\"Par13\">Protein quantification was determined with Bradford reagent using BSA as standard. The enzymatic activity was evaluated in a microplate assay by monitoring <italic>p</italic>-nitrophenyl butyrate (<italic>p</italic>NPB) hydrolysis for recombinant CALB and CALB-CLEAs. One hundred μL of 10 mM <italic>p</italic>NPB (20 mmol L⁻¹ MOPS buffer pH 7.2, 0.5 mmol L⁻¹ NaTDC, 150 mmol L⁻¹ NaCl, 5 mmol L⁻¹ CaCl2 and 3 g L⁻¹ β-cyclodextrin) were added to 20 μL of biocatalyst.</p>", "<p id=\"Par14\">The reaction course was followed at 410 nm for 15 min at 37 °C. One enzymatic activity unit (U) corresponds to 1 μmol of <italic>p</italic>NP released per min in the assay conditions.</p>", "<title>Preparation and characterization of CLEAs</title>", "<p id=\"Par15\">CALB-CLEAs were prepared with a mixture of glutaraldehyde (50%, v/v, in water) to a final concentration of 20–500 mmol L⁻¹ and precipitating agent (<italic>tert</italic>-butanol, isopropanol, acetone, acetonitrile, ethanol, polyethylene glycol (PEG) 20% (v/v), and saturated ammonium sulfate) were slowly added to recombinant CALB. Then, the aggregates were shaken in a Thermomixer (Eppendorf, Hamburg, Germany) at 30 °C, 750 rpm for 30–120 min. Immediately after, the reaction was stopped with MOPS 100 mmol L⁻¹ pH 7.2 at a ratio of 1:9 and the formed CLEAs were centrifuged, washed thrice with MOPS 100 mmol L⁻¹, pH 7.2 and lyophilized until further use.</p>", "<p id=\"Par16\">CLEAs were characterized in terms of retained activity according to the following calculation (Sheldon and Van Pelt ##REF##23532151##2013##):</p>", "<title>Punicic acid extraction and purification</title>", "<p id=\"Par17\">Whole pomegranates were peeled and de-seeded to reduce waste interference in the extraction process. The seeds were pressed to remove the juice present in them and then they were subjected to a pulp removal by constant stirring in presence of NaOH, thus providing the de-pulped seeds, these seeds were then left to dry completely before further use. Dried seeds were grounded and added to a significant amount of hexane to extract the oil present in them; the organic phase was filtrated, and the hexane removed with the use of a rotary evaporator.</p>", "<p id=\"Par18\">Once the oil was extracted, 10 mL of <italic>C. rugosa</italic> lipase (50 mg mL⁻¹) in MOPS buffer pH 7.2 (100 mmol L⁻¹) were added to 20 mL of the pomegranate oil obtained and incubated 12 h at 40 °C. To stop the reaction 100 mL of HCl 3 mol L⁻¹ were added and the lipidic fraction was extracted using 150 mL of hexane containing 1% BHT (1 mg mL⁻¹), a liquid/liquid extraction was performed and the organic phase was then treated with MgSO₄ in order to dry the solution, it was centrifuged afterwards and the solvent was removed at 40 °C with the use of a rotary evaporator; sample was stored under nitrogen atmosphere at -20 °C for further purification.</p>", "<p id=\"Par19\">Punicic acid was purified by flash chromatography on silica gel (petroleum ether: diethyl ether, 90:10, v/v). Fractions were analyzed by thin layer chromatography (TLC) using heptane: diethyl ether: acetic acid (55:45:1, v/v/v) as eluent. Fractions containing UV absorbing free fatty acids were collected and the solvent evaporated.</p>", "<title>Synthesis and purification of capsaicin analogues</title>", "<p id=\"Par20\">Capsaicin analogues were synthetized according to an optimized protocol in our research group (Diaz-Vidal et al. ##REF##30883025##2019##). Briefly, reactions were carried out in an IKA Magnetic Stirrer at equimolar concentrations of vanillylamine hydrochloride (VAM-HCl) and acyl donor (oleic acid, linoleic acid, DHA, and punicic acid) at 50 °C in 5 mL amber glass vials with a total reaction volume of 1 mL. Previously, VAM-HCl was incubated with DIPEA at a ratio of 1:10 to release the salt derivative. The synthesis was performed with 1 U in <italic>p</italic>NPB hydrolysis of CALB-CLEAs and CALB-150 in anhydrous <italic>tert</italic>-Amyl alcohol (2M2B).</p>", "<p id=\"Par21\">Reaction progress was followed by thin-layer chromatography (TLC) using as mobile phase a mixture of petroleum ether/ethyl acetate (50/50, v/v), and spots were visualized by iodine vapors. Reactions were centrifuged at 7000<italic> g</italic> for 5 min for the total removal of immobilized enzyme and molecular sieves. Next, the reaction solvent was fully evaporated in a rotatory evaporator and the residue resuspended in a mixture of petroleum ether/ethyl acetate at variable proportions. Purifications were carried out with silica gel flash chromatography (Silica gel 60 A, 230–400 mesh particle size) using a mobile phase of petroleum ether/ethyl acetate at variable proportions.</p>", "<title>Spectroscopic analysis</title>", "<p id=\"Par22\">¹H NMR spectra was obtained using a Bruker Ascend 400 (Billerica, Massachusetts, USA). The chemical shift values were recorded in parts per million (ppm) using CDCl3 as solvent. NMR data were obtained for <italic>N</italic>-(4-hydroxy-3-methoxybenzyl)oleamide (olvanil), (4Z,7Z,10Z,13Z,16Z,19Z)-<italic>N</italic>-(4-hydroxy-3-methoxybenzyl)docosa-4,7,10,13,16,19-hexaenamide (dohevanil), (9Z,12Z)-<italic>N</italic>-(4-hydroxy-3-methoxybenzyl)octadeca-9,12- dienamide (livanil), and (9Z,11E,13Z)-<italic>N</italic>-(4-hydroxy-3-methoxybenzyl)octadeca-9,11,13- trienamide (punivanil) synthetized by enzymatic means (Table ##TAB##0##1##). The expanded ¹H-NMR spectrum in the region of 0.7 to 7.2 ppm for all the synthetized capsaicinoids is shown in Table ##SUPPL##0##S1##, Supplementary Information.</p>", "<p id=\"Par23\"><italic>N</italic>-(4-hydroxy-3-methoxybenzyl) oleamide (olvanil):</p>", "<p id=\"Par24\">¹H NMR (600 MHz, CDCl₃) δH 6.85 (1H, d, J = 8.0 Hz, H6), 6.80 (1H, d, J = 2.0 Hz, H2), 6.75 (1H, dd, J = 8.0, 2.0 Hz, H5), 5.62 (1H, br. s, NH), 5.58 (1H, s, OH), 5.43 – 5.23 (2H, m, H9’, H10’, + oleic acid residues), 4.35 (2H, d, J = 5.6 Hz, H7), 4.21 (m, unknown), 3.87 (3H, s, CH3O), 3.68 (m, unknown), 3.64 (3H, d, J = 0.8 Hz, unknown), 2.32 (2H, dt, J = 14.9, 7.6 Hz, H2’), 2.18 (2H, p, J = 9.1, 7.6 Hz, H8’), 2.08 – 1.95 (2H, m, H11’, + oleic acid residues), 1.76 – 1.54 (2H, m, H3’, + oleic acid residues), 1.44 – 1.16 (20H, m, H4’-H6’, H13’-H17’, + oleic acid residues), 0.87 (3H, m, H18’, + oleic acid residues).</p>", "<p id=\"Par25\"><italic>N</italic>-(4-hydroxy-3-methoxybenzyl) octadeca-9,12-dienamide (livanil):</p>", "<p id=\"Par26\">¹H NMR (600 MHz, CDCl₃) δH 6.85 (1H, d, J = 8.0 Hz, H6), 6.80 (1H, d, J = 2.0 Hz, H2), 6.75 (1H, dd, J = 8.0, 2.0 Hz, H5), 5.62 (1H, br. s, NH), 5.58 (1H, s, OH), 5.45 – 5.26 (4H, m, H9’, H10’, H12’, H13’, + linoleic acid residues), 4.35 (2H, d, J = 5.5 Hz, H7), 3.87 (3H, s, CH3O), 3.64 (1H, s, unknown), 2.76 (2H, t, J = 6.8, 5.7 Hz, H11’, + linoleic acid residues), 2.33 (2H, dt, J = 15.0, 7.6 Hz, H2’, + linoleic acid residues), 2.19 (2H, dt, J = 15.0, 7.6 Hz, H8’, + linoleic acid residues), 2.03 (2H, q, J = 7.2, 6.1 Hz, H14’, + linoleic acid residues), 1.63 (4H, h, J = 7.5 Hz, H3’, H15’, + linoleic acid residues), 1.51 – 1.28 (12H, m, H4’-H7’, H16’, H17’, + linoleic acid residues), 0.95 – 0.77 (3H, m, H18’, + linoleic acid residues).</p>", "<p id=\"Par27\"><italic>N</italic>-(4-hydroxy-3-methoxybenzyl) docosa-4,7,10,13,16,19-hexaenamide (dohevanil):</p>", "<p id=\"Par28\">¹H NMR (600 MHz, CDCl₃) δH 6.84 (1H, d, <italic>J</italic> = 8.0 Hz, H6), 6.78 (1H, d, <italic>J</italic> = 2.0 Hz, H2), 6.74 (1H, dd, <italic>J</italic> = 8.0, 2.0 Hz, H5), 5.73 (1H, br s, NH), 5.46 – 5.24 (12H, m, H4’, H5’, H7’, H8’, H10’, H11’, H13’, H14’, H16’, H17’, H19’, H20’, + DHA residues), 4.33 (2H, d, <italic>J</italic> = 5.6 Hz, H7), 3.86 (3H, s, CH3O), 3.01 – 2.70 (10H, m, H6’, H9’, H12’, H15’, H18’, + DHA residues), 2.51 – 2.32 (2H, m, H2’, + DHA residues), 2.32–2.21 (2H, m, H3’, + DHA residues), 2.06 (2H, m, H21’, + DHA residues), 1.60 (1H, s, unknown), 1.49 (1H, q, <italic>J</italic> = 7.5, unknown), 1.37–1.22 (m, unknown), 1.19 (s, unknown), 0.96 (3H, td, <italic>J</italic> = 7.5, 1.5 Hz, H22’, + DHA residues), 0.91 (t, <italic>J</italic> = 7.5 Hz, unknown), 0.87 (t, <italic>J</italic> = 7.0 Hz, unknown).</p>", "<p id=\"Par29\">(9Z,11E,13Z)-<italic>N</italic>-(4-hydroxy-3-methoxybenzyl) octadeca-9,11,13-trienamide (punivanil):</p>", "<p id=\"Par30\">¹H NMR (600 MHz, CDCl₃) δH 6.49–641 (2H, m, H11’, H12’), 6.04 (2H, tt, <italic>J</italic> = 10.7, 1.8, H10’, H13’), 5.43 (2H, dq, <italic>J</italic> = 10.7, 8.1 Hz, H9’, H14’), 2.34 (2H, t, J = 7.5 Hz, H2’, + punicic acid residues), 2.33–2.12 (4H, m, H8’, H15’, + punicic acid residues), 2.10 – 1.96 (m, unknown), 1.66 – 1.56 (2H, m, H3’, + punicic acid residues), 1.39–1.27 (8H, m, H4’- H7’, + punicic acid residues), 1.26–1.21 (4H, m, H16’, H17’, + punicic acid residues), 1.19 (s, unknown), 0.98 – 0.79 (3H, m, H18’, + punicic acid residues).</p>", "<p id=\"Par31\">The molecular mass of olvanil, livanil, dohevanil, and punivanil was determined by UHRQ- TOF mass spectrometer (Xevo G2-XS QTOF, Waters, Milford, Massachusetts, USA) coupled with an ESI source. The sample was resuspended in different solvent mixtures and directly infused to an ESI source. The UHR-Q-TOF instrument was operated in positive ion mode (ES +) electrospray ionization with a capillary voltage of 2.5 kV. Data of spectrum was recorded over the mass/charge (m/z) range of 50–1200 Da and analyzed with Waters Masslynx™ Mass Spectrometry software. The molecular masses obtained are summarized in Table ##SUPPL##0##S2##, Supplementary Information, and the obtained ion chromatographs are shown in Fig. ##SUPPL##0##S1##, Supplementary Information.</p>", "<title>Scanning electron microscopy images of CLEAs</title>", "<p id=\"Par32\">Scanning electron micrographs of CLEAs were recorded using a Mira3 LMU field emission scanning electronic microscope (FE-SEM, TESCAN, Czech Republic). Prior, the samples were freeze-dried and coated with sputtered gold.</p>", "<title>Cell culture</title>", "<p id=\"Par33\">Human glioblastoma multiforme (GBM) cells U138-MG-HBT16 (U-138), U-87 MGHTB14 (U-87) and NCTC clone 929 [L cell, L-929, derivative of Strain L] were obtained from the American Type Culture Collection (ATCC, Rockville, MD). GBM cells and L-929 were grown at 37 °C in a humidified incubator under 5% CO₂ and cultured in DMEM supplemented with fetal bovine serum (10%, w/v), penicillin (10,000 U mL⁻¹), streptomycin (10,000 μg mL⁻¹), and amphotericin B (25 μg mL⁻¹). The culture medium was replaced daily until attaining 80% confluence.</p>", "<title>Viability assay</title>", "<p id=\"Par34\">Capsaicin, olvanil, livanil, dohevanil, and punivanil were dissolved in dimethylsulfoxide (DMSO) at a final concentration of 100 mmol L⁻¹. Temozolomide was selected as positive control, and the dilution was performed as instructed by the supplier. The solutions were then sterilized with syringe filters and kept frozen until use.</p>", "<p id=\"Par35\">U-138, U-87 and L-929 (as control) cells (5,000 cells/well in 200 μL of DMEM) were cultivated in 96-well plates for 72 h at 37 °C, under 5% CO₂, using the 3D model based on Matrigel™, (Corning, Matrigel, Matrix basement membrane) at 50%. Next, the cells were incubated with 50, 100, 200, and 400 μmol L⁻¹ of capsaicin analogues and temozolomide (300, 600, 900, and 1200 μmol L⁻¹) diluted in DMEM for GBM cells and 200, 300 and 500 µmol L⁻¹ for L-929 cells. The cytotoxicity of the vehicle (DMSO, 1%, v/v) in DMEM) was also tested. After 24 h of incubation, the cytotoxic effect of capsaicin, capsaicin analogues, temozolomide, and DMSO was determined using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay as per manufacturer’s instruction. The absorbance was measured at 570 nm in a microplate reader (Bio-Rad). Three replicates were used for each capsaicin, capsaicin analogue, temozolomide, and vehicle concentration.</p>", "<title>Induction of cell death by Apoptosis</title>", "<title>Detection of phosphatidylserine externalization</title>", "<p id=\"Par36\">For this determination, monolayer cultured GBM were used with a density of 200,000 cells per well in a 24-well plate in triplicate. After 24 h, the medium was removed and the studied molecules were added at the following concentrations: capsaicin at 300 μmol L⁻¹, olvanil and dohevanil at 200 μmol L⁻¹, and temozolomide (TMZ) at 600 μmol L⁻¹. After 3 h of incubation, the molecules were removed, the cells were detached with EDTA at 2 mmol L⁻¹ and worked according to the Annexin V protocol (Annexin V conjugated with Alexa-Fluor 488, Invitrogen Cat. No. 13201 PHN1010 and PHN1008). The detection of phosphatidylserine externalization was measured at 533 nm and 575 nm using a Flow Cytometer (Guava EasyCyte 5, Millipore).</p>", "<title>Caspase-3 activation</title>", "<p id=\"Par37\">3D culture of GBM cells with the Matrigel base model was performed in a culture chamber system on an 8-well slide (Thermo-Scientific, Cat. No. 154461-PK, Nunc Lab-Tek™ II Chamber Slide System), at a density of 20,000 cells per well. The cells were incubated for 72 h with culture medium at 37 °C with an air atmosphere of CO₂ 5%. Then, the following capsaicin analogue concentrations were added: capsaicin and livanil at 300 μmol L⁻¹, dohevanil at 200 μmol L⁻¹. The culture was incubated for 6 h. Next, the culture medium was removed and incubated with a solution of paraformaldehyde 4% (v/v) in 0.1 mol L⁻¹ phosphate buffer at pH 7.4 (PBS), for 2 h. Immunofluorescence assay for caspase 3 (Abcam, ab-13847 cysteine-protease-3) was performed with a dilution of 1:500 and allowed to incubate overnight at 4 °C. Alexa-Fluor 488 secondary antibody was bound for 2 h in the dark (1:500, Vector Laboratories), protected with a drop of mounting medium with 4',6-diamidino-2-phenylindole, di-hydrochloride (Fluoroshield, Abcam 104,139), and later analyzed under fluorescence microscopy (Leica DM4 DF7000T, Leica Biosystems, Wetzlar, Germany). The obtained images were analyzed with the Leica Application Suite software (LAS). For each taken image taken, the degree of fluorescence intensity was kept constant. The total cells (DAPI) and cells labeled with Caspase 3 (Green) were counted in 10 fields (1.5 mm2) for each well and each group (3 wells). The percentage of labeled cells was calculated using the double-blind technique.</p>", "<title>Statistical analysis</title>", "<p id=\"Par38\">All data are expressed as mean ± standard deviation (SD). Statistical analysis was conducted with the GraphPad Prism software, v. 6 (GraphPad Software, San Diego, CA, USA). Differences on cell viability were analyzed by one-way and two-way analysis of variance (ANOVA) followed by Tukey post-hoc to determine whether the differences from the studies groups were significant from those of the capsaicin analogues treated groups. In all cases, the level of statistical significance was set to <italic>p</italic> &lt; 0.05, 0.001, 0.0005 or 0.0001.</p>" ]

[ "<title>Results</title>", "<title>Preparation and characterization of CLEAs</title>", "<p id=\"Par39\">Prior to the preparation of CALB-CLEAs, the crude fermentation extract of <italic>P. pastoris</italic> containing recombinant CALB, among contaminant proteins, was concentrated 32 times and dialyzed with Milli-Q water by ultrafiltration with a 10 kDa membrane, in order to remove salts from the medium. The concentrated crude fermentation extract of CALB contained 0.8 g L⁻¹ of total protein. The enzymatic activity of CALB prior to immobilization was 38 U mL⁻¹.</p>", "<p id=\"Par40\">Before the CLEAs preparation, the best precipitation conditions were initially established. For this, 1 part of CALB was incubated with 9 parts of different precipitating agents for 30 min at 30 °C. In a previous work from our group, we described the preparation and optimization of CLEAs of recombinant CALB for the synthesis of olvanil (Diaz-Vidal et al. ##REF##30883025##2019##). The results indicated that CALB precipitated with isopropanol and cross-linked with 150 mmol L⁻¹ for 60 min gave active and highly efficient crystal-shape immobilizates. Thus, we selected the same precipitation and cross-linking conditions for the present synthesis of capsaicin analogues.</p>", "<title>Scanning electron microscopy images of CLEAs</title>", "<p id=\"Par41\">The morphology of CLEAs depends on enzyme type, precipitant agent and the microenvironment of the enzyme when cross-linking (Zerva et al. ##UREF##21##2018##). SEM micrographies revealed the formation of clusters with irregular, cluster shapes and low porosity for CALB-CLEAs (Fig. ##FIG##0##1##).</p>", "<title>Synthesis of capsaicin analogues</title>", "<p id=\"Par42\">The synthesis of capsaicin analogues was conducted on 2M2B at 50 °C with equimolar concentrations of VAM-HCl and oleic acid, linoleic acid, DHA, and punicic acid as acyl donors. The amount of biocatalyst was equivalent to 1 U on the hydrolysis of <italic>p</italic>NPB (20 mg and 38 mg of CALB-CLEAs and CALB-150, respectively). Table ##TAB##1##2## shows the concentration and conversion values of livanil, dohevanil and punivanil synthesis using CALB-150 at 50 °C for 24, 48 and 72 h. The highest conversion was achieved when punicic acid was used as acyl donor. At 48 h of reaction, 19.4 g L⁻¹ of punivanil were synthetized with 73% of conversion. Surprisingly, at 72 h, the conversion of punivanil dramatically decreased 3.3-fold. In contrast, the synthesis of livanil increased steadily through time, achieving the maximum conversion yield at 72 h (58.3% conversion to livanil). Dohevanil was obtained in moderate amounts, and similar conversion values were obtained at 48 and 72 h.</p>", "<p id=\"Par43\">The concentration and conversion values obtained in the synthesis of livanil, dohevanil, and punivanil catalyzed by recombinant CALB-CLEAs is resumed in Table ##TAB##2##3##. Overall, the catalytic performance displayed by CALB-CLEAs was low in comparison to commercial CALB-150. In contrast to CALB-150, CALB-CLEAs displayed a strong preference for linoleic acid as acyl donor. At 72 h, the conversion to livanil was 69.7%, the highest conversion value obtained in comparison to the rest of acyl donors. In contrast, DHA gave the poorest catalytic results, and only 8.3% of conversion to dohevanil was achieved at 72 h. Similar to CALB-150, the synthesis of punivanil reached a maximum at 48 h, followed by a decrease in conversion, where presumably the hydrolysis of the product predominated. The ¹H NMR spectra of the isolated capsaicinoids showed typical chemical shifts of the vanillyl ring, 3-OCH₃, 4-OH, NH group, and long-chain acyl moieties for olvanil, livanil, and dohevanil (Kobata et al. ##REF##20192218##2010##; Roby et al. ##REF##25308686##2015##). For punivanil, the chemical signals of 3-OCH₃, double bonds, and C-bonds of the aliphatic chain were easily detected; however, we were unable to completely identify the H and NH group peaks of the vanillyl ring. This could be explained by an aromatic solvent induced shift (Cao et al. ##REF##17204261##2007##). The enzymatically synthetized capsaicin analogues were also subjected to mass spectrometry analysis. The theoretical molecular masses were in agreement with the experimentally measured m/z values (Supplementary Table ##SUPPL##0##S2## and Fig. ##SUPPL##0##S1##).</p>", "<title>Effect of capsaicin and capsaicin analogues on the cytotoxicity of glioblastoma cells</title>", "<p id=\"Par44\">The viability of U-138 and U-87 glioblastoma cells treated with increasing concentrations of capsaicin, capsaicin analogues (olvanil, livanil, dohevanil, and punivanil), and temozolomide for 24 h was determined by the MTT assay. Capsaicin analogue type and concentration had a statistical effect on cell viability. Increasing concentrations of capsaicin, olvanil, and dohevanil had a significant effect on the viability of U-138 and U-87 cells, whereas livanil and punivanil did not show a significant cytotoxic effect (Fig. ##FIG##1##2## and ##FIG##2##3##). Photomicrographs of viable and non-viable cell lines due to capsaicinoid exposition are shown in Supplementary Fig. ##SUPPL##0##S2##.</p>", "<p id=\"Par45\">U-138 cells treated with capsaicin maintained their viability at capsaicin concentrations ≤ 100 μmol L⁻¹. However, at capsaicin concentrations ≥ 400 μmol L⁻¹, the viability was reduced to 65 ± 3.6%. In contrast, U-87 cells required less capsaicin concentration to induce a cytotoxic effect. The viability was reduced to 91.7% at the lowest capsaicin concentration assessed (50 μmol L⁻¹), and the maximum cytotoxic effect was observed with 400 μmol L⁻¹ of capsaicin with a viability of 60.66 ± 2.7%. The viability of U-138 cells treated with olvanil at concentrations ≥ 100 μmol L⁻¹ had a significant effect in cytoxicity, recording a minimum of 21.1 ± 0.4% in viability at the highest olvanil concentration evaluated (400 μmol L⁻¹). U-87 cells treated with olvanil responded similar to U-138 cells. Concentrations ≥ 200 μmol L⁻¹ significantly reduced the cell viability from 77.3 ± 2.2% with 100 μmol L⁻¹ olvanil to 18.8 ± 4.6% with 400 μmol L⁻¹. The cytotoxic effect of olvanil was more notorious for U-87 cells, as also observed for capsaicin.</p>", "<p id=\"Par46\">U-138 cell viability was diminished to 79.9 ± 1.7% when exposed to dohevanil concentration of 100 μmol L⁻¹. However, at a concentration of 200 μmol L⁻¹, the cell viability drastically decreased to 22.3 ± 0.2%. Increasing the concentration of dohevanil at 400 μmol L⁻¹ had no effect on the cytotoxicity of U-138 cells. For U-87 cells, the cytotoxic effect of dohevanil was more notorious at lower concentrations (50 and 100 μmol L⁻¹) with a cell viability of 85.1 ± 5.1% and 76.8 ± 4.5%, respectively. The cell viability effect at concentrations ≥ 200 μmol L⁻¹ was similar to that observed for U-138 cells (24.1 ± 0.9 20.6 ± 3.1 for 200 and 400 μmol L⁻¹, respectively).</p>", "<p id=\"Par47\"> Conversely, the studied concentrations of livanil and punivanil (50–400 μmol L⁻¹) had no significant effect on the cytotoxicity of U-87 and U-138 cells.</p>", "<p id=\"Par48\">The induction of cell death by apoptosis in GBM cells due to the effect of capsaicin and its analogues was determined by the detection of phosphatidylserine externalization and the expression of caspase-3. Capsaicin analogues tested after 3 h promoted the binding of annexin V to externalized phosphatidylserine with a positive percentage of cells of 60.6 ± 7.2, 65.5 ± 5.7 and 67.5 ± 3.9% for capsaicin (300 μmol L⁻¹), olvanil and dohevanil (200 μmol L⁻¹), respectively. The positive control temozolomide (600 μmol L⁻¹) promoted a value of 40.8 ± 7.2% (Supplementary Fig. ##SUPPL##0##S3##).</p>", "<p id=\"Par49\">The expression of active caspase-3 in GBM cells could be observed by fluorescense photomicrographs (Supplementary Fig. ##SUPPL##0##S4##). For cells without the caspase-3 labeling marker using Alexa-Fluor 488 (green), only the nucleus was stained with DAPI (blue). After 6 h of exposure, the positivity for capsaicin and dohevanil was 19.1 ± 2.6% and 73.5 ± 7.6%, respectively, with a difference to the control group of 5.6 ± 1.6. As expected, livanil did not promote the expression of caspase-3, showing a positivity percentage of 3.5 ± 1.5% with no significant differences compared to the control group.</p>", "<p id=\"Par50\">The cytotoxicity test in the L-929 line presented a lower level of cytotoxicity compared to GBM cells (Fig. ##FIG##3##4##). The utilization of dohevanil at a concentration of 500 µmol L⁻¹ in L-929 cells results in an average cell viability of 34%. Meanwhile, at a concentration of 400 µmol L⁻¹, the average viability was 22% and 24% in U-138 and U-87 cells, respectively. </p>", "<p id=\"Par51\">Likewise, cells incubated with olvanil showed a viability of 47% at a dose of 500 µmol L⁻¹, whereas in lines U-138 and U-87, the viability at 400 µmol L⁻¹ was 21% and 18%, respectively. Punivanil did not show any type of cytotoxicity.</p>" ]

[ "<title>Discussion</title>", "<p id=\"Par52\">Capsaicin analogues from punicic acid, linoleic acid, and DHA were obtained by a chemoenzymatic process catalyzed by commercial CALB-150 and CALB-CLEAs. The capability of CALB to efficiently synthetize and hydrolyze amides has been previously described (Anderson et al. ##UREF##2##1998##; Torres-Gavilan et al. ##UREF##20##2006##). In particular, commercial CALB (Novozym 435) has mediated the synthesis of olvanil, rinvanil, and <italic>N</italic>-vanillyltetradecanamide with efficacies greater than 70% (Kobata et al. ##UREF##11##1999##; Reyes-Duarte et al. ##UREF##17##2002##; Castillo et al. ##UREF##5##2008##).</p>", "<p id=\"Par53\">The catalytic efficiency of commercial CALB-150 was compared to recombinant CALB-CLEAs. The CLEAs were obtained directly from the fermentation extract of a deficient protein strain of <italic>P. pastoris</italic>. In a previous work, we observed that recombinant CALB precipitated with isopropanol and further cross-linked with 150 mmol L⁻¹ of glutaraldehyde for 60 min led to active, robust, and efficient CLEAs in the synthesis of olvanil (Diaz-Vidal et al. ##REF##30883025##2019##). In the present work, the same immobilization conditions were selected for the synthesis of long-chain <italic>N</italic>-vanillylamides.</p>", "<p id=\"Par54\">Overall, the performance of commercial immobilized CALB on immobead 150 was greater than that of recombinant CALB-CLEAs. This might indicate that the CLEA preparation conditions selected for the synthesis of these particular long-chain capsaicin analogues were not optimum. Immobilization protocols can greatly affect the selectivity of a certain enzyme in relation to changes in the tridimensional structure of the enzyme (Rodrigues et al. ##REF##23059445##2013##). Hydrophobic supports tend to improve the catalytic performance of lipases due to interfacial activation (Fernandez-Lafuente et al. ##REF##9720258##1998##; Rodrigues et al. ##REF##23059445##2013##). This could explain the poor catalytic performance obtained with CALB-CLEAs in contrast to commercial CALB-150. Although the CLEA methodology is a carrier-free method, different approaches can be aimed to cause an interfacial activation on an enzyme without the need of hydrophobic supports. In the presence of an imprinting template, such as polymers, substrates, surfactants, detergents, etc., an open conformation can be mimicked and further locked by the addition of a cross-linker (Mingarro et al. ##REF##7724558##1995##; Abahazi et al. ##REF##25006788##2014##; Zhang et al. ##REF##29215562##2017##). This technique is known as molecular bioimprinting, and besides its simplicity and low cost, it can modify the specificity, stability, and selectivity of lipolytic enzymes (Fishman and Cogan ##UREF##7##2003##; Foresti et al. ##UREF##8##2005##).</p>", "<p id=\"Par55\">As many parameters influence the catalytic performance of CLEAs, it is important to optimize its preparation by screening a variety of precipitant agents, cross-linking agent type and concentration, agitation rate, additives, etc. (Sheldon ##REF##21887507##2011b##). In this work, we selected the optimum CLEA preparation conditions for the synthesis of olvanil, but as observed, these conditions are unfavorable for the synthesis of other <italic>N</italic>-vanillylamides.</p>", "<p id=\"Par56\">Therefore, in order to increase the yield of livanil, dohevanil, and punivanil synthesis, additional CLEA optimization procedures should be performed for each reaction. Although the synthesis of livanil and dohevanil has been previously described by chemical means (Melck et al. ##REF##10448105##1999##; Jin et al. ##UREF##10##2002##; Sumithran et al. ##REF##23102773##2012##), this is the first report concerning the lipase mediated synthesis of these compounds. However, as far as we are concerned, our report is the first and only concerning the synthesis of punivanil, a capsaicin analogue from punicic acid.</p>", "<p id=\"Par57\">According to the morphology of the CALB-CLEAs obtained in this work, the immobilizates can be classified as <italic>“type 2”</italic>, which are non-defined clusters (Schoevaart et al. ##REF##15329933##2004##). In general, the structures had a highly irregular, clustered shape, which is a typical feature of highly glycosylated, hydrophilic enzymes. However, at some magnifications, some “<italic>ball type or type 1”</italic> structures could be observed among the flat surface (Schoevaart et al. ##REF##15329933##2004##). The formation of <italic>“type 1”</italic> structures is caused when the enzyme is highly lipophilic, as in the case of CALB. As the CLEAs in this work were immobilized directly from the fermentation broth of <italic>P. pastoris</italic>, the presence of contaminant proteins of unknown hydrophobicity and lipophilicity is expected. This mixture can help explain why CALB-CLEAs are a combination of both <italic>“type 1”</italic> and <italic>“type 2”</italic> structures. However, based on our results, the CLEA preparation conditions selected for our CALB-CLEAs generated immobilizates with poor catalytic performance in the synthesis of capsaicin analogues.</p>", "<p id=\"Par58\">As expected, capsaicin analogues and temozolomide demonstrated a dose-response cytotoxic effect for U-87 and U-138 glioblastoma cell lines. Although the molecular mechanisms underlying the cytotoxicity on U-138 cells has not been elucidated, similar reports with U-87 cells pointed out a TRPV1-independent mechanism in where the apoptosis pathway is activated. Jeon and colleagues found that cell viability of U-87 cells incubated with capsaicin decreased in a dose-dependent manner (Jeon et al. ##UREF##9##2012##). Capsaicin analogues, especially dohevanil and olvanil, were able to promote the extracellular expression of phosphatidylserine in MG U-138 cells, as well as caspase 3, which serve as indicators that these compounds could be acting in apoptotic pathways as observed in prior studies. Morphological changes, down-regulation of BCL-2 expression, up-regulation of Bax expression, and DNA fragmentation proved that apoptosis occurred during capsaicin induced cytotoxicity of U-87 cells. Thus, apoptosis occurred via activation of the p-38 MAPK signaling pathway and the mitochondrial pathway of BCL-2/Bax. In contrast to what has been reported for other cell lines, caspases did not participate in the capsaicin-induced apoptosis of U-87 cells (Jeon et al. ##UREF##9##2012##). However, the reported cell viability values were slightly lower than the ones obtained in this work. Values of ~ 60% and ~ 50% cell viability were determined after incubation with 200 and 400 μmol L⁻¹ of capsaicin, respectively.</p>", "<p id=\"Par59\">A similar loss of cell viability (~ 80%) was also observed for LN-18 glioblastoma cells after 24 h of incubation with 200 μmol L⁻¹ capsaicin (Szoka and Palka ##REF##33038582##2020##). However, the effect of 400 μmol L⁻¹ capsaicin after 24 h of incubation was more detrimental on cell viability, and values around ~ 30% were determined. Similarly, capsaicin activated the intrinsic apoptosis pathway of LN-18 cells, which is regulated by Bcl-2 proteins, and increased levels of PPARɣ expression. Indeed, a combination therapy of capsaicin analogues with PPARɣ agonists, such as thiazolidinediones, is a promising strategy for the treatment of several cancer cell lines (Hurley et al. ##REF##27196129##2017##; Szoka and Palka ##REF##33038582##2020##).</p>", "<p id=\"Par60\">Dohevanil, a capsaicin analogue from DHA, was the most cytotoxic capsaicin analogue on both U-138 and U-87 cells, tested both in cytotoxicity tests with MTT, as well as apoptotic pathways, expressed by the increase in phosphatidylserine translocation and the expression of caspase 3, as shown in other research with other types of cancers. Dohevanil required less dose to achieve a significant cytotoxic effect. The cytotoxic effect of dohevanil has also been studied for MCF-7 human breast cancer cells. Similar to our results, Tuoya et al<italic>.</italic> observed that the apoptosis induction caused by dohevanil was more potent than that of capsaicin (Tuoya et al. ##REF##16260002##2006##). The cytotoxic effect of olvanil was also significant on both U-138 and U-87 cells and the data suggests that the potency of olvanil might be greater than that of capsaicin. Similar results have also been seen with human small cell lung cancer cells (Hurley et al. ##REF##27196129##2017##) and C6 rat glioma cells and EFM-19 breast cancer cells (Melck et al. ##REF##10448105##1999##).</p>", "<p id=\"Par61\">Livanil and punivanil did not show a significant cytotoxic effect on U-87 and U-138 glioblastoma cells. However, both capsaicin analogues increased cell viability by ~ 9–30%. The prospective application of these capsaicin analogues is still unexploited, but according to our results, these compounds can be envisaged as cell growth promoters in cases where cell protection is required.</p>", "<p id=\"Par62\">L-929 cells are mouse connective tissue cells, with fibroblast morphology from the ATCC. As these cells do not present any pathology, they are commonly used to carry out toxicity studies. Nevertheless, these capsaicin analogues were employed for testing, revealing cytotoxic properties. Yet, upon analyzing specific doses and comparing these cells with tumor cells, they exhibited a lower level of cytotoxicity.</p>", "<p id=\"Par63\">If capsaicin analogues prove effective as antitumor therapies, their utilization alongside specific adjuncts could enable targeted action towards tumors without affecting healthy cells. Nevertheless, at lower doses, their cytotoxicity in healthy cells is comparatively lower than in tumor cells.</p>" ]

[]

[ "<title>Abstract</title>", "<p id=\"Par1\">Glioblastoma is one of the most lethal tumors, displaying striking cellular heterogeneity and drug resistance. The prognosis of patients suffering from glioblastoma after 5 years is only 5%. In the present work, capsaicin analogues bearing modifications on the acyl chain with long-chain fatty acids showed promising anti-tumoral activity by its cytotoxicity on U-87 and U-138 glioblastoma multiforme cells. The capsaicin analogues were enzymatically synthetized with cross-linked enzyme aggregates of lipase B from <italic>Candida antarctica </italic>(CALB). The catalytic performance of recombinant CALB-CLEAs was compared to their immobilized form on a hydrophobic support. After 72 h of reaction, the synthesis of capsaicin analogues from linoleic acid, docosahexaenoic acid, and punicic acid achieved a maximum conversion of 69.7, 8.3 and 30.3% with CALB-CLEAs, respectively. Similar values were obtained with commercial CALB, with conversion yields of 58.3, 24.2 and 22% for capsaicin analogues from linoleic acid, DHA and punicic acid, respectively. Olvanil and dohevanil had a significant cytotoxic effect on both U-87 and U-138 glioblastoma cells. Irrespective of the immobilization form, CALB is an efficient biocatalyst for the synthesis of anti-tumoral capsaicin derivatives.</p>", "<title>Key points</title>", "<p id=\"Par2\">\n<italic>• This is the first report concerning the enzymatic synthesis of capsaicin analogues from docosahexaenoic acid and punicic acid with CALB-CLEAs.</italic>\n</p>", "<p id=\"Par3\">\n<italic>• The viability U-87 and U-138 glioblastoma cells was significantly affected after incubation with olvanil and dohevanil.</italic>\n</p>", "<p id=\"Par4\">\n<italic>• Capsaicin analogues from fatty acids obtained by CALB-CLEAs are promising candidates for therapeutic use as cytotoxic agents in glioblastoma cancer cells.</italic>\n</p>", "<title>Supplementary Information</title>", "<p>The online version contains supplementary material available at 10.1007/s00253-023-12856-y.</p>", "<title>Keywords</title>" ]

[ "<title>Supplementary Information</title>", "<p>Below is the link to the electronic supplementary material.</p>" ]

[ "<title>Authors’ contribution</title>", "<p>JCMD, AACA, and JAR conceived and designed research, TDV, VPAP, LCRR, RBMP, and YKGM conducted experiments. TDV, JCMD, AACA, LCRR, and JAR analyzed data. TDV wrote the manuscript. All authors read and approved the manuscript.</p>", "<title>Funding</title>", "<p>This work was supported by Secretaria de Educación Pública-Consejo Nacional de Ciencia y Tecnología (SEP-CONACYT) grant 242544–2014 and Fondo Sectorial de Investigación en Salud y Seguridad Social (FOSISS) grant B-S-34029–2018. TDV thanks CONACYT for her doctoral scholarship.</p>", "<title>Data and code availability</title>", "<p> The data that support the findings of this study are available from the corresponding author, JAR, upon reasonable request.</p>", "<title>Declarations</title>", "<title>Conflicts of interest</title>", "<p id=\"Par64\">The authors declare no conflicts of interest.</p>", "<title>Ethical statement</title>", "<p id=\"Par65\">This article does not contain any studies with human participants or animals performed by any of the authors.</p>" ]

[ "<fig id=\"Fig1\"><label>Fig. 1</label><caption><p>Scanning electron micrographs of the structure of CALB-CLEAs at <bold>A)</bold> 1,030 × magnifications, <bold>B)</bold> 2,200 × magnifications, <bold>C)</bold> 2,000 × magnifications, and <bold>D)</bold> 5,000 × magnifications. CLEA preparation conditions: isopropanol as precipitating agent, 150 mM glutaraldehyde for 60 min at 30 °C</p></caption></fig>", "<fig id=\"Fig2\"><label>Fig. 2</label><caption><p>Average viability percentage of U-138 cell line in a concentration-dependent manner: <bold>A</bold>) 50 μmol L⁻¹, <bold>B</bold>) 100 μmol L⁻¹, <bold>C</bold>) 200 μmol L⁻¹, and <bold>D</bold>) 400 μmol L.⁻¹. Data are expressed as the average viability percentage ± standard deviation at different doses of capsaicin, capsaicin analogues, control (culture medium), temozolomide (TMZ, as positive control) and vehicle (DMSO) and analyzed using one-way ANOVA test followed by Tukey post-hoc. Differences were considered significant when *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.001, ***<italic>p</italic> &lt; 0.0005 or **** <italic>p</italic> &lt; 0.0001</p></caption></fig>", "<fig id=\"Fig3\"><label>Fig. 3</label><caption><p>Average viability percentage of U-87 cell line in a concentration-dependent manner: <bold>A</bold>) 50 μmol L⁻¹, <bold>B</bold>) 100 μmol L⁻¹, <bold>C</bold>) 200 μmol L⁻¹, and <bold>D</bold>) 400 μmol L.⁻¹. Data are expressed as the average viability percentage ± standard deviation at different doses of capsaicin, capsaicin analogues, control (culture medium), temozolomide (TMZ, as positive control) and vehicle (DMSO) and analyzed using one-way ANOVA test followed by Tukey post-hoc. Differences were considered significant when *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.001, ***<italic>p</italic> &lt; 0.0005 or **** <italic>p</italic> &lt; 0.0001</p></caption></fig>", "<fig id=\"Fig4\"><label>Fig. 4</label><caption><p>Average viability percentage of L929 cell line in a concentration-dependent manner: <bold>A</bold>) 200 µmol L⁻¹, <bold>B</bold>) 300 µmol L⁻¹ and <bold>C</bold>) 500 µmol L.⁻¹. Data is expressed as the average viability percentage ± standard deviation at different doses of capsaicin, capsaicin analogues, control (culture medium), temozolomide (TMZ, as positive control) and vehicle (DMSO) and analyzed using one-way ANOVA test followed by Tukey post-hoc. Differences were considered significant when *<italic>p</italic> &lt; 0.05, **<italic>p</italic> &lt; 0.001, ***<italic>p</italic> &lt; 0.0005 or **** <italic>p</italic> &lt; 0.0001</p></caption></fig>" ]