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Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps . | <meaning-changed> Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps . | Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the L\'{e measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps . | meaning-changed | 0.99903995 | 0902.2479 | 1 |
Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps . Moreover , the smooth-fit property is shown via the global regularity of the value function . | <meaning-changed> Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps . Moreover , the smooth-fit property is shown via the global regularity of the value function . | Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1 , the smooth-fit property is shown via the global regularity of the value function . | meaning-changed | 0.9992969 | 0902.2479 | 1 |
Moreover , the smooth-fit property is shown via the global regularity of the value function . | <meaning-changed> Moreover , the smooth-fit property is shown via the global regularity of the value function . | Moreover , the smooth-fit property holds and the value function is C^{2,1 . | meaning-changed | 0.9994166 | 0902.2479 | 1 |
Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 . | <meaning-changed> Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 . | Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 . | meaning-changed | 0.7698215 | 0902.2479 | 2 |
Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 . | <coherence> Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a result, the smooth-fit property holds and the value function is C^{2,1 . | Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . | coherence | 0.927137 | 0902.2479 | 2 |
Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . | <meaning-changed> Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . | Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . | meaning-changed | 0.99939954 | 0902.2479 | 3 |
Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . | <meaning-changed> Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . | Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with infinite activity jumps is W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds . | meaning-changed | 0.99914384 | 0902.2479 | 3 |
The value function of an optimal stopping problem for a process with L\'{e is known to be a generalized solution of a variational inequality. | <meaning-changed> The value function of an optimal stopping problem for a process with L\'{e is known to be a generalized solution of a variational inequality. | The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. | meaning-changed | 0.99896383 | 0902.2479 | 4 |
Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | <fluency> Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | fluency | 0.99844354 | 0902.2479 | 4 |
Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | <meaning-changed> Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | meaning-changed | 0.9985629 | 0902.2479 | 4 |
Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | <meaning-changed> Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} . As a consequence, the smooth-fit property holds. | Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} with p\in(1, \infty) . As a consequence, the smooth-fit property holds. | meaning-changed | 0.99932003 | 0902.2479 | 4 |
In this manual , we describe how to use the software together with COMSOL Multiphysics 3.4 and Matlab to set up simulations. We provide a detailed account of the code structure and of the available interfaces. This makes modifications and extensions of the code possible. We also give two detailed examples, in which we describe the process of simulating and visualizing two models from the systems biology literature in a step-by-step manner . | <meaning-changed> In this manual , we describe how to use the software together with COMSOL Multiphysics 3.4 and Matlab to set up simulations. We provide a detailed account of the code structure and of the available interfaces. This makes modifications and extensions of the code possible. We also give two detailed examples, in which we describe the process of simulating and visualizing two models from the systems biology literature in a step-by-step manner . | This manual describes version 1.1 of the software . | meaning-changed | 0.9860016 | 0902.2912 | 1 |
The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation. | <clarity> The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation. | The underlying algorithm is the next subvolume method , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation. | clarity | 0.9939857 | 0902.2912 | 2 |
The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation. | <fluency> The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation. | The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from a finite element formulation of the corresponding macroscopic equation. | fluency | 0.99917233 | 0902.2912 | 2 |
This manual describes version 1.1 of the software . | <meaning-changed> This manual describes version 1.1 of the software . | This manual describes version 1.2 of the software . | meaning-changed | 0.99874216 | 0902.2912 | 2 |
This manual describes version 1.1 of the software . | <meaning-changed> This manual describes version 1.1 of the software . | This manual describes version 1.1 of the software . URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. Additionally, support for basic SBML has been added along with the possibility to compile in stand-alone mode . | meaning-changed | 0.999509 | 0902.2912 | 2 |
This manual describes version 1.2 of the software. | <meaning-changed> This manual describes version 1.2 of the software. | This manual describes version 1.3 of the software. | meaning-changed | 0.9897166 | 0902.2912 | 3 |
URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. | <meaning-changed> URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. | URDME 1.3 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. | meaning-changed | 0.9647494 | 0902.2912 | 3 |
URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. Additionally, support for basic SBML has been added along with the possibility to compile in stand-alone mode . | <meaning-changed> URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. Additionally, support for basic SBML has been added along with the possibility to compile in stand-alone mode . | URDME 1.2 includes support for Comsol Multiphysics 5.x and PDE Toolbox version 1.5 and above . | meaning-changed | 0.9994467 | 0902.2912 | 3 |
This manual describes version 1.3 of the software. | <meaning-changed> This manual describes version 1.3 of the software. | This manual describes version 1.4 of the software. | meaning-changed | 0.9850343 | 0902.2912 | 4 |
URDME 1.3 includes support for Comsol Multiphysics 5.x and PDE Toolbox version 1.5 and above . | <meaning-changed> URDME 1.3 includes support for Comsol Multiphysics 5.x and PDE Toolbox version 1.5 and above . | Refer to URL for the latest updates . | meaning-changed | 0.5325719 | 0902.2912 | 4 |
This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | <meaning-changed> This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | The conflict can be understood on the basis that the multiplicative models used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | meaning-changed | 0.99633276 | 0902.2965 | 1 |
This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | <clarity> This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | This incompatibility goes away by noticing that the model used in both approaches are non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | clarity | 0.9839336 | 0902.2965 | 1 |
This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | <clarity> This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic which leads to ensemble-average returns differ from time-average returns in a single realization . | clarity | 0.999154 | 0902.2965 | 1 |
This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | <fluency> This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differing from time-average returns in a single realization . | fluency | 0.9993754 | 0902.2965 | 1 |
This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | <fluency> This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in a single realization . | This incompatibility goes away by noticing that the model used in both approaches , geometric Brownian motion, is a non-ergodic process, in the sense that ensemble-average returns differ from time-average returns in single realizations . | fluency | 0.99936837 | 0902.2965 | 1 |
The classic papers on portfolio theoryuse ensemble-average returns. The Kelly-result is obtained by considering time-average returns. | <clarity> The classic papers on portfolio theoryuse ensemble-average returns. The Kelly-result is obtained by considering time-average returns. | The classic treatments, from the very beginning of probability theory, use ensemble-averages, whereas the Kelly-result is obtained by considering time-average returns. | clarity | 0.7592107 | 0902.2965 | 1 |
The Kelly-result is obtained by considering time-average returns. | <meaning-changed> The Kelly-result is obtained by considering time-average returns. | The Kelly-result is obtained by considering time-averages. Maximizing the time-average returns. | meaning-changed | 0.99914396 | 0902.2965 | 1 |
The Kelly-result is obtained by considering time-average returns. The averages differ by a logarithm. In portfolio theory this logarithm can be implemented as a logarithmic utility function. It is important to distinguish between effects of non-ergodicity and genuine utility constraints. For instance, ensemble-average returns depend linearly on leverage. | <meaning-changed> The Kelly-result is obtained by considering time-average returns. The averages differ by a logarithm. In portfolio theory this logarithm can be implemented as a logarithmic utility function. It is important to distinguish between effects of non-ergodicity and genuine utility constraints. For instance, ensemble-average returns depend linearly on leverage. | The Kelly-result is obtained by considering time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage. | meaning-changed | 0.9990984 | 0902.2965 | 1 |
This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . | <clarity> This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . | The latter measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . | clarity | 0.5909659 | 0902.2965 | 1 |
This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . | <clarity> This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . | This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average growth and overall market stability . | clarity | 0.99630475 | 0902.2965 | 1 |
This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . | <meaning-changed> This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . | This measure can thus incentivize investors to maximize leverage, which is detrimental to time-average returns and overall market stability . The Sharpe ratio is insensitive to leverage. Its relation to optimal leverage is discussed . | meaning-changed | 0.9993673 | 0902.2965 | 1 |
Molecular motors are biogenic force generators acting in the nanometer range . | <clarity> Molecular motors are biogenic force generators acting in the nanometer range . | Molecular motors are single macromolecules that generate forces at the piconewton range and nanometer scale . | clarity | 0.99353963 | 0902.3301 | 1 |
They convert chemical energy into mechanical work and move along filamentous structures. | <coherence> They convert chemical energy into mechanical work and move along filamentous structures. | They convert chemical energy into mechanical work by moving along filamentous structures. | coherence | 0.6499556 | 0902.3301 | 1 |
In this research, we will discuss the velocity of molecular motors, in framework of a mechanochemical network theory. | <clarity> In this research, we will discuss the velocity of molecular motors, in framework of a mechanochemical network theory. | In this paper, we study the velocity of molecular motors, in framework of a mechanochemical network theory. | clarity | 0.9985644 | 0902.3301 | 1 |
In this research, we will discuss the velocity of molecular motors, in framework of a mechanochemical network theory. | <meaning-changed> In this research, we will discuss the velocity of molecular motors, in framework of a mechanochemical network theory. | In this research, we will discuss the velocity of two-head molecular motors in the framework of a mechanochemical network theory. | meaning-changed | 0.9989838 | 0902.3301 | 1 |
Our network modelis based on the distinct mechanochemical states of molecular motors. It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. | <clarity> Our network modelis based on the distinct mechanochemical states of molecular motors. It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. | The network model, a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. | clarity | 0.96223587 | 0902.3301 | 1 |
It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. | <clarity> It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. | It can be regarded as a generalization of the recently work of Liepelt and Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. | clarity | 0.9972844 | 0902.3301 | 1 |
It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) . | <meaning-changed> It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) . The method used in this research is similar as the one used by Michael E. Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) . | It can be regarded as a generalization of the one used by Steffen Liepelt and Reinhard Lipowsky (PRL 98, 258102 (2007)) , is based on the discrete mechanochemical states of a molecular motor with multiple cycles. By generalizing the mathematical method developed by Fisher and Kolomeisky for single cycle motor (PNAS(2001) 98(14) P7748-7753) . | meaning-changed | 0.99919313 | 0902.3301 | 1 |
Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) . Generally, the formulation of the velocity of molecular motors can be obtained . | <clarity> Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) . Generally, the formulation of the velocity of molecular motors can be obtained . | Fisher and Anatoly B. Kolomeisky (PNAS(2001) 98(14) P7748-7753) , we are able to obtain an explicit formula for the velocity of a molecular motor . | clarity | 0.9928341 | 0902.3301 | 1 |
In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached. | <clarity> In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached. | In accordance with the prevailing model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached. | clarity | 0.9980463 | 0902.3413 | 1 |
In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached. | <clarity> In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LDs that bud-off when a critical size is reached. | In accordance with the standard model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LD that bud-off when a critical size is reached. | clarity | 0.99703753 | 0902.3413 | 1 |
Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs. | <meaning-changed> Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs. | Mathematically, LD were modeled as spherical protuberances in an otherwise planar ER membrane. We estimated the local phospholipid composition, and calculated the change in the elastic free energy of the membrane caused by nascent LDs. | meaning-changed | 0.9994797 | 0902.3413 | 1 |
Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs. | <fluency> Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs. | Relying on this mechanism, we have calculated the change in elastic free energy of the membrane caused by nascent LDs. | fluency | 0.9989247 | 0902.3413 | 1 |
Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs. We found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. | <clarity> Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs. We found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. | Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LD. Based on this model calculation, we found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. | clarity | 0.99842227 | 0902.3413 | 1 |
We found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. | <clarity> We found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. | We found a gradual demixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. | clarity | 0.9941578 | 0902.3413 | 1 |
As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth . | <clarity> As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth . | During demixing , the phospholipid monolayer was able to gain energy during LD growth . | clarity | 0.99534434 | 0902.3413 | 1 |
As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth . This suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing. | <coherence> As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth . This suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing. | As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth , which suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing. | coherence | 0.98530465 | 0902.3413 | 1 |
This suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing. In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. | <meaning-changed> This suggested that the formation of curved interfaces , necessary for the creation of a lipid droplet, were driven or supported by the process of lipid de-mixing. In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. | This suggested that the formation of curved interfaces was supported by or even driven by lipid demixing. In addition, we show that demixing is thermodynamically necessary as LD cannot bud-off otherwise. In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. | meaning-changed | 0.8941307 | 0902.3413 | 1 |
In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. | <clarity> In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. | In the case of Saccharomyces cerevisiae our model predicts a LD bud-off diameter of about 30-50 nm. | clarity | 0.9936539 | 0902.3413 | 1 |
In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. We concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process. | <meaning-changed> In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm. We concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process. | In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 13 nm. This diameter is far below the experimentally determined size of typical yeast LD. Thus, we concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process. | meaning-changed | 0.999464 | 0902.3413 | 1 |
We provide a simple and accurate analytical model for infrastructure IEEE 802.11 WLANs. | <meaning-changed> We provide a simple and accurate analytical model for infrastructure IEEE 802.11 WLANs. | We provide a simple and accurate analytical model for multi-cell infrastructure IEEE 802.11 WLANs. | meaning-changed | 0.9987098 | 0903.0096 | 1 |
Our model applies if the cell radius, R, is much smaller than the distance , R_{cs} , up to which carrier sensing is effective. | <clarity> Our model applies if the cell radius, R, is much smaller than the distance , R_{cs} , up to which carrier sensing is effective. | Our model applies if the cell radius, R, is much smaller than the carrier sensing range , R_{cs} , up to which carrier sensing is effective. | clarity | 0.9980914 | 0903.0096 | 1 |
Our model applies if the cell radius, R, is much smaller than the distance , R_{cs} , up to which carrier sensing is effective. The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate. | <clarity> Our model applies if the cell radius, R, is much smaller than the distance , R_{cs} , up to which carrier sensing is effective. The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate. | Our model applies if the cell radius, R, is much smaller than the distance , R_{cs} . We argue that, the condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate. | clarity | 0.99903584 | 0903.0096 | 1 |
The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate. | <clarity> The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high Physical (PHY) rate. | The condition R_{cs} >> R is likely to hold in a dense deployment of Access Points (APs) where, for every client or station (STA), there is an AP very close to the STA such that the STA can associate with the AP at a high physical rate. | clarity | 0.99506795 | 0903.0096 | 1 |
We develop a scalable cell level model for such WLANs with saturated AP and STA queues as well as for TCP-controlled long file transfers . | <fluency> We develop a scalable cell level model for such WLANs with saturated AP and STA queues as well as for TCP-controlled long file transfers . | We develop a scalable cell level model for such WLANs with saturated AP and STA queues as well as for TCP-controlled long file transfers . | fluency | 0.9989906 | 0903.0096 | 1 |
We develop a scalable cell level model for such WLANs with saturated AP and STA queues as well as for TCP-controlled long file transfers . | <meaning-changed> We develop a scalable cell level model for such WLANs with saturated AP and STA queues as well as for TCP-controlled long file transfers . | We develop a scalable cell level model for such WLANs with saturated AP and STA queues as well as for TCP-controlled long file downloads . | meaning-changed | 0.54756767 | 0903.0096 | 1 |
The accuracy of our model is demonstrated by comparison with ns-2 simulations. | <fluency> The accuracy of our model is demonstrated by comparison with ns-2 simulations. | The accuracy of our model is demonstrated by comparison with ns-2 simulations. | fluency | 0.9974502 | 0903.0096 | 1 |
Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | <clarity> Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | Based on the insights provided by our analytical model, we propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | clarity | 0.93931544 | 0903.0096 | 1 |
Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | <fluency> Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | fluency | 0.9993641 | 0903.0096 | 1 |
Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | <fluency> Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | fluency | 0.9993641 | 0903.0096 | 1 |
Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | <meaning-changed> Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{ in as many steps as there are channels. | meaning-changed | 0.68556637 | 0903.0096 | 1 |
Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | <meaning-changed> Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput in as many steps as there are channels. | Based on the insights provided by our analytical model, we also propose a simple decentralized algorithm which provides static channel assignments that are \textit{Nash equilibria in pure strategies for the objective of maximizing \textit{normalized network throughput normalized network throughput. Our channel assignment algorithm requires neither any explicit knowledge of the topology nor any message passing, and provides assignments in only as many steps as there are channels. | meaning-changed | 0.99944526 | 0903.0096 | 1 |
In contrast to prior work, our approach to channel assignment is based on the \textit{throughput metric . | <fluency> In contrast to prior work, our approach to channel assignment is based on the \textit{throughput metric . | In contrast to prior work, our approach to channel assignment is based on the \textit{throughput metric . | fluency | 0.9991936 | 0903.0096 | 1 |
We propose a new generic framework for option price modelling, using quantum neural computation formalism. | <clarity> We propose a new generic framework for option price modelling, using quantum neural computation formalism. | We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. | clarity | 0.99379975 | 0903.0680 | 1 |
Briefly, when we apply a classical nonlinear neural-network learning to a quantum linear Schr\"odinger equation, as a result we get a nonlinear Schr\"odinger equation (NLS), performing as a quantum stochastic filter. | <meaning-changed> Briefly, when we apply a classical nonlinear neural-network learning to a quantum linear Schr\"odinger equation, as a result we get a nonlinear Schr\"odinger equation (NLS), performing as a quantum stochastic filter. | Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schr\"odinger equation, as a result we get a nonlinear Schr\"odinger equation (NLS), performing as a quantum stochastic filter. | meaning-changed | 0.7214846 | 0903.0680 | 1 |
This stiff pair of NLS equations is numerically solved using the method of lines with adaptive step-size integrator. | <meaning-changed> This stiff pair of NLS equations is numerically solved using the method of lines with adaptive step-size integrator. | This stiff pair of NLS equations is numerically solved using the method of lines with adaptive step-size integrator. Keywords: Option price modelling, Quantum neural computation, nonlinear Schr\"odinger equations, leverage effect, bidirectional associative memory | meaning-changed | 0.9995764 | 0903.0680 | 1 |
After reviewing the strengthened hypotheses of the Shannon-MacMillan-Breiman Theorem, versus the standard statement of the Noiseless Coding Theorem, we state and prove a similar result for relative information , otherwise known as information gain. If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ). | <clarity> After reviewing the strengthened hypotheses of the Shannon-MacMillan-Breiman Theorem, versus the standard statement of the Noiseless Coding Theorem, we state and prove a similar result for relative information , otherwise known as information gain. If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ). | This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger ( 2002 ). | clarity | 0.9976096 | 0903.2243 | 1 |
If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ). The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). | <meaning-changed> If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ). The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). | If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy Coding Theorems, two of the most important results of Shannon's theory, we begin the paper by defining a pragmatic information rate, showing that all of the relevant limits make sense, and interpreting them as the improvement in compression obtained from using the correct distribution of transmitted symbols. The first of two applications of the theory extends the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). | meaning-changed | 0.99953854 | 0903.2243 | 1 |
The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races. | <coherence> The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races. | The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races. | coherence | 0.9965957 | 0903.2243 | 1 |
We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races. | <meaning-changed> We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races. | We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some stationary process, including, but not limited to the history of previous races. | meaning-changed | 0.92141885 | 0903.2243 | 1 |
Also, if the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings can be interpreted as the pragmatic information of the messages. | <coherence> Also, if the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings can be interpreted as the pragmatic information of the messages. | If the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings can be interpreted as the pragmatic information of the messages. | coherence | 0.9976284 | 0903.2243 | 1 |
Also, if the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings can be interpreted as the pragmatic information of the messages. | <clarity> Also, if the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings can be interpreted as the pragmatic information of the messages. | Also, if the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings is bounded by the pragmatic information of the messages. | clarity | 0.9977192 | 0903.2243 | 1 |
Both the theorem proven herein and the application to trading make a compelling case for Weinberger's definition of pragmatic information . | <meaning-changed> Both the theorem proven herein and the application to trading make a compelling case for Weinberger's definition of pragmatic information . | A second application is to the question of market efficiency. An efficient market is, by definition, a market in which the pragmatic information of the "tradable past" with respect to current prices is zero. Under this definition, markets whose returns are characterized by a GARCH(1,1) process cannot be efficient. Finally, a pragmatic informational analogue to Shannon's Noisy Coding Theorem suggests that a cause of market inefficiency is that the underlying fundamentals are changing so fast that the price discovery mechanism simply cannot keep up. This may happen most readily in the run-up to a financial bubble, where investors' willful ignorance degrade the information processing capabilities of the market . | meaning-changed | 0.99927574 | 0903.2243 | 1 |
In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field " ). Convergence also holds for optimal policies. | <fluency> In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field " ). Convergence also holds for optimal policies. | In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the `` optimal mean field " ). Convergence also holds for optimal policies. | fluency | 0.9993007 | 0903.2352 | 1 |
In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field " ). Convergence also holds for optimal policies. | <fluency> In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field " ). Convergence also holds for optimal policies. | In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field '' ). Convergence also holds for optimal policies. | fluency | 0.9985079 | 0903.2352 | 1 |
Inverse of the average dwell time satisfies a `` Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | <fluency> Inverse of the average dwell time satisfies a `` Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | Inverse of the average dwell time satisfies a " Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | fluency | 0.99936193 | 0903.2608 | 1 |
Inverse of the average dwell time satisfies a `` Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | <fluency> Inverse of the average dwell time satisfies a `` Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | Inverse of the average dwell time satisfies a `` Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | fluency | 0.99935764 | 0903.2608 | 1 |
Inverse of the average dwell time satisfies a " Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | <fluency> Inverse of the average dwell time satisfies a " Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | Inverse of the average dwell time satisfies a `` Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | fluency | 0.9993656 | 0903.2608 | 2 |
Inverse of the average dwell time satisfies a " Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | <fluency> Inverse of the average dwell time satisfies a " Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | Inverse of the average dwell time satisfies a " Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. | fluency | 0.99931216 | 0903.2608 | 2 |
We investigate the distribution of flavonoid , a major category of plant secondary metabolites, across species. | <fluency> We investigate the distribution of flavonoid , a major category of plant secondary metabolites, across species. | We investigate the distribution of flavonoids , a major category of plant secondary metabolites, across species. | fluency | 0.9994037 | 0903.2883 | 1 |
Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | <fluency> Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | Flavonoids are known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | fluency | 0.9993667 | 0903.2883 | 1 |
Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | <fluency> Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | Flavonoid is known to show high species specificity, and were once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | fluency | 0.9993754 | 0903.2883 | 1 |
Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | <fluency> Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of URLanisms. | Flavonoid is known to show high species specificity, and was once considered as chemical markers for understanding adaptive evolution and characterization of URLanisms. | fluency | 0.99912614 | 0903.2883 | 1 |
We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. | <fluency> We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. | We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved among several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. | fluency | 0.9982121 | 0903.2883 | 1 |
We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. | <fluency> We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. | We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power-law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. | fluency | 0.99937075 | 0903.2883 | 1 |
We provide an axiomatic foundation for the representation of numeraire-invariant preferences of agents acting in a financial market. | <meaning-changed> We provide an axiomatic foundation for the representation of numeraire-invariant preferences of agents acting in a financial market. | We provide an axiomatic foundation for the representation of numeraire-invariant preferences of economic agents acting in a financial market. | meaning-changed | 0.8978253 | 0903.3736 | 1 |
With the addition of a transitivity requirement, this last preference relation is extended to expected logarithmic utility maximization . | <meaning-changed> With the addition of a transitivity requirement, this last preference relation is extended to expected logarithmic utility maximization . | With the addition of a transitivity requirement, this last preference relation has an extension that can be numerically represented by expected logarithmic utility maximization . | meaning-changed | 0.99772745 | 0903.3736 | 1 |
With the addition of a transitivity requirement, this last preference relation is extended to expected logarithmic utility maximization . | <clarity> With the addition of a transitivity requirement, this last preference relation is extended to expected logarithmic utility maximization . | With the addition of a transitivity requirement, this last preference relation is extended to expected logarithmic utility . | clarity | 0.99880075 | 0903.3736 | 1 |
We also discuss the previous in a dynamic environment, where consumption streams are the objects of choice. | <clarity> We also discuss the previous in a dynamic environment, where consumption streams are the objects of choice. | We also treat the case of a dynamic environment, where consumption streams are the objects of choice. | clarity | 0.99900407 | 0903.3736 | 1 |
There, a novel result concerning a canonical representation of optional measures with unit mass enables one to explicitly solve the investment-consumption problem by completely separating the two aspects of investment and consumption. | <clarity> There, a novel result concerning a canonical representation of optional measures with unit mass enables one to explicitly solve the investment-consumption problem by completely separating the two aspects of investment and consumption. | There, a novel result concerning a canonical representation of unit-mass optional measures enables to explicitly solve the investment-consumption problem by completely separating the two aspects of investment and consumption. | clarity | 0.998747 | 0903.3736 | 1 |
There, a novel result concerning a canonical representation of optional measures with unit mass enables one to explicitly solve the investment-consumption problem by completely separating the two aspects of investment and consumption. | <clarity> There, a novel result concerning a canonical representation of optional measures with unit mass enables one to explicitly solve the investment-consumption problem by completely separating the two aspects of investment and consumption. | There, a novel result concerning a canonical representation of optional measures with unit mass enables one to explicitly solve the investment-consumption problem by separating the two aspects of investment and consumption. | clarity | 0.7290925 | 0903.3736 | 1 |
Finally, we give an application to the problem of optimal numeraire investment with a random-time horizon . | <fluency> Finally, we give an application to the problem of optimal numeraire investment with a random-time horizon . | Finally, we give an application to the problem of optimal numeraire investment with a random time-horizon . | fluency | 0.9993291 | 0903.3736 | 1 |
We provide an axiomatic foundation for the representation of numeraire-invariant preferences of economic agents acting in a financial market. | <fluency> We provide an axiomatic foundation for the representation of numeraire-invariant preferences of economic agents acting in a financial market. | We provide an axiomatic foundation for the representation of num\'{e preferences of economic agents acting in a financial market. | fluency | 0.598722 | 0903.3736 | 2 |
We also treat the case of a dynamic environment , where consumption streams are the objects of choice. | <fluency> We also treat the case of a dynamic environment , where consumption streams are the objects of choice. | We also treat the case of a dynamic environment where consumption streams are the objects of choice. | fluency | 0.99938595 | 0903.3736 | 2 |
There, a novel result concerning a canonical representation of unit-mass optional measures enables to explicitly solve the investment-consumption problem by separating the two aspects of investment and consumption. | <coherence> There, a novel result concerning a canonical representation of unit-mass optional measures enables to explicitly solve the investment-consumption problem by separating the two aspects of investment and consumption. | There, a novel result concerning a canonical representation of unit-mass optional measures enables us to explicitly solve the investment-consumption problem by separating the two aspects of investment and consumption. | coherence | 0.67275226 | 0903.3736 | 2 |
There, a novel result concerning a canonical representation of unit-mass optional measures enables to explicitly solve the investment-consumption problem by separating the two aspects of investment and consumption. | <fluency> There, a novel result concerning a canonical representation of unit-mass optional measures enables to explicitly solve the investment-consumption problem by separating the two aspects of investment and consumption. | There, a novel result concerning a canonical representation of unit-mass optional measures enables to explicitly solve the investment--consumption problem by separating the two aspects of investment and consumption. | fluency | 0.9992718 | 0903.3736 | 2 |
Finally, we give an application to the problem of optimal numeraire investment with a random time-horizon. | <fluency> Finally, we give an application to the problem of optimal numeraire investment with a random time-horizon. | Finally, we give an application to the problem of optimal num\'{e investment with a random time-horizon. | fluency | 0.9970409 | 0903.3736 | 2 |
Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | <fluency> Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions , which ultimately generate the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | fluency | 0.9994056 | 0903.4215 | 1 |
Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | <fluency> Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cells . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | fluency | 0.9993449 | 0903.4215 | 1 |