text
stringlengths 2
2.82M
⌀ |
|---|
#include <elle/das/tuple.hh>
#include <elle/test.hh>
#include <elle/serialization/json.hh>
#include <elle/das/Symbol.hh>
#include <elle/das/serializer.hh>
ELLE_DAS_SYMBOL(foo);
ELLE_DAS_SYMBOL(bar);
static
void
basics()
{
auto t = elle::das::make_tuple(foo = 3, bar = "lol");
BOOST_CHECK_EQUAL(t.foo, 3);
BOOST_CHECK_EQUAL(t.bar, "lol");
}
static
void
move()
{
elle::das::make_tuple(foo = elle::make_unique<int>(42),
bar = std::vector<int>());
auto f = elle::make_unique<int>(42);
auto b = std::vector<int>();
elle::das::make_tuple(foo = std::move(f), bar = b);
}
static
void
print()
{
auto t = elle::das::make_tuple(foo = 3, bar = "lol");
BOOST_CHECK_EQUAL(elle::sprintf("%s", t), "(foo = 3, bar = lol)");
}
static
void
serialize()
{
auto t = elle::das::make_tuple(foo = 3, bar = std::string("lol"));
auto s = elle::serialization::json::serialize(t);
auto j = elle::json::read(s.string());
BOOST_CHECK(j["foo"] == 3);
BOOST_CHECK(j["bar"] == "lol");
auto d = elle::serialization::json::deserialize<decltype(t)>(s);
BOOST_CHECK(d.foo == t.foo);
BOOST_CHECK(d.bar == t.bar);
}
static
void
hash()
{
using elle::das::make_tuple;
BOOST_TEST(
hash_value(elle::das::make_tuple()) ==
hash_value(elle::das::make_tuple()));
BOOST_TEST(
hash_value(elle::das::make_tuple(foo = 3, bar = std::string("lol"))) ==
hash_value(elle::das::make_tuple(foo = 3, bar = std::string("lol"))));
BOOST_TEST(
hash_value(elle::das::make_tuple(foo = 3, bar = std::string("lol"))) !=
hash_value(elle::das::make_tuple(foo = 4, bar = std::string("lol"))));
BOOST_TEST(
hash_value(elle::das::make_tuple(foo = 3, bar = std::string("lol"))) !=
hash_value(elle::das::make_tuple(foo = 3, bar = std::string("bar"))));
BOOST_TEST(
hash_value(elle::das::make_tuple(foo = 3, bar = std::string("lol"))) !=
hash_value(elle::das::make_tuple(bar = std::string("lol"), foo = 3)));
}
static
void
compare()
{
BOOST_TEST(
elle::das::make_tuple() ==
elle::das::make_tuple());
BOOST_TEST(
elle::das::make_tuple(foo = 3, bar = std::string("lol")) ==
elle::das::make_tuple(foo = 3, bar = std::string("lol")));
BOOST_TEST(
elle::das::make_tuple(foo = 3, bar = std::string("lol")) !=
elle::das::make_tuple(foo = 4, bar = std::string("lol")));
BOOST_TEST(
elle::das::make_tuple(foo = 3, bar = std::string("lol")) !=
elle::das::make_tuple(foo = 3, bar = std::string("bar")));
}
/*-------.
| Driver |
`-------*/
ELLE_TEST_SUITE()
{
auto& master = boost::unit_test::framework::master_test_suite();
master.add(BOOST_TEST_CASE(basics));
master.add(BOOST_TEST_CASE(move));
master.add(BOOST_TEST_CASE(print));
master.add(BOOST_TEST_CASE(serialize));
master.add(BOOST_TEST_CASE(hash));
master.add(BOOST_TEST_CASE(compare));
}
|
Questions or Need Help Related to The Hunting Report Newsletter.Call us at 800-272-5656 or 305-253-5301
Search:
HuntingReport.com
This news bulletin was sent exclusively to Email Extra subscribers of The Hunting Report at least 24 hours prior to becoming available to other viewers.
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New Move To open Hunting In Zambia
(posted December 17, 2001)
In a move that appears to signal a reopening of hunting next year,
the Zambia National Tender Board today officially asked safari operators
to submit bids for the control of the country's hunting concessions.
The deadline for submitting bids is January 4. "I'm definitely
taking this to mean hunting will reopen next year," Mike Faddy
told The Hunting Report this morning. Faddy is head of the Zambia
Professional Hunters Association, and he has his finger on the pulse
of hunting developments.
The other good news on hunting in Zambia is, a Director General
of Zambia Wildlife Authority (ZAWA) has finally been named. We hope
to have more information on the new director as early as tomorrow.
Suffice it to say, the new director is getting rave reviews so far.
The call for tenders is directly related to his being named, according
to sources we spoke with this morning.
ZAWA, you'll recall, is the new quasi-private organization that
was slated to take over all wildlife-related matters in Zambia more
than a year ago, which is when the old National Parks Department
was disbanded. Since then, Zambia has been without any kind of game
department at all. The European Union during this period has had
millions of dollars ready to help ZAWA get rolling, but has refused
to release the funds until a director general and support staff
are in place. Presumably those funds will now be released. If so,
Zambia's wildlife programs could be on their way to a complete recovery
shortly.
To be sure, there are some open questions still. The most important
revolves around the possible impact of the presidential election,
which is slated for December 27. Will the current tender process
be acceptable to whoever wins the election? Or will still another
tender process be initiated by the winner? No one we spoke with
had any idea how to answer those questions. In fact, no one we have
spoken with for months has been willing to predict just who will
win the election. It's no secret that the closure of hunting in
Zambia was linked to presidential politics. Surely, its reopening
will be too.
The other open question at this point is the condition of Zambia's
game. With no game department in place for more than a year, and
with concessions empty of personnel for an entire summer, poaching
has been widespread.
Doubts and questions aside, the underlying news here is good. A
definitive move has been made toward the reopening of hunting in
Zambia. We're hoping for the best, and we are keeping our fingers
crossed. More details soon. - Don Causey.
Get important news bulletins like this sent directly to your email 24 hours before anyone else sees them, plus unlimited access to our database of hunt reports and past articles, a special expanded electronic version of our newsletter and more! Upgrade your Hunting Report subscription to Email Extra today. Click here for more information. |
Self-assembled high-strength hydroxyapatite/graphene oxide/chitosan composite hydrogel for bone tissue engineering.
Graphene hydrogel has shown greatly potentials in bone tissue engineering recently, but it is relatively weak in the practical use. Here we report a facile method to synthesize high strength composite graphene hydrogel. Graphene oxide (GO), hydroxyapatite (HA) nanoparticles (NPs) and chitosan (CS) self-assemble into a 3-dimensional hydrogel with the assistance of crosslinking agent genipin (GNP) for CS and reducing agent sodium ascorbate (NaVC) for GO simultaneously. The dense and oriented microstructure of the resulted composite gel endows it with high mechanical strength, high fixing capacity of HA and high porosity. These properties together with the good biocompatibility make the ternary composite gel a promising material for bone tissue engineering. Such a simultaneous crosslinking and reduction strategy can also be applied to produce a variety of 3D graphene-polymer based nanocomposites for biomaterials, energy storage materials and adsorbent materials. |
From dissipative dynamics to studies of heat transfer at the nanoscale: analysis of the spin-boson model.
We study in a unified manner the dissipative dynamics and the transfer of heat in the two-bath spin-boson model. We use the Bloch-Redfield (BR) formalism, valid in the very weak system-bath coupling limit, the noninteracting-blip approximation (NIBA), applicable in the nonadiabatic limit, and iterative, numerically exact path integral tools. These methodologies were originally developed for the description of the dissipative dynamics of a quantum system, and here they are applied to explore the problem of quantum energy transport in a nonequilibrium setting. Specifically, we study the weak-to-intermediate system-bath coupling regime at high temperatures kBT/ħ > ε, with ε as the characteristic frequency of the two-state system. The BR formalism and NIBA can lead to close results for the dynamics of the reduced density matrix (RDM) in a certain range of parameters. However, relatively small deviations in the RDM dynamics propagate into significant qualitative discrepancies in the transport behavior. Similarly, beyond the strict nonadiabatic limit NIBA's prediction for the heat current is qualitatively incorrect: It fails to capture the turnover behavior of the current with tunneling energy and temperature. Thus, techniques that proved meaningful for describing the RDM dynamics, to some extent even beyond their rigorous range of validity, should be used with great caution in heat transfer calculations, because qualitative-serious failures develop once parameters are mildly stretched beyond the techniques' working assumptions. |
Circuitry for the positioning of the electron beam in CRT display systems such as exemplified by the M. S. Granberg, et al., U.S. Pat. Nos. 3,434,135 and 3,489,946 includes X and Y deflection coil current drive systems of various designs. These prior art systems include digital logic that selectively switches in or out constant current sources of individually fixed but separately different incremental current magnitudes or levels such that the desired deflection-determining current level is caused to flow through the X (and Y) deflection coil.
In CRT display systems, the cathode ray tube face is usually a flat surface. Equal increments of deflection-determining current move the electron beam along the face in increasing incremental lengths for increasing distances away from the center of the face producing a distortion called the "pin-cushion" or "non-linear effect." Prior art CRT display systems have included various correction features to compensate for such distortion. Aslo included were constant current drivers and electronic switches to maintain fixed increments of deflection-determining current and to prevent switching induced transients that further distort the display. The present invention is directed toward a CRT display system that eliminates these above noted causes of display distortion. |
Q:
Creating object in C++
I am new to C++. Here's my problem.
I declare bus, stepper as private instances in the h file:
class Motor_control
{
public:
...
private:
IICBus bus ;
IICStepper stepper ;
IICStepper stepper_r ;
IICStepper stepper_l ;
};
And then initiate them in the constructor
Motor_control::Motor_control(){
IICBus bus ("/dev/i2c-2",0,"");
IICStepper stepper (bus,0x00, "Global addr");
IICStepper stepper_r (bus,0x6e, "Stepper Modul");
IICStepper stepper_l (bus,0x66, "Stepper Modul");
}
IICStepper was declared in .cpp:
IICStepper::IICStepper(IICBus& bus, int addr, const string& name) : IICBase(bus,addr, name) { } in cpp
and in .h:
class IICStepper : public IICBase { public: IICStepper(IICBus& bus, int addr, const std::string& name); virtual ~IICStepper(){}; ...}
It compalins
../src/Motor_control.h:15: error: no matching function for call to 'IICStepper::IICStepper()'
../src/Stepper.h:41: note: candidates are: IICStepper::IICStepper(IICBus&, int, const std::string&)
../src/Stepper.h:38: note: IICStepper::IICStepper(const IICStepper&)
../src/Motor_control.h:15: error: no matching function for call to 'IICBus::IICBus()'
../src/Bus.h:28: note: candidates are: IICBus::IICBus(const std::string&, int, const std::string&)
../src/Bus.h:17: note: IICBus::IICBus(const IICBus&)
../src/Motor_control.h:15: error: no matching function for call to 'IICStepper::IICStepper()'
../src/Stepper.h:41: note: candidates are: IICStepper::IICStepper(IICBus&, int, const std::string&)
../src/Stepper.h:38: note: IICStepper::IICStepper(const IICStepper&)
../src/Motor_control.h:15: error: no matching function for call to 'IICStepper::IICStepper()'
../src/Stepper.h:41: note: candidates are: IICStepper::IICStepper(IICBus&, int, const std::string&)
../src/Stepper.h:38: note: IICStepper::IICStepper(const IICStepper&)
../src/Motor_control.h:15: error: no matching function for call to 'IICStepper::IICStepper()'
../src/Stepper.h:41: note: candidates are: IICStepper::IICStepper(IICBus&, int, const std::string&)
../src/Stepper.h:38: note: IICStepper::IICStepper(const IICStepper&)
A:
Before the constructor body enters, all user types are initialized. Because you don't have default constructors for IICStepper, you'll get the errors.
You need to use initializer lists:
Motor_control::Motor_control() :
bus("/dev/i2c-2", 0, ""),
stepper(bus, 0, "Global addr"),
stepper_r(bus, 0x6e, "Stepper Modul"),
stepper_l(bus, 0x66, "Stepper Modul")
{
}
Your version not only doesn't initialize the members, it creates new temporary objects which you never use afterwards.
|
Border problem: A pipeline of children
Jul. 15, 2014
|
A teenage boy looks out the window of his sleeping area on June 19, 2014, at the Instituto Nacional del Migracion, a municipal shelter in Reynosa, Mexico, for child migrants that is receiving growing numbers of children caught by Mexican authorities and will be deported to their countries of origin. / David Wallace, David Wallace/The Republic
by USA TODAY Network, USA TODAY
by USA TODAY Network, USA TODAY
According to the U.S. Customs and Border Protection agency, more than 47,000 unaccompanied children have crossed the border into the U.S. in the past fiscal year, a number that could double in the coming months. The vast majority of these kids are coming from the troubled Central American countries of Honduras, El Salvador and Guatemala.
The Arizona Republic has a team of journalists reporting from Central America and the McAllen, Texas-Mexico border working on a project that will attempt to fill in this pipeline from the impoverished neighborhoods these kids are leaving, to the Mexican-Guatemala border, then the rugged journey to the Rio Grande and the raft ride across the river, where they are almost immediately picked up by the Border Patrol.
Reporter Bob Ortega and photographer Michael Chow are reporting from Central America, based in San Salvador and Guatemala.
Reporter Daniel Gonzalez and photographer David Wallace are reporting from the Rio Grande Valley, both sides of the border, based in McAllen, Texas.
Upcoming stories:
Finding shelter. Many of the kids stop in shelters before they cross into the U.S. We will paint a picture with photos and words of the scene there. Do they know where their parents are? What do they expect in America?
Videos:
The team is making daily videos from reporting locales available via the Gannett Video Production Center (VPC). |
Schools' actual budget becomes clearer
A final accounting shows that cuts made in December were important.
For the past year, the most important question facing the Hernando County school system has been about the health of the district's budget.
It was a year during which the district had three budget directors: one who said the sky was falling, another who said there were no worries and a third who tried to sort out the truth.
It was a year in which then-superintendent John Sanders and the School Board at times didn't know whom to believe or where things stood. Eventually, they sought a middle road, agreeing in December to cut their budget back by $2.4-million.
Now, a final accounting of the books shows that the December cuts were much-needed but that a financial meltdown feared by some never materialized. In short:
The district spent $85.5-million last year on day-to-day expenses, about $100,000 less than the revenue it took in.
Before the cuts, the board was on pace to spend about $2-million more than it took in.
The cuts not only brought the budget in line but also added $143,000 to the district's slim rainy day reserve, which now stands at $1.3-million.
Medical costs in the school district's self-funded health insurance plan outstripped the money put into the plan by $2.9-million, creating an internal debt that must be repaid with cash that could otherwise be spent on the classroom.
The new numbers bring clarity to a budget that was anything but clear in the past year.
The fog developed when budget director Vince Benedict, who resigned last summer for health reasons, and Sara Perez, his successor, came to vastly different conclusions about the district's financial state.
Benedict, a veteran who relied on his experience and his insight as much as raw data, predicted that 2000-2001 would be a tight year. But, with some routine adjustments, he predicted that his final budget would prove accurate.
Perez, who put her faith in hard numbers instead of gut feelings, said Benedict's original budget was on pace to spend $5.9-million above its expected revenues.
Carol MacLeod, a former auditor who took over the budget office in December after Perez resigned for family reasons, was asked to sort out the truth.
By then, the board had cut its budget, enacted a hiring freeze and put strict limits on new spending. The cuts weren't devastating. But they were far more drastic than Benedict's past practice of covering shortfalls in one area of the budget with surpluses from other parts.
Jo Ann Hartge, who was president of the Hernando Classroom Teachers Association last year, said cuts meant the district wouldn't pay for substitute teacher's aides when regulars were out sick, leaving teachers to fly solo in crowded classrooms.
They meant that a handful of teachers working outside the classroom, including two that taught rookie teachers survival skills and helped struggling veterans improve, had to fill teaching vacancies. Their previous jobs were simply eliminated.
For a time, Hartge said, it also meant that supplies ranging from workbook materials to art supplies were hard to get and professional training was reduced. Toward the end of the year, things eased up some. But, Hartge said, "I don't want to repeat that again."
MacLeod has refused to declare a winner in the Perez-Benedict debate. But she has some thoughts on the problems in the budget.
Benedict, who was on chemotherapy for bladder and prostate cancer at the time, didn't leave any clear documentation of what early adjustments Perez needed to make to the budget.
At the same time, MacLeod said people overreacted to Perez's worst-case prediction that the budget was $5.9-million out of line. Even Perez knew that routine retirements and resignations would result in less-than-expected payroll spending, she said.
In the end, MacLeod said the school district was never in a budget "crisis." Budgets are spending plans, she said, and they are not etched in stone. By definition, they require constant tweaking. But she agrees that a $2.4-million cut is nothing to laugh at.
"I would have hoped we would have done our front-end work better so we wouldn't have needed to do that," MacLeod said. "But there is nothing wrong with that."
The school district faces two financial audits in the next few months that are mandated by the state. And MacLeod plans to give a clearer view of where the December cuts were made.
Both should shed further light on the budget.
For now, the district has an $86.8-million budget, slightly larger than last year's. But schools have been ordered to cut back on spending money they have discretion over -- one final safeguard to keep history from repeating itself.
- Times staff writer Robert King covers education in Hernando County and can be reached at 754-6127. Send e-mail to [email protected]. |
Q:
CSS to rotate an image/icon(spinner) in IE11
Css to convert an icon/image into spinner
add following properties to the class of that icon/image
.spinner{
-webkit-animation: load3 1.4s infinite linear;
animation: load3 1.4s infinite linear;
-ms-transform: translateZ(0);
transform: translateZ(0);
}
A:
add this to your CSS and you'll have a rotating image
@keyframes load3 {
from {
-ms-transform: rotate(0deg);
-moz-transform: rotate(0deg);
-webkit-transform: rotate(0deg);
-o-transform: rotate(0deg);
transform: rotate(0deg);
}
to {
-ms-transform: rotate(360deg);
-moz-transform: rotate(360deg);
-webkit-transform: rotate(360deg);
-o-transform: rotate(360deg);
transform: rotate(360deg);
}
}
|
In 5 Minutes, He Lets the Blind See - laex
http://www.nytimes.com/2015/11/08/opinion/sunday/in-5-minutes-he-lets-the-blind-see.html?_r=0
======
Elte
My mom used to tell me about a similar procedure she would perform to help
people with cateracts in Africa 30 years ago, so I'm a bit confused. I'm not
saying this isn't awesome or special, just a bit curious what has changed to
make it particularly special _now_.
EDIT: So I asked her, it seems the main difference is the new lens they're
putting in. With a cateract the lens is clouded and the essence of this
procedure is cutting out that lens so that light reaches the retina once more.
30 years back they did not have new lenses to put in though, so (quote) "we
would send everyone home with +10 glasses". She also recalls the expeditions
into Nepal going into the mountains to operate cateracts 14 consecutive days
full time even back then (takes a while to get up to 100.000 I suppose :]).
So it used to be they were getting people who saw nothing to see something.
Now they get people who see nothing to see really well, which is of course
huge.
~~~
eps
Lower cost, probably. But if your mom is around, perhaps just ask her instead
of HN?
~~~
Elte
That e-mail went out before I posted here, and I fully intend on providing the
answer myself ;). Should've probably made that more obvious. EDIT: Updated
with the answer!
------
stevetrewick
Quite a few things bug me about this piece.
>I’m on my annual win-a-trip journey, in which I take a university student
with me on a trip to the developing world to cover underreported issues.
Firstly, I don't think this is 'under reported', I've seen at least two full
length documentaries about this procedure in Nepal, the project has its own
Facebook page [0] and a Google search for 'Nepal cataract' turns up lots of
trad media results.
Secondly, if the author has taken a student to cover things, why aren't e
reading the student's piece ?
Lastly, the author - like most people who haven't undergone this type of
surgery - falls into the trap of breathlessly hailing this as a miraculous
cure for blindness. It's not. While the restored sight is absolutely better
than having cataracts and will indeed cheer you up in the immediate term, the
vision provided by the replacement lenses is a far cry from a person's natural
vision, for one thing these lenses have a fixed focus. Another issue is the
limited life span - eventually they fur up, but don't go hard like UV induced
cataracts - which necessitates replacement or laser surgery.
Humans - particularly the kind that live up mountains in Nepal - are adaptable
and can cope, but as someone who has had this surgery (and the follow up laser
surgery) it annoys me that reportage routinely fails to mention these kinds of
things.
In this particular case, it is also quite peculiar that the author fails to
point out that handing out a $5 pair of sunglasses would prevent the cataracts
in the first place (these are pretty much all UV induced). Education and
prevention in this respect _are_ very much under reported.
[0]
[https://www.facebook.com/cureblindness/](https://www.facebook.com/cureblindness/)
~~~
IkmoIkmo
> handing out a $5 pair of sunglasses would prevent the cataracts in the first
> place (these are pretty much all UV induced).
I've also heard that vitamin sufficiency prevents UV induced cataracts, is
this true and on what scale would vitamins be sufficient? Introducing a
particular crop with the particular vitamin to the local farmers, potentially
a GMO crop, or selling supplements or adding vitamins to food (e.g. in the
Netherlands I know virtually all bread has government-encouraged iodine to
prevent iodine deficiency illnesses and effects, not sure if it's a worldwide
standard, but iodising table salt is common practice for the majority of the
world, too) might be a practical alternative.
------
curiousAl
Modern (science-based) medicine is a miracle of biblical proportions.
~~~
fasteo
Cataract surgery is not exactly modern medicine. There are records [1] of
cataract surgery as far as 2500 BC, that is, more than 4000 years ago.
[1] [http://cdn.intechopen.com/pdfs/42710/InTech-
The_history_of_c...](http://cdn.intechopen.com/pdfs/42710/InTech-
The_history_of_cataract_surgery.pdf)
~~~
afsina
Removing the infected lens is something, replacing it with an artificial
intraocular lens implant is something else.
------
pmontra
Bypass of the NY login: original text from
[https://translate.google.com/translate?hl=es&sl=en&tl=es&u=h...](https://translate.google.com/translate?hl=es&sl=en&tl=es&u=http:%2F%2Fwww.nytimes.com%2F2015%2F11%2F08%2Fopinion%2Fsunday%2Fin-5-minutes-
he-lets-the-blind-see.html%3F_r%3D0&anno=2&sandbox=1)
------
rokhayakebe
This guy needs a kickstarter, or GoFundMe, or some other easy way to give him
$25. Imagine a "LET'S FREAKING END CATARACT BLINDNESS" movement.
~~~
_mgr
[http://www.hollows.org.nz](http://www.hollows.org.nz)
The Fred Hollows Foundation has been doing this since at least 1992 around the
world including Nepal where Dr. Hollows and Dr. Ruit worked closely together.
Unfortunately Dr. Hollows passed away years ago but the foundation continues
his work.
------
Kiro
I can recommend "Inside North Korea" (National Geographic) where he's treating
cataracts in NK.
------
ck2
I'm curious what $25 per eye translates into American healthcare prices?
$1000? $2500?
~~~
psykovsky
$25,000 probably.
|
TDP-43 regulates endogenous retrovirus-K viral protein accumulation.
The concomitant expression of neuronal TAR DNA binding protein 43 (TDP-43) and human endogenous retrovirus-K (ERVK) is a hallmark of ALS. Since the involvement of TDP-43 in retrovirus replication remains controversial, we sought to evaluate whether TDP-43 exerts an effect on ERVK expression. In this study, TDP-43 bound the ERVK promoter in the context of inflammation or proteasome inhibition, with no effect on ERVK transcription. However, over-expression of ALS-associated aggregating forms of TDP-43, but not wild-type TDP-43, significantly enhanced ERVK viral protein accumulation. Human astrocytes and neurons further demonstrated cell-type specific differences in their ability to express and clear ERVK proteins during inflammation and proteasome inhibition. Astrocytes, but not neurons, were able to clear excess ERVK proteins through stress granule formation and autophagy. In vitro findings were validated in autopsy motor cortex tissue from patients with ALS and neuro-normal controls. We further confirmed marked enhancement of ERVK in cortical neurons of patients with ALS. Despite evidence of enhanced stress granule and autophagic response in ALS cortical neurons, these cells failed to clear excess ERVK protein accumulation. This highlights how multiple cellular pathways, in conjunction with disease-associated mutations, can converge to modulate the expression and clearance of viral gene products from genomic elements such as ERVK. In ALS, ERVK protein aggregation is a novel aspect of TDP-43 misregulation contributing towards the pathology of this neurodegenerative disease. |
Murder of Anni Dewani
Anni Ninna Dewani (née Hindocha; 12 March 1982 – 13 November 2010) was a Swedish woman of Indian origin who was murdered while on her honeymoon in South Africa after the taxi in which she and her husband were travelling was hijacked.
Arrests were made in the days following the crime; hijackers Mziwamadoda Qwabe and Xolile Mngeni, and hotel receptionist Monde Mbolombo admitted to their involvement in an unintentionally fatal robbery and kidnapping. Facing life in prison, Qwabe and Mbolombo later changed their stories to allege the crime had been a premeditated murder for hire at the behest of Anni's husband Shrien Dewani. Taxi driver Zola Tongo initially claimed to be an innocent victim of the incident but, faced with the weight of evidence implicating him in the crime and in the wake of his fellow conspirators' allegations of a "murder for hire" plot, he too changed his story to allege the husband was the instigator. Attractive plea bargains were offered to the conspirators in exchange for future testimony in legal proceedings related to the crime. The allegation of the husband's involvement made global headlines; Shrien Dewani's supporters emphatically denied the accusations, saying it was "ludicrous" to suggest he had solicited an attack on his wife from the first taxi driver he met within hours of their arrival in Cape Town.
Zola Tongo pleaded guilty to murder in December 2010 and was sentenced to 18 years in prison. Mziwamadoda Qwabe pleaded guilty to murder in August 2012 and was sentenced to 25 years in prison. Xolile Mngeni was tried and convicted of murder in November 2012 and was sentenced to life in prison. Monde Mbolombo admitted his involvement but was offered immunity in exchange for testimony against the other men alleged to have been involved in the crime.
South African prosecutors formulated charges against Shrien Dewani based on the later-discredited confessions of Tongo, Qwabe and Mbolombo, who were found to have committed perjury. Charges were brought on the basis Anni had been the victim of a premeditated kidnapping and murder for hire that was staged to appear as a random carjacking at the alleged behest of her husband. Following a long legal battle, Shrien was extradited from the UK to South Africa to face trial. He was exonerated by a Western Cape High Court, which in December 2014 ruled there was no credible evidence to support the allegations against him nor to support the allegation the crime was a premeditated murder for hire.
Background
Anni Dewani
The Hindocha family was forced to leave Uganda in the early 1970s after the country's president Idi Amin expelled all Asians living there. They were granted residence in Sweden and settled in Mariestad, where their daughter Anni was born and raised.
Marriage
Anni Hindocha met Shrien Dewani in London in 2009; they maintained a long-distance relationship until Hindocha moved to the UK in March 2010, where they became engaged in May that year. The couple, whose relationship was sometimes troubled, married at Lake Powai near Mumbai, India, on 29 October 2010. They were planning to hold a civil ceremony in the UK in 2011 for friends who could not attend their wedding in India.
Robbery, kidnapping and murder
After landing at Cape Town International Airport on 7 November 2010, Dewani and her husband took a domestic flight and stayed at Kruger National Park for four nights. On 12 November, the couple returned to Cape Town International Airport, where they met and engaged taxi driver Zola Tongo to drive them to the five-star Cape Grace Hotel.
On 13 November, having retained Tongo as a tour guide, the couple were driven through the city in his VW Sharan into Gugulethu. Tongo drove past a BBQ restaurant (Mzolis) and they continued to Surfside Restaurant in Strand, where the couple dined. After their meal, Tongo drove the Dewanis back into Gugulethu. Shortly after turning off the main road, two armed men hijacked the vehicle. After driving a short distance, Tongo was ejected from the taxi. Shrien Dewani was robbed of his money, wallet, designer watch and mobile telephone, and after being driven for about 20 minutes, he was also ejected from the vehicle. On the street, a bystander assisted him by calling the police.
At 07:50 on 14 November, in Lingelethu West, Anni Dewani was found dead in the back of the VW Sharan taxi. She had suffered a single gunshot wound to her neck. Police later confirmed Anni's Giorgio Armani wristwatch, a white-gold and diamond bracelet, her handbag and her BlackBerry mobile telephone were missing, and assumed they were stolen. The items stolen in the robbery had an estimated value of R90,000.
Post-mortem examination, repatriation and cremation
Anni Dewani's body was taken to a Cape Town hospital. The post-mortem examination revealed bruising on her inner leg, indicating she had been involved in a struggle. It also indicated she had died from a single gunshot that passed through her hand and neck, severing an artery. There was no sign of sexual assault. On 17 November, Dewani's body was released by the South African authorities and returned to the United Kingdom on a British Airways flight, accompanied by her husband. Six months after her death, in a Hindu ceremony, her family scattered her ashes in her favourite area of the Vänern lake, close to her home town, Mariestad, Sweden.
Investigation: sequence of arrests and confessions
As a result of a palm print found on the abandoned taxi, Xolile Mngeni was arrested on Tuesday 16 November 2010. Mngeni made a videotaped confession in the presence of Captain Jonker of the South African Police Service, admitting involvement in a hijack, armed robbery and kidnapping operation. He described Shrien and Anni Dewani as victims and said Qwabe shot Anni Dewani during a struggle for her handbag.
Mziwamadoda Qwabe was arrested at around 01:00 on Thursday 18 November 2010 as a result of a tip-off from a trusted township informant. After initial denials, Qwabe was allowed to consult with arrested co-conspirators Mbolombo and Mngeni, and subsequently admitted involvement in the hijack, armed robbery and kidnapping. He described Shrien and Anni Dewani as victims. He changed his story during an interview recorded at 17:21 that day, saying the incident was a murder planned at the behest of Shrien Dewani.
Monde Mbolombo was arrested in the early hours of Thursday 18 November 2010 as a result of Qwabe providing his name to the police. After initially denying involvement, Mbolombo made a recorded confession at 16:30, admitting arranging a hijacking and armed robbery operation. The confession did not mention a planned murder or Shrien Dewani's involvement. The following day, Mbolombo changed his story, saying the operation was a planned murder at the behest of Shrien Dewani.
Taxi driver Zola Tongo reported the hijacking to a police station in Gugulethu after he was ejected from the vehicle, and made a statement saying he was an unknowing victim. On 17 November, Tongo gave a statement to Officer Hendrikse of the SAPS, again saying he was an innocent victim. The following day, Tongo appointed attorney William De Grass, and on Saturday 20 November he surrendered to police and said the operation was a planned murder that was staged to appear as a random hijacking at the behest of Shrien Dewani.
Media coverage
In South Africa, there was much media coverage of the case following the discovery of the body. With an economy reliant on tourism, tour operators reported an immediate drop in bookings as potential visitors became aware of the country's murder rate; on average, 46 per day. There were also concerns the killing would negate the goodwill resulting from the 2010 FIFA World Cup. The assignment of the Police Hawks team, and the early arrests, conviction and statement implicating Shrien Dewani led to increased media coverage.
BBC Panorama episode
An episode of the BBC television documentary series Panorama in March 2012 reported that the original South African post-mortem report showed the bullet that killed Anni Dewani had passed through her left hand followed by her chest, and that the wound on her neck was an exit wound. The report said the bullet left "an irregular gunshot exit wound", which suggested there had been a struggle. A second Panorama programme broadcast in September 2013 revisited the case and highlighted numerous inconsistencies between the physical evidence, witness testimony, and the South African prosecutors' purported version of events. In particular it said the forensic evidence had not been collected properly and that it indicated an accidental shooting during a struggle rather than a deliberate killing.
Trials, convictions and sentencing
Plea bargains
Mziwamadoda Qwabe and Zola Tongo were offered reduced sentences in exchange for guilty pleas and the promise of truthful testimony against Shrien Dewani and in other criminal proceedings related to the crime. These plea deals were granted in accordance with Section 105A of the Criminal Procedure Act. Monde Mbolombo was granted full immunity from prosecution in exchange for his promise of truthful testimony against Shrien Dewani and in other criminal proceedings related to the crime. This plea deal was granted in accordance with Section 204 of the Criminal Procedure Act.
Conviction and sentencing of Zola Tongo
On 7 December 2010, Zola Tongo appeared in the Western Cape High Court; in accordance with his plea deal under Section 105A of the Criminal Procedure Act, he pleaded guilty to the armed robbery, kidnapping and murder of Anni Dewani—crimes he alleged were committed at the behest of Shrien Dewani. According to the terms of his Section 105A agreement, Tongo was sentenced to 18 years in prison, contingent on him testifying truthfully against Dewani in any future legal proceedings.
Tongo was expected to give evidence in the trials of Mngeni and Qwabe in 2011 and 2012. Qwabe avoided trial by pleading guilty pursuant to a Section 105A plea deal. Tongo was not called as a witness at Mngeni's trial in 2012.
, Tongo was serving his 18-year sentence in Malmesbury Prison, and will be eligible for release in 2019.
Conviction and sentencing of Mziwamadoda Qwabe
In pre-trial hearings on 18 February at Wynberg Magistrates Court, counsel for Mziwamadoda Qwabe said the court was unable to provide a fair trial for his client. Thabo Nogemane said, "I am instructed that some unknown police officer assaulted him by means of a big torch. He was hit all over his body. He said the statement was a suggestion put to him by the police. They already had the allegations so they told him: 'Just sign here'. I wouldn't refer to it as a confession, just a statement." According to the terms of his Section 105A agreement, Qwabe was sentenced to 25 years in prison, contingent on him testifying truthfully in future legal proceedings relating to the case. Qwabe will be eligible for release in 2027.
Trial of Xolile Mngeni and surrounding events
In 2011, Mngeni's lawyer Vusi Tshabalala said his client had been suffocated with a plastic bag before signing a statement admitting his involvement in the killing, further saying police resorted to "irregular methods" because of the pressure they were under to solve the high-profile case. The start of Mngeni's trial was delayed, and on 13 June 2011 it was announced he had undergone brain surgery to remove a tumour.
Despite having admitted to his role in the robbery and kidnapping of Anni Dewani in a videotaped confession, Mngeni pleaded not guilty at the start of his 2012 trial, saying he had an alibi and was not at the scene of the crime. Mngeni's lawyers said his initial confession should be ruled inadmissible as evidence because it was allegedly extracted using torture. Justice Robert Henney ruled against Mngeni and said the confession was admissible. Before testifying in the Mngeni trial, key witness Monde Mbolombo read out a prepared statement confessing to lying in his two previous affidavits and promised to tell the truth when testifying.
On 19 November 2012, Mngeni was convicted of murder and sentenced to life in jail. The court accepted Mziwamadoda Qwabe's and Monde Mbolombo's version of events, according to which the crime was a contract killing. Mngeni was ruled to have been the person who shot Anni Dewani. The court's findings were superseded by the judgement in the later trial of Shrien Dewani, in which the court found the earlier determinations had been made on the basis of flawed forensic evidence, and perjury of Qwabe and Mbolombo, the two key witnesses.
In July 2014, it was confirmed that a medical parole application had been made for Mngeni, who was terminally ill with a brain tumour. He was denied parole and died in jail at the Goodwood Centre of Excellence on 18 October 2014.
Extradition and trial of Shrien Dewani
After a long legal battle, Shrien Dewani was extradited from the United Kingdom to South Africa on 7 April 2014. Upon arrival he was arrested, charged and ordered to stand trial for allegedly arranging the murder of his wife. He was charged with five offences; conspiracy to commit kidnapping, robbery with aggravating circumstances, murder, kidnapping and obstructing the administration of justice. He pleaded not guilty to all five charges.
Dewani's trial began on 6 October 2014. Under cross examination, the key witnesses who alleged Dewani's involvement—Zola Tongo, Mziwamadoda Qwabe and Monde Mbolombo—contradicted their previous statements and each other on most of the key elements of the "murder for hire" story. Tongo and Mbolombo were found to have fabricated telephone calls and text messages that did not exist and refused to identify a fifth conspirator referred to in taped recordings. Qwabe refused to explain to the court why Anni was driven into a residential area.
On 24 November 2014, after the close of the prosecution's case, Dewani's counsel argued for the case to be dismissed under Section 174 of the Criminal Procedure Act, citing a lack of credible evidence linking his client to the crime. On 8 December, the application for dismissal under Section 174 was granted by the Honourable Judge Traverso; Dewani was acquitted and exonerated of all involvement with the crimes. In her judgement, Traverso ruled there was no credible evidence linking Shrien Dewani to the crime and explained her ruling by saying:
The court overturned the finding of Justice Henney in the Mngeni trial, ruling that Xolile Mngeni could not have been the person who shot Anni, and that some of the key conclusions reached in the 2012 Mngeni trial were erroneous, being based on flawed forensic evidence and the admitted lies of Monde Mbolombo. The court also ruled that Monde Mbolombo had again committed perjury and would not be granted indemnity from prosecution. Judge Traverso said, "Before Mr. Mbolombo proceeded with his evidence, he delivered a pre-prepared speech which, from the record, appears to be virtually identical to a similarly emotive speech which he gave the court in the Mngeni trial, before blatantly lying about material aspects."
Monde Mbolombo
Monde Mbolombo has not been prosecuted or punished for his self-confessed role in the crime, nor for his self-confessed perjury whilst testifying. On 19 November 2015 the Director of Public Prosecutions decided Mbolombo could not be prosecuted.
Complaint about judicial conduct
On 22 January 2015, a complaint was lodged by the Higher Education Transformation Network (HETN), alleging judicial bias and prejudiced behaviour of Judge Traverso in the trial of Shrien Dewani. On 25 April that year, a Judicial Conduct Committee dismissed the HETN's complaint, describing it as "frivolous" and lacking in substance. The National Prosecuting Authority declined to appeal the judgement or lodge any complaint against Judge Traverso.
Coroner's inquest
After Shrien Dewani's exoneration in December 2014, Anni Dewani's family asked for a coroner's court in the UK to reopen the inquest into her death and to compel Dewani to publicly answer questions. On 9 September 2015, at Brent Coroner's Court in North London, Coroner Andrew Walker said he did not consider a full inquest was appropriate because a criminal trial had been conducted in South Africa. On 9 October, Walker confirmed there was insufficient cause to resume an inquest. He told the court he was prohibited from reaching a conclusion that was inconsistent with the findings of the South African courts.
Hindocha family statement
On 4 August 2018, Anni Hindocha's uncle, acting as spokesperson for the Hindocha family in response to media reports of Shrien Dewani's same-sex relationship, said: "We accept he did not murder Anni, but he lied to us and had a very secret gay life. He owes us an apology for his lies".
References
Category:2010 crimes in South Africa
Category:2010 in England
Category:Deaths by firearm in South Africa
Category:2010 murders in Africa
Category:People murdered in South Africa
Category:Swedish murder victims
Category:Swedish people murdered abroad
Category:Deaths by person
Category:Kidnappings in South Africa
Category:Swedish people of Indian descent
Category:2010s murders in South Africa |
@echo off
reg Query "HKLM\Hardware\Description\System\CentralProcessor\0" | find /i "x86" > NUL && set UNAME=i686 || set UNAME=amd64
set PATH=%PATH%;C:\Program Files\7-Zip;C:\Program Files\Git\bin
FOR /F "tokens=1 delims=" %%A in ('git describe --abbrev^=0 --tags') do SET VERSION=%%A
set DIR=%0\..\..
set DISTNAME=glitch-windows-%UNAME%-%VERSION%
set DISTDIR=%DIR%\dist\%DISTNAME%
mkdir %DISTDIR%
windres -i %DIR%\dist\glitch.rc -O coff -o %DIR%\cmd\glitch\glitch_rc.syso
go generate github.com/naivesound/glitch/cmd/glitch
go test github.com/naivesound/glitch/...
go vet github.com/naivesound/glitch/...
go build -ldflags "-H windowsgui" -o %DISTDIR%\glitch.exe github.com/naivesound/glitch/cmd/glitch
copy /y %DIR%\LICENSE %DISTDIR%\LICENSE.txt
xcopy /y %DIR%\API.md %DISTDIR%
xcopy /i /y %DIR%\examples %DISTDIR%\examples
xcopy /i /y %DIR%\samples %DISTDIR%\samples
cd %DIR%/dist
7z a %DISTNAME%.zip %DISTNAME%
|
Bacterial colonisation in the gut of Phlebotomus duboseqi (Diptera: Psychodidae): transtadial passage and the role of female diet.
Bacteria isolated from the gut of different developmental stages of Philebotomus duboseqi Neveu-Lcmaire, 1906 belonged almost all to aerobic or facultatively anaerobic gram-negative rods. In females, the highest bacterial counts were observed two days after bloodfeeding; seven days after bloodfeeding the bacterial counts returned to pre-feeding levels. Most isolates were identified phenotypically as Ochrobactrum sp. The distinctiveness and homogeneity of the phenotypic and genotypic characteristics of Ochrobactrum isolates indicated that they belonged to a single strain (designated AK). This strain was acquired by larvae from food and passaged transtadially: it was isolated from the guts of fourth-instar larvae shortly before pupation, from pupae as well from newly emerged females. Most other bacteria found in females were acquired from the sugar solution fed to adults. To determine if the midgut lectin activity may serve as antibacterial agent females were membrane-fed on blood with addition of inhibitory carbohydrates. No significant differences in bacterial infections were found between experimental and control groups and we suppose that the lectin activity has no effect on gram-negative bacteria present in sandfly gut. |
Q:
Rapidshare premium download (c#)
Is there a way to download a file using a rapidshare premium account with c# or java?
A:
RapidShare has an API you might want to look into.
|
Vitamin B12-binding proteins in serum and plasma in various disorders. Effect of anticoagulants.
Because of recent developments in the study of vitamin B12-binding proteins, the levels of the three serum binders were compared in serum and plasma samples from subjects with various disorders. The results allow the following conclusions: (1) As previously reported, transcobalamin (TC) III and to a lesser extent TC I are artifactually elevated in serum. The appear to be released in vitro during the clotting process, presumably from granulocytes. (2) Blood cells of patients with polycythemia vera release exceedingly large amounts of TC I and TC III in vitro. (3) The above findings support, but do not prove, at least a partial granulocytic source of TC I. Nevertheless, factors other than granulocytes influence TC I levels, as disorders characterized by increased TC I (most prominently chronic myelogenous leukemia but also several cases of cancer) manifest relatively little cellular release of TC I in vitro. (4) Despite the serum artifact, the serum abnormalities described in various conditions were seen in plasma also, even though the actual values of themselves were lower in plasma. The chief exception was TC III, which was elevated in plasma only in polycythemia vera (and in a few cases of leukocytosis). (5) EDTA-NaF anticoagulant is not suitable, as it causes plasma dilution, thus explaining previous reports of TC II level differences between serum and plasma. EDTA is therefore a preferable anticoagulant for vitamin B12-binding protein studies, although it too may not be ideal. |
1. Field of the Invention
The present invention relates to a drive unit for a hybrid vehicle.
2. Description of the Related Art
Electrically driven vehicles conventionally have been provided with a drive unit including a drive motor, a generator-motor and an inverter unit. Further, in the inverter for the drive motor formed by a bridge circuit, direct current supplied from a battery is converted into three phase alternating current, and the alternating current is supplied to the drive motor. Further, by an inverter for the generator-motor, formed by a bridge circuit, three phase alternating current supplied from the generator-motor is converted into direct current and the direct current is supplied to the battery.
A pulse-width modulating signal is generated by the control unit and that signal is output to the respective bridge circuits to thereby switch transistors of the respective bridge circuits.
However, it has previously been necessary to provide for separate connection of an inverter to the drive motor and of an inverter to the generator-motor and, accordingly, the drive unit must be sufficiently sized to accommodate such connections.
Further, with a smoothing condenser, common to the respective bridge circuits, for stabilizing voltage generated when the transistors of the respective bridge circuits are switched ON and OFF, the lead wires connecting the respective transistors with the drive motor and the generator-motor are lengthy and the wiring is complicated.
Further, particularly in a drive unit in which a drive motor and a generator-motor are arranged on two different axes, there is no design integrating the inverter for the drive motor, the inverter for the generator-motor and the drive unit casing so that the drive unit is necessarily large-sized. |
This is a hybrid collective/class action FLSA/Pennsylvania state minimum wage law case arising from work in the gas fields of our region. The Court has previously written on matters related to this case, including substantial recitations of the underlying facts, so they will not be repeated here.
By prior Order, the Court authorized the mailing of notice of FLSA opt-in procedures to certain current and former employees of the Defendant related to certain of its Pennsylvania operations, and its facility in Decatur, Texas. The opt-in period will soon expire, and the Court directed the parties to meet and confer and to then submit a proposed case management order relating to further pretrial activities, including discovery. Counsel has met to do that, and while many matters relative to such an Order have been agreed upon, not all were, so the Court convened an extensive status conference with counsel in an effort to resolve those open issues. Some were, and some were not, and after consideration of the positions and proposals of each party, the Court will enter the Third Amended Case Management Order ("Order") of this date.
The Court provides this Opinion in order to explain its rulings on some of the disputed matters, and to set out its further expectations of counsel.
Counsel for the Plaintiffs has urged the Court to permit somewhat more limited discovery followed by comparatively prompt summary judgment practice as to the application (or not) of the "Motor Carrier Exemption" to the FLSA in this case, contending that doing it that way would protect the material interests of the parties, would foster fruitful settlement discussions, and would minimize anticipated costs. Counsel for the Defendants, on the other hand, says that unless and until discovery as to a significant portion of the actual/potential claimants occurs, his clients cannot fairly and accurately assess the likelihood or magnitude of liability, [1] something necessary both to defend the case and to be in any position to meaningfully think about (let alone discuss) potential settlement. Defendants also point out that for quite some time now, the Plaintiffs have propounded, and the Defendants have responded to, lots of "paper" discovery (100 interrogatories and requests for production of documents). Without saying so directly, the Defendants seem to contend that just as they are getting into the discovery they think that they need to both size up and fully litigate or settle the case, the Plaintiffs are urging that discovery now be truncated, when doing so would be inappropriate and would materially prejudice them.[2]
Given the current status of this case, the discovery and proceedings to date, the procedural posture of the proceedings, the complexity of the factual and legal issues resolved and to be resolved, and what the Plaintiffs say may well be the amount in controversy, the Court concludes that the Defendants have somewhat the better of the argument, and that further discovery as authorized by the Order is appropriate to permit the parties to prepare and advance their claims and defenses, which will also facilitate meaningful ADR proceedings.
The currently open issues seem to come in several categories: pretty significant (location of depositions), somewhat important (the number of certain discovery requests and dates for amendments to pleadings), rather unusual (what to do if deponents just don't show up as noticed?), and essentially meaningless (must reply briefs to summary judgment motions coming months from now be filed, if at all, in 14 or 20 days?).
As to the identity and location of depositions, the Court will direct that counsel meet and confer (a teleconference or video conference is OK), and come up with a "master list" of all anticipated deponents for both sides. Once that is done, counsel should endeavor to group them by day/series of days to cut down on travel costs for all concerned, and also to determine whether they can be handled by video, [3] and if not, where is the most logical, fair, economical place for those depositions.
As to "in-person" depositions, if they are to occur, they should be done where they are most logical, convenient and cost-effective. While the Defendant is correct in the broader sense that plaintiffs should ordinarily be deposed in the judicial district where an action is pending, that is not necessarily the case here. The nature of the business and operations involved here presumed that crews will move around. While those persons that opt-in as Plaintiffs in a FLSA case are just that, "party plaintiffs" (to use the verbiage of 29 U.S.C. § 216(b)), if they are no longer present here, and there is no reasonable anticipation that they will be returning here in the near future, and it is reasonable to depose them along with other deponents in a single location elsewhere, that may be the "just, speedy, and inexpensive" thing to do.[4] By the same token, such persons are, by statute, "party plaintiffs", so they have some responsibility to participate in the lawsuit that they have joined. The long and short of it is that counsel should apply logic and reason to resolving such locational matters, and any thorny issue as to such matters as to which reasonable minds could differ can be resolved by the Court.
As to the number of "paper" discovery requests, the Court has considered the proposals of each side, and the Order issued this date strikes what is in the Court's judgment the appropriate balance of interests given the nature and context of the case.
The parties have attempted to address the circumstance of a deponent failing to appear for a noticed deposition. As the Court observed at a recent status conference, just not showing up at a deposition is a new concept for the Court, and one not countenanced by the Civil Rules. The Order issued by the Court provides what appears to be a mechanism for the parties to confirm the dates/time/attendance of depositions and deponents that is structured to avoid the incurring of unnecessary costs and preparation. In these regards, the Court would also note that it expects any party or witness of a party in this litigation to show up when and where they are supposed to be, absent extenuating, unavoidable/unexpected circumstances. That is one of the responsibilities of being a party in a federal lawsuit, and it will be enforced here.
As to the "date" for the filing of any motions for leave to file amended pleadings, the Court believes that prevailing Circuit law requires that it give rather wide latitude for the filing of such motions. Of course, any such motion may well be met with vigorous opposition if the proposed amendment causes real prejudice to the substantial rights of a party, would result in the avoidable duplication or delay in the disposition of the case, complication or repetition of discovery, or other issues that the law recognizes are properly considered in the grant or denial (or limitation) of any amendment effort. Should such a motion be filed, any opposing party will be given plenty of time to respond, and the Court will then rule on the merits of such motion to amend.
Finally, the Court has in the Order resolved the minor, rather meaningless differences in timelines for the filing of briefs that would be due months from now.
The Court finds and concludes that the Third Amended Case Management Order Dated this date complies with the applicable provisions of the Federal Rules of Civil Procedure, does not prejudice the material interests of the parties, is consistent with the nature and context of this civil action, and furthers the just, speedy and inexpensive disposition of this action.
An appropriate Order will be entered.
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Last Thursday at Comic-Con, Guillermo del Toro (Hellboy, Pan’s Labyrinth) announced that he will co-write and produce–and may also direct–a movie based on Disney’s Haunted Mansion attraction. He also took pains to emphasize that it will have no relationship to that hideous Eddie Murphy thing.* And thank gawd for that.
It’s apparently going to be family-oriented but “scary.” Walt Disney Studios also unveiled a new piece of artwork for the movie (seen above, with a larger version at the Disney blog), which looks promising.
I’m assuming the story will be based on the whole “phantom bride” thing that’s hinted at in Disneyland’s version of the ride and fleshed out more fully in EuroDisney’s Phantom Manor. Given del Toro’s fantastical imagery in his other movies, this could really be pretty cool. |
Q:
How to check if QSpinBox value changed by keyboard or buttons(mouse wheel)
I need to set spinbox value to one of 1, 10, 100, 1000, 10000 if value changed by spinbox buttons or mouse wheel or up or down keys. But if value changed by keyboard I need other behavior.
Here is my code for buttons, mouse wheel, up and down keys.
void Dlg::onValueChanged(int value)
{
if (value > _value)
value = (value - 1) * 10;
value = log10(value);
value = _Pow_int(10, value);
_ui->spinBoxs->setValue(_value = value);
}
How can I make other behavior for value changing by keyboard?
A:
In this case I think you will have create your custom spinbox derived from QSpinBox. And you will need to reimplement at least the following functions:
virtual void keyPressEvent( QKeyEvent* event );
virtual void wheelEvent( QWheelEvent* event );
with your specification.
|
Feedback wanted: Any demand for 18x24 Business Model Canvas posters? - mgav
http://aintnojive.com/
======
mgav
@rman666 - Thank you! Yes, I wanted to print the free PDF on Friday last week,
so I looked on the Kinkos website (and a host of others) and all showed $45-
to $50- for one 20x24 poster, which seemed ridiculous and made me think there
might be something here. Based your experience, it's now obvious there isn't.
I'll zip to Kinkos, spend $4 and be on my way. THANK YOU AGAIN!
------
mgav
Thank you for generously sharing your feedback about whether anyone wants
these or not (better to find out now, before buying inventory)
------
rman666
The BMC is a free PDF. I took it to FedEx (Kinko's) and they printed it 18x24
for $4.
|
Everyone knows there are gays and lesbians in everybodys family. And no office would be complete without a sassy gay character. And just about every other kid in high school is wresting with his sexuality. I know. I watch TV.
Except it isnt true, and the Centers for Disease Control just proved it. A new comprehensive study by the CDC with over 33,000 participants has confirmed earlier estimates; less than 3 percent of the U.S. population self-identifies as gay, lesbian or bisexual. Earlier, much smaller-scale surveys have put that number at 4 percent.
The National Health Interview Survey (NHIS), published July 15 by the CDC, was the first large-scale study of its kind. Data was collected from the Census Bureau, as The Washington Post reported, and 33,557 adults between the ages of 18 and 64 participated in the study, which included in-person interviews as well as follow-up phone questions.
The NHIS study found that, while 96.6 percent of adults identified as straight, 1.6 percent identified as gay or lesbian, and 0.7 percent called themselves bisexual. 1.1 percent responded I dont know or said they were something else not listed.
That sure doesnt sound like society according to Hollywood, or the news media, which have young Americans convinced 30 percent of the population is gay.
Maybe thats because gay characters pop up in just about every product out of Hollywood. Men dress as women, give lap dances to other men and even get married in national awards shows likethe Grammys and Tony Awards. Media festivals likeSouth by Southwest and Sundance celebrate gay sex and all other kinds of relationships as completely normal. TV shows like Modern Family, The New Normal and The Fosters attempt to show that gay families are just as common and normal as any other family.
The news media does their part too. CNN has a particularly cozy relationship with GLAAD, the gay speech police. CNNs Paul Begala claimed in 2011, One out of 10 Americans is gay...At Least 10 percent of us are gay or lesbian. The media attacks businesses and churches as being out of step with reality, and calls for childrens organizations like the Boy Scouts to include gay scout leaders.
Meanwhile the media highlights stories of transgender toddlers and invokes pity for the handful of gay students who go to Christian colleges and are open about their sexuality, then complain when they are asked to abide by the schools religious rules.
Gay activists who say hateful things get a pass from the media too. Take Dan Savage, who has said all kinds of vile comments towards conservatives, Christians, and women, yet the media ignores his hate. The moment a Christian refers to the Bible on homosexuality, the media relentlessly attacks the person, their family, and tries to take away their livelihood. They did that with Phil Robertson of Duck Dynasty and Chic-Fil-As Dan Cathy.
A much higher percentage of the population believes marriage should be between man and a woman. The annual March for Marriage is the largest march of its kind yet themedia refuse to report on it each year.
I'm really getting tired of being reminded that about 3% of men like to ---- other men everywhere I turn. All the time, everywhere. Can't watch TV, can't see a movie, can't go to the store, can't go to work, can't watch a damn cartoon even!
"Have a nice day 'cause about 3% of men like to ---- other men!" "Would you like a free appetizer? We're having a special because about 3% of men like to ---- other men." "The all new 2015 POS Sedan! Because about 3% of men like to ---- other men!" "On the next "All My Widgets" Steve and Kim discuss how about 3% of men like to ---- other men." "And now the news. Our top story again tonight- Approximately 3% of men still like to ---- other men." At work- "This month is '3% of Men Like to ---- Other Men' Month."
It's really getting aggravating. Seriously. It is now literally impossible for me to go 24hrs and not be reminded by something or someone that anal sex between dudes is a 'thing.' And I bet gay advocates think that is just peachy.
The word “gay” is misunderstood. It is a self-identifier. It is possible that the number of men that have or have had sex with another man is 10% and the number of “gay” people are still 2%. So really, it is all about how the question is asked. Young, “heterosexual” women have been having sex with each other at high rates for about 20 years. Now, young heterosexual men are doing it and that is of particular concern given the public health fallout.
Well, it would be fair to say that whatever the answer is, politics is not it.
I say that the answer is faith, which is something that goes beyond “religion” and even transcends it. I used to think people were quibbling who made a distinction between faith and religion, but now I know from experience it isn’t a quibble. Religion is all outward. It doesn’t guarantee that there is anything in the heart behind it. Faith is inward... in fact it results when you actually believe that God loves you. Religion could be a response to a conviction that either God does not care or is chiefly bent on hating you.
19
posted on 07/15/2014 11:08:58 AM PDT
by HiTech RedNeck
(Embrace the Lion of Judah and He will roar for you and teach you to roar too. See my page.)
I don’t call them “gay”. That is a bastardazation of the word. Similar to the rainbow flag. I call them queers. And so do a lot of FReepers. The word gay and the rainbow has been usurped by the homos and is now engrained with the connection of that life style. The same way the swastija became synonomis with the Nazi party. It’s inseperable. I prefer to call them what they really call themselves, queers. And as for their use of the term gay marriage, THAT is a huge misnomer. Whatever it is, it IS NOT a true marriage.
31
posted on 07/15/2014 11:56:14 AM PDT
by NCC-1701
(You have your fear, which might become reality; and you have Godzilla, which IS reality.)
Everyone knows there are gays and lesbians in everybodys family. And no office would be complete without a sassy gay character. And just about every other kid in high school is wresting with his sexuality. I know. I watch TV.
Except it isnt true, and the Centers for Disease Control just proved it. A new comprehensive study by the CDC with over 33,000 participants has confirmed earlier estimates; less than 3 percent of the U.S. population self-identifies as gay, lesbian or bisexual. Earlier, much smaller-scale surveys have put that number at 4 percent.
The National Health Interview Survey (NHIS), published July 15 by the CDC, was the first large-scale study of its kind. Data was collected from the Census Bureau, as The Washington Post reported, and 33,557 adults between the ages of 18 and 64 participated in the study, which included in-person interviews as well as follow-up phone questions.
The NHIS study found that, while 96.6 percent of adults identified as straight, 1.6 percent identified as gay or lesbian, and 0.7 percent called themselves bisexual. 1.1 percent responded I dont know or said they were something else not listed.
Maybe thats because gay characters pop up in just about every product out of Hollywood. Men dress as women, give lap dances to other men and even get married in national awards shows likethe Grammys and Tony Awards. Media festivals likeSouth by Southwest and Sundance celebrate gay sex and all other kinds of relationships as completely normal. TV shows like Modern Family, The New Normal and The Fosters attempt to show that gay families are just as common and normal as any other family.
Meanwhile the media highlights stories of transgender toddlers and invokes pity for the handful of gay students who go to Christian colleges and are open about their sexuality, then complain when they are asked to abide by the schools religious rules.
Gay activists who say hateful things get a pass from the media too. Take Dan Savage, who has said all kinds of vile comments towards conservatives, Christians, and women, yet the media ignores his hate. The moment a Christian refers to the Bible on homosexuality, the media relentlessly attacks the person, their family, and tries to take away their livelihood. They did that with Phil Robertson of Duck Dynasty and Chic-Fil-As Dan Cathy.
A much higher percentage of the population believes marriage should be between man and a woman. The annual March for Marriage is the largest march of its kind yet themedia refuse to report on it each year.
But Major League Baseball just deemed that 3% so important to America's game that Bud Selig named Billy Bean as Ambassador for Inclusion. Not a single major leaguer identifies himself as gay, but Bean is desperately needed to "help create educational initiatives against sexism, homophobia and prejudice, presenting at annual events like the winter meetings and rookie career development program."
It’s less than 1%. And that 1% has changed what the definition of marriage was since the beginning of recorded history. None of this degenerate, immoral garbage would would have happened if not for the election of the homosexual in the White House, wiht an assist from the spineless, worthless republicans cowering down to him like a dog in heat.
Disclaimer:
Opinions posted on Free Republic are those of the individual
posters and do not necessarily represent the opinion of Free Republic or its
management. All materials posted herein are protected by copyright law and the
exemption for fair use of copyrighted works. |
Q:
Why is a (non-)degenerate semiconductor called (non-)degenerate?
In a non-degenerate semiconductor with (Ec-Ef) > 4kT separation, Maxwell-Boltzmann distribution can be used for simplification. I do not get why the term non-degenerate is used in this context? Degeneracy refers to multiple states having equal energies. Does the term degeneracy have different meanings in different contexts? Points where different bands cross are also referred to as degenerate points. At high dopings, dopants also form a band which can interact with the semiconductor bands. Is this interaction (band crossing) causing the degeneracy leading to a the term degenerate semiconductor? Can someone shed some light on this concept of degeneracy?
Thanks
A:
When used in reference to a semiconductor, the term "degenerate" means that it is doped so much that the material has metallic properties such as a Fermi surface and high electrical conductivity.
To be strictly correct, it is more appropiate to say that the semiconductor "has degenerate electron statistics" when said statistics are only appropiately described by a Fermi-Dirac distribution at thermal equilibrium, which is the case when the semiconductor is highly doped. However, the phrase "degenerate semiconductor" is considered acceptable shorthand for the term "semiconductor with degenerate electron statistics".
Evidently, this concept of degeneracy is different from the degeneracy of energy states, in which the term is also often used in solid-state physics. However, the degeneracy of the energy of the eigenstates of a Hamiltonian is just an instance of a broader mathematical concept of degeneracy, which applies when multiple members of a set share a common characteristic, such as the value of their energy. Off the top of my head, a classical system of coupled harmonic oscillators may have degenerate oscillation modes, sharing a common frequency. Propagating electromagnetic modes in a waveguide can be said to be degenerate if they have the same propagation constant.
The concept of degenerate electron bands, as you say, is then that of two different bands which share states with common Bloch wave vector (up to the addition of a reciprocal lattice vector) and energy. This concept is clearly different from that of the degeneracy of the electron statistics of a doped semiconductor, which, again, qualifies if Fermi-Dirac statistics are necessary to describe the occupation of electronic states in thermal equilibrium.
|
Contents
Following the independence of Bangladesh in 1971, Manabendra Narayan Larma founded the Parbatya Chattagram Jana Samhati Samiti (PCJSS) on February 15, 1972, seeking to build an organization representing all the tribal peoples of the Chittagong Hill Tracts. Larma was elected to the BangladeshJatiya Sangsad, the national legislature of Bangladesh as a candidate of the PCJSS in 1973.[4] When Larma's continued efforts to make the government recognize the rights of the tribal peoples through political discussions had failed,[5] Larma and the PCJSS began organizing the Shanti Bahini (Peace Corps), an armed force operating in the Hill Tracts area. It was formed in 1972 and fought for many years against the government.[6]
Members of Shanti Bahini in Khagrachari on 5 May 1994.
Shanti Bahini began attacking Bangladesh Army convoys in 1977.[7] They carried out kidnappings and extortion.[8][9][10] Larma subsequently went into hiding from government security forces.[8][10] Factionalism within the PCJS weakened Larma's standing and he was assassinated on November 10, 1983.[8][10] On 23 June 1981 the Shanti Bahini attacked a camp of Bangladesh rifles, killing 13 people. They later captured and executed 24 members of the Bangladesh rifles.[11] In the 1980s the Government of Bangladesh started to provide land for thousands of landless Bengali . Many Bengali were forced to move to secure regions because of the insurgency, abandoning their land to the tribal communities.[12] On 29 April 1986, Shanti Bahini massacred 19 Bengali.[13][14] On 26 June 1989 the Shanti Bahini burned down villages where inhabitants had voted in Bangladeshi elections.[15] In 1996 Shanti Bahini abducted and killed 30 Bengali.[16] On 9 September 1996, the Shanti Bahini massacred a group of Bengali woodcutters, who were under the impression they'd been called to a meeting.[17] Members of Shanti Bahini extorted some four million dollars from the local population in the name of toll collection.[18]
The Shanti Bahini abandoned militancy when the Bangladesh Awami League negotiated the Chittagong Hill Tracts Peace Accord between the government and the PCJSS on 2 December 1997.[19] Members of Shanti Bahini surrendered their weapons in a stadium in Khagrachari. The treaty saw the lifting of nighttime curfew and the return of 50 thousand refugees.[20] However, some members opposed to the peace deal formed a dissident group.[21] Some of those who opposed the peace treaty formed the United People's Democratic Front as an alternate to the PCJSS.[22] The treaty was also criticised by the Bangladesh Nationalist Party[23] and has not been fully implemented.[24] Some members of Shanti Bahini became police officers after the peace treaty. On November 2012, two of those members of Bangladesh police were arrested for stealing ammunition from the police.[25] On August 2014 Indian security forces arrested members of Shanti Bahini, two Bangladeshi and three Indian nationals, with weapons in Mizoram.[26]
The spokesman for the Shanti Bahini, Bimal Chakma alleged Indian involvement by stating that after the assassination of Sheikh Mujibur Rahman and the removal of Bangladesh Awami League from power in 1975, [27] India provided support and shelter to the members of Shanti Bahini.[28][29][30] Members of Shanti Bahini were trained in Chakrata, India.[31][32] |
Phase-dependent excitation and ionization in the multiphoton ionization regime.
We theoretically study the dependence of atomic excitation and ionization on the carrier envelope phase of few-cycle laser pulses in the multiphoton ionization regime. Our theoretical results for the hydrogen atom based on the solution of the 3D time-dependent Schrödinger equation show that the strong phase dependence can be seen in not only total ionization, but also bound-state population under the weak laser intensity regime. |
Q:
How to do in-code bindings on Windows Phone 8
I'm trying to do in-code binding on Windows Phone 8, like in the question "How to do CreateBindingSet() on Windows Phone?"
How to do CreateBindingSet() on Windows Phone?
I think I have done the steps as suggested by Stuart, but I keep getting exception error or output error
"MvxBind:Warning: 9,86 Failed to create target binding for binding _update for TextUpdate"
In Droid it works very well, so what am I doing wrong, missing or don't see?
Any suggestions?
I have the following setup in the Phone part.
Setup.cs:
using Cirrious.CrossCore.Platform;
using Cirrious.MvvmCross.BindingEx.WindowsShared;
using Cirrious.MvvmCross.ViewModels;
using Cirrious.MvvmCross.WindowsPhone.Platform;
using Microsoft.Phone.Controls;
namespace DCS.Phone
{
public class Setup : MvxPhoneSetup
{
public Setup(PhoneApplicationFrame rootFrame) : base(rootFrame)
{
}
protected override IMvxApplication CreateApp()
{
return new Core.App();
}
protected override IMvxTrace CreateDebugTrace()
{
return new DebugTrace();
}
protected override void InitializeLastChance()
{
base.InitializeLastChance();
var builder = new MvxWindowsBindingBuilder();
builder.DoRegistration();
}
}
}
ServerView.xaml:
<views:MvxPhonePage
x:Class="DCS.Phone.Views.ServerView"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:phone="clr-namespace:Microsoft.Phone.Controls;assembly=Microsoft.Phone"
xmlns:shell="clr-namespace:Microsoft.Phone.Shell;assembly=Microsoft.Phone"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:views="clr-namespace:Cirrious.MvvmCross.WindowsPhone.Views;assembly=Cirrious.MvvmCross.WindowsPhone"
xmlns:converters="clr-namespace:DCS.Phone.Converters"
FontFamily="{StaticResource PhoneFontFamilyNormal}"
FontSize="{StaticResource PhoneFontSizeNormal}"
Foreground="{StaticResource PhoneForegroundBrush}"
SupportedOrientations="Portrait" Orientation="Portrait"
mc:Ignorable="d"
shell:SystemTray.IsVisible="True">
<!--LayoutRoot is the root grid where all page content is placed-->
<Grid x:Name="LayoutRoot" Background="Transparent">
<!--used as dummy bool to call Update callback through converter -->
<CheckBox x:Name ="DummyUpdated" Height ="0" Width ="0" Content="" Visibility="Visible" IsChecked="{Binding TextUpdate, Converter={StaticResource Update }, ConverterParameter=ServerView}"></CheckBox>
<ScrollViewer x:Name="ScrollView" Height="760" Width ="480" VerticalAlignment="Top">
<Canvas x:Name="View" Top="0" Left="0" Margin ="0" Background="Transparent" Height="Auto" Width ="Auto"/>
</ScrollViewer>
</Grid>
</views:MvxPhonePage>
ServerView.xaml.cs:
using System.Windows;
using Cirrious.MvvmCross.Binding.BindingContext;
using Cirrious.MvvmCross.WindowsPhone.Views;
using DCS.Core;
using DCS.Core.ViewModels;
using DCS.Phone.Controls;
namespace DCS.Phone.Views
{
public partial class ServerView : MvxPhonePage,IMvxBindingContextOwner
{
private bool _isUpdating;
private bool _update;
private DcsText _text;
private DcsInput _input;
private DcsList _list;
private DcsButton _button;
public IMvxBindingContext BindingContext { get; set; }
public ServerView(){
InitializeComponent();
BindingContext = new MvxBindingContext();
Loaded += new RoutedEventHandler(MainPage_Loaded);
}
private void MainPage_Loaded(object sender, RoutedEventArgs e){
CreateControls();
}
private void CreateControls() {
//User controls
_text = new DcsText(View);
_input = new DcsInput(View, View, DummyUpdated);
_list = new DcsList(View);
_button = new DcsButton(View);
//Bindings
var set = this.CreateBindingSet<ServerView, ServerViewModel>();
set.Bind(this).For(v => v._update).To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
for (int i = 0; i < Constants.MaxButton; i++){
set.Bind(_button.Button[i]).To(vm => vm.ButtonCommand).CommandParameter(i);
}
set.Apply();
AppTrace.Trace(string.Format("OnCreate Finish"));
}
protected override void OnNavigatedTo(System.Windows.Navigation.NavigationEventArgs e){
base.OnNavigatedTo(e);
BindingContext.DataContext = this.ViewModel;
}
}
}
I get the following errors when I try to do set.Apply();
Exception at set.Apply();
var set = this.CreateBindingSet<ServerView, ServerViewModel>();
for (int i = 0; i < Constants.MaxButton; i++){
set.Bind(_button.Button[i]).To(vm => vm.ButtonCommand).CommandParameter(i);
}
set.Apply();
System.NullReferenceException was unhandled by user code
HResult=-2147467261
Message=Object reference not set to an instance of an object.
Source=Cirrious.MvvmCross.BindingEx.WindowsPhone
StackTrace:
at Cirrious.MvvmCross.BindingEx.WindowsShared.MvxDependencyPropertyExtensionMethods.EnsureIsDependencyPropertyName(String& dependencyPropertyName)
at Cirrious.MvvmCross.BindingEx.WindowsShared.MvxDependencyPropertyExtensionMethods.FindDependencyPropertyInfo(Type type, String dependencyPropertyName)
at Cirrious.MvvmCross.BindingEx.WindowsShared.MvxDependencyPropertyExtensionMethods.FindDependencyProperty(Type type, String name)
at Cirrious.MvvmCross.BindingEx.WindowsShared.MvxBinding.MvxWindowsTargetBindingFactoryRegistry.TryCreatePropertyDependencyBasedBinding(Object target, String targetName, IMvxTargetBinding& binding)
at Cirrious.MvvmCross.BindingEx.WindowsShared.MvxBinding.MvxWindowsTargetBindingFactoryRegistry.TryCreateReflectionBasedBinding(Object target, String targetName, IMvxTargetBinding& binding)
at Cirrious.MvvmCross.Binding.Bindings.Target.Construction.MvxTargetBindingFactoryRegistry.CreateBinding(Object target, String targetName)
at Cirrious.MvvmCross.Binding.Bindings.MvxFullBinding.CreateTargetBinding(Object target)
at Cirrious.MvvmCross.Binding.Bindings.MvxFullBinding..ctor(MvxBindingRequest bindingRequest)
at Cirrious.MvvmCross.Binding.Binders.MvxFromTextBinder.BindSingle(MvxBindingRequest bindingRequest)
at Cirrious.MvvmCross.Binding.Binders.MvxFromTextBinder.<>c__DisplayClass1.<Bind>b__0(MvxBindingDescription description)
at System.Linq.Enumerable.WhereSelectArrayIterator`2.MoveNext()
at Cirrious.MvvmCross.Binding.BindingContext.MvxBindingContextOwnerExtensions.AddBindings(IMvxBindingContextOwner view, IEnumerable`1 bindings, Object clearKey)
at Cirrious.MvvmCross.Binding.BindingContext.MvxBindingContextOwnerExtensions.AddBindings(IMvxBindingContextOwner view, Object target, IEnumerable`1 bindingDescriptions, Object clearKey)
at Cirrious.MvvmCross.Binding.BindingContext.MvxBindingContextOwnerExtensions.AddBinding(IMvxBindingContextOwner view, Object target, MvxBindingDescription bindingDescription, Object clearKey)
at Cirrious.MvvmCross.Binding.BindingContext.MvxBaseFluentBindingDescription`1.Apply()
at Cirrious.MvvmCross.Binding.BindingContext.MvxFluentBindingDescriptionSet`2.Apply()
at DCS.Phone.Views.ServerView.CreateControls()
at DCS.Phone.Views.ServerView.MainPage_Loaded(Object sender, RoutedEventArgs e)
at MS.Internal.CoreInvokeHandler.InvokeEventHandler(Int32 typeIndex, Delegate handlerDelegate, Object sender, Object args)
at MS.Internal.JoltHelper.FireEvent(IntPtr unmanagedObj, IntPtr unmanagedObjArgs, Int32 argsTypeIndex, Int32 actualArgsTypeIndex, String eventName)
InnerException:
Output at set.Apply();
var set = this.CreateBindingSet<ServerView, ServerViewModel>();
set.Bind(this).For(v => v._update).To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
set.Apply();
MvxBind:Warning: 9,86 Failed to create target binding for binding _update for TextUpdate
Just to clerify.
set.Bind(this).For(v => v._update).To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
gave the warning on set.Apply()
MvxBind:Warning: 9,86 Failed to create target binding for binding _update for TextUpdate
Using the public bool Update did solve the set.Apply() problem, but I don't get the binding.
In Droid all these are working
set.Bind(this).For("_update").To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
set.Bind("_update").To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
set.Bind(this).For(v=>v._update).To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
set.Bind(this).For(v=>v.Update).To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
set.Bind("Update").To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
set.Bind(_button.Button[i]).To(vm => vm.ButtonCommand).CommandParameter(i);
gave the exception:
A:
Looking at the stack trace, the code is failing on: https://github.com/MvvmCross/MvvmCross/blob/v3.1/Cirrious/Cirrious.MvvmCross.BindingEx.WindowsPhone/MvxDependencyPropertyExtensionMethods.cs#L113
private static void EnsureIsDependencyPropertyName(ref string dependencyPropertyName)
{
if (!dependencyPropertyName.EndsWith("Property"))
dependencyPropertyName += "Property";
}
So this would suggest that the dependencyPropertyName name being passed to the method is null.
My guess is that this is because _update is not a property and not public. MvvmCross binding works on properties - and .Net security forces it to only work with public (although you could use internal with a little assembly:InternalsVisibleTo code).
Try replacing _update with a public property with both get and set access - e.g.:
public bool Update {
get { return _update; }
set { _update = value; /* do something with the new value? */ }
}
with:
set.Bind(this).For(v => v.Update).To(vm => vm.TextUpdate).OneWay().WithConversion("Update", this);
Aside: In non-Windows binding this problem would result in a much nicer error message - Empty binding target passed to MvxTargetBindingFactoryRegistry from https://github.com/MvvmCross/MvvmCross/blob/v3.1/Cirrious/Cirrious.MvvmCross.Binding/Bindings/Target/Construction/MvxTargetBindingFactoryRegistry.cs#L34 - will put on the todo list for Windows too.
|
// Copyright 2001-2019 Crytek GmbH / Crytek Group. All rights reserved.
#pragma once
namespace Designer
{
class Model;
enum ECompilerFlag
{
eCompiler_CastShadow = BIT(1),
eCompiler_Physicalize = BIT(2),
eCompiler_General = eCompiler_CastShadow | eCompiler_Physicalize
};
//! This class plays a role of creating engine resources used for rendering and physicalizing out of the Designer::Model instance.
class ModelCompiler : public _i_reference_target_t
{
public:
ModelCompiler(int nCompilerFlag);
ModelCompiler(const ModelCompiler& compiler);
virtual ~ModelCompiler();
bool IsValid() const;
void Compile(CBaseObject* pBaseObject, Model* pModel, ShelfID shelfID = eShelf_Any, bool bUpdateOnlyRenderNode = false);
void DeleteAllRenderNodes();
void DeleteRenderNode(ShelfID shelfID);
IRenderNode* GetRenderNode() { return m_pRenderNode[0]; }
void UpdateHighlightPassState(bool bSelected, bool bHighlighted);
bool GetIStatObj(_smart_ptr<IStatObj>* pStatObj);
bool CreateIndexdMesh(Model* pModel, IIndexedMesh* pMesh, bool bCreateBackFaces);
void SaveToCgf(const char* filename);
void SetViewDistRatio(int nViewDistRatio) { m_viewDistRatio = nViewDistRatio; }
int GetViewDistRatio() const { return m_viewDistRatio; }
void SetRenderFlags(uint64 nRenderFlag) { m_RenderFlags = nRenderFlag; }
uint64 GetRenderFlags() const { return m_RenderFlags; }
void SetStaticObjFlags(int nStaticObjFlag);
int GetStaticObjFlags();
void SetSelected(bool bSelect);
void AddFlags(int nFlags) { m_nCompilerFlag |= nFlags; }
void RemoveFlags(int nFlags) { m_nCompilerFlag &= (~nFlags); }
bool CheckFlags(int nFlags) const { return (m_nCompilerFlag & nFlags) ? true : false; }
void SaveMesh(CArchive& ar, CBaseObject* pObj, Model* pModel);
bool LoadMesh(CArchive& ar, CBaseObject* pObj, Model* pModel);
bool SaveMesh(int nVersion, std::vector<char>& buffer, CBaseObject* pObj, Model* pModel);
bool LoadMesh(int nVersion, std::vector<char>& buffer, CBaseObject* pObj, Model* pModel);
private:
bool UpdateMesh(CBaseObject* pBaseObject, Model* pModel, ShelfID nShelf);
void UpdateRenderNode(CBaseObject* pBaseObject, ShelfID nShelf);
void RemoveStatObj(ShelfID nShelf);
void CreateStatObj(ShelfID nShelf);
IMaterial* GetMaterialFromBaseObj(CBaseObject* pObj) const;
void InvalidateStatObj(IStatObj* pStatObj, bool bPhysics);
private:
mutable IStatObj* m_pStatObj[cShelfMax];
mutable IRenderNode* m_pRenderNode[cShelfMax];
uint64 m_RenderFlags;
int m_viewDistRatio;
int m_nCompilerFlag;
};
}
|
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The ONLY political and religious thread allowed on Chiefscrowd
0
Clinton, McCain emerge as comeback winners in New Hampshire primary
WASHINGTON - Democrat Hillary Clinton pulled off an unexpected narrow victory in New Hampshire on Tuesday, dramatically rescuing her bid for the White House in a tense battle with Barack Obama.
Clinton, who's fighting to become the first woman in the Oval Office, mounted a surprisingly strong showing after bracing for a second defeat following her devastating third-place showing in Iowa.
Republican John McCain also nabbed a major comeback victory, putting him solidly back in his party's nomination race.
While Obama, vying to make history as the first black U.S. president, scored big among independents and voters between 18 and 24, Clinton attracted lower-income voters and seniors and did best among voters citing the economy as their top concern.
But a big factor for Clinton was women voters, who had gone over to Obama in large numbers in Iowa. Nearly half in New Hampshire were once again supporting her, while Obama got only a third.
You can come to Germany and see how we treat our people better with paying about the same tax rate as in some states in the USA. You all saying it is going to get bad, no matter who won or lost, the United States needs to be United.
"A democracy cannot exist as a permanent form of government. It can only exist until the majority discovers it can vote itself largess out of the public treasury. After that, the majority always votes for the candidate promising the most benefits with the result the democracy collapses because of the loose fiscal policy ensuing, always to be followed by a dictatorship, then a monarchy." Make no mistake; this was a vote for more handouts by the permanently dependent. Until they finish burying the Constitution, which Obama will do as fast as he can, it's still the best country in the world.
"A democracy cannot exist as a permanent form of government. It can only exist until the majority discovers it can vote itself largess out of the public treasury. After that, the majority always votes for the candidate promising the most benefits with the result the democracy collapses because of the loose fiscal policy ensuing, always to be followed by a dictatorship, then a monarchy." Make no mistake; this was a vote for more handouts by the permanently dependent. Until they finish burying the Constitution, which Obama will do as fast as he can, it's still the best country in the world.
You guy make it sound like the end of the USA. It just needs politicians to meet in the middle, on all sides of the issues. I also think if the republicans would leave religion out of politics, then they would have a good chance in 2016.
You guy make it sound like the end of the USA. It just needs politicians to meet in the middle, on all sides of the issues. I also think if the republicans would leave religion out of politics, then they would have a good chance in 2016.
I personally believe that we are well on our way, look closely at Greece; I believe that could well be us in four years.
We have a president who touts getting Bin Laden and then hangs four of our own out to dry in Libya and the media by in large gives him a pass because the mere insinuation of impropriety on the administrations part is "offensive" to the President. Well, sometimes the truth hurts, and here's the truth as I understand it: The consulate was denied the security forces required to protect it despite numerous requests. In spite of using the term "terror" in his address to the nation in the White House rose garden Obama and his surrogates spent nearly the next two weeks blaming a spontaneous "protest", which never happened, that had gotten out of control over some ridiculous You Tube video. As far as I'm concerned the president can be offended all he wants to but it doesn't change the facts in the matter.
Lastly, unless everyone thinks we'll be just fine going 20+ trillion dollars in debt and maintaining trillion dollar deficits over the course of the next four years, selling more and more debt to China and devaluation our own currency by simply printing more money, then we are headed for ruins IMO.
The House Speaker and the rest of the Republicans want to keep their jobs so they'll cower in the corner with their tails tucked between their legs to protect what’s left of their genitals allowing the President to run roughshod all over them being unfettered and unchecked now that he doesn't have to worry about re-election. Obama now has more "flexibility" to lighten up on the Iran sanctions for Putin making the world a more dangerous place. I'm not real optimistic about our country's future.
That attack in Libya was not the first attack that killed Americans at an Embassy. It happened many times before and it will happen again no matter who is President. It is sad and it sucks but if these groups, terrorist or not, want to attack us, they will.
I just see how we are too far to either the left side or the right side. If we do not get back to the middle, then we will end up like Greece. The USA does not have a "Germany" to bail them out so I truly believe in being fiscal conservative. At the same time though we have to pay for the things that are and have been on the books before Obama became President, the other 10t debt.
No, I do not want more debt so we should cut the social programs and put in check and controls making sure only those who really need it get it. Still though, we have to pay and I rather see the Bush tax cuts for those making more than 250k to go back up that 3%. I just do not believe the budget can be balanced just on reducing the social programs alone.
Like I said, if we do not get to the middle, then the future of the USA will not be a good one.
That attack in Libya was not the first attack that killed Americans at an Embassy. It happened many times before and it will happen again no matter who is President. It is sad and it sucks but if these groups, terrorist or not, want to attack us, they will.
I just see how we are too far to either the left side or the right side. If we do not get back to the middle, then we will end up like Greece. The USA does not have a "Germany" to bail them out so I truly believe in being fiscal conservative. At the same time though we have to pay for the things that are and have been on the books before Obama became President, the other 10t debt.
No, I do not want more debt so we should cut the social programs and put in check and controls making sure only those who really need it get it. Still though, we have to pay and I rather see the Bush tax cuts for those making more than 250k to go back up that 3%. I just do not believe the budget can be balanced just on reducing the social programs alone.
Like I said, if we do not get to the middle, then the future of the USA will not be a good one.
Agreed, but that doesn't excuse ignoring and denying the need for additional security even after several requests for it.
I agree that the approach needs to be increased tax revenue combined with spending cuts. However, this can be done by doing away with loopholes rather than raising the tax rate which has a way of "tickling down" to those of us making under that 250k.
...And that first ten trillion you make mention of was racked up by all the other Presidents in US history combined. The last 6+ trillion is new debt racked up by Obama in just the last four years. |
Buddleja alternifolia
Buddleja alternifolia, known as alternate-leaved butterfly-bush, is a species of flowering plant in the figwort family, which is endemic to Gansu, China. A substantial deciduous shrub growing to tall and wide, it bears grey-green leaves and graceful pendent racemes of scented lilac flowers in summer.
Description
B. alternifolia is a vigorous deciduous shrub reaching tall with long, slender, pendulous stems. The leaves are alternate, entire, and lanceolate, 4–10 cm long by 0.6–1 cm wide, glabrous and dark green above. The inflorescences of the plants in cultivation are bright lilac-purple, and comprise flowers so densely crowded in clusters along the branch as to often obscure it. However, specimens from the Tsangpo valley in Tibet originally named B. tsetangensis by Marquand have creamy flowers. Flowering occurs in early summer; the flowers are fragrant, but less so than other buddlejas. 2n = 38.
In its native territory it grows along river banks in thickets at elevations of .
Taxonomy
In his 1979 revision of the taxonomy of the African and Asiatic species of Buddleja, the Dutch botanist Anthonius Leeuwenberg sank two species, B. legendrei and B. tsetangensis, as B. alternifolia on the basis of the similarity in the individual flowers, dismissing the variations in plant structure, flower colour and leaf as attributable to environmental factors. It was Leeuwenberg's taxonomy which was adopted in the Flora of China published in 1996. Until DNA analysis can prove otherwise, it is this classification which is accepted here.
Cultivation
In the West this plant was first described and named by the Russian botanist Carl Maximowicz in 1880. It was not introduced to cultivation in the West until 1915, by Purdom and Farrer.
The species has become very common in cultivation, a popular shrub for the larger garden, and is readily available from most garden centres in the UK. Fully hardy, it prefers a sunny position and loamy soil; pruning should immediately follow flowering. Like most buddlejas, the species is easily propagated from cuttings. Hardiness: RHS H5, USDA zones 7 – 9.
B. alternifolia was accorded the Royal Horticultural Society's Award of Garden Merit (record 674) in 1993.
Cultivars
Buddleja alternifolia ‘Argentea’.
References
Hillier & Sons. (1977). Hilliers' Manual of Trees and Shrubs. David & Charles, Newton Abbot, UK
alternifolia
Category:Flora of China |
About Pathophilia
Allergan Files “Free-Speech” Complaint Against Govt
The latest in the conflict between Constitutionally granted free speech and the government’s prohibition of off-label drug discussions by pharma.
Last week, Allergan, maker of Botox (onabotulinumtoxinA), announced a suit against the US government, seeking “declaratory relief” from such long-time federally mandated off-label speech restrictions.* The complaint, filed in US District Court for the District of Columbia, specifically applies to the sharing of information about Botox Therapeutic (not Botox Cosmetic) and recent requirements of the FDA’s Risk Evaluation and Mitigation Strategies (REMS) program. In its complaint, the company is represented by Paul Clement, former Solicitor General and a current partner in the DC law firm of King & Spalding.
Allergan’s suit was filed with respect to the FDA’s REMS program for botulinum toxin products. The program was instituted this year because of postmarketing reports of toxin spread after injections for off-label conditions—namely, spasticity in children with cerebral palsy and arm spasticity in adults. In the program, the FDA requires manufacturers to create a “communication plan” that provides information to physicians about the risk of the distant spread of botulinum toxin after local injection.
But Allergan argues that the FDA’s required communication plan puts the company in a double bind—effectively mandating proactive discussions about the safety of off-label Botox Therapeutic, while simultaneously prohibiting proactive off-label discussions. Allergan claims that it cannot reasonably abide by the FDA’s REMS program for Botox Therapeutic (ie, “proactively provide comprehensive information to physicians about these off-label uses [emphasis added]”) without fear of prosecution. The company writes, “Allergan seeks a judgment that would permit it to provide currently available and truthful information to doctors for common off-label uses of [Botox].”
In a conference call on Friday, Allergan’s General Counsel, Douglas Ingram, provided additional information about the complaint and fielded questions. Ingram stressed that the company’s suit applies to the provision of “truthful,” “nonmisleading,” and “comprehensive” information about the off-label uses of Botox Therapeutic. Ingram would not comment on a recent investigation of the company by the US Attorney’s Office for the Northern District of Georgia, which issued a subpoena in March to the California-based firm regarding the alleged off-label promotion of Botox for headache. Both Ingram and Allergan CEO, David Pyott, stressed that the company’s current complaint does not relate to alleged past activities. Ingram also declined to comment on Pfizer’s recent record-breaking $2.3-billion settlement with the government concerning off-label drug promotion.
* Mandated by the Federal Food, Drug, and Cosmetic Act of 1938. The FDCA dictates that an approved drug is “misbranded,” if it is marketed (in interstate commerce) for an unapproved use. The act stipulates that the product’s approved label, in this case, does not provide “adequate directions for use.”
A native East Tennessean, Barbara Martin is a formerly practicing, board-certified neurologist who received her BS (psychology, summa cum laude) and MD from Duke University before completing her postgraduate training (internship, residency, fellowship) at the Hospital of the University of Pennsylvania in Philadelphia. She has worked in academia, private practice, medical publishing, drug market research, and continuing medical education (CME). For the last 3 years, she has worked in a freelance capacity as a medical writer, analyst, and consultant. Follow Dr. Barbara Martin on Google + and Twitter. |
Response surface optimization and physicochemical properties of polysaccharides from Nelumbo nucifera leaves.
Dynamic high pressure microfluidization (DHPM)-assisted extraction (DHPMAE) of lotus (Nelumbo nucifera) leaves polysaccharides (LLPs) was optimized by response surface methodology. The optimal extraction conditions were: liquid/solid ratio of 35:1 (v/m, mL/g), processing pressure of 180 MPa, processed two times, extraction temperature of 76°C, extraction time of 50 min. Under the optimal extraction conditions, DHPMAE produced a higher polysaccharides yield (6.31%) than leaching (2.95%). Scanning electron microscope (SEM) analysis revealed that DHPM could reduce the particles size and make the surface more unconsolidated. The LLPs prepared by both methods showed similar FT-IR spectrum, and were consisted of the same monosaccharides, including rhamnose, fucose, arabinose, xylose, mannose, glucose and galactose. The content of each monosaccharide in extracts, however, was quite different. The average molecular weight of LLPs prepared by DHPMAE is 550 kDa, smaller than 578 kDa obtained by leaching. The LLPs prepared by DHPMAE exhibited stronger DPPH scavenging ability (IC50 value of 0.38 mg/mL), HO scavenging ability (IC50 value of 0.61 mg/mL) and reducing power. Therefore, DHPMAE can be a promising alternative to traditional extraction techniques for polysaccharides from plants, and lotus leaves might be a potential resource of natural antioxidants. |
The Benefits of App-Based Mobile Research
Mobile Research: The Next Chapter
Research has certainly come a long way. From in-person interviews, to mailers, to phone centers; researchers have always been quick to harness new technologies. Yes, we still get the occasional phone survey, but research has largely relocated to the internet.
In the past, joining an online survey panel became a great way to make a few extra bucks and researchers gained direct access to respondents. But, these traditional panels aren’t without issues–
They tend to have a shallow reach, and it is difficult to fill them with a truly representative sample.
Their panelist can be “professional” survey takers, who know they are taking part in research.
Clever respondents can game the system, and commit fraud which hurts the value of your data.
To avoid these issues, many researchers are turning to mobile research. Mobile is the next chapter; and what better way to reach people than with the apps they use everyday?
Mobile research conducted with app-recruited respondents has many benefits. Here are just a few:
Broad Reach
Research done through mobile apps has been proven to reach a broad and diverse set of respondents. Everyone is plugged in. PEW research found that more than 95% of adults in the US have a cellphone, and the majority of those are smartphones.
Adults are also spending more and more time on those devices. People are spending almost twice as many hours on digital devices than they were in 2008, with more than half of that growth on mobile.
More people are spending more time on their phones, and this represents a great opportunity in research. We no longer have to rely on hand-picked or self-selecting groups of respondents that don’t represent the public’s real views. Since apps are so widely used, we can harness their broad reach to get our surveys into the hands of real people.
Professional Panelists vs App Survey-Takers
Respondents on traditional survey panels tend to take survey after survey. We all know that practice makes perfect, but with data you don’t want perfect; you want the truth. Many “professional panelists” are able to navigate questions more intelligently and manipulate the process to gain rewards. This sometimes leads to insincere results.
In comparison, app survey-takers are often new to the process and only take surveys every so often. These respondents tend to put more thought into how they answer, and are often more expressive. The experience of participating in research is still novel, and so their responses are more natural.
Virtual Rewards Means Less Fraud
Respondents taking surveys through mobile apps are awarded virtual rewards, such as in-game items or virtual currency. They are rewarded instantly, so there is no waiting for a monthly pay-out or gift card to come in the mail.
Instant in-app rewards are a great incentive, because they harness the power of useful (and sometimes addictive!) apps, while discouraging fraud. When the reward can only be spent in the app, people are much less likely to game the system.
Good News for Research
This new approach provides access to groups of people who were difficult to engage before, allows us to engage those users in a more natural way, and cuts down on fraud. This is great news for researchers who can use mobile app-recruited respondents to avoid the issues inherent in traditional panels. If you are interested in seeing the results for yourself email us, or go DIY with our easy to use tool. |
Exposure to toxic metals and polychlorinated biphenyls of adolescents and adults from two atolls in the Tuamotu Archipelago (French Polynesia).
The atoll of Hao, part of the Tuamotu Archipelago in French Polynesia, hosted an air base which was used by France Air Force and Naval Aviation during the nuclear tests. Following the publication of a report in 2012 indicating widespread contamination of the atoll, we conducted a biomonitoring survey to assess the exposure to toxic metals and polychlorinated biphenyls (PCBs) of Hao residents and residents of Makemo, a nearby atoll without any known sources of industrial pollution. Adults and adolescents (≥12 years) randomly sampled from Hao (n = 275) and Makemo (n = 268) provided blood samples for contaminant analyses. Whole blood samples were analysed for cadmium, lead and total mercury by inductively coupled plasma mass spectrometry. Plasma concentrations of PCBs were measured by gas chromatography mass spectrometry. Face-to-face interviews were conducted to document lifestyle and a food-frequency questionnaire was used to document dietary habits. Concentrations of contaminants were compared between atolls and associations with sociodemographic and personal characteristics of the participants were investigated. A significantly higher mean (geometric) of blood lead concentration was observed in Hao compared to Makemo (3.75 vs 3.40 μg/L, P = 0.02), whereas similar concentrations were noted for cadmium (0.49 vs 0.50 μg/L, P = 0.58) and mercury (11.4 vs 11.5 μg/L, P = 0.78). Mean total PCBs plasma concentration was significantly higher in Hao than in Makemo participants (0.75 vs 0.32 μg/L, P < 0.001). A significant proportion of participants exceeded toxicological reference values for mercury and lead in both atolls. The higher body burden of PCBs and Pb in Hao compared to Makemo residents may be linked to past air base activities in Hao. According to international standards, PCBs exposure is low; however, exposure to both mercury and lead is high and further investigations are required to identify specific sources of exposure. |
After you choose your school, the next most important decision you need to make is which computer you'll have for the next four years. Start your short list with these top-rated, value-focused laptops.
Powerful virtualization utilities let you run Windows and all its apps on your OS X or Linux system, host older versions of Windows on newer systems, isolate your main operating system by running a virtual OS in a sandbox, and much more. |
Thursday, December 13, 2012
Breaking Her Stunned And Traumatized Silence
Quick roundup - US initial claims continue to bounce around frenetically, but that is because of seasonal adjustment. Actual claims, allowing for the Thanksgiving delay in processing, are pretty steady. They are not very different from the prior year's. This is the current release, and with it I grumpily concede that claims are in the 380s rather than the 370s where I wanted them to be. While not dire, this is an unfavorable development.All-important inventories to sales ratios - Total business remains where it has been cycling, which obscures the unhappy fact that the reason we are seeing the slow down in production-type PMIs is that it is cycling - businesses are notching down employment in order to keep it cycling. The forward impetus you get by looking at wholesalers, and there we get news of another downward notch. Again, not dire, but again, unfavorable.Wholesalers adjust their buys so that inventory doesn't accumulate too much, which then passes through to manufacturers.Retail sales for November were okay, but not if you were a department store or a grocery chain operator. There is an obvious slowing in YoY gains for retail sales. Table 2 gives you rolling three month comparisons YoY and for the previous 3 months. The YoY is now 4.3%, but the previous 3 months is 2%. This data is not price-adjusted, of course. There is a relatively high current error in this report for each month's data, but the three-month totals should have much less variance. Grocery store sales dropped in November in comparison to October, which is a sign that consumers aren't that flush. Food spending dropped in Q4 last year as well; consumers cut their food expenditures to pay for other spending. This, btw, is the biggest single indicator that we are in a recession, and it is truly an amazing one, due to the continued expansion of the SNAP (food stamp) program. It is Table 2.3.6, real-dollar food and beverages purchased for off-premises consumption, and since Q2 2011 it has not moved. But the population has increased and our subsidy for food has increased. SNAP expenditures continue to rise by month, and they are roughly equivalent to a 1.5% payroll tax cut.
In fiscal year 2012, we spent 74.6 billion on SNAP, which is 9% of the total annualized BEA reported off-premises food consumption. (Table 2.3.5). In comparison, in fiscal year 2008 we spent 34.6 billion versus 740 billion total, or 4.7%. If this doesn't scare you witless, nothing will. Your mind is gone. You have exited the reality highway. You have achieved the nirvana of total mental drift, and you are floating in a warm sea of disassociation. There is also WIC, which at 4.8 billion in FY 2012 gets us to more like 9.5% of basic food expenditures.All this money, and the increasing population is buying less food per capita? This is Japanese-style deflation. The following BEA-generated chart shows CURRENT-dollar food trends:
It might be time to stop importing immigrants that need government subsidies to feed themselves. All we are doing is crushing the working-class population into the ground. In this context, it's easy to see why the Fed is launching a Treasury bond-buying program, which at an annual total of 540 billion, would amount to funding close to half the fiscal year 2012 federal deficit. But the reality is that any measure which does not restore the ability of the general population to buy food at at least a continuous per-capita level is doomed to fail as an economic stimulus. I do have one favorable thing to say of MMT versus current more mainstream economics - the MMTers generally do seem to really get that a theoretical increase in the money supply does not equate to an actual increase in the money supply. You can dump "money" into the system all day long, but without a circulating mechanism, the "money" does not exist in fact. Another aspect of our current future expectations is that GASB is gradually tightening up the standards for government pensions. The current change in standards will fully take effect in 2014, and it will force higher contribution levels for government pensions, which will further cramp a lot of state and local governmental budgets. Of course there is a loophole which would allow and indeed force marginally funded plans to use a higher discount rate for the first-pass calculation in order to avoid the forced low-end discount rate. But some plans don't have this option, and this should be an adventure in fiscal reality.
Well, I could write more, but I think I have come to the conclusion that the best way to proceed is to focus on real money supply in the context of theory and evidence. We can discuss what I think is happening to it, what MMT thinks it is, and what the Fed thinks it is doing to it!
We've gone to the lowest price food goods we can go...next stop is the dumpster behind the store...lol. Probably should've started there, the trip would've been shorter.I look forward to seeing your take on the MMT'ers and their (nominal versus real) financial prestidigitation. It's a neat trick, their use of operational identities as their proof of "theory" while unmooring the feedback between the nominal and the real economy. Global 3-card monte...AnonPA
TJ, I think you're right. Most of the people I know, myself included, are in a state of low confidence. Lots of money in CDs, MMAs, bonds, under the mattresses, and in gold/silver.
IMO, a restoration of confidence would release a torrent of investing and spending. Only one thing standing in its way - government policy. The regulations to strangle coal, tight formation fracking, and even regular oil/gas production are now ready to go.
A small businessman of my acquaintance has a big cash hoard. He's waiting for something that gives him the confidence to put it to work. Imagine that multiplied by millions of small businesses. Sure, it could cause another bubble. But that would be a nice problem to have compared to another four years of stagnation.
Jimmy - it's not clear that the Fed alone can produce inflation, but your comments point out why some of the Fed Heads are worried about inflation. Once the fire starts, at 4 Trillion in how does the Fed get out? Trying to pull that much money out of the economy could only be done over a period of years, so likely the Fed would raise rates. It would be messy to say the least, and very resistant to attempts at calibration.
Of course, our problems are not likely to clear up so one may doubt an explosion of confidence.
The biggest fallacy of MMT, I don’t even know why we are talking about this, is that all the money printing goes to bonds first to finance government spending. If money printing is so good then just print it and deposit it to the US Treasury’s bank account at the Federal Reserve Bank. That goes for all the other 12 central banks that are printing. Just think of all the world resources that go into managing all that debt (and all that trauma) that could be diverted to more productive uses.
I guess as long as the Velocity of money is not zero the more the Fed pumps in the more it should help the economy. That said I think the velocity of money may be structurally zero.
As I've commented before we've passed the tipping point with the reelection of Obama. The class warfare he preaches will do nothing but widen the gulf between the haves and have nots. Pity. As in the "Only Nixon can go to China" theme he could sort out spending and entitlements but he's too wrapped up in the hate the rich meme to see the light or seize the opportunity.
Obama doesn't realize that Fed stimulus actually widens the income gap. He can try to ram through tax increases for the top 10%, but if he doesn't get the budget balanced and federal regulation/control reduced (and he is incapable of such) then there will be no choice but more Fed money printing which essentially undoes any income gap compression the tax increases would enable. |
Q:
listen for any div that goes from display: none to display:block
Is there any way to listen for elements being shown or hidden?
I would like categorically to--whenever an element goes from hidden to shown--put focus on the first input element within the newly shown element
I thought of attaching a click event to everything and putting it at the top of the document, thinking that would trigger before anything and I could track whether the clicked element's next("div") (or something) would have a css display property of none, then setting a small timeout, then setting the focus, but I get undefined when I try to access that CSS property
$("html").on("click", "body", function(){
alert($(this).next("div").css("display")); //undefined
});
Is there a way to do this?
A:
You can try something like this (it’s kind of a hack). If you monkey-patch the css/show/hide/toggle prototypes in jQuery, you can test if the element changes it’s :hidden attribute after a "tick" (I used 4ms). If it does, it has changed it’s visibility. This might not work as expected for animations etc, but should work fine otherwise.
DEMO: http://jsfiddle.net/Bh6dA/
$.each(['show','hide','css','toggle'], function(i, fn) {
var o = $.fn[fn];
$.fn[fn] = function() {
this.each(function() {
var $this = $(this),
isHidden = $this.is(':hidden');
setTimeout(function() {
if( isHidden !== $this.is(':hidden') ) {
$this.trigger('showhide', isHidden);
}
},4);
});
return o.apply(this, arguments);
};
})
Now, just listen for the showhide event:
$('div').on('showhide', function(e, visible) {
if ( visible ) {
$(this).find('input:first').focus();
}
});
Tada!
PS: I love monkeypatching
|
1. Field of the Invention
The present application relates to measuring devices, more specifically to coordinate measurement machines.
2. Description of the Related Art
Portable coordinate measurement machines (PCMMs) such as articulated arm PCMMs can be used to perform a variety of measurement and coordinate acquisition tasks. In one common commercially-available PCMM, an articulated arm having three transfer members connected by articulating joints allows easy movement of a probe head or tip about seven axes to take various measurements. In operation, when the probe head or tip contacts an object the PCMM outputs to a processing unit data regarding the orientation of the transfer members and articulating joints on the articulated arm. This data would then be translated into a measurement of a position at the probe head or tip.
Typical uses for such devices generally relate to manufacturing inspection and quality control. In these applications, measurements are typically taken only when a measuring point on the arm is in contact with an article to be measured. Contact can be indicated by strain-gauges, static charge, or user-input. Such devices have been commercially successful. Still there is a general need to continue to increase the accuracy of such instruments. |
simple interesting this coat hook design is the result of a challenge to take an everyday object u0026 remold rebuild repurpose it create entirely new item while using and interesting coat hooks bored panda. |
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Giacomo Po <[email protected]>
// Copyright (C) 2011 Gael Guennebaud <[email protected]>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include <cmath>
#include "../../test/sparse_solver.h"
#include <Eigen/IterativeSolvers>
template<typename T> void test_minres_T()
{
// Identity preconditioner
MINRES<SparseMatrix<T>, Lower, IdentityPreconditioner > minres_colmajor_lower_I;
MINRES<SparseMatrix<T>, Upper, IdentityPreconditioner > minres_colmajor_upper_I;
// Diagonal preconditioner
MINRES<SparseMatrix<T>, Lower, DiagonalPreconditioner<T> > minres_colmajor_lower_diag;
MINRES<SparseMatrix<T>, Upper, DiagonalPreconditioner<T> > minres_colmajor_upper_diag;
MINRES<SparseMatrix<T>, Lower|Upper, DiagonalPreconditioner<T> > minres_colmajor_uplo_diag;
// call tests for SPD matrix
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_I) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_I) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_diag) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_diag) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_uplo_diag) );
// TO DO: symmetric semi-definite matrix
// TO DO: symmetric indefinite matrix
}
void test_minres()
{
CALL_SUBTEST_1(test_minres_T<double>());
// CALL_SUBTEST_2(test_minres_T<std::compex<double> >());
}
|
Microarray analysis of differentially expressed genes in placental tissue of pre-eclampsia: up-regulation of obesity-related genes.
Susceptibility genes present in both mother and fetus most likely contribute to the risk of pre-eclampsia. Placental biopsies were therefore investigated by high-density DNA microarray analysis to determine genes differentially regulated within chorionic villous tissue in pre-eclampsia and normal pregnancy. The pooled RNAs of pre-eclamptic and normotensive subjects were hybridized to the HuGeneFL array representing sequences from approximately 5600 full-length human cDNAs. The differentially expressed genes that were detected could be categorized into nine groups: adhesion molecules, obesity-related genes, transcription factors/signalling molecules, immunological factors, neuromediators, oncogenic factors, protease inhibitors, hormones and growth factor-binding proteins. Among those, the obesity-related genes included putative candidate genes associated with the pathogenesis of pre-eclampsia. One of the most up-regulated transcripts was the obese gene (43.6-fold change), and this was reflected by elevated leptin protein levels. In the case of feto-maternal contribution of polymorphic genes to pre-eclampsia, expression analysis of placental tissue has lead to numerous target genes waiting for large scale genetic linkage analyses. |
Q:
How to remove a file from Git Pull Request
I have a pull request opened where I have some project.lock.json files which I do not want to merge while merging my branch to main branch. Is there a way to remove thos project.lock.json files from my Pull Request?
A:
Please do let me know if there is a better way of doing this. This is the workaround I have found.
list remote branches
git branch -va
checkout the PR branch
git checkout origin pr_branch
overwrite pr_branch's file with other_branch's file
git checkout other_branch -- ./path/to/file
commit changes
git commit -m "overwrite with other_branch's"
push your changes
git push origin pr_branch
A:
You need to remove file, commit changes and make next push to your branch.
If you want leave file in your branch, but not to merge it to main branch, you can delete it in one commit, then add again in another. Git allows you manually accept certain commits using git-cherry-pick. You can accept each commit except that in which you have added this file again.
|
[Massive hemorrhage in the small intestine].
Haemorrhage into the small intestine accounts only for cca 1% of all haemorrhages into the gastrointestinal tract. Profuse haemorrhage is very rare, it occurs in malignant tumours, sarcomas and also haemangiomas. Preoperative diagnosis is practically impossible not only because the small intestine is not readily accessible for examination but in case of profuse haemorrhage also because of lack of time. Therefore a decision on early laparotomy has to be taken. |
---
abstract: 'Using semi-empirical isochrones, we find the age of the Taurus star-forming region to be 3-4 Myr. Comparing the disc fraction in Taurus to young massive clusters suggests discs survive longer in this low density environment. We also present a method of photometrically de-reddening young stars using $iZJH$ data.'
---
Introduction
============
Taurus is a low-density star-forming region containing primarily low-mass stars and so represents an ideal laboratory for studying the environmental effects on circumstellar disc lifetimes [@Kenyon2008 (Kenyon et al. 2008)]. To investigate the impact of the low-density environment on the discs in Taurus, we used the Wide-Field Camera (WFC) on the 2.5m Isaac Newton Telescope (INT) on La Palma to obtain $griZ$ photometry of 40 fields in Taurus. Our fields are focused on the densest regions not covered by the Sloan Digital Sky Survey. The resultant INT-WFC survey mainly covers the L1495, L1521 and L1529 clouds.
We have augmented the WFC data with near-infrared $JHK$ data from 2MASS [@Cutri2003 (Cutri et al. 2003)]. To determine the age of Taurus we compare the semi-empirical isochrones discussed in [@Bell2013; @Bell2014 Bell et al. (2013, 2014)] to the observed colour-magnitude diagrams (CMDs). For a brief description of these isochrones see Bell et al. (these proceedings).
De-reddening
============
The extinction in Taurus is spatially variable across the different clouds, and so we require a method of de-reddening the stars individually. We have found that in an $i$-$Z$, $J$-$H$ colour-colour diagram the reddening vectors are almost perpendicular to the theoretical stellar sequence (Fig.\[fig:izjh\_age\]), whose position is almost independent of age, and so we can de-redden stars using photometry alone. We construct a grid of models over a range of ages (1 to 10 Myr) and binary mass ratios (single star to equal mass binary). We adopt the reddening law from [@Fitzpatrick1999 Fitzpatrick (1999)], apply it to the atmospheric models and fold the result through sets of filter responses to derive reddening coefficients in each photometric system.
[0.45]{} ![**Left:** $i$-$Z$, $J$-$H$ diagram for Taurus members. Asterisks are Class II sources, open circles are Class III sources. Overlaid as solid lines are a 2 and 4Myr isochrone. The dashed lines are reddening vectors in this colour space. **Right:** $r$, $r$-$i$ diagram for Taurus members identified as Class III. Isochrones of 1, 4 and 10Myr are overlaid. Asterisks indicate the position of a theoretical star with mass 0.75M$_\odot$. The black dashed line shows a reddening vector for A$_V$ = 1 mag. []{data-label="fig:izjh_age"}](izjh.eps "fig:"){width="\textwidth" height="5.5cm"} \[fig:izjh\_ccd\]
[0.45]{} ![**Left:** $i$-$Z$, $J$-$H$ diagram for Taurus members. Asterisks are Class II sources, open circles are Class III sources. Overlaid as solid lines are a 2 and 4Myr isochrone. The dashed lines are reddening vectors in this colour space. **Right:** $r$, $r$-$i$ diagram for Taurus members identified as Class III. Isochrones of 1, 4 and 10Myr are overlaid. Asterisks indicate the position of a theoretical star with mass 0.75M$_\odot$. The black dashed line shows a reddening vector for A$_V$ = 1 mag. []{data-label="fig:izjh_age"}](age.eps "fig:"){width="\textwidth" height="5.5cm"} \[fig:age\]
It is well known that for a fixed value of E(B-V), extinction in a given filter will vary with [$T_{\mathrm{eff}}$]{} (see e.g. [@Bell2013 Bell et al. 2013]). To account for this we use extinction tables to redden the isochrones for a grid of E($B$-$V$) and [$T_{\mathrm{eff}}$]{} values, and compare the reddened model grid to the data. We adopt a Bayesian approach and marginalise over binary mass, age and [$T_{\mathrm{eff}}$]{}. We take the extinction values from the model with the highest likelihood, and use this to de-redden the star.
Taurus
======
Plotting the de-reddened Taurus members in the $r$, $r$-$i$ CMD, we notice that a significant fraction of the Class II objects appear much fainter than the primary locus. This is likely an accretion effect, and if we were to fit for the age of these members we would derive an age that is erroneously old. To avoid this effect, we fit only the Class III sources. We note that those Class II sources that are not scattered below the sequence lie coincident with the Class III sources, and thus we believe the age derived from the Class III sources alone will be representative of the overall age. We plot our de-reddened Taurus members in an $r$, $r$-$i$ CMD to fit for the age (Fig.\[fig:izjh\_age\]). We find that isochrones of 3-4 Myr (older than is commonly quoted in the literature) trace the observed stellar sequence well. To ensure consistency with the [@Bell2013 Bell et al. (2013)] age scale we compare the position of a theoretical star with a mass of 0.75 M$_\odot$ to the middle of the observed sequence. We find consistency with the overall isochrone fitting, with an age of 3-4 Myr still providing a good fit. With a robust age for Taurus we then examined the disc fraction. Taurus has a disc fraction of 69% [@Luhman2010 (Luhman et al. 2010)]. If we compare this to the other clusters in [@Bell2013 Bell et al. (2013)], which are on the same age scale, we find that Taurus has the largest disc fraction in the sample, significantly higher than the group of young (2 Myr), massive clusters, suggesting that discs may have survived longer in the low density environment present in Taurus.
2013, *MNRAS*, 434, 806
2014, *MNRAS*, 445, 3496
2003, *2MASS All Sky Catalog of point sources.*
1999, *PASP*, 111, 63
2008, *Handbook of Star Forming Regions, Vol. 1*, p.405
2010, *ApJS*, 186, 111
|
/**
* Copyright (c) Rich Hickey. All rights reserved.
* The use and distribution terms for this software are covered by the
* Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php)
* which can be found in the file epl-v10.html at the root of this distribution.
* By using this software in any fashion, you are agreeing to be bound by
* the terms of this license.
* You must not remove this notice, or any other, from this software.
**/
using System.Reflection;
using System.Runtime.InteropServices;
// General Information about an assembly is controlled through the following
// set of attributes. Change these attribute values to modify the information
// associated with an assembly.
[assembly: AssemblyTitle("Clojure")]
[assembly: AssemblyDescription("")]
[assembly: AssemblyConfiguration("")]
[assembly: AssemblyCompany("")]
[assembly: AssemblyProduct("Clojure")]
[assembly: AssemblyCopyright("Copyright © 2009")]
[assembly: AssemblyTrademark("")]
[assembly: AssemblyCulture("")]
// Setting ComVisible to false makes the types in this assembly not visible
// to COM components. If you need to access a type in this assembly from
// COM, set the ComVisible attribute to true on that type.
[assembly: ComVisible(false)]
// The following GUID is for the ID of the typelib if this project is exposed to COM
[assembly: Guid("92a6be2b-759d-4d62-8912-9dde0052bc33")]
// Version information for an assembly consists of the following four values:
//
// Major Version
// Minor Version
// Build Number
// Revision
//
// You can specify all the values or you can default the Build and Revision Numbers
// by using the '*' as shown below:
// [assembly: AssemblyVersion("1.0.*")]
[assembly: AssemblyVersion("1.4.0.0")]
[assembly: AssemblyFileVersion("1.3")]
[assembly: System.Resources.NeutralResourcesLanguage("en-US")]
|
Index Herbariorum
The Index Herbariorum provides a global directory of herbaria and their associated staff. This searchable online index allows scientists rapid access to data related to 3,400 locations where a total of 350 million botanical specimens are permanently housed (singular, herbarium; plural, herbaria). The Index Herbariorum has its own staff and website. Overtime, six editions of the Index were published from 1952 to 1974. The Index became available on-line in 1997.
The index was originally published by the International Association for Plant Taxonomy, which sponsored the first six editions (1952–1974); subsequently the New York Botanical Garden took over the responsibility for the index. The Index provides the supporting institution's name (often a university, botanical garden, or not-for-profit organization) its city and state, each herbarium's acronym, along with contact information for staff members along with their research specialties and the important holdings of each herbarium's collection.
Editors
6th edition (1974) was co-edited by Patricia Kern Holmgren, Director of the New York Botanical Garden
7th printed edition, ed. by Patricia Kern Holmgren.
8th printed edition, ed. by Patricia Kern Holmgren.
Online edition, prepared by Noel Holmgren of the New York Botanical Garden
2008+, ed. by Barbara M. Thiers, Director of the New York Botanical Garden Herbarium
References
Category:Directories
Category:Herbaria |
Spray application of liquid smoke to reduce or eliminate Listeria monocytogenes surface inoculated on frankfurters.
In a simulated post process contamination scenario liquid smoke was sprayed on the frankfurters after peeling, and then inoculated with Listeria monocytogenes (Lm). Samples that did not receive a liquid smoke spray remained at approximately 2 log cfu/cm(2) during the 48h of storage while the levels on the liquid smoke treated frankfurters continued to decline until they were below detection level (1 cfu/100 cm(2)). A shelf-life study lasting 140 days indicated that liquid smoke suppressed the growth of Lm for up to 130 days. An application of 2 or 3 ml liquid smoke at packaging resulted in at least a 1 log reduction of Lm within 12h post packaging. |
Prophylaxis of atherosclerosis with marine omega-3 fatty acids. A comprehensive strategy.
Traditional approaches to prophylaxis of atherosclerosis have focused on one aspect of the pathogenesis of this multifactorial disease, such as platelet function or blood lipids, and therefore have had limited success. Epidemiologic studies show a striking inverse correlation of consumption of fish rich in the two omega-3 fatty acids, eicosapentaenoic acid and docosahexaenoic acid, and mortality from cardiovascular disease. In studies of volunteers and patients, reductions in platelet responsiveness, lowering of blood lipids, and improvements of blood flow, as well as improvements in other values implicated in the pathogenesis of atherosclerosis, were induced with eicosapentaenoic and docosahexaenoic acids. These findings indicate that these omega-3 fatty acids have a larger prophylactic potential than traditional approaches. This potential must be scrutinized in meticulously designed and conducted trials with clinical endpoints. |
Q:
What does it mean? A record deal? And hating on somebody?
Some people started hating on my friend when she got a record deal.
A record deal? what kind of a deal is it?
Does the word "hating" mean envious?
A:
In this context, a record deal could mean one of two things:
It could refer to a recording contract, where a performing artist signs a contract with a record label, also known as a recording studio. For example:
Beyonce signed a new record deal with Arista. Her new album will be released next year.
Or, it could refer to a deal that sets a new record (for something like salary) in any industry; for example, it would make your friend the highest-paid athlete in the history of her sport.
Rousey signed a record deal that will pay her 40 million dollars over the next five years.
There is no way to tell which your sentence means without surrounding context, which is why we often exhort users to provide context when they ask questions here on ELL.
And, yes, I would guess the word "hating" here refers to being envious.
|
Apple stores your Siri queries for up to two years
Apple keeps your Siri data in its servers for up to two years, it has been revealed.
Apple keeps your Siri data in its servers for up to two years, it has been revealed.
Apple spokesperson Trudy Muller told Wired that the company only collects Siri voice clips, which can include questions, messages and other commands, in order to improve the voice-activated personal assistant that was launched with the iPhone 4S in 2011. "Our customers' privacy is very important to us," she said, adding that Apple takes steps to ensure that the data is kept anonymous.
Wired explains that, when a user speaks to Siri, the voice-clip gets sent to Apple's data farm for analysis. Apple creates a random string of numbers to represent the user, therefore keeping their identity anonymous. Each time that user speaks to Siri, the same string of numbers (which is not an Apple ID or email address) will be associated to the voice clips collected.
After six months, Apple "disassociates" the number from the voice recording, but can keep the file for up to 18 more months in order to carry out further testing and help improve Siri, Muller said.
"Apple may keep anonymised Siri data for up to two years," Muller added. "If a user turns Siri off, both identifiers are deleted immediately along with any associated data."
You can turn Siri off on your supported iOS device by going to Settings > General > Siri.
While its understandable that Apple would want to keep Siri data in order to improve the service, American Civil Liberties Union lawyer Nicole Ozer says that Apple should make it clear to users that this is the case in its Siri FAQ, with a link to the Siri Privacy policy. At present, users can only find the Siri Privacy policy within the settings of an iPad or iPhone, so they aren't made aware of Apple's storage of voice clips until after purchasing an iOS device.
"There is no good reason for Apple not to include information about privacy practices on their Siri FAQ page," Ozer told Wired, adding that, while data is anonymous, "what you say to Siri could reveal sensitive things about you, your family, or business."
Gigaom's Erica Ogg highlights that Apple's two years of data storage is longer than Yahoo, Microsoft and Google's, all of which retain search data for 18 months.
How do you feel about Apple's storage of Siri data? Let us know in the comments section below, or on Twitter. |
The effect of intermittent scrotal hyperthermia on the Sprague-Dawley rat testicle.
Twenty-four mature male Sprague-Dawley rats were divided into 2 groups of 12. One group was exposed to intermittent hot baths for 1 month, while the other group was exposed to room temperature baths. The group that was exposed to the elevated temperature demonstrated histological testicular changes that included decreased tubular diameter, basement membrane thinning, and decreased spermatogenesis. Fertility rates were markedly reduced in the heat exposed group, but complete recovery of fertility occurred by 10 weeks after completion of the heat treatments. |
Q:
Take an unknown format string and return a UTF-8 string
The following two strings are different in format but identical in data:
str1 = '\xd7\x91\xd7\xa8\xd7\xa7'
str2 = u'\u05d1\u05e8\u05e7'
I need to implement the following function:
Take a string in either one of the formats above as input
Return the equivalent string in the first format as output
I know that I can encode a string from the second format into the first format.
But how do I determine that the input string is indeed given in the second format?
A:
For Python 3.x, the right thing to do would probably be to try to call encode. (For 3.5+, this will hopefully be as simple as try s.encode('utf-8') except AttributeError: s.)
But for 2.x, the encode will succeed even on str1—by first decoding the UTF-8 string as ASCII (or whatever sys.getdefaultencoding() returns) so it can re-encode it, so you definitely don't want that.
When there is no way to safely EAFP, you have no choice but to LBYL. So:
if isinstance(s, unicode):
return s.encode('utf-8')
else:
return s
Note that I'm using isinstance here, not calling type and comparing. As PEP 8 says:
Object type comparisons should always use isinstance() instead of comparing types directly.
Why? Because instances of subtypes (subclasses, classes registered with ABCs, etc.) are, by definition, supposed to always count as instances of their supertypes. There are some rare cases where you explicitly need to break that rule, in which case type comparisons are what you want. But otherwise, don't use them.
|
Viktor Pimenov
Vaynakh Television
March 11, 1996, in Grozny, Russia
Pimenov, a cameraman for Vaynakh Television, a Chechen station supported by Moscow-backed forces, was fatally shot in the back by a sniper positioned on the roof of a 16-story building in Grozny, the Chechen capital. Pimenov had been filming the devastation caused by the March 6-9 raid on the city. |
Knox Cameron
Knox Cameron (born September 17, 1983 in Kingston) is a Jamaican-born American soccer player who most recently played for AFC Ann Arbor in the National Premier Soccer League.
Career
College and Amateur
Cameron grew up in New York City, attended Cardinal Spellman High School in The Bronx, and played college soccer at the University of Michigan, where he is second in the school's all-time record for goals (28) and points (72), and was named Big Ten Player of the Year his junior year.
Playing in the indoor and rec league's while in Michigan, Cameron excelled in the bare-foot method of playing soccer, and once scored 14 goals in an indoor soccer game while playing with no shoes on.
During his college years Cameron also played in the USL Premier Development League for the Brooklyn Knights and the Michigan Bucks.
Knox also played for Pasco Soccer Club from Wayne, NJ during his high school years. He helped the team win countless tournaments and was one of a handful of players from the club to move on to play professional soccer.
Professional
Cameron suffered a serious knee injury while playing for the Michigan Bucks, and subsequently missed much of his senior year at Michigan. As a result of this, and doubts over his signability, Cameron slipped to the fourth round of the 2005 MLS SuperDraft, where he was drafted by Columbus Crew. He went on to play 30 games and score 4 goals for the team over the next two years, but following the 2006 season, he was waived by the team. During his time with the Crew he played a friendly against English side Everton and thanked them on the scoreboard for coming to Columbus so he could beat them.
Following his release by Crew, Cameron played for amateur team Canton Celtic, which plays in Michigan's MUSL Men's Open 1st Division. Celtic won the Michigan section of the USASA National Amateur Cup Championship, and represented the state at the 2008 USASA Regional tournament in Bowling Green, Kentucky.
Cameron returned to play for the Michigan Bucks in the USL Premier Development League in 2009, and then signed with Detroit City FC in 2012. He made his DCFC debut against the Erie Admirals on May 26, 2012, scoring the first goal in a 3-0 victory. He continued to play for DCFC in 2013, and scored two goals in their opener and another in the home opener. Cameron scored again in DCFC's 2-0 over Zanseville AFC, giving him 4 goals on the season.
Post-Professional
Cameron now is a co-owner and player for AFC Ann Arbor in Ann Arbor, Michigan. Cameron also helps with a youth soccer club called Saline FC.
International
Cameron elected to represent the United States internationally, and played for various youth national teams, being brought to UAE in 2003 for FIFA World Youth Championship.
References
External links
Columbus Crew player profile
Michigan bio
Category:1983 births
Category:Living people
Category:AFC Ann Arbor players
Category:African-American soccer players
Category:American soccer players
Category:Association football forwards
Category:Brooklyn Knights players
Category:Columbus Crew SC draft picks
Category:Columbus Crew SC players
Category:Jamaican emigrants to the United States
Category:Major League Soccer players
Category:Flint City Bucks players
Category:Michigan Wolverines men's soccer players
Category:National Premier Soccer League players
Category:Soccer players from New York (state)
Category:Sportspeople from the Bronx
Category:Sportspeople from Kingston, Jamaica
Category:United States men's under-20 international soccer players
Category:USL League Two players
Category:Cardinal Spellman High School (New York City) alumni |
Antenna arrays are widely used in communication and radar systems because of their high directivity and ability to control beam direction. Some examples of these systems are military radars, vehicles collision avoidance systems, cellular base stations, satellite communication systems, broadcasting, naval communication, weather research, radio-frequency identification (RFID) and synthetic aperture radars. Antenna arrays are excited using either a serial or a corporate feed network. Serially-fed antenna arrays are more compact than their corporate-fed counterparts (e.g., serially-fed antenna arrays have a substantially shorter feeding or transmission line than corporate-fed arrays). Furthermore, the ohmic and feed line radiation losses are smaller in serially-fed arrays than in corporate-fed arrays. Hence, the efficiency of serially-fed arrays can be higher than that of corporate-fed arrays.
Serially-fed antenna arrays are not without their drawbacks, however. For example, serially-fed antenna arrays have a narrow bandwidth due to the non-zero group delay of the feed network causing variation of the phase shift with frequency between the antennas of adjacent antenna units. Therefore, beam direction varies (beam squint) as the frequency changes, thereby reducing the array boresight gain and causing performance degradation, especially in narrow beam width systems.
More particularly, the main beam angle of an antenna array is determined by phase shifts between adjacent antennas of the array. In serially-fed antenna arrays, the phase shift is adjusted using a frequency dependent phase shifter. Therefore, the antenna array beam angle changes as the frequency changes resulting in beam squinting given by equation (1):
θ beam = sin - 1 ( θ f - θ f o K o d E ) ( 1 ) where: θbeam is the main beam angle, θfo and θf are the phase shifts between any two of the adjacent antennas at the center frequency and at an offset frequency, respectively, and dE is the inter-element spacing (i.e., the space between adjacent antennas in the antenna array). According to equation (1), the beam squint occurs because the phase shift between the adjacent antennas varies with frequency. In order to eliminate the beam squint, the phase shift between the antennas must be frequency independent. In other words, the group delay, which is calculated from equation (2) below, between adjacent antennas must be zero.
Group Delay = - 1 2 π d θ f d f ( 2 )
To obtain a zero group delay between the adjacent antennas (and thereby eliminating, or at least substantially reducing, beam squint), one or more NGD circuit(s) may be integrated between the adjacent antennas. In such an instance, the NGD value must be equal to the value of the positive group delay of the interconnecting transmission lines. FIGS. 1A and 1B depict conventional serially-fed antenna array arrangements wherein NGD circuits are integrated between adjacent antennas to have an overall group delay of approximately zero. In FIG. 1A, and for each set of adjacent antennas, an NGD circuit comprising a lossy parallel resonance circuit is serially-integrated into the transmission line between the two antennas. In FIG. 1B, an NGD circuit comprising a lossy series resonator circuit is integrated into the transmission line in a shunt arrangement. In each of these arrangements, in order to have a uniformly excited antenna array, an amplifier and corresponding matching circuits can be used as illustrated in FIGS. 1A and 1B.
The use of conventional NGD circuits in this manner is not without its shortcomings, however. The conventional NGD circuits employ lossy elements (e.g., a lossy resonator) to generate a desirable amount of NGD. As such, these circuits suffer from a large amount of loss in order to generate NGD (e.g., certain conventional NGD circuits may have a typical loss of 6 dB or more, meaning that more than 70-75% of the power is dissipated in the NGD circuit), which significantly limits their application.
Accordingly, there is a need for NGD circuits that minimize and/or eliminate one or more of the above-identified deficiencies. |
General
Nha Trang is a seaside town, also the capital city of Khanh Hoa Province – on the South Central Coast of Vietnam. Nha Trang is becoming increasingly popular in recent years because of its pristine beach, best scuba diving center of Vietnam as well as lots of interesting places and delicious food to enjoy.
08h30: Pick-up at the hotel. Transfer to the National Oceanographic Institute, where performances various sea creatures. It was built at the begin of the century by French.
09h30: Visit Bao Dai Villa, it was built on the hill and surrounded by the poetic scenery.
10h00: Visit Long Son pagoda with the white huge Buhhda statue on the top of Trai Thuy hill, Ponagar tower a typical historic building of Cham people, Chong Ptomontory which is a beautiful sightseeing.
12h30: Have lunch and relax. Then you will soak and relax in Thap Ba Hot Mineral Spring Center (pay ticket which enjoy Mud Bath for yourself)
15h30: Shopping at Dam Market. Then you have a chance to listen about Nha Trang history at The Second of April Square, take photo with Tram Huong Tower and Opera House. Take an over view of Nha Trang city from the hight of Tram Huong Tower. |
-4
Suppose 2*c = -2*s + 38, s = -4*c + 2*c + 23. Let w = 37 - s. Solve 5*g + 3 + w = 0 for g.
-5
Let n(a) = a**2 + 12*a + 4. Let j be n(-12). Suppose 0 = 2*l - j*l + 4. Solve 0*b = l*b for b.
0
Suppose -5*w = -3*w. Suppose i - 6 = -4*q, 3*q - i = 8 - w. Suppose -5*x + 15 = 2*o, 5*o + 4 = 4*x - 8. Solve k - q = -o for k.
2
Let u(l) be the second derivative of l**5/4 + l**4/12 - l**3/2 + l**2/2 - l. Let t be u(2). Let i = t + -27. Solve -i = k + 2*k for k.
-4
Let m be (0 + 0)*(-3)/(-9). Solve -3*b + 6 + 6 = m for b.
4
Suppose 5*c = 0, -4*r + r - 24 = 3*c. Let i = 16 + r. Solve -i*v + 3*v = 10 for v.
-2
Let w(u) be the third derivative of -u**5/60 - u**4/3 - 3*u**3/2 + 3*u**2. Let j be w(-6). Suppose j*m + 1 = 7. Solve 5 = -m*y - 1 for y.
-3
Let g = 101 - 63. Suppose 4*v = -5*s - 46, -v - s - g = 3*v. Let x = 14 + v. Solve x*a - 25 = -0*a for a.
5
Let f be ((-9)/(-27))/(138/45 - 3). Solve f - 14 = -3*o for o.
3
Let j be -18*-2*(-1)/(-3). Suppose 3*s + 3 = j. Solve 0 = s*z - 15 - 0 for z.
5
Let s = -1 + 1. Let d be 8*14/70 + (-4)/(-10). Solve -d*o = -s*o + 4 for o.
-2
Let g = 5 - 1. Solve g*p = -0*p + 12 for p.
3
Let h(u) = -u - 7. Let n be h(-10). Suppose n*l = 6*l. Solve -5*a - 13 + 3 = l for a.
-2
Let l be (36/(-15) - -3)*5. Suppose 0 = -b + l. Solve -5 = b*u + 2*u for u.
-1
Let x(n) = -n**2 + n. Let i be x(-1). Let h be (57/(-6))/(1/i). Let a be h/2 + (-4)/8. Solve 25 = 4*f + a for f.
4
Let h = 9 - 4. Let z(v) = -v**3 - 7*v**2 + 6*v + 1. Let w be z(-8). Let x = w - h. Solve k + x = -3*k for k.
-3
Let h(n) = -n**2 - 5*n. Let y be h(-4). Suppose -2*g + g + 16 = 0. Solve -y*o + 0*o = g for o.
-4
Suppose d = -3*d + 8. Suppose m + 4*v + 4 = 0, 3 = d*v - 1. Let s be (-27)/(-18)*m/(-2). Solve 16 = -5*i - s for i.
-5
Suppose 2*l - 7*l = 2*i - 54, -4*i + 38 = 3*l. Let c(z) = z - 7. Let o be c(9). Solve -3*h - o = l for h.
-4
Suppose 27 + 3 = 3*h. Let m = 12 - h. Solve m = 3*v - 7 for v.
3
Let v be ((-8)/(-5))/(5/50). Let q = 17 - v. Solve 0*f = -f + q for f.
1
Let y be 0/(-2 - -2 - -2). Solve 3*q = 3 - y for q.
1
Suppose -c - 3 = 2*c + n, 4*n = 5*c - 12. Let o(p) = p + 1. Let a be o(c). Solve -a = 3*l - 4 for l.
1
Let o(w) = w**3 + 20*w**2 + 19*w + 2. Let i be o(-19). Solve -i*r = -7*r for r.
0
Let q = 8 - 19. Let m = q - -13. Solve -7 = g - m for g.
-5
Let q be ((-3)/4)/((-12)/64). Solve p + 2 = q for p.
2
Let n(j) = -2 + j - 10*j - 6*j. Let p be n(-8). Suppose 0 = 3*k - 0*s + 2*s - 86, -3*s - p = -5*k. Solve 6 = -4*g + k for g.
5
Suppose 2*h - h - 3 = 0. Suppose -1 = 5*p + m + 7, 4*m - 6 = -p. Let l be (3/p)/((-12)/32). Solve -5 = -h*v + l for v.
3
Let b = 4 - 6. Let i be (3/b)/((-3)/18). Solve j + i = 4*j for j.
3
Let n(s) = 3*s**2 - 33*s - 30. Let x(z) = z**2 - 11*z - 10. Let o(g) = -3*n(g) + 8*x(g). Let j be o(10). Solve -3*d - 2*d = -j for d.
4
Let y(c) = -c**2 + 13. Let f be y(0). Solve -5*o + 2 = -f for o.
3
Let i(y) = 3*y + 65. Let u be i(-20). Solve 2 = u*d - 8 for d.
2
Let j = 19 - 19. Suppose -5*d - 4 + 19 = 0. Solve s + j*s = d for s.
3
Let t(g) = -g**2 + 5*g. Let b be t(4). Let o(h) = -h - 2. Let z be o(-3). Solve 0 = -b*l + 9 - z for l.
2
Let c(f) = -f**2 - 11*f + 26. Let l be c(-13). Solve -u = -l*u + 4 for u.
-4
Let p be 2*(-12)/(-32)*4. Solve 0 = p*r - 2*r - 2 for r.
2
Suppose r - 12 = -0*r - 2*m, -10 = -5*m. Suppose 3*o + 20 = r*o. Solve 0 = -0*y + o*y for y.
0
Let m = -20 + 24. Let h be (-4)/(-1) - (0 - -1). Solve h*v - 5 = m for v.
3
Suppose -b + 3*d - 7 = -d, 2*d = 2*b - 4. Suppose b*a = -0*a. Solve 5*u = -a*u for u.
0
Suppose -11 + 61 = 5*d. Let l(y) = -4*y - 7. Let b be l(-7). Let q = -11 + b. Solve -q - d = 5*g for g.
-4
Let n(f) = -f**3 + 6*f**2 - 4*f - 4. Let j be n(5). Let w be (3/3)/j + 3. Solve w*i - 17 = -1 for i.
4
Let i be 0/(-3 + 2 + -1). Suppose -3*m + i*m = 0. Solve m = -4*y - 13 + 1 for y.
-3
Suppose -2*y = 4 - 14. Suppose 3*d - 3 = -3*i, y*d + i = -1 + 10. Let p(z) = z**2 - 3*z - 4. Let l be p(5). Solve d*m - l*m = -4 for m.
1
Let b(a) = a + 8. Let c be b(-6). Let p be 2 + 0 + 0 + c. Solve 3*j = p - 19 for j.
-5
Let x = -14 - -14. Solve -6*l + l + 5 = x for l.
1
Suppose 5 = 3*v - 7. Solve -v = 3*c - c for c.
-2
Let g be (-4)/2*35/(-14). Solve -t = -0*t - g for t.
5
Suppose 0 = -6*o + o + 75. Suppose 0*s + o = 3*s. Let j be (3/1)/(11/11). Solve 4*w - s*w = j for w.
-3
Let c be (2/3)/(8/(-12)). Let b = 2 - c. Solve -b*f + 4 = -f for f.
2
Let x(y) = 2*y**2 - 2 - y + y**3 - 3*y**2 + 0*y**2 - 2*y**3. Let m = 5 - 7. Let w be x(m). Solve 0 = v + 3 - w for v.
1
Suppose 27 + 33 = 12*p. Solve 3*d - p - 1 = 0 for d.
2
Suppose 0 = -4*l - 3*z - 13, -z = 2*l + 4 + 1. Let m = 0 - l. Let j = 1 - m. Solve j = 5*x - 2*x for x.
0
Suppose j - 4 = -3*p - 1, 5*p + 2*j - 6 = 0. Solve p = -m - 1 for m.
-1
Let k be 3/(-2) + 14/4. Solve 0*v + k*v = 8 for v.
4
Suppose -5*f + 4 = -p + 32, -3*p - 16 = 5*f. Solve 1 = c + p for c.
-2
Let p = 166 - 116. Suppose 0 = 3*t + 2*t - p. Solve t = 4*q - 9*q for q.
-2
Suppose -3*w = -0*w. Solve 4*k = -w*k for k.
0
Let b = 3 - 3. Suppose k + 2*t = 3, 0 = -0*k - 2*k + 4*t + 6. Solve b = -0*w + 3*w - k for w.
1
Suppose -5*m + 16 = -2*w, -m - 14 = -w - 4*m. Suppose 1 = -3*v - o + 3, -2*o - 4 = w*v. Suppose -5*d = 3*i - 88, 0*i = v*d + 3*i - 28. Solve d = -4*q + 4 for q.
-4
Suppose -20 = -j + 3*x, -2*x - 3*x - 15 = 2*j. Suppose 5 = r - 0. Suppose -3*s + 3*y + 10 = -4*s, -4*s - j*y - r = 0. Solve -4 - 6 = -s*p for p.
2
Let p be 309/21 - (-4)/14. Let s = 22 + -18. Solve -s*a + 1 = -p for a.
4
Let o(k) = -k**3 - 4*k**2 - 5*k - 2. Let w be o(-3). Let c be (-4)/(-2)*10/w. Solve -c*t - 10 = -3*t for t.
-5
Let j be 4/(-10) - (-36)/15. Let y(u) = u. Let h be y(0). Suppose -3*m + h*m - 12 = 0, 3*c - 4*m = 25. Solve -j*r - 15 = c*r for r.
-3
Let g be 4/(-7)*(4 - 11). Suppose 5*t + 0 = -5, 3*q - g*t = 13. Solve 2*x = -q*x - 10 for x.
-2
Suppose 0 = 2*f + 2*f - 108. Solve -11 + f = 4*v for v.
4
Let y be (2/1)/(10/(-45)). Let m = 14 + y. Solve -2*n = 3 + m for n.
-4
Let r be ((-12)/8)/((-2)/(-24)). Let a be (-4)/r + 4/(-18). Solve a = -0*l - 3*l for l.
0
Let o(d) be the third derivative of d**6/120 + d**5/20 - d**4/6 + d**3/3 + 2*d**2. Let l be o(-4). Solve 6*u - 4 = l*u for u.
1
Suppose 8*b = 10 + 14. Solve -b*w = -6*w + 9 for w.
3
Let z(i) = -2 - 8*i + 5*i + 2*i + 6. Let k be z(2). Let j be 10*k/12*3. Solve -j*d = -d - 12 for d.
3
Let h = -13 - -12. Let m = 3 - h. Solve q - m = -0*q for q.
4
Let u(c) = -7*c - 3. Let v(f) = 27*f + 11. Let g(a) = 22*u(a) + 6*v(a). Let i be g(1). Solve 7 + i = 5*l for l.
3
Let c = 3 - 0. Suppose -c*g = 2*g + 5. Let o be (1/g)/((-3)/9). Solve 0 = o*b - 4*b for b.
0
Let n(d) = -d + 1. Let k be n(4). Let i be -1 + -10 - (k - -1). Let o(l) = -l**3 - 9*l**2 - 2*l - 8. Let q be o(i). Solve -5*f - 10 = q for f.
-4
Let i be ((-1)/(-2))/(1/6). Let p(c) = c + c**2 + i - 1 - 2. Let k be p(-1). Solve -5*l = -k*l for l.
0
Let m = 25 - 16. Suppose -20 = -33*v + 28*v. Solve o = v*o - m for o.
3
Let g(m) = -m**2 + 6*m - 6. Let j be g(3). Solve 2*f + j*f = 20 for f.
4
Let p(b) = -7*b**2 - b + 10. Let w(a) = 11*a**2 + a - 15. Let h(t) = -8*p(t) - 5*w(t). Let s be h(-5). Solve v + s = 3 for v.
-2
Suppose 3*t - 46 = 7*t + 3*s, t + 2 = 4*s. Suppose -3*j + 25 - 70 = 0. Let g be (-86)/t + j/25. Solve -l - l = -g for l.
4
Let z be 8 + (-4)/(-12)*0. Solve -u = u - z for u.
4
Suppose -3*m + 5*w + 39 = -1, 0 = 5*m + 2*w - 46. Solve -m = 3*j - j for j.
-5
Let v be (-3)/(-2)*(-12)/(-6). Solve v*j + 0*j = 3 for j.
1
Let t = 32 + 14. Let z = 67 - t. Let j = -13 + z. Solve -5*h + j + 2 = 0 for h.
2
Let p = -15 + 21. Solve -p*s + s + 15 = 0 for s.
3
Suppose -2*c + 2*n + 7 = -1, -n = c + 2. Suppose -c = -5*h + 9. Solve -14 = -4*v + h for v.
4
Suppose -3*h = 2*h + 10. Let a be (-29)/9 + h/(-9). Let s be a/(-2)*16/6. Solve s*q = q for q.
0
Suppose 11 - 39 = 2*i. Let f = i + 20. Solve w = f*w for w.
0
Let c be -3*(5/(-3) - -1). Solve 3*d - c*d = -1 for d.
-1
Let f = -99 + 101. Solve -f*r = r + 9 for r.
-3
Let c(l) = -l**3 + l - 1. Let y be c(1). Let x = 3 + y. Let k be (-1)/x + (-5)/(-10). Solve k*v + 12 = -4*v for v.
-3
Let o be 9/2 - 9/18. Solve o*y = -3 - 5 for y.
-2
Let g(j) = 0*j**3 + 3*j**2 + 1 + j**3 + 3 - j**2 - 2*j. Let i be g(-3). Suppose 4*v - 7 - 9 = 0. Solve 7 = -v*r - i for r.
-2
Let o(k) = k**3 - 5*k**2 + |
Sarasota Reds
The Sarasota Reds were a professional minor league baseball team, located in Sarasota, Florida, as a member of the Florida State League. However team originally started play in Sarasota as the Sarasota White Sox in 1989. They remained in the city for the next 21 seasons, going through a series of name changes due to their affiliation changes. They were known as the White Sox from 1989–1993, as the Sarasota Red Sox from 1994–2004, and the Reds from 2004–2009. In Sarasota, the team played in Payne Park (1989) and then Ed Smith Stadium (1990–2009). They won two division championships, in 1989 and 1992, and made playoff appearances in 1989, 1991, 1992, 1994, and 2007.
However the roots of the Reds can be traced back, even further, to the Tampa Tarpons. In the 1980s rumors arose that a major league team would come to Tampa, which would threaten the viability of the Tarpons and other minor league teams in the Tampa Bay Area. In 1988 the Chicago White Sox replaced Cincinnati as the Tarpons' affiliate, launching murmurs that the White Sox would themselves relocate to the area. Fearing his team would soon be displaced, in 1989 Tarpons owner Mitchell Mick sold his franchise to the White Sox, who moved it to Sarasota, Florida as the Sarasota White Sox.
The team's Sarasota era produced many notable player who would go on to play in majors. Bo Jackson, Mike LaValliere, Dave Stieb, Hall of Famer Frank Thomas and Bob Wickman all played for the Sarasota White Sox. Meanwhile, Stan Belinda, David Eckstein, Nomar Garciaparra, Byung-hyun Kim, Jeff Suppan, Dustin Pedroia, Jonathan Papelbon, and Kevin Youkilis were alumni of the Sarasota Red Sox. The Sarasota Reds also produced many notable major league players such as Jay Bruce, Johnny Cueto, Joey Votto, Chris Heisey, and Drew Stubbs.
After the Reds' spring-training departure from Florida's Grapefruit League to Arizona's Cactus League in 2009, the Reds and Pittsburgh Pirates did an "affiliate-swap". The Pirates took over the Sarasota Reds, while the Reds became the parent club of the Pirates' former Class A-Advanced affiliate, the Lynchburg Hillcats of the Carolina League. The Pittsburgh Pirates have had their spring training facilities based in Bradenton, Florida since in 1969, when the city met with Pirates' general manager Joe Brown and owner John W. Galbreath and both sides agreed to a lease of 40 years, with an option for another 40 years. On November 10, 2009, baseball officials voted to allow the Pirates to purchase and uproot the Sarasota Reds. The Pirates moved the team to Bradenton, where they were renamed the Bradenton Marauders. The Marauders became the first Florida State League team located in Bradenton since the Bradenton Growers folded in 1926.
Logos and uniforms
The Sarasota teams' names, logos and team colors were all closely associated with each's parent club. For example, the logos for Sarasota White Sox, Red Sox and Reds were just slightly altered versions of the parent club logos. However, there were attempts to allow some of these teams to find their own unique identities. In 2000, the Sarasota Red Sox introduced their mascot Gordy the Gecko. The Red Sox front office felt that since the team was based in Florida, its mascot should be reflective to the area. Soon Gordy found his way on to the team's caps as an alternate logo.
Season-by-season record
Notable alumni
Former White Sox players
Former Red Sox players
Former Reds players
References
Category:Baseball teams established in 1989
Category:Defunct Florida State League teams
Category:Sports in Sarasota County, Florida
Category:Boston Red Sox minor league affiliates
Category:Chicago White Sox minor league affiliates
Category:Cincinnati Reds minor league affiliates
Category:Defunct baseball teams in Florida
Category:1989 establishments in Florida
Category:2009 disestablishments in Florida
Category:Baseball teams disestablished in 2009 |
Q:
iOS - Passing LaunchOptions to a sub-method
Im trying to add an asyncronous lookup for Push Notifications and I'm having a problem passing launchOptions to the*@selector. Can you please tell me what I need to change?
- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
{
/* Operation Queue init (autorelease) */
NSOperationQueue *queue = [NSOperationQueue new];
/* Create NSInvocationOperation to call loadDataWithOperation, passing in nil */
NSInvocationOperation *operation = [[NSInvocationOperation alloc] initWithTarget:self selector:@selector(setupPushNotifications) object:launchOptions];
[queue addOperation:operation]; /* Add the operation to the queue */
[operation release];
}
and
-(void)setupPushNotifications:(NSDictionary *)launchOptions
{
//Init Airship launch options
NSMutableDictionary *takeOffOptions = [[[NSMutableDictionary alloc] init] autorelease];
[takeOffOptions setValue:launchOptions forKey:UAirshipTakeOffOptionsLaunchOptionsKey];
// Create Airship singleton that's used to talk to Urban Airship servers.
// Please populate AirshipConfig.plist with your info from http://go.urbanairship.com
[UAirship takeOff:takeOffOptions];
NSLog(@"Registering for Notifications");
// Register for notifications
[[UIApplication sharedApplication]
registerForRemoteNotificationTypes:(UIRemoteNotificationTypeBadge |
UIRemoteNotificationTypeSound |
UIRemoteNotificationTypeAlert)];
}
A:
change
NSInvocationOperation *operation = [[NSInvocationOperation alloc] initWithTarget:self selector:@selector(setupPushNotifications) object:launchOptions];
to
NSInvocationOperation *operation = [[NSInvocationOperation alloc] initWithTarget:self selector:@selector(setupPushNotifications:) object:launchOptions];
|
---
abstract: 'Inspired by the paper of Tasaka [@tasaka], we study the relations between totally odd, motivic depth-graded multiple zeta values. Our main objective is to determine the rank of the matrix $C_{N,r}$ defined by Brown [@Brown]. We will give new proofs for (conjecturally optimal) upper bounds on ${\operatorname{rank}}C_{N,3}$ and ${\operatorname{rank}}C_{N,4}$, which were first obtained by Tasaka [@tasaka]. Finally, we present a recursive approach to the general problem, which reduces the evaluation of ${\operatorname{rank}}C_{N,r}$ to an isomorphism conjecture.'
address:
- 'Charlotte Dietze, Max-Planck-Institut für Mathematik,Vivatsgasse 7,53111 Bonn, Germany'
- 'Chorkri Manai, Max-Planck-Institut für Mathematik,Vivatsgasse 7,53111 Bonn, Germany'
- 'Christian Nöbel, Max-Planck-Institut für Mathematik,Vivatsgasse 7,53111 Bonn, Germany'
- 'Ferdinand Wagner, Max-Planck-Institut für Mathematik,Vivatsgasse 7,53111 Bonn, Germany'
author:
- Charlotte Dietze
- Chokri Manai
- Christian Nöbel
- Ferdinand Wagner
bibliography:
- 'mzv.bib'
date: September 2016
title: 'Totally Odd Depth-graded Multiple Zeta Values and Period Polynomials'
---
Introduction
============
In this paper we will be interested in $\mathbb{Q}$-linear relations among totally odd depth-graded multiple zeta values (MZVs), for which there conjecturally is a bijection with the kernel of a specific matrix $C_{N,r}$ connected to restricted even period polynomials (for a definition, see [@schneps] or [@gkz2006 Section 5]). For integers $n_1,\ldots,n_{r-1}\geq1$ and $n_r\geq2$, the MZV of $n_1,\ldots,n_r$ is defined as the number $$\begin{aligned}
\zeta(n_1,\ldots,n_r)\coloneqq \sum_{0<k_1<\cdots<k_r} \frac{1}{k_1^{n_1}\cdots k_r^{n_r}}{\,}.\end{aligned}$$ We call the sum $n_1+\cdots+n_r$ of arguments the weight and their number $r$ the depth of $\zeta(n_1,\ldots,n_r)$. One classical question about MZVs is counting the number of linearly independent $\mathbb Q$-linear relations between MZVs. It is highly expected, but for now seemingly out of reach that there are no relations between MZVs of different weight. Such questions become reachable when considered in the motivic setting. Motivic MZVs $\zeta^{\mathfrak m}(n_1,\ldots,n_r)$ are elements of a certain $\mathbb Q$-algebra $\mathcal H=\bigoplus_{N\geq 0}\mathcal H_N$ which was constructed by Brown in [@brownMixedMotives] and is graded by the weight $N$. Any relation fulfilled by motivic MZVs also holds for the corresponding MZVs via the period homomorphism $per\colon\mathcal H\to \mathbb R$.
We further restrict to depth-graded MZVs: Let $\mathcal Z_{N,r}$ and $\mathcal H_{N,r}$ denote the $\mathbb Q$-vector space spanned by the real respectively motivic MZVs of weight $N$ and depth $r$ modulo MZVs of lower depth. The depth-graded MZV of $n_1,\ldots,n_r$, that is, the equivalence class of $\zeta(n_1,\ldots,n_r)$ in $\mathcal Z_{N,r}$, is denoted by $\zeta_{\mathfrak D}(n_1,\ldots,n_r)$. The elements of $\mathcal H_{N,r}$ are denoted $\zeta_{\mathfrak D}^{\mathfrak m}(n_1,\ldots,n_r)$ analogously. The dimension of $\mathcal Z_{N,r}$ is subject of the Broadhurst-Kreimer Conjecture.
The generating function of the dimension of the space $\mathcal Z_{N,r}$ is given by $$\begin{aligned}
\sum_{N,r\geq0}\dim_{\mathbb Q}\mathcal Z_{N,r}\cdot x^N y^r\overset?= \frac{1- \mathbb E(x)y}{1-\mathbb O(x)y+\mathbb S(x) y^2 - \mathbb S(x)y^4}{\,},\end{aligned}$$ where we denote $\mathbb E(x)\coloneqq \frac{x^2}{1-x^2}=x^2+x^4+x^6+\cdots$, $\mathbb O(x)\coloneqq \frac{x^3}{1-x^2}=x^3+x^5+x^7+\cdots$, and $\mathbb S(x)\coloneqq \frac{x^{12}}{(1-x^4)(1-x^6)}$.
It should be mentioned that $\mathbb S(x)=\sum_{n>0}\dim\mathcal S_n\cdot x^n$, where $\mathcal S_n$ denotes the space of cusp forms of weight $n$, for which there is an isomorphism to the space of restricted even period polynomials of degree $n-2$ (defined in [@schneps] or [@gkz2006 Section 5]).
In his paper [@Brown], Brown considered the $\mathbb Q$-vector space $\mathcal Z_{N,r}^{{\operatorname{odd}}}$ (respectively $\mathcal H_{N,r}^{{\operatorname{odd}}}$) of totally odd (motivic) and depth-graded MZVs, that is, $\zeta_{\mathfrak D}(n_1,\ldots,n_r)$ (respectively $\zeta_{\mathfrak D}^{\mathfrak m}(n_1,\ldots,n_r)$) for $n_i\geq3$ odd, and linked them to a certain explicit matrix $C_{N,r}$, where $N=n_1+\cdots+n_r$ denotes the weight. In particular, he showed that any right annihilator $(a_{n_1,\ldots,n_r})_{(n_1,\ldots,n_r)\in S_{N,r}}$ of $C_{N,r}$ induces a relation $$\begin{aligned}
\sum_{(n_1,\ldots,n_r)\in S_{N,r}}a_{n_1,\ldots,n_r}\zeta_{\mathfrak D}^{\mathfrak m}(n_1,\ldots,n_r)=0{\,},\text{ hence also }\sum_{(n_1,\ldots,n_r)\in S_{N,r}}a_{n_1,\ldots,n_r}\zeta_{\mathfrak D}(n_1,\ldots,n_r)=0\end{aligned}$$(see Section \[sec:preliminaries\] for the notations) and conjecturally all relations in $\mathcal Z_{N,r}^{{\operatorname{odd}}}$ arise in this way. This led to the following conjecture (the uneven part of the Broadhurst-Kreimer Conjecture).
\[con:Brown\] The generating series of the dimension of $\mathcal Z_{N,r}^{{\operatorname{odd}}}$ and the rank of $C_{N,r}$ are given by $$\begin{aligned}
1+\sum_{N,r>0}{\operatorname{rank}}C_{N,r}\cdot x^Ny^r\overset?=1+\sum_{N,r>0}\dim_{\mathbb Q}\mathcal Z_{N,r}^{{\operatorname{odd}}}\cdot x^Ny^r\overset?=\frac1{1-\mathbb O(x)y+\mathbb S(x)y^2}{\,}.\end{aligned}$$
The contents of this paper are as follows. In Section \[sec:preliminaries\], we explain our notations and define the matrices $C_{N,r}$ due to Brown [@Brown] as well as $E_{N,r}$ and $E_{N,r}^{(j)}$ considered by Tasaka [@tasaka]. In Section \[sec:known results\], we briefly state some of Tasaka’s results on the matrix $E_{N,r}$. Section \[sec:main tools\] is devoted to further investigate the connection between the left kernel of $E_{N,r}$ and restricted even period polynomials, which was first discovered by Baumard and Schneps [@schneps] and appears again in [@tasaka Theorem 3.6]. In Section \[sec:main results\], we will apply our methods to the cases $r=3$ and $r=4$. The first goal of Section \[sec:main results\] will be to show
\[thm:case3\]Assume that the map from Theorem \[thm:injection\] is injective. We then have the lower bound $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,3}\cdot x^N\geq 2 \mathbb O(x)\mathbb S(x){\,},\end{aligned}$$ where $\geq$ means that for every $N>0$ the coefficient of $x^N$ on the right-hand side does not exceed the corresponding one on the left-hand side.
This was stated without proof in [@tasaka]. Furthermore, we will give a new proof by the polynomial methods developed in Section \[sec:main tools\] for the following result.
\[thm:case4\]Assume that the map from Theorem \[thm:injection\] is injective. We then have the lower bound $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,4}\cdot x^N\geq 3 \mathbb O(x)^2\mathbb S(x)-\mathbb S(x)^2{\,}.\end{aligned}$$
In the last two subsections of this paper, we will consider the case of depth 5 and give an idea for higher depths. For depth 5, we will prove that upon Conjecture \[con:isomorphism\] due to Tasaka ([@tasaka Section 3]), the lower bound predicted by Conjecture \[con:Brown\] holds, i.e. $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,5}\cdot x^N\geq 4 \mathbb O(x)^3\mathbb S(x)-3 \mathbb O(x)\mathbb S(x)^2{\,}.\end{aligned}$$ These bounds are conjecturally sharp (i.e. the ones given by Conjecture \[con:Brown\]). Finally, we will prove a recursion for value of $\dim_{\mathbb Q}\ker C_{N,r}$ under the assumption of a similar isomorphism conjecture stated at the end of Section \[sec:main tools\], which was proposed by Claire Glanois.
Acknowledgments {#acknowledgments .unnumbered}
---------------
This research was conducted as part of the Hospitanzprogramm (internship program) at the Max-Planck-Institut für Mathematik (Bonn). We would like to express our deepest thanks to our mentor, Claire Glanois, for introducing us into the theory of multiple zeta values. We are also grateful to Daniel Harrer, Matthias Paulsen and Jörn Stöhler for many helpful comments.
Preliminaries {#sec:preliminaries}
=============
Notations
---------
In this section we introduce our notations and we give some definitions. As usual, for a matrix $A$ we define $\ker A$ to be the set of right annihilators of $A$. Apart from this, we mostly follow the notations of Tasaka in his paper [@tasaka]. Let $$\begin{aligned}
S_{N,r}\coloneqq \left\{(n_1,\ldots,n_r)\in\mathbb Z^r\ |\ n_1+\cdots+n_r=N,\ n_1,\ldots,n_r\geq3\text{ odd}\right\}{\,},\end{aligned}$$ where $N$ and $r$ are natural numbers. Since the elements of the set $S_{N,r}$ will be used as indices of matrices and vectors, we usually arrange them in lexicographically decreasing order. Let $$\begin{aligned}
\mathbf V_{N,r}\coloneqq \left\langle \left.x_1^{m_1-1}\cdots x_r^{m_r-1}\ \right|\ (m_1,\ldots,m_r)\in S_{N,r}\right\rangle_\mathbb{Q}\end{aligned}$$denote the vector space of restricted totally even homogeneous polynomials of degree $N-r$ in $r$ variables. There is a natural isomorphism from $\mathbf V_{N,r}$ to the $\mathbb Q$-vector space ${\mathsf{Vect}}_{N,r}$ of $n$-tuples $(a_{n_1,\ldots,n_r})_{(n_1,\ldots,n_r)\in S_{N,r}}$ indexed by totally odd indices $(n_1,\ldots,n_r)\in S_{N,r}$, which we denote $$\begin{aligned}
\label{eq:natiso}
\begin{split}
\pi\colon\mathbf V_{N,r}&\overset{\sim\,}{\longrightarrow}{\mathsf{Vect}}_{N,r}\\
\sum_{(n_1,\ldots,n_r)\in S_{N,r}}a_{n_1,\ldots,n_r}x_1^{n_1-1}\cdots x_r^{n_r-1}&\longmapsto \left(a_{n_1,\ldots,n_r}\right)_{(n_1,\ldots,n_r)\in S_{N,r}}{\,}.
\end{split} \end{aligned}$$ We assume vectors to be row vectors by default.
Finally, let $\mathbf W_{N,r}$ be the vector subspace of $\mathbf V_{N,r}$ defined by $$\begin{aligned}
\mathbf W_{N,r}\coloneqq \left\{P\in\mathbf V_{N,r}\ |\ P(x_1,\ldots,x_r)\right.&=P(x_2-x_1,x_2,x_3,\ldots,x_r)\\&\left.\phantom=-P(x_2-x_1,x_1,x_3,\ldots,x_r)\right\}{\,}.\end{aligned}$$ That is, $P(x_1,x_2,x_3,\ldots,x_r)$ is a sum of restricted even period polynomials in $x_1,x_2$ multiplied by monomials in $x_3,\ldots,x_r$. More precisely, one can decompose $$\begin{aligned}
\mathbf W_{N,r}=\bigoplus_{\substack{1<n<N\\n\text{ even}}}\mathbf W_{n,2}\otimes \mathbf V_{N-n,r-2} \label{eq:decomposition}{\,},\end{aligned}$$ where $\mathbf W_{n,2}$ is the space of restricted even period polynomials of degree $n-2$. Since $\mathbf W_{n,2}$ is isomorphic to the space $\mathcal S_n$ of cusp forms of weight $n$ by Eichler-Shimura correspondence (see [@zagier]), leads to the following dimension formula.
\[lem:wnreq\] For all $r\geq 2$, $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\mathbf W_{N,r}\cdot x^N= \mathbb O(x)^{r-2} \mathbb S(x){\,}.\end{aligned}$$
Ihara action and the matrices $E_{N,r}$ and $C_{N,r}$
-----------------------------------------------------
We use Tasaka’s notation (from [@tasaka]) for the polynomial representation of the Ihara action defined by Brown [@Brown Section 6]. Let $$\begin{aligned}
{\mathbin{\underline{\circ}}}\colon\mathbb Q[x_1]\otimes\mathbb Q[x_2,\ldots,x_r]&\longrightarrow\mathbb Q[x_1,\ldots,x_r] \\
f\otimes g&\longmapsto f{\mathbin{\underline{\circ}}}g{\,},\end{aligned}$$where $f{\mathbin{\underline{\circ}}}g$ denotes the polynomial $$\begin{gathered}
(f{\mathbin{\underline{\circ}}}g)(x_1,\ldots,x_r)\coloneqq f(x_1)g(x_2,\ldots,x_r)+\sum_{i=1}^{r-1}\Bigl(f(x_{i+1}-x_i)g(x_1,\ldots,\hat x_{i+1},\ldots,x_r)\\
-(-1)^{\deg f}f(x_i-x_{i+1})g(x_1,\ldots,\hat x_i,\ldots,x_r)\Bigr){\,}.\end{gathered}$$ (the hats are to indicate, that $x_{i+1}$ and $x_i$ resp. are omitted in the above expression).
For integers $m_1,\ldots,m_r,n_1,\cdots,n_r \geq 1$, let furthermore the integer $e{{\textstyle\binom{m_1,\ldots,m_r}{n_1,\ldots,n_r}}}$ denote the coefficient of $x_1^{n_1-1}\cdots x_r^{n_r-1}$ in $x_1^{m_1-1} {\mathbin{\underline{\circ}}}\left(x_1^{m_2-1}\cdots x_{r-1}^{m_r-1}\right)$, i.e. $$\begin{aligned}
\label{eq:e}
x_1^{m_1-1} {\mathbin{\underline{\circ}}}\left(x_1^{m_2-1}\cdots x_{r-1}^{m_r-1}\right) = \sum_{\substack{n_1 + \cdots + n_r = m_1 + \cdots + m_r \\ n_1, \cdots, n_r \geq 1}} e{{\textstyle\binom{m_1,\ldots,m_r}{n_1,\ldots,n_r}}}x_1^{n_1-1}\cdots x_r^{n_r-1}{\,}.\end{aligned}$$ Note that $e{{\textstyle\binom{m_1,\ldots,m_r}{n_1,\ldots,n_r}}}=0$ if $m_1+\cdots+m_r\not=n_1+\cdots+n_r$.
One can explicitly compute the integers $e{{\textstyle\binom{m_1,\ldots,m_r}{n_1,\cdots,n_r}}}$ by the following formula: ([@tasaka Lemma 3.1]) $$\begin{gathered}
e{{\textstyle\binom{m_1,\ldots,m_r}{n_1,\ldots,n_r}}}=\delta{{\textstyle\binom{m_1,\ldots,m_r}{n_1\ldots,n_r}}}+\sum_{i=1}^{r-1}\delta{{\textstyle\binom{\hat m_1,m_2,\ldots,m_i,\hat m_{i+1},m_{i+2},\ldots,m_r}{n_1,\ldots,n_{i-1},\hat n_i,\hat n_{i+1},n_{i+2},\ldots,n_r}}}\\
\cdot\left((-1)^{n_i}\binom{m_1-1}{n_i-1}+(-1)^{m_1-n_{i+1}}\binom{m_1-1}{n_{i+1}-1}\right)$$ (again, the hats are to indicate that $m_1,m_{i+1},n_i,n_{i+1}$ are omitted), where $$\begin{aligned}
\delta{{\textstyle\binom{m_1,\ldots,m_{s}}{n_1,\ldots,n_{s}}}} \coloneqq
\begin{cases}
1\quad\text{if } m_i=n_i \text{ for all }i\in\{1,\ldots,s\} \\
0\quad\text{else}
\end{cases}\end{aligned}$$ denotes the usual Kronecker delta.
\[def:enrq\] Let $N,r$ be positive integers.
- We define the $|S_{N,r}|\times |S_{N,r}|$ matrix $$\begin{aligned}
E_{N,r}\coloneqq \left(e{{\textstyle\binom{m_1,\ldots,m_r}{n_1,\ldots,n_r}}}\right)_{(m_1,\ldots,m_r),(n_1,\ldots,n_r)\in S_{N,r}}{\,}.\end{aligned}$$
- For integers $r\geq j\geq 2$ we also define the $|S_{N,r}|\times |S_{N,r}|$ matrix $$\begin{aligned}
E_{N,r}^{(j)}\coloneqq \left(\delta{{\textstyle\binom{m_1,\ldots,m_{r-j}}{n_1,\ldots,n_{r-j}}}}e{{\textstyle\binom{m_{r-j+1},\ldots,m_r}{n_{r-j+1},\ldots,n_r}}} \right)_{(m_1,\ldots,m_r),(n_1,\ldots,n_r)\in S_{N,r}}{\,}.\end{aligned}$$
\[def:cnr\] The $|S_{N,r}|\times |S_{N,r}|$ matrix $C_{N,r}$ is defined as $$\begin{aligned}
C_{N,r}\coloneqq E_{N,r}^{(2)}\cdot E_{N,r}^{(3)}\cdots E_{N,r}^{(r-1)}\cdot E_{N,r}{\,}.
\end{aligned}$$
Known Results {#sec:known results}
=============
Recall the map $\pi\colon\mathbf V_{N,r}\rightarrow{\mathsf{Vect}}_{N,r}$ (equation ). Theorem \[thm:Schneps\] due to Baumard and Schneps [@schneps] establishes a connection between the left kernel of the matrix $E_{N,2}$ and the space $\mathbf W_{N,2}$ of restricted even period polynomials. This connection was further investigated by Tasaka [@tasaka], relating $\mathbf W_{N,r}$ and the left kernel of $E_{N,r}$ for arbitrary $r\geq2$.
\[thm:Schneps\] For each integer $N>0$ we have $$\begin{aligned}
\pi\left(\mathbf W_{N,2}\right)=\ker{\prescript{t\!}{}{E}}_{N,2}{\,}.\end{aligned}$$
\[thm:injection\] Let $r\geq2$ be a positive integer and $F_{N,r}=E_{N,r}-{\operatorname{id}}_{{\mathsf{Vect}}_{N,r}}$. Then, the following $\mathbb Q$-linear map is well-defined: $$\begin{aligned}
\label{eq:TasakasFail}
\begin{split}
\mathbf W_{N,r}&\longrightarrow \ker{\prescript{t\!}{}{E}}_{N,r}\\
P(x_1,\ldots,x_r)&\longmapsto\pi(P)F_{N,r}{\,}.
\end{split}
\end{aligned}$$
\[con:isomorphism\]For all $r\geq2$, the map described in Theorem \[thm:injection\] is an isomorphism.
\[rem:isor2\] For now, only the case $r=2$ is known, which is an immediate consequence of Theorem \[thm:Schneps\]. In [@tasaka], Tasaka suggests a proof of injectivity, but it seems to contain a gap, which, as far as the authors are aware, couldn’t be fixed yet. However, assuming the injectivity of morphisms one has the following relation.
\[cor:enrineq\]For all $r\geq2$, $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker{\prescript{t\!}{}{E}}_{N,r}\cdot x^N\geq\mathbb O(x)^{r-2}\mathbb S(x){\,}.
\end{aligned}$$
Main Tools {#sec:main tools}
==========
Decompositions of $E_{N,r}^{(j)}$
---------------------------------
We use the following decomposition lemma:
\[lem:blockdia\] Let $2\leq j\leq r-1$ and arrange the indices $(m_1,\ldots,m_r),(n_1,\ldots,n_r)\in S_{N,r}$ of $E_{N,r}^{(j)}$ in lexicographically decreasing order. Then, the matrix $E_{N,r}^{(j)}$ has block diagonal structure $$\begin{aligned}
E_{N,r}^{(j)}={\operatorname{diag}}\left(E_{3r-3,r-1}^{(j)},E_{3r-1,r-1}^{(j)},\ldots,E_{N-3,r-1}^{(j)}\right){\,}.\end{aligned}$$
This follows directly from Definition \[def:enrq\].
\[cor:blockdia\] We have $$\begin{aligned}
E_{N,r}^{(2)}E_{N,r}^{(3)}\cdots E_{N,r}^{(r-1)}={\operatorname{diag}}\left(C_{3r-3,r-1},C_{3r-1,r-1},\ldots,C_{N-3,r-1}\right){\,}.
\end{aligned}$$
Multiplying the block diagonal representations of $E_{N,r}^{(2)},E_{N,r}^{(3)},\ldots,E_{N,r}^{(r-1)}$ block by block together with Definition \[def:cnr\] yields the desired result.
\[cor:enrjocnr\] For all $r\geq 3$, $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker\left(E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}\right)\cdot x^N=\mathbb O(x)\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,r-1}\cdot x^N{\,}.
\end{aligned}$$
According to Corollary \[cor:blockdia\], the matrix $E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}$ has block diagonal structure, the blocks being $C_{3r-3,r-1},C_{3r-1,r-1},\ldots,C_{N-3,r-1}$. Hence, $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker\left(E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}\right)\cdot x^N &= \sum_{N>0} \left( \sum_{k=3r-3}^{N-3}\dim_{\mathbb Q}\ker C_{k,r-1} \right) \cdot x^N \\
&=\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,r-1}\left(x^{N+3}+x^{N+5}+x^{N+7}+\cdots\right)\\
&=\mathbb O(x)\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,r-1}\cdot x^N{\,},
\end{aligned}$$ thus proving the assertion.
Connection to polynomials
-------------------------
Motivated by Theorem \[thm:injection\], we interpret the right action of the matrices $E_{N,r}^{(2)},\ldots,E_{N,r}^{(r-1)},E_{N,r}^{(r)}=E_{N,r}$ on ${\mathsf{Vect}}_{N,r}$ as endomorphisms of the polynomial space $\mathbf V_{N,r}$. Having established this, we will prove Theorems \[thm:case3\] and \[thm:case4\] from a polynomial point of view.
\[def:phij\] The *restricted totally even part* of a polynomial $Q(x_1,\ldots,x_r)\in\mathbf V_{N,r}$ is the sum of all of its monomials, in which each exponent of $x_1,\ldots,x_r$ is even and at least 2. Let $r\geq j$. We define the $\mathbb Q$-linear map $$\begin{aligned}
{\varphi^{(r)}_{j}}\colon\mathbf V_{N,r}\longrightarrow\mathbf V_{N,r}{\,},
\end{aligned}$$ which maps each polynomial $Q(x_1,\ldots,x_r)\in \mathbf V_{N,r}$ to the restricted totally even part of $$\begin{gathered}
Q(x_1,\ldots,x_r)+\sum_{i=r-j+1}^{r-1}\Bigl(Q(x_1,\ldots,x_{r-j},x_{i+1}-x_i,x_{r-j+1},\ldots,\hat x_{i+1},\ldots,x_r)\\ -Q(x_1,\ldots,x_{r-j},x_{i+1}-x_i,x_{r-j+1},\ldots,\hat x_i,\ldots,x_r)\Bigr){\,}.
\end{gathered}$$
Note that ${\varphi^{(r)}_{1}}\equiv{\operatorname{id}}_{\mathbf V_{N,r}}$.
The following lemma shows that the map ${\varphi^{(r)}_{j}}$ corresponds to the right action of the matrix $E_{N,r}^{(j)}$ on ${\mathsf{Vect}}_{N,r}$ via the isomorphism $\pi$.
\[lem:phij\] Let $r\geq j$. Then, for each polynomial $Q\in\mathbf V_{N,r}$, $$\begin{aligned}
\pi\left({\varphi^{(r)}_{j}}(Q)\right)=\pi(Q)E_{N,r}^{(j)}{\,}.\end{aligned}$$ or equivalently, the following diagram commutes:
\(a) at (0,2) [$\mathbf V_{N,r}$]{}; (b) at (3,2) [$\mathbf V_{N,r}$]{}; (c) at (0,0) [${\mathsf{Vect}}_{N,r}$]{}; (d) at (3,0) [${\mathsf{Vect}}_{N,r}$]{}; (e) at (0,-0.5) [$v$]{}; (f) at (3,-0.5) [$v\cdot E_{N,r}^{(j)}$]{}; (c1) at (e) ; (d1) at (f) ; (a) – (b) node\[pos=0.5,above\][${\varphi^{(r)}_{j}}$]{}; (c) – (d); (a) – (c) node\[pos=0.5,sloped,above=-2pt\][$\sim$]{} node\[pos=0.5,left\][$\pi$]{}; (b) – (d) node\[pos=0.5,sloped,above=-2pt\][$\sim$]{} node\[pos=0.5,left\][$\pi$]{}; (c1) – (d1);
We proceed by induction on $r$. Let $r=j$ and $$\begin{aligned}
Q(x_1,\ldots,x_j)=\sum_{(n_1,\ldots,n_j)\in S_{N,j}}q_{n_1,\ldots,n_j}x_1^{n_1-1}\cdots x_r^{n_j-1}{\,}.\end{aligned}$$Then, $E_{N,j}^{(j)}=E_{N,j}$ and thus $$\begin{aligned}
\pi(Q)E_{N,j}=\left(\sum_{(m_1,\ldots,m_j)\in S_{N,j}}q_{n_1,\ldots,n_j}e{{\textstyle\binom{m_1,\ldots,m_j}{n_1,\ldots,n_j}}}\right)_{(n_1,\ldots,n_j)\in S_{N,j}}{\,}.\end{aligned}$$ By and linearity of the Ihara action ${\mathbin{\underline{\circ}}}$, the row vector on the right-hand side corresponds to $\pi$ applied to the restricted totally even part of the polynomial $$\begin{aligned}
\label{eq:phiihara}
\sum_{(n_1,\ldots,n_j)\in S_{N,j}}q_{n_1,\ldots,n_j}x_1^{n_1-1}{\mathbin{\underline{\circ}}}\left(x_1^{n_2-1}\cdots x_{j-1}^{n_j-1}\right){\,}.\end{aligned}$$ On the other hand, plugging $r=j$ into Definition \[def:phij\] yields that ${\varphi^{(j)}_{j}}(Q(x_1,\ldots,x_j))$ corresponds to the restricted totally even part of some polynomial, which by definition of the Ihara action ${\mathbin{\underline{\circ}}}$ coincides with the polynomial defined in . Thus, the claim holds for $r=j$.
Now suppose that $r\geq j+1$ and the claim is proven for all smaller $r$. Let us decompose $$\begin{aligned}
Q(x_1,\ldots,x_r)=\sum_{\substack{n_1=3\\n_1\text{ odd}}}^{N-(3r-3)}x_1^{n_1-1}\cdot Q_{N-n_1}(x_2,\ldots,x_r){\,},\end{aligned}$$where the $Q_k$ are restricted totally even homogeneous polynomials in $r-1$ variables. In particular, $Q_k\in\mathbf V_{k,r-1}$ for all $k$. Arrange the indices of $\pi(Q)$ in lexicographically decreasing order. Then, by grouping consecutive entries, $\pi(Q)$ is the list-like concatenation of $\pi(Q_{3r-3}),\ldots,\pi(Q_{N-3})$, which we denote by $$\begin{aligned}
\pi(Q)=\big(\pi(Q_{3r-3}),\pi(Q_{3r-1}),\ldots,\pi(Q_{N-3})\big){\,}.\end{aligned}$$ Since we have lexicographically decreasing order of indices, the block diagonal structure of $E_{N,r}^{(j)}$ stated in Lemma \[lem:blockdia\] yields $$\begin{aligned}
\pi(Q)E_{N,r}^{(j)}&=\left(\pi(Q_{3r-3})E_{3r-3,r-1}^{(j)},\pi(Q_{3r-1})E_{3r-1,r-1}^{(j)},\ldots,\pi(Q_{N-3})E_{N-3,r-1}^{(j)}\right)\\
&=\left(\pi\left({\varphi^{(r-1)}_{j}}(Q_{3r-3})\right),\pi\left({\varphi^{(r-1)}_{j}}(Q_{3r-1})\right),\ldots,\pi\left({\varphi^{(r-1)}_{j}}(Q_{N-3})\right)\right)\\
&=\pi\left({\varphi^{(r)}_{j}}(Q)\right)\end{aligned}$$by linearity of ${\varphi^{(r)}_{j}}$ and the induction hypothesis. This shows the assertion.
\[cor:phiEiso\] For all $r\geq2$, $$\begin{aligned}
{\operatorname{Im}}{\prescript{t\!}{}{\left(E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}\right)}}\cap\ker{\prescript{t\!}{}{E}}_{N,r}\cong\ker{\varphi^{(r)}_{r}}\cap{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ\cdots\circ{\varphi^{(r)}_{2}}\right){\,}.\end{aligned}$$
By the previous Lemma \[lem:phij\], the following diagram commutes:
\(a) at (0,2) [$\mathbf V_{N,r}$]{}; (b) at (3,2) [$\mathbf V_{N,r}$]{}; (c) at (6,2) [$\cdots$]{}; (d) at (9,2) [$\mathbf V_{N,r}$]{}; (e) at (12,2) [$\mathbf V_{N,r}$]{}; (A) at (0,0) [${\mathsf{Vect}}_{N,r}$]{}; (B) at (3,0) [${\mathsf{Vect}}_{N,r}$]{}; (C) at (6,0) [$\cdots$]{}; (D) at (9,0) [${\mathsf{Vect}}_{N,r}$]{}; (E) at (12,0) [${\mathsf{Vect}}_{N,r}$]{}; /in[a/A,b/B,d/D,e/E]{}[ () – () node\[pos=0.5,sloped,above=-2pt\][$\sim$]{} node\[pos=0.5,left\][$\pi$]{}; ]{} //in[a/b/2,b/c/3,c/d/r-1,d/e/r]{}[ () – () node\[pos=0.5,above\][${\varphi^{(r)}_{\j}}$]{}; ]{} //in[A/B/2,B/C/3,C/D/r-1,D/E/r]{}[ () – () node\[pos=0.5,above\][${}\cdot E_{N,r}^{(\j)}$]{}; ]{}
From this, we have ${\operatorname{Im}}{\prescript{t\!}{}{\left(E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}\right)}}\cong{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ\cdots\circ{\varphi^{(r)}_{2}}\right)$ and $\ker{\prescript{t\!}{}{E}}_{N,r}\cong\ker{\varphi^{(r)}_{r}}$. Thereby, the claim is established.
\[lem:kerphi\]Let $j\leq r-1$. Then, $$\begin{aligned}
\ker{\varphi^{(r)}_{j}}\cong\bigoplus_{n<N}\mathbf V_{N-n,r-j}\otimes\ker E_{n,j}{\,}.
\end{aligned}$$
Let $Q\in\mathbf V_{N,r}$. We may decompose $$\begin{aligned}
Q(x_1,\ldots,x_r)=\sum_{n<N}\ \sum_{(n_1,\ldots,n_{r-j})\in S_{N-n,r-j}}x_1^{n_1-1}\cdots x_{r-j}^{n_{r-j}-1}R_{n_1,\ldots,n_{r-j}}(x_{r-j+1},\ldots,x_r){\,},\end{aligned}$$ where $R_{n_1,\ldots,n_{r-j}}\in\mathbf V_{n,j}$ is a restricted totally even homogeneous polynomial. Note that we have $Q\in\ker{\varphi^{(r)}_{j}}$ if and only if ${\varphi^{(j)}_{j}}(R_n)=0$ holds for each $R_n$ in the above decomposition. By Lemma \[lem:phij\], ${\varphi^{(j)}_{j}}(R_n)=0$ if and only if $\pi(R_n)\in\ker E_{n,j}$. Now, the assertion is immediate.
\[cor:phijres\] Let $2\leq j\leq r-2$. The restricted map $$\begin{aligned}
{\varphi^{(r)}_{j}\big|_{\mathbf W_{N,r}}}\colon\mathbf W_{N,r}\longrightarrow\mathbf W_{N,r}
\end{aligned}$$ is well-defined and satisfies $$\begin{aligned}
\ker{\varphi^{(r)}_{j}\big|_{\mathbf W_{N,r}}}\cong\bigoplus_{n<N}\mathbf W_{N-n,r-j}\otimes\ker E_{n,j}{\,}.
\end{aligned}$$
Since $j\leq r-2$, for each $Q\in\mathbf V_{N,r}$ the map $Q(x_1,\ldots,x_r)\mapsto{\varphi^{(r)}_{j}}(Q)$ does not interfere with $x_1$ or $x_2$ and thus not with the defining property of $\mathbf W_{N,r}$. Hence, ${\varphi^{(r)}_{j}\big|_{\mathbf W_{N,r}}}$ is well-defined. The second assertion is done just like in the previous Lemma \[lem:kerphi\].
\[lem:fnr\] Let $r\geq3$. For all $P\in\mathbf W_{N,r}$, $$\begin{aligned}
\pi(-P)E_{N,r}^{(r-1)}=\pi(P)F_{N,r}{\,}.\end{aligned}$$
Recall that by Lemma \[lem:phij\], $$\begin{aligned}
\pi(-P)E_{N,r}^{(r-1)}&=\pi\left( {\varphi^{(r)}_{r-1}}\big(-P(x_1,\ldots,x_r)\big)\right)\\
&=\begin{multlined}[t]
\pi\bigg(-P(x_1,\ldots,x_r)+\sum_{i=2}^{r-1}\Big(-P(x_1,x_{i+1}-x_i,x_2,\ldots, \hat x_{i+1},\ldots,x_r)\\
+P(x_1,x_{i+1}-x_i,x_2,\ldots, \hat x_i,\ldots,x_r)\Big)\bigg)
\end{multlined}\\
&=\begin{multlined}[t]
\pi\bigg(-P(x_1,\ldots,x_r)+\sum_{i=2}^{r-1}\Big(P(x_{i+1}-x_i,x_1,\ldots, \hat x_{i+1},\ldots,x_r)\\
-P(x_{i+1}-x_i,x_1,\ldots, \hat x_i,\ldots,x_r)\Big)\bigg){\,},
\end{multlined}\end{aligned}$$ since $-P$ is antisymmetric with respect to $x_1\leftrightarrow x_2$. In the same way we compute $$\begin{aligned}
\pi(P)F_{N,r}&=\pi(P)\left(E_{N,r}-{\operatorname{id}}_{{\mathsf{Vect}}_{N,r}}\right)=\pi\big({\varphi^{(r)}_{r}}(P(x_1,\ldots,x_r))\big)-\pi(P)\\
&=\begin{multlined}[t]
\pi\bigg(P(x_1,\ldots,x_r)+\sum_{i=1}^{r-1}\Big(P(x_{i+1}-x_i,x_1,\ldots, \hat x_{i+1},\ldots,x_r)\\
-P(x_{i+1}-x_i,x_1,\ldots, \hat x_i,\ldots,x_r)\Big)\bigg)-\pi(P){\,}.
\end{multlined}\end{aligned}$$ Now the desired result follows from $$\begin{aligned}
P(x_1,x_2,\ldots,x_r)+P(x_2-x_1,x_1,x_3,\ldots,x_r)-P(x_2-x_1,x_2,\ldots,x_r)=0{\,},\end{aligned}$$ since $P$ is in $\mathbf W_{N,r}$.
\[cor:kerimineq\] Assume that the map from Theorem \[thm:injection\] is injective. Then, for all $r\geq 3$, $$\begin{aligned}
\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{E}}_{N,r}^{(r-1)}\cap\ker{\prescript{t\!}{}{E}}_{N,r}\right)\geq\dim_{\mathbb Q}\mathbf W_{N,r}{\,}.\end{aligned}$$
This is immediate by the previous Lemma \[lem:fnr\].
\[lem:imphi\] For all $r\geq3$, $$\begin{aligned}
{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ{\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)\subseteq\ker {\varphi^{(r)}_{r}}\cap{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ\cdots\circ{\varphi^{(r)}_{2}}\right){\,}.\end{aligned}$$
We may replace the right-hand side by just $\ker{\varphi^{(r)}_{r}}$. Note that by Corollary \[cor:phijres\] the composition of restricted ${\varphi^{(r)}_{j}\big|_{\mathbf W_{N,r}}}$ on the left-hand side is well-defined. Moreover, each $Q\in{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ{\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)$ can be represented as $Q={\varphi^{(r)}_{r-1}}(P)$ for some $P\in\mathbf W_{N,r}$ and thus $Q\in\ker{\varphi^{(r)}_{r}}$ according to Lemma \[lem:fnr\] and Theorem \[thm:injection\].
Similar to Conjecture \[con:isomorphism\] we expect a stronger result to be true, which is stated in the following conjecture due to Claire Glanois:
\[con:imiso\] For all $r\geq 3$, $$\begin{aligned}
{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ{\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)=\ker {\varphi^{(r)}_{r}}\cap{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ\cdots\circ{\varphi^{(r)}_{2}}\right){\,}.\end{aligned}$$
Note that intersecting $\ker{\varphi^{(r)}_{r}}\cap{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ\cdots\circ{\varphi^{(r)}_{2}}\right)$, Conjecture \[con:imiso\] does not need the injectivity from Conjecture \[con:isomorphism\]. However, we haven’t been able to derive Conjecture \[con:imiso\] from Conjecture \[con:isomorphism\], so it is not necessarily weaker.
Main Results {#sec:main results}
============
Throughout this section we will assume that the map from Theorem \[thm:injection\] is injective, i.e. the injectivity part of Conjecture \[con:isomorphism\] is true. This was also the precondition for Tasaka’s original proof of Theorem \[thm:case4\].
Proof of Theorem \[thm:case3\].
-------------------------------
By Corollary \[cor:enrjocnr\], Remark \[rem:isor2\] and the fact that $E_{N,2}=C_{N,2}$ we obtain $$\begin{aligned}
\label{eq:case3ineq1}
\sum_{N>0}\dim_{\mathbb Q}\ker E_{N,3}^{(2)}\cdot x^N=\mathbb O(x)\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,2}\cdot x^N=\mathbb O(x)\mathbb S(x){\,}.\end{aligned}$$ We use Corollary \[cor:kerimineq\] and Lemma \[lem:wnreq\] to obtain $$\begin{aligned}
\label{eq:case3ineq2}
\sum_{N>0}\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{E}}_{N,3}^{(2)} \cap \ker{\prescript{t\!}{}{E}}_{N,3}\right)\cdot x^N \geq \sum_{N>0}\dim_{\mathbb Q}\mathbf W_{N,3}\cdot x^N
= \mathbb O(x) \mathbb S(x){\,}.\end{aligned}$$ Now observe that since $C_{N,3}=E_{N,3}^{(2)}E_{N,3}$, we have $$\begin{aligned}
\dim_{\mathbb Q}\ker C_{N,3}=\dim_{\mathbb Q}\ker{\prescript{t\!}{}{E}}_{N,3}^{(2)}+\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{E}}_{N,3}^{(2)} \cap \ker{\prescript{t\!}{}{E}}_{N,3}\right){\,}.\end{aligned}$$ By and , the assertion is proven.
Proof of Theorem \[thm:case4\].
-------------------------------
Since $C_{N,4}=E_{N,4}^{(2)}E_{N,4}^{(3)}E_{N,4}$, we may split $\dim_{\mathbb Q}\ker C_{N,4}$ into $$\begin{aligned}
\dim_{\mathbb Q}\ker C_{N,4}=\dim_{\mathbb Q}\ker{\prescript{t\!}{}{\left( E_{N,4}^{(2)}E_{N,4}^{(3)}\right)}}+\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{\left( E_{N,4}^{(2)}E_{N,4}^{(3)}\right)}}
\cap \ker{\prescript{t\!}{}{E}}_{N,4}\right){\,}.\end{aligned}$$ The two summands on the right-hand side are treated separately. For the first one, by Corollary \[cor:enrjocnr\] and Theorem \[thm:case3\] one has $$\begin{aligned}
\label{eq:case4ineq1}
\sum_{N>0}\dim_{\mathbb Q}\ker{\prescript{t\!}{}{\left( E_{N,4}^{(2)}E_{N,4}^{(3)}\right)}}\cdot x^N\geq2\mathbb O(x)^2\mathbb S(x){\,}.\end{aligned}$$ For the second one, we use Corollary \[cor:phiEiso\] and Lemma \[lem:imphi\] to obtain $$\begin{aligned}
\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{\left( E_{N,4}^{(2)}E_{N,4}^{(3)}\right)}} \cap \ker{\prescript{t\!}{}{E}}_{N,4}\right)&\geq\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(4)}_{3}}\circ{\varphi^{(4)}_{2}\big|_{\mathbf W_{N,4}}}\right)\\
&=\dim_{\mathbb Q}{\operatorname{Im}}{\varphi^{(4)}_{2}\big|_{\mathbf W_{N,4}}}{\,},\end{aligned}$$ since we assume ${\varphi^{(4)}_{3}}$ to be injective on $\mathbf W_{N,r}$ according to Conjecture \[con:isomorphism\]. According to Corollary \[cor:phijres\] and Theorem \[thm:Schneps\], $$\begin{aligned}
\ker{\varphi^{(4)}_{2}\big|_{\mathbf W_{N,4}}}\cong\bigoplus_{n<N}\mathbf W_{N-n,2}\otimes\ker E_{n,2}\cong\bigoplus_{n<N}\mathbf W_{N-n,2}\otimes\mathbf W_{n,2}{\,}.\end{aligned}$$ Now, by $\dim_{\mathbb Q}{\operatorname{Im}}{\varphi^{(4)}_{2}\big|_{\mathbf W_{N,4}}}=\dim_{\mathbb Q}\mathbf W_{N,4}-\dim_{\mathbb Q}\ker{\varphi^{(4)}_{2}\big|_{\mathbf W_{N,4}}}$ we obtain $$\begin{aligned}
\label{eq:case4ineq2}
\sum_{N>0}\dim_{\mathbb Q}{\operatorname{Im}}{\varphi^{(4)}_{2}\big|_{\mathbf W_{N,4}}}\cdot x^N=\mathbb O(x)^2\mathbb S(x)-\mathbb S(x)^2{\,}.\end{aligned}$$ Combining and , the proof is finished.
The case $r=5$ assuming Conjecture \[con:isomorphism\].
-------------------------------------------------------
In addition to the injectivity of , we now assume Conjecture \[con:isomorphism\] is true in the case $r=3$, i.e. $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker{\prescript{t\!}{}{E}}_{N,3}\cdot x^N=\mathbb O(x)\mathbb S(x)\label{eq:case5eq1}\end{aligned}$$ by Corollary \[cor:enrineq\]. Our goal is to prove the lower bound $$\begin{aligned}
\sum_{N>0}\dim_{\mathbb Q}\ker C_{N,5}\cdot x^N\geq 4 \mathbb O(x)^3\mathbb S(x)-3 \mathbb O(x)\mathbb S(x)^2{\,},\label{eq:case5}\end{aligned}$$ which as an equality would be the exact value predicted by Conjecture \[con:Brown\]. Again we use the decomposition $C_{N,5}=E_{N,5}^{(2)}E_{N,5}^{(3)}E_{N,5}^{(4)}E_{N,5}$ to split $\dim_{\mathbb Q}\ker C_{N,5}$ into $$\begin{aligned}
\dim_{\mathbb Q}\ker C_{N,5}=\dim_{\mathbb Q}\ker{\prescript{t\!}{}{\left( E_{N,5}^{(2)}E_{N,5}^{(3)}E_{N,5}^{(4)}\right)}}+\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{ \left( E_{N,5}^{(2)}E_{N,5}^{(3)}E_{N,5}^{(4)}\right)}} \cap \ker{\prescript{t\!}{}{E}}_{N,5}\right){\,}.\end{aligned}$$ Applying Corollary \[cor:enrjocnr\] and Theorem \[thm:case4\] to the first summand on the right-hand side, we obtain $$\begin{aligned}
\label{eq:case5ineq1}
\sum_{N>0}\dim_{\mathbb Q}\ker E_{N,5}^{(2)}E_{N,5}^{(3)}E_{N,5}^{(4)}\cdot x^N\geq3\mathbb O(x)^3\mathbb S(x)-\mathbb O(x)\mathbb S(x)^2{\,}.\end{aligned}$$ Again, for the second summand Corollary \[cor:phiEiso\] and Lemma \[lem:imphi\] yield $$\begin{aligned}
\begin{split}
\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{\left( E_{N,5}^{(2)}E_{N,5}^{(3)}E_{N,5}^{(4)}\right)}} \cap \ker{\prescript{t\!}{}{E}}_{N,5}\right)&\geq\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(5)}_{4}}\circ{\varphi^{(5)}_{3}\big|_{\mathbf W_{N,5}}}\circ{\varphi^{(5)}_{2}\big|_{\mathbf W_{N,5}}}\right)\\
&=\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(5)}_{3}\big|_{\mathbf W_{N,5}}}\circ{\varphi^{(5)}_{2}\big|_{\mathbf W_{N,5}}}\right){\,},
\end{split}\end{aligned}$$ since ${\varphi^{(5)}_{4}}$ is injective on $\mathbf W_{N,r}$ by our assumption. According to Corollary \[cor:phijres\] and Theorem \[thm:Schneps\], $$\begin{aligned}
\ker{\varphi^{(5)}_{2}\big|_{\mathbf W_{N,5}}}\cong\bigoplus_{n<N}\mathbf W_{N-n,3}\otimes\ker E_{n,2}\cong\bigoplus_{n<N}\mathbf W_{N-n,3}\otimes\mathbf W_{n,2}\end{aligned}$$ and by , $$\begin{aligned}
\ker{\varphi^{(5)}_{3}\big|_{\mathbf W_{N,5}}}\cong\bigoplus_{n<N}\mathbf W_{N-n,2}\otimes\ker E_{n,3}\cong\bigoplus_{n<N}\mathbf W_{N-n,2}\otimes\mathbf W_{n,3}{\,}.\end{aligned}$$ Now, by $$\begin{aligned}
\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(5)}_{3}\big|_{\mathbf W_{N,5}}}\circ{\varphi^{(5)}_{2}\big|_{\mathbf W_{N,5}}}\right)\geq\dim_{\mathbb Q}\mathbf W_{N,5}-\dim_{\mathbb Q}\ker{\varphi^{(5)}_{2}\big|_{\mathbf W_{N,5}}}-\dim_{\mathbb Q}\ker{\varphi^{(5)}_{3}\big|_{\mathbf W_{N,5}}}\end{aligned}$$ we arrive at $$\begin{aligned}
\label{eq:case5ineq2}
\sum_{N>0}\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(5)}_{3}\big|_{\mathbf W_{N,5}}}\circ{\varphi^{(5)}_{2}\big|_{\mathbf W_{N,5}}}\right)\cdot x^N\geq\mathbb O(x)^3\mathbb S(x)-2\mathbb O(x)\mathbb S(x)^2{\,}.\end{aligned}$$ Combining and yields the desired result.
A recursive approach to the general case $r\geq2$
-------------------------------------------------
In this section, we show that one can recursively derive the exact value of $\dim_{\mathbb Q}\ker C_{N,r}$ from Conjecture \[con:imiso\]. Let us fix some notations:
For $r\geq2$, let us define the formal series $$\begin{aligned}
B_r(x)&\coloneqq \sum_{N>0}\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ{\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)\cdot x^N\tag i\\
T_r(x)&\coloneqq \sum_{N>0}\dim_{\mathbb Q}\ker C_{N,r}\cdot x^N\tag{ii}{\,}.\end{aligned}$$ We set $T_0(x),T_1(x)\coloneqq 0$.
The main observation is the following lemma:
\[lem:recursion\] Assume that Conjecture \[con:imiso\] is true and that the map from Theorem \[thm:injection\] is injective. Then, for $r\geq 3$ the following recursion holds: $$\begin{aligned}
B_r(x)=\mathbb O(x)^{r-2}\mathbb S(x)-\sum_{j=2}^{r-2}\mathbb O(x)^{r-j-2}\mathbb S(x)B_j(x){\,}.\end{aligned}$$
We have $$\begin{gathered}
\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ{\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)\\
=\begin{aligned}[t]
\dim_{\mathbb Q}\mathbf W_{N,r}&-
\sum_{j=2}^{r-2}\dim_{\mathbb Q}\ker{\varphi^{(r)}_{j}\big|_{\mathbf W_{N,r}}}\cap{\operatorname{Im}}\left({\varphi^{(r)}_{j-1}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)\\
&-\dim_{\mathbb Q}\ker{\varphi^{(r)}_{r-1}}\cap{\operatorname{Im}}\left({\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right){\,}.
\end{aligned}\end{gathered}$$ Since we assume ${\varphi^{(r)}_{r-1}}$ to be injective on $\mathbf W_{N,r}$, the last summand on the right-hand side vanishes. Let $2\leq j\leq r-2$. As the restriction to $\mathbf W_{N,r}$ only affects $x_1$ and $x_2$, whereas ${\varphi^{(r)}_{j}}$ acts on $x_{r-j+1},\ldots,x_r$, we obtain $$\begin{gathered}
\ker{\varphi^{(r)}_{j}\big|_{\mathbf W_{N,r}}}\cap{\operatorname{Im}}\left({\varphi^{(r)}_{j-1}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)\\
\begin{aligned}[t]
&=\bigoplus_{n<N}\mathbf W_{N-n,r-j}\otimes\left(\ker{\varphi^{(j)}_{j}}\cap{\operatorname{Im}}\left({\varphi^{(j)}_{j-1}}\circ\cdots\circ{\varphi^{(j)}_{2}}\right)\right)\\
&=\bigoplus_{n<N}\mathbf W_{N-n,r-j}\otimes{\operatorname{Im}}\left({\varphi^{(j)}_{j-1}}\circ{\varphi^{(j)}_{j-2}\big|_{\mathbf W_{n,j}}}\circ\cdots\circ{\varphi^{(j)}_{2}\big|_{\mathbf W_{n,j}}}\right){\,},
\end{aligned}\end{gathered}$$ where the last equality follows from Conjecture \[con:imiso\]. Hence, if we denote $$\begin{aligned}
a_{N,r}=\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ{\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right){\,},\end{aligned}$$we obtain the recursion $$\begin{aligned}
\label{eq:casercauchy}
a_{N,r}=\dim_{\mathbb Q}\mathbf W_{N,r}-\sum_{j=2}^{r-2}\sum_{n<N}\dim_{\mathbb Q}\mathbf W_{N-n,r-j}\cdot a_{n,j}{\,}.\end{aligned}$$ By Lemma \[lem:wnreq\] and the convolution formula for multiplying formal series, equation establishes the claim.
\[thm:recursion\] Upon Conjecture \[con:imiso\] and the injectivity of , for all $r\geq3$ the following recursion is satisfied: $$\begin{aligned}
T_r(x)=\mathbb O(x)T_{r-1}(x)-\mathbb S(x)T_{r-2}(x)+\mathbb O(x)^{r-2}\mathbb S(x){\,}.\end{aligned}$$
As we assume Conjecture \[con:imiso\], we get from Definition \[def:cnr\] and Corollary \[cor:phiEiso\] $$\begin{aligned}
\dim_{\mathbb Q}\ker C_{N,r}&=
\begin{multlined}[t]
\dim_{\mathbb Q}\ker{\prescript{t\!}{}{\left( E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}\right)}}\\+\dim_{\mathbb Q}\left({\operatorname{Im}}{\prescript{t\!}{}{\left( E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}\right)}} \cap \ker{\prescript{t\!}{}{E}}_{N,r}\right)
\end{multlined}\\
&=\begin{multlined}[t]
\dim_{\mathbb Q}\ker{\prescript{t\!}{}{\left( E_{N,r}^{(2)}\cdots E_{N,r}^{(r-1)}\right)}}\\+\dim_{\mathbb Q}{\operatorname{Im}}\left({\varphi^{(r)}_{r-1}}\circ{\varphi^{(r)}_{r-2}\big|_{\mathbf W_{N,r}}}\circ\cdots\circ{\varphi^{(r)}_{2}\big|_{\mathbf W_{N,r}}}\right)
\end{multlined}\end{aligned}$$ and thus, by Corollary \[cor:enrjocnr\], $$\begin{aligned}
T_r(x)=\mathbb O(x)T_{r-1}(x)+B_r(x){\,}.\end{aligned}$$ Using Lemma \[lem:recursion\], we obtain $$\begin{aligned}
T_r(x)&=\mathbb O(x)T_{r-1}(x)+\mathbb O(x)^{r-2}\mathbb S(x)-\sum_{j=2}^{r-2}\mathbb O(x)^{r-j-2}\mathbb S(x)\big(T_j(x)-\mathbb O(x)T_{j-1}(x)\big)\\
&=\mathbb O(x)T_{r-1}(x)+\mathbb O(x)^{r-2}\mathbb S(x)-\mathbb S(x)T_{r-2}(x)+\mathbb O(x)^{r-3}\mathbb S(x)T_1(x)\\
&=\mathbb O(x)T_{r-1}(x)-\mathbb S(x)T_{r-2}(x)+\mathbb O(x)^{r-2}\mathbb S(x){\,},\end{aligned}$$where by definition $T_1(x)=0$. The conclusion follows.
Note that by our choice of $T_0(x)$ and $T_1(x)$, Theorem \[thm:recursion\] remains true for $r=2$ since we know from [@schneps] that $T_2(x)=\mathbb S(x)$. Under the assumption of Conjecture \[con:imiso\] and injectivity in , we are now ready to prove that the generating series of ${\operatorname{rank}}C_{N,r}$ equals the explicit series $\frac{1}{1-\mathbb O(x)y+\mathbb S(x)y^2}$ as was claimed in Conjecture \[con:Brown\]. This (under the same assumptions though) proves the motivic version of Conjecture \[con:Brown\] (i.e. with $\mathcal Z_{N,r}^{{\operatorname{odd}}}$ replaced by $\mathcal H_{N,r}^{{\operatorname{odd}}}$).
Let $R_r(x)=\mathbb O(x)^r-T_r(x)$ and note that by Theorem \[thm:recursion\] $$\begin{aligned}
R_r(x)=\mathbb O(x)R_{r-1}(x)-\mathbb S(x)R_{r-2}(x)\end{aligned}$$for all $r\geq2$. Hence, $$\begin{aligned}
\left(1-\mathbb O(x)y+\mathbb S(x)y^2\right)\sum_{r\geq0}R_r(x)y^r&=
\begin{aligned}[t]
&\sum_{r\geq2}\big(R_r(x)-\mathbb O(x)R_{r-1}(x)+\mathbb S(x)R_{r-2}(x)\big)y^r\\
&+R_0(x)+R_1(x)y-\mathbb O(x)R_0(x)y
\end{aligned}\\
&=R_0(x)+\mathbb O(x)y-\mathbb O(x)y\\
&=1\end{aligned}$$and thus $$\begin{aligned}
1+\sum_{N,r>0}{\operatorname{rank}}C_{N,r}\cdot x^Ny^r=\sum_{r\geq0}R_r(x)y^r=\frac1{1-\mathbb O(x)y+\mathbb S(x)y^2}{\,},\end{aligned}$$ which is the desired result.
|
Q:
Can you get the filename of the jsp file using a taglib in the taglib code
Is it possible to get the filename of the jsp file that uses a taglib from the java code?
I.e.
public int doStartTag() throws JspException
{
try
{
String xxx = pageContext.?
Where xxx would get the filename of the jsp file (which of course could be a nested include file)
br
/B
A:
It's not possible to get the name of the JSP file simply because at this point it has been compiled and you're dealing with compiled version rather than source JSP file.
You can get the name of the class JSP has been compiled into via
pageContext.getPage().getClass().getName();
and try to derive the JSP name from it but the naming scheme differs between JSP containers.
|
Relationship of classical and non-classical risk factors with genetic variants relevant to coronary heart disease.
In addition to the well established cardiovascular risk factors, evidence suggests a possible role of genetic and non-classical risk factors in the development and progression of atherothrombosis. We aimed to determine the relationship of classical and non-classical cardiovascular risk factors with candidate gene polymorphisms potentially involved in cardiovascular risk in the general Mediterranean population. Cross-sectional study. We have determined the prevalence of classical (lipid profile, blood pressure, glycaemia, diabetes, smoking, body mass index, menopause and family history of coronary heart disease) and non-classical cardiovascular risk factors (infectious processes, homocysteinaemia, oxidative status, C-reactive protein, lipoprotein (a) and fibrinogen) in a population-based study. We analysed the relationship of these risk factors with the following five gene polymorphisms potentially involved in cardiovascular risk: ATP-binding cassette transporter A1-R219K, Peroxisome proliferator-activated receptor (PPAR)-alpha-L162V, Lipoprotein lipase (LPL)-HindIII, Paraoxonase (PON)1-Q192R, and Tumour necrosis factor (TNF)-alpha-G-308A. We found PPAR-alpha-V and LPL-H alleles to be associated with decreased high-density lipoprotein-cholesterol (HDL-c) concentration and with increased total cholesterol : HDL-c and triglyceride : HDL-c ratios. Regarding the non-classical risk factors, C-reactive protein concentration was higher for the PPAR-alpha-V allele. A higher oxidative status was shown in homozygotes for LPL-H and TNF-alpha-G alleles, although the latter also had lower homocysteinaemia. Three of the genetic variants analysed, PPAR-alpha-L162V, LPL-HindIII, and TNF-alpha-G-308A, were associated with non-classical risk factors, specifically lipid profile, inflammation, and oxidative status. |
647 F.Supp. 1035 (1986)
James MESSER, Jr., Appellant,
v.
Ralph KEMP, Warden, Georgia Diagnostic and Classification Center, Respondent.
Civ. A. No. C86-173R.
United States District Court, N.D. Georgia, Rome Division.
July 7, 1986.
*1036 Howard J. Manchel, Atlanta, Ga., for appellant.
Mary Beth Westmoreland, Asst. Atty. Gen., Atlanta, Ga., for respondent.
ORDER
ROBERT H. HALL, District Judge.
James Messer, Jr., who is scheduled to be executed before July 9, 1986, petitions this court for a writ of Habeas Corpus, pursuant to 28 U.S.C. § 2254. This court has stayed petitioner's execution pending a full review of the issues raised by the petition. For the reasons set forth herein, the court DENIES prisoner's petition, and accordingly lifts the stay of execution.
FACTS
Petitioner, James E. Messer, Jr., was indicted by the grand jury of Polk County, Georgia, during the November Term, 1979, for kidnapping with bodily injury and for the murder of Rhonda Tanner. A special plea of insanity was filed on behalf of the petitioner. After two subsequent state sponsored psychiatric examinations established that petitioner was mentally competent to stand trial, the special plea of insanity was withdrawn. At his trial petitioner pleaded not quilty. Following a trial by jury on February 7, 1980, petitioner was found guilty on both charges and sentenced to death for both offenses. Petitioner received the death penalty for murder after the jury found the presence of two statutory aggravating circumstances, (1) that the murder was committed during the course of another capital felony, the kidnapping with bodily injury, and (2) that the murder was outrageously and wantonly vile, horrible or inhuman in that it involved torture to the victim. The jury found one aggravating circumstance with respect to the kidnapping with bodily injury charge, that the crime was outrageously or wantonly vile, horrible or inhuman in that it involved aggravated battery and torture to the victim. The death sentence was imposed *1037 on February 8, 1980. Petitioner's motion for a new trial was denied after hearing on May 20, 1980.
On direct appeal, the petitioner raised six issues, including denial of the motion for an independent psychiatric examination. The Supreme Court of Georgia considered these allegations and also conducted a sentence review, finding that the evidence supported the verdict, that the sentence was not imposed under passion or prejudice, that the evidence supported the aggravating circumstances, that the death penalty was not disproportionate and that the charge at the sentencing phase was proper. Thus, the court affirmed both the convictions and the sentences. Messer v. State, 247 Ga. 316, 276 S.E.2d 15 (1981). A motion for rehearing was denied on March 18, 1981.
Petitioner subsequently filed a petition for a writ of certiorari in the Supreme Court of the United States challenging the denial of an independent psychiatric examination. This petition was denied on October 5, 1981. Messer v. Georgia, 454 U.S. 882, 102 S.Ct. 367, 70 L.Ed.2d 193 (1981).
Petitioner then filed a petition for habeas corpus relief in the Superior Court of Butts County, Georgia, on January 5, 1982. On or about January 25, 1982, the petitioner filed an amendment to the petition and a brief in support. Petitioner did not raise the denial of the motion for independent psychiatric examination. The state habeas corpus court denied relief without a hearing on February 23, 1982. Petitioner's Application for Certificate of Probable Cause to Appeal was denied on April 20, 1982. Subsequently, a petition for a writ of certiorari was filed in which the petitioner challenged the admission of his confession and asserted that he was arrested without probable cause. Certiorari was denied on October 4, 1982. Messer v. Zant, 459 U.S. 882, 103 S.Ct. 182, 74 L.Ed.2d 148, rehng. den., sub. nom, Cape v. Zant, 459 U.S. 1059, 103 S.Ct. 479, 74 L.Ed.2d 626 (1982).
Petitioner filed an application for habeas corpus relief in the United States District Court for the Northern District of Georgia, Rome Division, on November 23, 1982. In that petition, the petitioner raised the denial by the trial court of the motion for an independent psychiatric examination and funds for an expert.
The case was transferred to the Atlanta Division and an evidentiary hearing was held before United States Magistrate Joel M. Feldman on August 5, 1983. On February 1, 1984, the magistrate entered a report and recommendation recommending that relief be denied as to the conviction, but suggesting that relief be granted as to the sentencing phase finding that counsel was ineffective during the closing argument at the sentencing phase. On March 30, 1984, this court entered an order adopting all portions of the magistrate's report and recommendation except that portion dealing with the effectiveness of counsel at the sentencing phase. This court concluded that petitioner had failed to show any prejudice resulting from this allegation. Messer v. Francis, No. C82-419A (N.D.Ga. March 30, 1984) (Hall, J.). This court also ruled on certain other allegations not addressed by the magistrate and denied a certificate for probable cause to appeal. Id. The Eleventh Circuit Court of Appeals granted the certificate on June 1, 1984.
Subsequently, a panel of the Eleventh Circuit Court of Appeals affirmed this court's decision denying habeas corpus relief in an opinion dated April 30, 1985. Messer v. Kemp, 760 F.2d 1080 (11th Cir. 1985). Only three issues were raised on appeal; the denial of the motion for a mistrial, the allegation of ineffective assistance of counsel and the question of whether jury instructions were correct on the kidnapping with bodily injury charge. A petition for rehearing en banc was denied on August 23, 1985. Petitioner then filed a petition for a writ of certiorari in the Supreme Court of the United States which was denied on January 21, 1986. Messer v. Kemp, ___ U.S. ___, 106 S.Ct. 864, 88 L.Ed.2d 902 (1986).
On June 17, 1986, an order was signed setting a new execution time frame beginning at noon on July 2, 1986, and ending at *1038 noon on July 9, 1986. Petitioner filed a petition for habeas corpus relief in the Superior Court of Butts County, Georgia on June 26, 1986, raising five allegations, including the allegation that he had been denied funds for an independent psychiatric examination and that the death penalty was applied in a discriminatory fashion. No evidence was proffered to the state habeas corpus court by the petitioner, nor did petitioner assert that any was available.
On June 27, 1986, respondent filed a motion to dismiss the petition. At 8:00 a.m. on that day, a hearing was held before the Honorable Hal Craig on the petition, request for a stay and motion to dismiss. At 3:10 p.m. on that date, an order was filed denying the stay, dismissing the petition as successive as to four counts and finding the remaining count to be without merit. Petitioner filed a notice of appeal and an application for certificate of probable cause to appeal that afternoon. On Monday morning, June 30, 1986, petitioner filed an amendment to his application for a certificate of probable cause. Respondent filed a response to the application. On that same date, the Supreme Court of Georgia denied the application for a certificate of probable cause to appeal. Petitioner then filed the current petition with this court on July 1, 1986. This court orally granted petitioner's motion to proceed in forma pauperis.
DISCUSSION
Petitioner contends that he was convicted and sentenced to death in violation of the Georgia Constitution and the Fifth, Sixth, Eighth and Fourteenth Amendments to the United States Constitution. Petitioner argues that under Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985) he was denied funds to have an independent psychiatrist to aid in his defense, in violation of his rights under the Fourteenth Amendment. (Petition for Writ of Habeas Corpus custody ("Petition")). Petitioner also argues that the imposition of the death penalty violates the Eighth Amendment's prohibition of cruel and unusual punishment because it will be applied in a racially discriminatory manner. As an initial matter, the court finds that petitioner's claim that imposition of the death penalty violates the Eighth Amendment's prohibition of cruel and unusual punishment because it will be applied in a racially discriminatory manner, is without merit and cannot provide a basis for the relief sought. McCleskey v. Kemp, 753 F.2d 877 (11th Cir.1985) (en banc).[1]
Respondent pleads abuse of the writ under Rule 9(b) of the Rules Governing § 2254 cases. Specifically, respondent asserts that all claims raised in the instant petition have been raised in a prior federal habeas corpus petition. (Respondent's Answer/Response, "Response").[2] Therefore, to determine whether any ground for relief is properly before this court, the court must consider whether petitioner has abused the writ in bringing a successive petition.
This court holds that petitioner abused the writ in raising his Ake (denial of independent psychiatric evaluation) claim in his second habeas petition. Rule 9(b) of the Rules Governing 28 U.S.C. § 2254 provides:
A second or successive petition may be dismissed if the judge finds that it fails to allege new or different grounds for relief and if the prior determination was on the merits, or if new and different grounds are alleged, the judge finds that the failure of the petitioner to assert those grounds in a prior petition constitutes an abuse of the writ. *1039 28 U.S.C. § 2254 (1977). However, a petitioner may rebut the state's contention that he abused the writ in a successive petition in one of two ways:
"(a) If the ground was previously addressed in a federal habeas corpus proceeding, the petitioner must demonstrate that the decision was not on the merits, or the ends of justice would be served by reconsideration on the merits ...
(b) If the ground was not previously presented in a federal habeas corpus proceeding, the petitioner must demonstrate the failure to present the ground in the prior proceeding was neither the result of an intentional abandonment or withholding nor the product of inexcusable neglect." Witt v. Wainwright, 755 F.2d 1396, 1397 (11th Cir.1985), rev'd on other grounds 469 U.S. 412, 105 S.Ct. 844, 83 L.Ed.2d 841 (1985) (emphasis supplied) see also, Sanders v. United States, 373 U.S. 1, 83 S.Ct. 1068, 10 L.Ed.2d 148 (1963).
In the instant case, it is not disputed that petitioner properly raised the claim of the unconstitutional denial of an independent psychiatric evaluation in his first habeas petition.[3]
Because this court finds that petitioner's denial of independent psychiatric evaluation claim constitutes a successive petition that has been decided on the merits in the previous habeas corpus proceeding, the court now turns to whether the "ends of justice" would be served by a reconsideration of this claim. Petitioner contends that reconsideration is required by an intervening change in the law applicable to the constitutionality of denying petitioner's request for an independent psychiatric evaluation for the purpose of preparing a defense of insanity. This court cannot agree.
Respondent urges that the Supreme Court's recent decision in Kuhlmann v. Wilson, ___ U.S. ___, 106 S.Ct. 2616, 2626, 91 L.Ed.2d 364 (1986) addressing the "ends of justice" standard, controls the instant case.[4]Kuhlmann involved a Sixth *1040 Amendment claim of denial of right to counsel based on court's denial of motion to suppress statements made to a jailhouse informant. The prisoner, in a successive petition for a writ, claimed that the change in the law occasioned by the Supreme Court's decision in United States v. Henry, 447 U.S. 264, 100 S.Ct. 2183, 65 L.Ed.2d 115 (1980) mandated reconsideration of the Sixth Amendment claim. An opinion written by Justice Powell and joined in pertinent part by Chief Justice Burger, Justices Rehnquist and O'Connor, stated that:
In light of the historic purpose of habeas corpus and the interest implicated by successive petitions for federal habeas relief from a state conviction, we conclude that "the ends of justice" require federal courts to entertain such petitions only where the prisoner supplements his constitutional claim with a colorable showing of factual innocence.
Kuhlmann v. Wilson, 106 S.Ct. at 2626. The plurality stated that its purpose in requiring a "colorable showing of factual innocence" was to provide a specific guideline for district courts to use in resolving the "ends of justice" issue.
For several reasons, this court finds that Kuhlmann is not controlling precedent with respect to the "ends of justice" determination. First, the precedential value of a four justice opinion is highly suspect.[5] Simply stated, a position that does not garner the votes of at least five justices cannot be binding precedent where there is a contrary body of Supreme Court decisions. In Marks v. United States, 430 U.S. 188, 97 S.Ct. 990, 51 L.Ed.2d 260 (1977), the Supreme Court restated the familiar notion that a four justice plurality opinion has no binding effect.[6]
Second, this court's belief that a majority of the court rejected the notion that the "colorable showing of factual innocence" is the only element to consider in deciding the "ends of justice" issue is supported by Justice Stevens' dissent. Justice Stevens explicitly rejected Justice Powell's "single factor" approach, contending that whether the petitioner has advanced a colorable claim of innocence is but "one of the facts that may be properly considered." Id. (Stevens, J. dissenting). Justices Stevens, Brennan and Marshall explicitly endorsed the court's traditional approach under Sanders, supra that the decision whether to hear a successive petition was committed "to the sound discretion of federal trial judges." Sanders, 373 U.S. at 18, 83 S.Ct. at 1079. Thus, based on a mere plurality of four votes, Kuhlmann does not change the basic approach of Sanders.[7]
*1041 Petitioner urged at oral argument that the recently decided case of Fleming v. Kemp, 794 F.2d 1478 (11th Cir.1986) should control the outcome of the case. In Fleming the Eleventh Circuit, without deciding the merits of that prisoner's habeas petition, stayed the scheduled execution pending further order of that court. Id. In deciding that the prisoner did not abuse the writ in raising an identical claim on a successive habeas petition, the circuit court reached the question of whether the "ends of justice" would be served by a second review of the claim. Id. The court reiterated that the "ends of justice" are defined by objective factors, such as whether there was a full and fair hearing on the original petition, or whether there was an intervening chanqe in the facts of the case or the applicable law. Id. There, the alleged intervening change in the applicable law was the Supreme Court's decision in Batson v. Kentucky, ___ U.S. ___, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986) (juror exclusion based on race held unconstitutional).
The Fleming court, however, did not discuss the Supreme Court's ruling in Kuhlmann, which was handed down the day before. Because the circuit did not consider and discuss the Kuhlmann case, this court feels Fleming's precedential value is questionable with respect to the "ends of justice" determination.
Additionally, Fleming contains no discussion of the many other objective factors courts consider when making the "ends of justice" determination. In Fleming, the fact that there was an intervening change in the applicable law alone was held to be enough to grant reconsideration of the petition. The Fleming court failed to discuss any other factor. In essence, that court proposed its own "single factor" approach, and ignored the Sanders line of cases which leave it to the sound discretion of the district courts to weigh these factors. No opinion in Kuhlmann supports the position that an intervening change in the applicable law standing alone requires reconsideration of a successive petition.
Although this court finds the Kuhlmann decision does not control the outcome of this case, this court cannot ignore the fact that four justices supported an opinion that would make a "colorable showing of factual innocence" the sole factor to consider when deciding the "ends of justice" question. Thus, to the extent the Fleming court did not explicitly consider whether the petitioner there had made a "colorable showing of factual innocence in making its "ends of justice" determination, this court feels Fleming is not controlling.
This court finds that neither Kuhlmann nor Fleming essentially alter the traditional approach to the "ends of justice" test set forth in Sanders v. United States, 373 U.S. 1, 83 S.Ct. 1068, 10 L.Ed.2d 148 (1963). The burden lies with the petitioner to demonstrate that a reconsideration would serve the ends of justice. Sanders, 373 U.S. at 15-19, 83 S.Ct. at 1077-79; Bass v. Wainwright, 675 F.2d 1204 (11th Cir.1982). In Sanders the court held:
If factual issues are involved, the applicant is entitled to a new hearing upon showing that the evidentiary hearing on the prior application was not full and fair ... If purely legal questions are involved, the applicant may be entitled to a new hearing upon showing an intervening change in the law or some other justification for having failed to raise a crucial point or argument in the prior *1042 application. Id. at 16-17, 83 S.Ct. at 1078.
The court went on to qualify its remarks in the following ways:
First, the foregoing enumeration is not intended to be exhaustive; the test is "the ends of justice" and it cannot be too finely particularized. Second, the burden is on the applicant to show that, although the ground of the new application was determined against him on the merits on a prior application, the ends of justice would be served by a redetermination of the ground. Id. at 17, 83 S.Ct. at 1078.
The Eleventh Circuit has elucidated the Sanders holding stating that "the `ends of justice' are defined by objective factors, such as whether there was a full and fair hearing on the original petition or whether there was an intervening change of the facts of the case or the applicable law." Witt v. Wainwright, 755 F.2d 1396, 1397 (11th Cir.1985). Briefly stated then, the law of Sanders leaves the decision to grant reconsideration of a successive petition to the sound discretion of the district court which may properly consider several objective factors in reaching this decision. Courts have considered the following factors proper in making the "ends of justice" determination.
First, the plurality opinion in Kuhlmann indicates that four justices were willing to adopt the "colorable showing of factual innocence" test as the sole factor in making the "ends of justice" inquiry. Indeed, Justice Stevens' dissent acknowledges this test as "one of the facts that may properly be considered," although he did not feel it was an essential element to the reconsideration of a successive petition. Kuhlmann (Stevens, J. dissenting). Justice Stevens went on to conclude that the district court did not abuse its discretion because Kuhlmann was "one of those close cases in which the district court could have properly decided that a second review of the same contention was not required despite the intervening decision...." Id. Thus, at a minimum, five justices agree that whether petitioner has made a colorable showing of factual innocence is properly a factor to consider in making the "ends of justice" determination.
In the instant case, petitioner has made no such showing. Petitioner's counsel declined this court's invitation to make such a showing, arguing alternatively that the mere allegation that petitioner was insane established a "colorable showing", or that petitioner's claim regarding the "ends of justice" issue was established by other factors under Sanders such as an intervening change in the applicable law. (Transcript of oral argument on petition for habeas corpus p. 8-12, "Transcript"). When asked by this court whether petitioner had any claim of factual innocence, petitioner's counsel responded "there is a claim of innocence here. It's not a claim of factual innocence, it's a claim of legal innocence by reason of insanity." (Transcript at 10) Thus, by his own words counsel disavowed any showing that could establish the existence of this factor. Where, as here, both this court and the Eleventh Circuit in reviewing petitioner's first petition explicitly stated that the evidence of petitioner's guilt was "overwhelming", without making any showing of factual innocence whatsoever, petitioner has not made out a "colorable showing.[8]Messer v. Francis, No. C82-419R at 3 (N.D.Ga. March 30, 1984) (Hall, J. unpublished opinion) aff'd sub nom, Messer v. Kemp, 760 F.2d 1080, 1084 (11th Cir.1985).
Petitioner contends that other countervailing objective factors demonstrate that the "ends of justice" would be served by granting reconsideration. Namely, petitioner contends that the intervening change in law announced in Ake supra requires such a result. This court disagrees. Even assuming arguendo (1) that Ake did change the law relevant to the constitutionality *1043 of denying this petitioner an independent psychiatric evaluation for the preparation of his defense, and (2) that Ake applies retroactively to this petitioner on collateral review, this court feels an intervening change in law alone is insufficient to warrant reconsideration. In light of the plurality opinion in Kuhlmann that indicates the importance of the "colorable showing of factual innocence" factor, and three dissents in that case that emphasize the multiplicity of factors that may properly be considered, this court feels it would be inappropriate to give the change in intervening law alone controlling weight.[9]
The petitioner's failure to appeal an adverse ruling on his prior habeas petition is a factor to be considered in the "ends of justice" calculus of the Sanders test. Johnson v. Wainwright, 702 F.2d 909 (11th Cir.1983); Bass v. Wainwright, 675 F.2d 1204 (11th Cir.1982). Here, this court ruled on the merits of Messer's first petition on March 30, 1984. The court explicitly considered and denied relief on the denial of an independent psychiatric evaluation along with seven other grounds. Messer v. Francis, supra at 15. The Ake decision, the intervening change in law argued by petitioner as grounds for reconsideration of this opinion, was decided February 26, 1985. Ake supra. Petitioner on appeal from this court's denial of relief on his first petition did not raise Ake as a ground of appeal. This court has already ruled that this omission does not amount to "abandonment" of the claim, but as a factor to be considered under the ends of justice calculus it does weigh against petitioner. See discussion supra.
There are other factors that may be properly considered by this court, which are relevant to whether the ends of justice would be served by allowing reconsideration of a prisoner's second petition. The fact that a man's life is at stake is a weighty factor that this court fully appreciates. Potts v. Zant, 638 F.2d 727, 752 (11th Cir.1981). Also relevant is possible prejudice to the state e.g., here whether the state has access to witnesses that would be necessary to rebut petitioner's claim of insanity at the time of the offense. Id. Finality, here serves the state's legitimate punitive interests. When a prisoner is freed on a successive petition, often many years after the crime, the state may be unable successfully to retry him. Peyton v. Rowe, 391 U.S. 54, 62, 88 S.Ct. 1549, 1553, 20 L.Ed.2d 426 (1968) see Pate v. Robinson, 383 U.S. 375, 86 S.Ct. 836, 15 L.Ed.2d 815 (1966). The state has offered no showing to support such a conclusion on this case. However, the litany of direct appeals and collateral attack in this case, demonstrates the point. See facts supra.
After weighing all the above-mentioned factors and carefully examining the record in this case, the court feels the "ends of justice" would not be served by reaching the merits of the successive petition. First, petitioner has chosen to make no showing of factual innocence. Thus, petitioner fails to satisfy this factor. It is the concern of at least five members of the Supreme Court that a "colorable showing of factual innocence" be one of the factors properly considered by a district court in ruling on reconsideration of a successive petition. Although this court assumes arguendo that Ake supra is an intervening change in the law applicable to the facts of petitioner's case, and that it applies retroactively to this petitioner, standing alone such is insufficient to require reconsideration. Where (1) petitioner has made no showing of factual innocence, (2) the evidence of petitioner's guilt was found to be "overwhelming" by both this court and the circuit court, and (3) petitioner had the opportunity, yet failed to raise the Ake ground of relief on appeal from this court's *1044 order denying petitioner's first petition, the court feels the "ends of justice" do not require reconsideration.
CONCLUSION
In conclusion, the court considers this petition for a writ of habeas corpus to be a successive petition, and because this court feels the "ends of justice" would not be served by reconsideration, this court accordingly DENIES petitioner a writ of habeas corpus. The stay of execution ordered by this court is hereby lifted effective at noon July 8, 1986.
NOTES
[1] The United States Supreme Court granted certiorari in McCleskey v. Kemp, No. ___ U.S. ___, 106 S.Ct. 3331, 92 L.Ed.2d 737 (1986), to consider whether the death penalty is being applied in a racially discriminatory manner. This court feels the grant of certiorari should not alter the court's denial of the petition in the case at bar.
[2] In its Response, respondent pleads exhaustion contending that all the qrounds raised in the instant petition have not been previously raised in state proceedings. (Response at 2) However, respondent does not pursue this contention in its brief and the court does not feel compelled to discuss its merits.
[3] Respondent raised at oral argument a conceptually distinct problem arising from the posture of this case. As the court holds, petitioner properly stated his denial of independent psychiatric evaluation as a ground for relief in his first habeas petition. However, he did not renew this argument on appeal. Respondent argues petitioner, thus, intentionally abandoned his claim.
The "intentional abandonment or withholding" doctrine applies on a second habeas only where petitioner has not "previously presented [the ground for relief] in a federal habeas corpus proceeding." Witt; supra; Cf. Sanders v. United States, 373 U.S. 1, 83 S.Ct. 1068, 10 L.Ed.2d 148 (1963).
Here, petitioner did present this ground in the first habeas petition, and this court considered and rejected his arguments. Messer v. Francis, No. C82-419R (March 30, 1984) (Hall, J.) (unpublished opinion). aff'd Messer v. Kemp, 760 F.2d 1080 (11th Cir.1985) reh denied, ___ U.S. ___, 106 S.Ct. 864, 88 L.Ed.2d 902 (1986).
Once this ground was raised in the first habeas petition, as required under Witt and Sanders supra, no abandonment for abuse of writ purposes could occur. Fleming v. Kemp, 794 F.2d 1478 (11th Cir.1986). Additionally, there is no evidence that the failure of petitioner to brief the issue on appeal was to "vex, harass, or delay" Sanders supra 373 U.S. at 18, 83 S.Ct. at 1078. Therefore, any contention that petitioner abused the writ by this "abandonment" is groundless.
[4] Kuhlmann involved a situation in which defendant, after arraignment on charges of a 1970 robbery and murder, was confined in a cell with another prisoner who had previously agreed to act as a police informant. The defendant made incriminating statements, and the informant reported them to the police. Prior to trial, defendant moved to suppress the statements on the ground that they were obtained in violation of his Sixth Amendment right to counsel. The trial court denied the motion finding that the informant had obeyed a police officer's instructions not to question defendant about the crimes and that defendant's statements were "spontaneous" and "unsolicited". In 1972, defendant was convicted for common law murder and felonious possession of a weapon. The State Appellate Court affirmed. In 1973, defendant sought federal habeas corpus relief, asserting a Sixth Amendment violation based on the same grounds. The district court denied the writ, and the Court of Appeals affirmed. After the 1980 decision in United States v. Henry, 447 U.S. 264 100 S.Ct. 2183, 65 L.Ed.2d 115 (1980), which applied the "deliberately elicited" test of Massiah v. United States, 377 U.S. 201, 84 S.Ct. 1199, 12 L.Ed.2d 246 (1964) to suppress statements made to a paid jailhouse informant, defendant unsuccessfully sought to have his conviction vacated by the state courts. In 1982, defendant filed a habeas corpus petition in district court, again raising the Sixth Amendment claim. The district court denied relief, but the court of appeals reversed.
[5] Powell, J. announced the judgment of the court. Burger CJ., Rehinquist and O'Connor, JJ., joined Powell's discussion of the "ends of justice" test. Brennan, J. dissented joined by Marshall, J. Stevens, J. dissented separately. White and Blackmun, JJ., did not join Powell's "ends of justice" discussion.
[6] The most commonly recognized theory on dealing with four vote pluralities is the statement in Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976) that "when a fragmented court decides a case and no single rationale explaining the result enjoys the assent of five justices, `the holding of the court may be viewed as that position taken by those members who concurred in the judgment on the narrowest grounds.'" See Note, The Precedential Value of Supreme Court Plurality Decisions, 80 Columbia L.Rev. 756 (1980) for a fuller discussion of the "narrowest grounds" approach.
[7] If it is truly apparent that a "single factor" test is needed for the policy reasons set forth in Justice Powell's Kuhlmann opinion, this court feels the better analysis would be to extend the test of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), used in evaluating effectiveness of counsel issues on original habeas petitions, to the "ends of justice" question on successive petitions. This test would contemplate allowing reconsideration where there is a "reasonable probability that, but for [the denial of an independent psychiatric evaluation in preparation of an insanity defense that would have been a significant factor a trial], the result of the proceeding would have been different." Id. at 694, 104 S.Ct. at 2068. Restated simply, if the denial of the independent psychiatric evaluation in preparation for trial could reasonably have resulted in a different outcome, then reconsideration should be granted. This test has also been used as the test for materiality of exculpatory information not disclosed to the defense by the prosecution, United States v. Agurs, 427 U.S. 97, 104, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976), and in the test for materiality of testimony made unavailable to the defense by government deportation of a witness, United States v. Vallenzuela-Bernal, 458 U.S. 858, 102 S.Ct. 3440, 73 L.Ed.2d 1193 (1982).
This test would achieve the goals desired by Justice Powell and the three justices that joined his Kuhlmann opinion by (1) providing a clear rule for the district courts to apply, and (2) denying reconsideration to prisoners who have no chance of prevailing at retrial because "guilt is conceded or plain" Kuhlmann, 106 S.Ct. at 2626. The proposed test would also avoid problems where the "colorable showing of factual innocence" test does not logically apply. One example of these problems arises where a prisoner alleges constitutional error in the sentencing phase of a capital case. Guilt or innocence seems to be irrelevant in that context. See Kuhlmann, 106 S.Ct. p. 2622, n. 7 (Brennan, J. dissenting).
[8] In Kuhlmann, the plurality noted the circuit below stated that the evidence of prisoner's guilt in that case "was nearly overwhelming." Kuhlmann, 106 S.Ct. at 2628. Here, the Eleventh Circuit stated, "[i]f ever there was an open and shut case, this is it ..."
[9] Before Kuhlmann, a change in applicable law seemed to guarantee reconsideration in the Eleventh Circuit. This court is aware of no published case regarding successive petitioners in which the Eleventh Circuit has ever denied reconsideration where there was an intervening change in law which applied retroactively to a prisoner. Cf Young v. Kemp, 758 F.2d 514 (11th Cir.1985); Smith v. Kemp, 715 F.2d 1459 (11th Cir.1983); Fleming supra (granting reconsideration where intervening change applicable law occurred.)
|
Five Crazy Headlines: Babies for sale, a DUI hood ornament and a cartoon getaway van
How much is a baby worth nowadays? In China, one was enough to buy a new iPhone and a motorbike.
A young couple were arrested in China after they sold their 18-day-old baby to a man they met through the Chinese messaging app QQ. The couple planned on using the money from the sale to buy several different items including a motorbike and an iPhone.
The 19-year-old father was sentenced by a judge to three years in jail, while the underage mother of the baby received a two and a half year suspended sentence since she had not yet completed her schooling.
After hearing about the arrests of the parents, the man who bought the baby turned himself in to authorities, but it is unclear at this time if he has been sentenced to jail time. The baby is now being raised by the sister of the buyer, as the judge determined that the conditions the birth parents currently faced were too difficult for raising a child.
At a city-run pregnancy seminar, the mayor of Tangerang City, Indonesia gave expectant mothers a warning.
Feeding babies instant noodles or milk formula will make them gay.
Arief R. Wismansyah explained that because parents today are so busy that they feed their babies instant foods and formula, it has a negative impact on children’s development. He added that it is because of this that there have recently been more gay people.
Homosexuality is not widely accepted in Indonesia, but it is also not illegal except for in the province of Aceh, which follows Sharia law.
Source: DNA India
No officer, I’m not drunk. It’s a hood ornament!
If you are drunk and try to drive, just know you aren’t as subtle as you think you are.
Recently an officer in Roselle, Illinois pulled over and arrested a man for driving under the influence.
The officer suspected something was wrong when he saw a car driving along with a 15-foot-tall tree stuck in the front grill. When he got closer he noticed the airbags had been deployed inside the car. He then arrested the man for DUI. His case is still pending.
A video of the incident was posted on the department’s Facebook page, where it has now been shared almost 20,000 times.
Source: NBC Chicago
A couple dollars for you and a couple million dollars for me
Brothers James and Bob Stocklas hit it big recently, when they combined to win $291,000,007 from the Florida lottery.
James won the $291 million Powerball jackpot. Bob won $7.
James Stocklas, a judge from Pennsylvania, was eating breakfast at his favorite restaurant when he discovered he had won the jackpot. To celebrate his winnings, he paid for the meal of everyone in the restaurant at the time.
To commemorate the pair of winners, the Florida State Lottery also printed off a full-size winner’s check for Bob’s $7 prize.
Source: CNN
Like, zoinks! The cops are after us!
A 51-year-old woman in Redding, California is being sought after by police after she led them on a high-speed chase last week in a van painted up to look like the Mystery Machine from the Scooby-Doo cartoons.
Sharon Kay Turman was wanted for violating her probation when an officer from the Redding Police Department tried to pull her over.
Turman then led police on a high-speed chase, speeding through major roads and highways before running a red light and crashing into four cars. She managed to continue driving after the crash, and later abandoned her van and fled on foot. |
Q:
How to bind web service in jquery easy ui CRUD DataGrid
I am developing an website in c# asp.net using jQuery EasyUI CRUD datagrid.
But i need to replace the .php files with my web service to bind the datagrid as in the following snippet.Please suggest me a way to do so.
<table id="dg" title="My Users" style="width:700px;height:250px"
toolbar="#toolbar" pagination="true" idField="id"
rownumbers="true" fitColumns="true" singleSelect="true">
<thead>
<tr>
<th field="firstname" width="50" editor="{type:'validatebox',options:{required:true}}">First Name</th>
<th field="lastname" width="50" editor="{type:'validatebox',options:{required:true}}">Last Name</th>
<th field="phone" width="50" editor="text">Phone</th>
<th field="email" width="50" editor="{type:'validatebox',options:{validType:'email'}}">Email</th>
</tr>
</thead>
</table>
<script type="text/javascript">
$(function(){
$('#dg').edatagrid({
url: 'get_users.php',
saveUrl: 'save_user.php',
updateUrl: 'update_user.php',
destroyUrl: 'destroy_user.php'
});
});
</script>
A:
You can use jQuery Ajax, with jTemplate.
$.ajax({
url: "Your webservice path",
type: "POST",
data: "JSON formated data to pass in the webservice",
contentType: "application/json; charset=utf-8",
dataType: "json",
cache: false,
success: function (data) {
//You can further use jTemplate to output the data.
},
error: function (data) {
}
});
The following link shows a simple example for jTemplate:
http://www.codeproject.com/Articles/45759/jQuery-jTemplates-Grid
|
We are excited that you will be attending the Madison Mission Trip! The trip will be exciting opportunity for participants to strengthen their relationship with Jesus, step out of their comfort zone, learn the needs of the Madison area, serve our community and have fellowship with members of all three church sites. It is a four day mission trip in our own backyard from Sunday, April 13th to Wednesday, April 16th. Everyone is welcome- young, old, families, couples, singles. Whether you have gifts to share, or you're not sure how God can use you in Madison, you are welcome to join us on this adventure!
To participate in the mission trip you must complete this form by Saturday March 1st. |
Assessment of quality of life in head and neck cancer patients.
Seventy-five consecutive patients were selected to evaluate a disease-specific quality-of-life questionnaire (UW QOL). The new test was compared to two established equality of life evaluation tools, the Karnofsky scale and the Sickness Impact Profile (SIP). Each test was administered on three separate occasions: (1) several days preoperatively; (2) immediately postoperatively; and (3) 3 months postoperatively. The Karnofsky scale is relatively crude and lacks the ability to measure subtle changes. The SIP is a detailed questionnaire that is quite sensitive to change. However, due to its length, the SIP is inefficient and expensive to administer, and patient non-compliance is often a problem. The three questionnaires were compared according to the following factors: Acceptability: 97% of the patients favored the UW QOL scale compared with the SIP because it was more concise and easier to complete. VALIDITY indicates the ability of the test under investigation to measure what it was intended to measure. Using the SIP as a gold standard, the UW QOL scale demonstrated an average criterion validity of 0.849, whereas the Karnofsky average criterion validity was 0.826. Reliability: Reliability is a measurement of the reproducibility of the data. The UW QOL questionnaire scored > 0.90 on reliability coefficients versus 0.80 for the Karnofsky and 0.87 for the SIP scale. Responsiveness: Responsiveness is the ability of the test to measure clinical change. The UW QOL scale faired better than the Karnofsky and the SIP scale in detecting change. The UW QOL scale is comparable to the Karnofsky and SIP scales when tested for validity and reliability. It was the preferred test format of 97% of patients and provided the greatest responsiveness to clinical change. |
Introduction {#Sec1}
============
Psoriasis is a chronic, immune-mediated, inflammatory skin disorder that is currently incurable. Consequently, the majority of people with psoriasis require long-term treatment to maintain disease control. Traditional immunosuppressive systemic treatments, such as acitretin, methotrexate, cyclosporine, hydroxyurea, and thioguanine, may be effective in controlling psoriasis in some patients but significant toxicity and the need to closely monitor patients limit the viability of these treatments for long-term, continuous use \[[@CR23]\]. Recently developed systemic therapies that selectively target specific pathways in the inflammatory cascade of psoriasis generally have a much improved safety profile compared with traditional therapies \[[@CR26]\].
Efalizumab (anti-CD11a; Raptiva^®^) is a recombinant humanized monoclonal IgG~1~ antibody that has been approved for the treatment of moderate-to-severe chronic plaque psoriasis. It interferes with the pathogenesis of psoriasis via multiple mechanisms, including inhibition of T-lymphocyte trafficking and T-lymphocyte activation and reactivation \[[@CR1], [@CR10], [@CR11], [@CR21], [@CR25]\]. The safety and efficacy profile of efalizumab has been established in numerous clinical trials, in which more than 3,500 patients were enrolled and treatment was assessed for up to 3 years \[[@CR4]--[@CR6], [@CR12]--[@CR17], [@CR22]\].
Although psoriasis can be associated with the co-morbidity of psoriatic arthritis, a minority of patients with psoriasis (7--30%) will develop this joint disease \[[@CR27]\]. Nevertheless, psoriatic arthritis constitutes a major consideration in patients who are receiving long-term treatment for their psoriasis. A Nordic study of more than 5,000 patients with psoriasis showed that patients with arthritis exhibited greater impairment of psoriasis-related quality of life (QoL), longer disease duration, and greater self-reported disease severity, compared with patients who had psoriasis but no co-morbid arthritis \[[@CR27]\].
A low incidence of arthropathy adverse events (AEs; any form of joint disease) associated with efalizumab treatment has been reported in both clinical studies and routine clinical practice \[[@CR8], [@CR12]\]. However, anecdotal reports of arthropathy in routine clinical practice have expressed concern that efalizumab may be associated with exacerbation of arthropathy \[[@CR8]\]. To address this concern, we conducted a large-scale pooled analysis of safety data from five Phase III clinical trials (including open-label extensions of two of these studies) and two Phase III open-label clinical trials of efalizumab to explore whether arthropathy AEs were associated with efalizumab treatment in patients with psoriasis.
Methods {#Sec2}
=======
The primary objective of this pooled safety analysis was to assess the incidence of arthropathy AEs in patients who had received either efalizumab or placebo. Safety data were pooled from five randomized, double-blind, placebo-controlled clinical trials (including data from two open-label extension studies of two of these trials) and two open-label clinical trials of efalizumab \[[@CR4]--[@CR6], [@CR12]--[@CR17], [@CR22]\]. Patients included in these Phase III studies were aged ≥18 years and had moderate-to-severe chronic plaque psoriasis, a psoriasis area and severity index (PASI) score of ≥12 at screening, and plaque psoriasis covering ≥10% of body surface area. All patients were candidates for either systemic anti-psoriatic therapy or had received systemic anti-psoriatic therapy. Patients included in these trials received subcutaneous injections with efalizumab, 1--4 mg/kg once weekly or 2 mg/kg once-every-other week, or placebo. Details of individual study methodologies are described in other publications \[[@CR4]--[@CR6], [@CR12]--[@CR17], [@CR22]\].
Arthropathy AEs were defined according to the Coding Symbols for Thesaurus of Adverse Reaction Terms (COSTART) \[[@CR3]\] preferred terms 'arthritis' and 'arthrosis', or the Medical Dictionary for Regulatory Activities (MedDRA, <http://www.meddramsso.com/NewWeb2003/index.htm>) preferred terms 'arthritis not otherwise specified (NOS)', 'psoriatic arthropathy', 'arthropathy NOS', 'monoarthritis', 'polyarthritis', and 'osteoarthritis NOS'.
Treatment groups analyzed {#Sec3}
-------------------------
Due to the variety of study designs, five analyses were considered: 'first-treatment phase', 'first exposure phase', 'extended treatment phase', 're-treatment phase', and 'long-term treatment' (see Table [1](#Tab1){ref-type="table"}). Table 1Summary of the Phase III data from five placebo-controlled clinical trials (including data from two open-label extension studies of two of these trials) and two open-label clinical trials of efalizumab included in the pooled safety analysisPublication (protocol number)Study designNumber of patients in each analysisFirst treatment (0--12 weeks)Efalizumab sc 1--4 mg/kg qw or 2 mg/kg qowFirst exposure\
Extended treatment (13--24 weeks)Long-term treatment^a^(≤36 months)Re-treatmentPlaceboEfalizumab 1 mg/kgEfalizumab 2 mg/kgLeonardi \[[@CR13]\] (ACD2058g)Randomized, double-blind, parallel-group, placebo-controlled170162166462123--55Lebwohl \[[@CR12]\] (ACD2059g)Randomized, double-blind, parallel-group, placebo-controlled122232243579289----Gordon \[[@CR4]\] (ACD2390g)Randomized, double-blind, parallel-group, placebo-controlled187368--368------Papp \[[@CR17]\] (ACD2600g)Randomized, double-blind, parallel-group, placebo-controlled236449--449--449--Sterry \[[@CR22]\] (IMP24011)Randomized, double-blind, parallel-group, placebo-controlled264529--772308--145Papp \[[@CR16]\] (ACD2062g)Open-label------34137--365Gottlieb \[[@CR5], [@CR6]\] (ACD2243g)Open-label------339^b^290339--Menter \[[@CR14]\] (ACD2391g)Open-label extension^c^of study ACD2390g \[[@CR4]\]------174342----Menter \[[@CR15]\] (ACD2601g)Open-label extension^c^of study ACD2600 g \[[@CR17]\]------217622635^d^--Pooled analysis97917404093,3942,111n.a.^e^565*qow* once-every-other week, *qw* once weekly, *sc* subcutaneous^a^Number of patients at start^b^Patients received combined therapy with fluocinolone acetate (*n* = 169) or petrolatum (*n* = 170) for weeks 9--12; for months 3--15, the dose of efalizumab could be escalated to 4 mg/kg per week for up to 4 weeks if clinically indicated^c^Some patients are included in the analyses more than once because patients in the open-label extension studies are also included in analyses of the parent studies^d^Included patients who received either efalizumab or placebo in the parent study \[[@CR17]\]^e^Not applicable because data are analyzed and reported separately for the study by Gottlieb et al. \[[@CR6]\] and the study published by Papp \[[@CR17]\] and Menter \[[@CR15]\]
It is worth noting that most of the studies included in this pooled analysis were designed and conducted before efalizumab had received regulatory approval and before it was known that doses of more than 1 mg/kg once weekly (the approved dose) did not confer additional treatment benefit (EMEA, Raptiva Summary of Product Characteristics; FDA US, FDA Prescribing Information for Raptiva). For this reason, only the efalizumab 1 mg/kg once-weekly dose data are reported for the 'first treatment phase' of the analysis. Due to the wide variety of study designs included in the pooled analysis, data for patients receiving any dose of efalizumab are combined for all other treatment phases analyzed.
The 'first treatment phase' analysis included 0--12-week data from patients in the five placebo-controlled studies who received either efalizumab 1 mg/kg once weekly or placebo. This analysis allows a comparison between the efalizumab and placebo treatment groups.
The 'first exposure phase' included 12-week data from all studies in patients who had their first exposure to any dose of efalizumab and, thus, did not include placebo data. This analysis was conducted to include the maximum number of patients who received efalizumab for their first 12 weeks of treatment (i.e., it included those patients who first received efalizumab treatment after crossing over from a placebo group, as well as the patients who first received efalizumab during weeks 0--12).
The 'extended treatment phase' analysis included 13--24-week data in patients given any dose of efalizumab who had already received efalizumab during the first treatment phase.
The 'long-term treatment phase' analysis included all patients who received continuous long-term treatment (up to 36 months) with any dose of efalizumab. Data were analyzed in 12-week segments to assess change in the incidence of arthropathy AEs over time. This analysis included data from two long-term studies \[[@CR6], [@CR15], [@CR17]\], which were analyzed separately due to differences in study design.
The 're-treatment phase' analysis included all patients who re-started treatment with efalizumab following a treatment-free observation period.
Statistical analyses {#Sec4}
--------------------
Descriptive statistics were used to explore the association between efalizumab and the occurrence of arthropathy AEs. Results are expressed as point-estimates of the incidence rates (ratio of the number of patients with an arthropathy AE to the total number of patient-years at risk of an arthropathy AE) with their 95% confidence intervals (CIs). Descriptive comparisons are provided; no formal statistical tests were performed.
Analyses were also conducted to explore the relationship between onset of arthropathy AEs during efalizumab treatment and a previous history of arthropathy (reported as a narrative by patients at the baseline visit) and the incidence of arthropathy AEs and clinical response to efalizumab treatment \[measured at 12 weeks using the Physician Global Assessment (PGA) and PASI scales\]. Differences in patient and psoriasis characteristics at baseline were also compared between patients who had arthropathy AEs and those who did not. An additional analysis of data from patients included in the first treatment phase of the study by Sterry et al. \[[@CR22]\] (Table [1](#Tab1){ref-type="table"}) was conducted to assess the incidence of psoriatic arthropathy in these patients. This was the only study to define arthropathy AEs according to MedDRA; other studies used the COSTART, which did not include 'psoriatic arthropathy' specifically as a preferred term.
Baseline demographics and psoriasis characteristics and the proportion of patients with a previous history of arthropathy (as reported by patients at the baseline visit) were tabulated by presence/absence of an arthropathy event.
Results {#Sec5}
=======
The number of patients included in each of the pooled safety analyses from each of the seven trials and two open-label extensions is summarized in Table [1](#Tab1){ref-type="table"}. Up to 3,394 patients received at least one dose of efalizumab. A total of 2,719 patients were included in the first treatment phase analysis, of whom the majority (64%; 1,740 patients) received efalizumab 1 mg/kg per week; 979 patients (36%) received placebo. Efalizumab 2 mg/kg per week regimen was given to 409 patients (15%) in two of the five studies \[[@CR12], [@CR13]\]; consequently, these patients were not included in the first treatment analysis. Patient demographics and baseline psoriasis characteristics were similar between treatment groups in the first treatment phase (Table [2](#Tab2){ref-type="table"}). Table 2Baseline demographic and disease characteristics for patients in the placebo-controlled first treatment phaseCharacteristicsPlacebo (*n* = 979)Efalizumab 1 mg/kg per week (*n* = 1,740)Efalizumab 2 mg/kg per week (*n* = 409)Mean age (years), mean (SD)45 (12)45 (12)45 (13)Weight (kg), mean (SD)90.0 (20.0)89.4 (19.6)93.6 (20.5)Mean BMI^a^ (kg/m^2^)30.4 (6.4)30.2 (6.3)31.4 (6.6)Race,*n* (%) Caucasian891 (91)1,569 (90)356 (87) Other88 (9)171 (10)53 (13)Duration of psoriasis, mean number of years (SD)19.2 (11.4)19.1 (11.4)17.6 (11.7)History of arthritis,*n* (%)286 (29.2)529 (30.4)141 (34.5)*BMI* body mass index^a^Due to missing height data, BMI was calculated for 971 patients in the placebo group, 1,719 patients in the efalizumab 1 mg//kg per week group and 404 patients in the efalizumab 2 mg/kg per week group
First treatment phase (weeks 0--12) {#Sec6}
-----------------------------------
During the first 12 weeks of treatment a similar proportion of patients had an arthropathy AE in the efalizumab 1 mg/kg group (3.3%) and the placebo group (3.5%; Fig. [1](#Fig1){ref-type="fig"}a). Correspondingly, the incidence of arthropathy AEs per patient-year was 0.15 in the efalizumab 1 mg/kg group (95% CI 0.11--0.19) and 0.16 in the placebo group (95% CI 0.11--0.22; Fig. [1](#Fig1){ref-type="fig"}b). The majority of the arthropathy AEs was mild-to-moderate in intensity in both the efalizumab (41/58 events; 71%; 95% CI 57--82%) and placebo groups (31/34 events; 91%; 95% CI 76--98%). Fig. 1**a** Proportion of patients who had arthropathy adverse events (AEs) during each phase of the safety analysis and **b** incidence of arthropathy AEs per patient-year for each phase
The additional analysis of data from the study by Sterry et al. \[[@CR22]\] demonstrated that the incidence of psoriatic arthropathy per patient-year was lower in the group treated with efalizumab 1 mg/kg per week (0.10; 95% CI 0.05--0.18) than in the placebo group (0.17; 95% CI 0.08--0.30); the proportion of patients with psoriatic arthropathy was 2.3% (12/529 patients) in the efalizumab group and 3.8% (10/264 patients) in the placebo group.
First exposure phase {#Sec7}
--------------------
In total, 3,394 efalizumab-treated patients were included in this analysis. A small proportion of patients had an arthropathy AE (3.6%; Fig. [1](#Fig1){ref-type="fig"}a) and the incidence of arthropathy AEs per patient-year was also low (0.16; 95% CI 0.14--0.19; Fig. [1](#Fig1){ref-type="fig"}b).
The incidence of arthropathy AEs in this group of patients was similar to that in the placebo group in the first treatment phase, as indicated by the overlap in CIs.
Extended treatment phase (weeks 13--24) {#Sec8}
---------------------------------------
In total, 2,111 patients were included in the extended treatment phase analysis. During this phase, a low proportion of patients had an arthropathy AE (3.8%; Fig. [1](#Fig1){ref-type="fig"}a) and the incidence of arthropathy AEs per patient-year was also low (0.17; 95% CI 0.14--0.22; Fig. [1](#Fig1){ref-type="fig"}b). Overlap in the CIs indicates that the incidence of arthropathy AEs in this group of patients was also similar to that in the placebo group in the first treatment phase.
Long-term treatment phase {#Sec9}
-------------------------
The results of two long-term studies were analyzed separately to assess the incidence of arthropathy AEs in patients treated with efalizumab. In both of these studies (Fig. [2](#Fig2){ref-type="fig"}), there was no overall increase in the incidence of arthropathy AEs over time. Furthermore, the incidence of arthropathy remained similar to that of the placebo group in the first treatment phase and stable between 12-week periods. Fig. 2Incidence of arthropathy AEs in long-term studies of patients treated with efalizumab **a** for up to 36 months and compared indirectly with pooled placebo data from the first treatment (FT) phase \[[@CR5], [@CR6]\] and **b** for up to 15 months and compared with the study's placebo group during month 0--12 \[[@CR15], [@CR17]\]. \*Following the first 3-month double-blind, placebo-controlled phase of this study, patients in the placebo group who continued were switched to open-label treatment with efalizumab. Consequently, the month 6, 9, 12 and 15 results included patients who had received placebo during the initial 3 months of the study
In total, 339 patients were included in the analysis of the study by Gottlieb et al. \[[@CR6]\]. These patients received continuous treatment with efalizumab 2 mg/kg once weekly for weeks 1--12 (fluocinolone acetate or petrolatum was co-administered during weeks 9--12), followed by continuous maintenance treatment with efalizumab 1 mg/kg once weekly for up to 36 months in patients who had a ≥ 50% improvement in PASI score. For months 3--15, the dose of efalizumab could be escalated to 4 mg/kg per week for up to 4 weeks if clinically indicated, then maintained at 2 mg/kg per week. During the entire study period, there was little variation in the incidence of arthropathy AEs (range 0.06--0.19; Fig. [2](#Fig2){ref-type="fig"}a). Reasons for discontinuation were diverse and were representative of the overall population; refer to Gottlieb et al. \[[@CR6], [@CR7]\] for details of discontinuations.
For the other long-term study, the analysis included 3-month data from 449 efalizumab-treated patients in the placebo-controlled first treatment phase of the study \[[@CR17]\] and data from 635 patients who entered the open-label extension phase and received efalizumab treatment \[[@CR15]\]; 218 of the 635 patients included in the open-label extension had switched from placebo to efalizumab after completing the first treatment phase. Patients who entered the open-label extension phase continued to receive, or initiated treatment with, efalizumab 1 mg/kg once weekly for up to 15 months continuously. As in the long-term study by Gottlieb et al. \[[@CR6]\], there was little variation in the incidence of arthropathy AEs during the entire study period (range 0.06--0.12; Fig. [2](#Fig2){ref-type="fig"}b).
Re-treatment phase {#Sec10}
------------------
In total, 565 efalizumab-treated patients were included in the re-treatment phase of the analysis. In this phase, a lower proportion of patients had an arthropathy AE (2.7%; Fig. [1](#Fig1){ref-type="fig"}a) compared with the first treatment phase, and the incidence of arthropathy AEs per patient-year was also lower (0.12; 95% CI 0.07--0.19; Fig. [1](#Fig1){ref-type="fig"}b). The incidence of arthropathy AEs in this group of patients was lower than in the placebo group in the first treatment phase.
Baseline characteristics and previous history of arthropathy {#Sec11}
------------------------------------------------------------
There were no differences in baseline demographics or disease characteristics between the patients who had arthropathy AEs and those who did not. Patients who experienced an arthropathy AE during treatment with efalizumab appeared to be more likely to have a history of arthropathy prior to treatment. Of the patients who never developed an arthropathy AE during efalizumab treatment, 27% reported a previous history of arthropathy compared with 59% in patients who did have an arthropathy AE.
During the first treatment phase, 88% (*n* = 34) and 76% (*n* = 79) of patients who developed an arthropathy AE had a history of arthropathy prior to receiving placebo or efalizumab 1 mg/kg once weekly, respectively.
Arthropathy AEs and clinical response to efalizumab {#Sec12}
---------------------------------------------------
Arthropathy AEs appeared to be less likely to occur in patients who had a good clinical response to treatment (≥75% improvement in PASI score; 2.3% of patients had events) than in patients who had a partial response (50--74% improvement in PASI score; 3.5% of patients had events; Fig. [3](#Fig3){ref-type="fig"}) and non-responders (\<50% improvement in PASI score; 4.5% of patients had events). The corresponding incidences of arthropathy AEs per patient-year were 0.10 in patients with a good clinical response (95% CI 0.05--0.18), 0.17 in patients with a partial clinical response (95% CI 0.11--0.25), and 0.21 in patients who did not respond (95% CI 0.15--0.28). Fig. 3**a** Proportion of patients with an arthropathy AE by response category on the psoriasis area and severity index (PASI) and physician global assessment (PGA) scales and **b** incidence of arthropathy AEs per patient-year by response category on the PASI and PGA scales
When assessed using the PGA scale, arthropathy AEs also appeared to be less likely to occur in patients who had better clinical responses to treatment with efalizumab (Fig. [3](#Fig3){ref-type="fig"}). During the extended treatment phase, the incidence of arthropathy AEs per patient-year was 0.17 in patients with responses categorized as 'cleared', 'excellent' or 'good' on the PGA scale (95% CI 0.10--0.25) and 0.25 in patients with responses categorized as 'fair', 'slight', 'unchanged' or 'worse' on the PGA scale (95% CI 0.17--0.35).
Discussion {#Sec13}
==========
The placebo-controlled results of this large-scale pooled analysis of arthropathy data from seven clinical trials show that efalizumab does not appear to increase the risk of developing arthropathy AEs compared with placebo during the first 12 weeks of treatment. In addition, for patients treated with efalizumab, the incidence of arthropathy AEs did not appear to increase over time. The proportion of patients who had an arthropathy AE within any 12-week treatment period was low (\<4.1%) through all treatment phases (first treatment, first exposure, extended treatment, re-treatment, long-term treatment).
Joint disease has also been reported as a side-effect of other approved biological treatments for psoriasis, namely infliximab (EMEA public statement on infliximab, <http://www.emea.eu.int/pdfs/human/press/pus/444500en.pdf>) \[[@CR2], [@CR18], [@CR19]\], alefacept (Biogen safety presentation on Alefacept to the FDA, <http://www.fda.gov/ohrms/dockets/ac/02/slides/3865S1_04_Biogen-Safety/sld007.htm>) \[[@CR20], [@CR24]\], and etanercept (EMEA Scientific discussion for the approval of Enbrel, <http://www.emea.eu.int/humandocs/PDFs/EPAR/Enbrel/014600en6.pdf>). Indeed, placebo-controlled studies of infliximab and alefacept indicate that in patients with moderate-to-severe psoriasis the incidence of arthralgia (joint pain) is 7 and 5%, respectively (Biogen safety presentation on Alefacept to the FDA, <http://www.fda.gov/ohrms/dockets/ac/02/slides/3865S1_04_Biogen-Safety/sld007.htm>) \[[@CR18], [@CR24]\]. Psoriatic arthritis has been reported as serious treatment-related AE in three placebo-controlled studies of etanercept in the treatment of chronic plaque psoriasis (incidence data have not been published) (EMEA Scientific discussion for the approval of Enbrel, <http://www.emea.eu.int/humandocs/PDFs/EPAR/Enbrel/014600en6.pdf>). The incidence of arthropathy AEs in the current analysis of efalizumab appears to be similar to that for arthralgia in studies of infliximab and alefacept. Moreover, the term 'arthropathy', used in the current study encompasses a variety of joint diseases, not just a single joint condition such as arthralgia or psoriatic arthritis, and therefore has greater potential to include more patients. However, this between-study comparison is indirect and thus should be treated with caution. Moreover, no arthropathy event (defined by any of the MedDRA or COSTART preferred terms) was excluded from the analysis. Also, data from first treatment phase of the study by Sterry et al. \[[@CR22]\] indicate that the proportion of patients with psoriatic arthropathy specifically was low (2.3%) in patients treated with efalizumab 1 mg/kg per week---in fact, lower than in the placebo group (3.8%). It should be noted, however, that psoriatic arthropathy events were not confirmed by a rheumatologist---this is a potential limitation of the study. However, the umbrella term 'arthropathy' was designed to capture all joint diseases, including 'psoriatic arthropathy'. Also, the incidence of psoriatic arthropathy in the study by Sterry et al. was in line with the incidence of 'arthropathy' in the overall pooled analysis.
To put the results of this pooled analysis, which by its very nature included select patient populations (determined by the inclusion/exclusion criteria and study designs), in the context of routine clinical practice, post-marketing surveillance data were assessed. During post-marketing surveillance of efalizumab, which accounts for approximately 17,500 patient-years to date, serious arthropathies requiring hospitalization were reported with a frequency of about 4.8 per 1,000 patient-years in patients receiving efalizumab. It should be noted, however, that underreporting of AEs in routine clinical practice setting may lead to an underestimate of the true incidence of arthropathy.
For both the 12-week first treatment and first exposure phases of the current analyses, the proportions of patients reporting an arthropathy AE appeared to be lower in the efalizumab groups than in the placebo group in the first treatment phase. Correspondingly, the incidences of AEs per patient-year in these treatment phases were also lower in the efalizumab groups than that observed in the placebo group in the first treatment phase. However, the proportion of AEs that were moderate or severe was greater in the efalizumab groups than in the placebo groups; too few patients had events to draw any meaningful conclusions.
During the extension phase (weeks 13--24), the incidence of arthropathy AEs in efalizumab-treated patients remained similar to the placebo group in the first treatment phase. Previous history of arthropathy and poor clinical response may potentially indicate a risk for occurrence of new arthropathy AEs during treatment. Indeed, arthropathy AEs were most frequent in patients who did not respond to therapy with efalizumab or in patients with a history of arthropathy.
Importantly, the data from the two long-term studies of efalizumab indicate that the incidence of arthropathy AEs remains stable and low for up to 3 years of continuous treatment. These results, coupled with efficacy data showing that the clinical improvements of the skin after 3 months of efalizumab therapy are maintained throughout 36 months of continuous dosing \[[@CR5]\], support the suitability of efalizumab for the chronic, continuous treatment of patients with psoriasis. Reasons for patients' discontinuations in the 36-month study by Gottlieb et al. \[[@CR6], [@CR7]\] were diverse and representative of the overall population included in this analysis and have been described previously. When considering the long-term analysis of the 36-month study (Fig. [2](#Fig2){ref-type="fig"}a), it should be noted that the number of patients who remained in the study decreased over time. This discontinuation rate is not unexpected for a study that is 3 years in duration but, by month 36, there is a small number of patients on which to base comparisons with the first treatment phase. Another factor that may confound between-phase analysis comparisons was the possible use of concomitant medications for psoriasis after the first treatment phase in the study by Gottlieb et al. \[[@CR6]\], which permitted the use of topical corticosteroids and ultraviolet B phototherapy. Accordingly, it should be noted that comparisons of the results between any of the treatment phases of this analysis are observational (i.e., not direct) but do confirm the results of the long-term treatment phase and the placebo-controlled 12-week first treatment phase studies, suggesting that the risk of joint disease is not increased with continued efalizumab treatment and that the incidence of arthropathy is low and similar to placebo. Further investigation is needed to confirm the results of this preliminary analysis of arthropathy events during long-term treatment with efalizumab.
In patients who re-started treatment for a further 12 weeks following an intervention-free period, the proportion of patients who had an arthropathy AE was lower than during the first treatment phase; the same was true for the incidence of arthropathy AEs per patient-year in re-treated patients. Although this scenario is likely to occur infrequently in clinical practice, these data show that if a patient needs to stop (e.g., during pregnancy) and then restart treatment, there appears to be no increased risk of arthropathy AEs.
Although arthritis in patients with psoriasis has a significant impact on QoL \[[@CR9], [@CR27]\], it can, in most cases, be managed effectively \[[@CR8]\]. In the small minority of patients who develop arthropathy during treatment, the symptoms can be managed successfully with non-steroidal anti-inflammatory drugs \[[@CR8]\].
In conclusion, the results of this pooled analysis show that efalizumab does not appear to increase the risk of developing arthropathy AEs compared with placebo. Long-term studies of efalizumab indicate that the incidence of arthropathy AEs remains stable and low for up to 3 years of continuous treatment.
This study was sponsored by Serono International S.A. The authors thank Tom Potter, MSc, for his assistance with manuscript preparation.
|
Optically variable devices are used in a wide variety of applications, both decorative and utilitarian. Optically variable devices can be made in multitude of ways to achieve a variety of effects. Optically variable devices (OVDs) such as holograms are imprinted on credit cards and authentic software documentation; color-shifting images are printed on banknotes, and OVDs enhance the surface appearance of items such as motorcycle helmets and wheel covers.
Optically variable devices can be made as a film or a foil that is pressed, stamped, glued, or otherwise attached to an object, and can also be made using optically variable pigments. One type of optically variable pigment is commonly called a color-shifting pigment because the perceived color of images appropriately printed with such pigments changes as the angle of view and/or illumination is tilted. A common example is the number “20” printed with color-shifting pigment in the lower right-hand corner of a U.S. twenty-dollar banknote, which serves as an anti-counterfeiting device.
Some anti-counterfeiting devices are covert, while others are overt intended to be noticed. Unfortunately, some optically variable devices that are intended to be noticed are not widely known because the optically variable aspect of the device is not sufficiently dramatic or distinguishable from its background. For example, the amount of color-shift of an image printed with color-shifting pigment might not be noticed under uniform fluorescent ceiling lights, but may be more noticeable in direct sunlight or under single-point illumination. This can make it easier for a counterfeiter to pass counterfeit notes without the optically variable feature because the recipient might not be aware of the optically variable feature, or because the counterfeit note might look substantially similar to the authentic note under certain conditions.
Optically variable devices can also be made with magnetic pigments. These magnetic pigments may be aligned with a magnetic field after applying the pigment (typically in a carrier such as an ink vehicle or a paint vehicle) to a surface. However, painting with magnetic pigments has been used mostly for decorative purposes. For example, use of magnetic pigments has been described to produce painted cover wheels having a decorative feature that appears as a three-dimensional shape. A pattern was formed on the painted product by applying a magnetic field to the product while the paint medium still was in a liquid state. The paint medium had dispersed magnetic non-spherical particles that aligned along the magnetic field lines. The field had two regions. The first region contained lines of a magnetic force that were oriented parallel to the surface and arranged in a shape of a desired pattern. The second region contained lines that were non-parallel to the surface of the painted product and arranged around the pattern. To form the pattern, permanent magnets or electromagnets with the shape corresponding to the shape of desired pattern were located underneath the painted product to orient in the magnetic field non-spherical magnetic particles dispersed in the paint while the paint was still wet. When the paint dried, the pattern was visible on the surface of the painted product as the light rays incident on the paint layer were influenced differently by the oriented magnetic particles.
Similarly, a process for producing of a pattern of flaked magnetic particles in fluoropolymer matrix has been described. After coating a product with a composition in liquid form, a magnet with desirable shape was placed on the underside of the substrate. Magnetic flakes dispersed in a liquid organic medium orient themselves parallel to the magnetic field lines, tilting from the original planar orientation. This tilt varied from perpendicular to the surface of a substrate to the original orientation, which included flakes essentially parallel to the surface of the product. The planar oriented flakes reflected incident light back to the viewer, while the reoriented flakes did not, providing the appearance of a three dimensional pattern in the coating.
By way of background prior art, United States Patent Application 20050106367, incorporated herein by reference, published May 19, 2005 in the name of Raksha et al., assigned to JDS Uniphase Corporation, describes a method and apparatus for orienting magnetic flakes such as optically variable flakes.
Although some of the aforementioned methods for providing visually appealing and useful optical effects are now nearly ubiquitous, these devices require enhancements and additional features to make them more recognizable as an authentic article; for example it would be preferable to have the ability to provide yet additional security features.
For example it would be highly desirous to have a security device which provided a color shift with change in incident light or viewing angle including magnetically aligned flakes and optical features associated therewith; and, providing such a device which had a reasonable amount of tactility would be highly advantageous. It would also be preferably to have such a device wherein there was significant contrast and sharpness between regions of the device that Were functionally different. For example a magnetically aligned region of thin film color shifting flakes directly adjacent an embossed region could offer benefits not realizable in two adjacent different magnetically aligned regions.
It is an object of this invention to provide a method for forming an image of a plurality of contrasting, discernible regions, wherein at least one region has magnetic flakes thereon aligned by an applied magnetic field having a predetermined orientation, and another of the discernible regions adjacent to the first discernible region having flakes thereon or an absence of flakes caused by mechanically impressing or pushing away flakes from said second region.
It is an object of this invention to provide a tactile image wherein a tactile transition can be sensed by touching a transition between at least the first and second discernible regions.
It is an object of this invention to provide a banknote or security document which has tactile properties to assist the blind in verifying the authenticity of the note or document.
It is an object of this invention to provide an image having an optically variable region and having a tactile region about the optically variable region. |
Struma ovarii: hyperthyroidism in a postmenopausal woman.
A rare case of struma ovarii producing hyperthyroidism in a postmenopausal woman is reported. The ovarian tumor demonstrated uptake of both [99mTc]pertechnetate and 131I, allowing preoperative diagnosis of the condition. In females with unexplained hyperthyroidism and low 131I uptake by the cervical thyroid gland, imaging of the pelvis should be considered. |
Fray Mocho (magazine)
Fray Mocho was an Argentine weekly magazine that published general interest topics. Its first number was published on May 3, 1912, with historian and journalist Carlos Correa Luna being its first director. Fray Mocho'''s staff included former collaborators of Caras y Caretas who had left the magazine in disagreement with its editorial line.
The magazine was named after José Sixto Álvarez (1858–1903), writer and journalist who was notable for his humorous texts, apart of having been the founder of Caras y Caretas. Fray Mocho published 196 issues until its closure in 1929.
History
The magazine was founded with the purpose of continuing the editorial line of Caras y Caretas that had significantly changed since the death of Sixto Alvarez in 1903. Some of Fray Mocho founders and main collaborators were Carlos Correa Luna, Spanish illustrator José María Cao, writer Luis Pardo (under the seudonym "Luis García"), Félix Lima, painter Juan Peláez, Czech cartoonist José Friedriech,La Revista Fray Mocho y un tango dedicado by León Benarós on Todo Tango website and artist Juan Hohmann.Fray Mocho was an alternative to general-interest magazines such as Caras y Caretas or PBT, with an average of 80,000 copies printed. In 1922 the magazine added more articles about classical culture and art, ceasing the use of illustrations on its covers and adding more photographs and paintings until 1929 when it ceased to be published.
The magazine covered a wide range of topics, some of its permanent sections were theatre activities, provinces, women, Montevideo, readers' letters, children's literature, horse racing, other countries' traditions and costumes, and everyday life, among others.
Visual styleFray Mocho's visual aesthetic had influences of the romanticism and art nouveau styles at its first steps, then changing to art deco.
The rise of art nouveau in Argentina in the 1900s influenced not only magazines' visual styles but facades of private houses, and was quickly adopted by the middle class. That aesthetic renovation was also visible on typography, illustration and design of Fray Mocho, as well as advertisement, facades of public buildings and even clothing in the Argentine society of that age.
See also
Caras y Caretas''
Notes
References
Category:Argentine satirical magazines
Category:Magazines established in 1912
Category:Magazines disestablished in 1929
Category:Media in Buenos Aires
Category:Argentine political magazines
Category:Argentine political satire
Category:Spanish-language magazines
Category:Weekly magazines |
#define YEAR 2013
#define STATUS "release"
#ifndef ROOT_DIR
#define ROOT_DIR ".."
#endif
#define BUILD_DIR ROOT_DIR + "/build/NetBox/
#ifndef SOURCE_DIR
#define SOURCE_DIR ROOT_DIR + "/src/NetBox"
#endif
#ifndef OUTPUT_DIR
#define OUTPUT_DIR ROOT_DIR + "/build"
#endif
#ifndef BINARIES_DIR_FAR2
#define BINARIES_DIR_FAR2 BUILD_DIR + "/Far2"
#endif
#ifndef BINARIES_DIR_FAR3
#define BINARIES_DIR_FAR3 BUILD_DIR + "/Far3"
#endif
#ifndef PUTTY_SOURCE_DIR
#define PUTTY_SOURCE_DIR "C:/Program Files/Putty"
#endif
#define FileSourceMain_Far2x86 BINARIES_DIR_FAR2 + "/x86/NetBox.dll"
#define FileSourceMain_Far2x64 BINARIES_DIR_FAR2 + "/x64/NetBox.dll"
#define FileSourceMain_Far3x86 BINARIES_DIR_FAR3 + "/x86/NetBox.dll"
#define FileSourceMain_Far3x64 BINARIES_DIR_FAR3 + "/x64/NetBox.dll"
#define FileSourceEng SOURCE_DIR + "/NetBoxEng.lng"
#define FileSourceRus SOURCE_DIR + "/NetBoxRus.lng"
#define FileSourceChangeLog ROOT_DIR + "/ChangeLog"
#define FileSourceReadmeEng ROOT_DIR + "/README.md"
#define FileSourceReadmeRu ROOT_DIR + "/README.RU.md"
#define FileSourceLicense ROOT_DIR + "/LICENSE.txt"
#define PluginSubDirName "NetBox"
#define Major
#define Minor
#define Rev
#define Build
#expr ParseVersion(FileSourceMain_Far2x86, Major, Minor, Rev, Build)
#define Version Str(Major) + "." + Str(Minor) + (Rev > 0 ? "." + Str(Rev) : "") + \
(STATUS != "" ? " " + STATUS : "")
[Setup]
AppId=netbox
AppMutex=NetBox
AppName=NetBox plugin for Far2/Far3
AppPublisher=Michael Lukashov
AppPublisherURL=https://github.com/michaellukashov/Far-NetBox
AppSupportURL=http://forum.farmanager.com/viewtopic.php?f=39&t=6638
AppUpdatesURL=http://plugring.farmanager.com/plugin.php?pid=859&l=en
VersionInfoCompany=Michael Lukashov
VersionInfoDescription=Setup for NetBox plugin for Far2/Far3 {#Version}
VersionInfoVersion={#Major}.{#Minor}.{#Rev}.{#Build}
VersionInfoTextVersion={#Version}
VersionInfoCopyright=(c) 2011-{#YEAR} Michael Lukashov
DefaultDirName={pf}\Far Manager\Plugins\{#PluginSubDirName}
UsePreviousAppDir=false
DisableProgramGroupPage=true
LicenseFile=licence.setup
; UninstallDisplayIcon={app}\winscp.ico
OutputDir={#OUTPUT_DIR}
DisableStartupPrompt=yes
AppVersion={#Version}
AppVerName=NetBox plugin for Far2/Far3 {#Version}
OutputBaseFilename=FarNetBox-{#Major}.{#Minor}.{#Rev}_Far2_Far3_x86_x64
Compression=lzma2/ultra
SolidCompression=yes
PrivilegesRequired=none
Uninstallable=no
MinVersion=5.1
DisableDirPage=yes
; AlwaysShowDirOnReadyPage=yes
ArchitecturesInstallIn64BitMode=x64
[Types]
Name: full; Description: "Full installation"
; Name: compact; Description: "Compact installation"
Name: custom; Description: "Custom installation"; Flags: iscustom
; Languages: en ru
[Components]
Name: main_far2_x86; Description: "NetBox for Far2/x86"; Types: full custom; check: IsFar2X86Installed
Name: main_far2_x64; Description: "NetBox for Far2/x64"; Types: full custom; check: IsWin64 and IsFar3X64Installed
Name: main_far3_x86; Description: "NetBox for Far3/x86"; Types: full custom; check: IsFar3X86Installed
Name: main_far3_x64; Description: "NetBox for Far3/x64"; Types: full custom; check: IsWin64 and IsFar3X64Installed
; Name: pageant; Description: "Pageant (SSH authentication agent)"; Types: full
; Name: puttygen; Description: "PuTTYgen (key generator)"; Types: full
[Files]
Source: "{#FileSourceMain_Far2x86}"; DestName: "NetBox.dll"; DestDir: "{code:GetPlugin2X86Dir}"; Components: main_far2_x86; Flags: ignoreversion
Source: "{#FileSourceMain_Far2x64}"; DestName: "NetBox.dll"; DestDir: "{code:GetPlugin2X64Dir}"; Components: main_far2_x64; Flags: ignoreversion
Source: "{#FileSourceMain_Far3x86}"; DestName: "NetBox.dll"; DestDir: "{code:GetPlugin3X86Dir}"; Components: main_far3_x86; Flags: ignoreversion
Source: "{#FileSourceMain_Far3x64}"; DestName: "NetBox.dll"; DestDir: "{code:GetPlugin3X64Dir}"; Components: main_far3_x64; Flags: ignoreversion
Source: "{#FileSourceEng}"; DestName: "NetBoxEng.lng"; DestDir: "{code:GetPlugin2X86Dir}"; Components: main_far2_x86; Flags: ignoreversion
Source: "{#FileSourceEng}"; DestName: "NetBoxEng.lng"; DestDir: "{code:GetPlugin2X64Dir}"; Components: main_far2_x64; Flags: ignoreversion
Source: "{#FileSourceEng}"; DestName: "NetBoxEng.lng"; DestDir: "{code:GetPlugin3X86Dir}"; Components: main_far3_x86; Flags: ignoreversion
Source: "{#FileSourceEng}"; DestName: "NetBoxEng.lng"; DestDir: "{code:GetPlugin3X64Dir}"; Components: main_far3_x64; Flags: ignoreversion
Source: "{#FileSourceRus}"; DestName: "NetBoxRus.lng"; DestDir: "{code:GetPlugin2X86Dir}"; Components: main_far2_x86; Flags: ignoreversion
Source: "{#FileSourceRus}"; DestName: "NetBoxRus.lng"; DestDir: "{code:GetPlugin2X64Dir}"; Components: main_far2_x64; Flags: ignoreversion
Source: "{#FileSourceRus}"; DestName: "NetBoxRus.lng"; DestDir: "{code:GetPlugin3X86Dir}"; Components: main_far3_x86; Flags: ignoreversion
Source: "{#FileSourceRus}"; DestName: "NetBoxRus.lng"; DestDir: "{code:GetPlugin3X64Dir}"; Components: main_far3_x64; Flags: ignoreversion
Source: "{#FileSourceChangeLog}"; DestName: "ChangeLog"; DestDir: "{code:GetPlugin2X86Dir}"; Components: main_far2_x86; Flags: ignoreversion
Source: "{#FileSourceChangeLog}"; DestName: "ChangeLog"; DestDir: "{code:GetPlugin2X64Dir}"; Components: main_far2_x64; Flags: ignoreversion
Source: "{#FileSourceChangeLog}"; DestName: "ChangeLog"; DestDir: "{code:GetPlugin3X86Dir}"; Components: main_far3_x86; Flags: ignoreversion
Source: "{#FileSourceChangeLog}"; DestName: "ChangeLog"; DestDir: "{code:GetPlugin3X64Dir}"; Components: main_far3_x64; Flags: ignoreversion
Source: "{#FileSourceReadmeEng}"; DestName: "README.md"; DestDir: "{code:GetPlugin2X86Dir}"; Components: main_far2_x86; Flags: ignoreversion
Source: "{#FileSourceReadmeEng}"; DestName: "README.md"; DestDir: "{code:GetPlugin2X64Dir}"; Components: main_far2_x64; Flags: ignoreversion
Source: "{#FileSourceReadmeEng}"; DestName: "README.md"; DestDir: "{code:GetPlugin3X86Dir}"; Components: main_far3_x86; Flags: ignoreversion
Source: "{#FileSourceReadmeEng}"; DestName: "README.md"; DestDir: "{code:GetPlugin3X64Dir}"; Components: main_far3_x64; Flags: ignoreversion
Source: "{#FileSourceReadmeRu}"; DestName: "README.RU.md"; DestDir: "{code:GetPlugin2X86Dir}"; Components: main_far2_x86; Flags: ignoreversion
Source: "{#FileSourceReadmeRu}"; DestName: "README.RU.md"; DestDir: "{code:GetPlugin2X64Dir}"; Components: main_far2_x64; Flags: ignoreversion
Source: "{#FileSourceReadmeRu}"; DestName: "README.RU.md"; DestDir: "{code:GetPlugin3X86Dir}"; Components: main_far3_x86; Flags: ignoreversion
Source: "{#FileSourceReadmeRu}"; DestName: "README.RU.md"; DestDir: "{code:GetPlugin3X64Dir}"; Components: main_far3_x64; Flags: ignoreversion
Source: "{#FileSourceLicense}"; DestName: "LICENSE.txt"; DestDir: "{code:GetPlugin2X86Dir}"; Components: main_far2_x86; Flags: ignoreversion
Source: "{#FileSourceLicense}"; DestName: "LICENSE.txt"; DestDir: "{code:GetPlugin2X64Dir}"; Components: main_far2_x64; Flags: ignoreversion
Source: "{#FileSourceLicense}"; DestName: "LICENSE.txt"; DestDir: "{code:GetPlugin3X86Dir}"; Components: main_far3_x86; Flags: ignoreversion
Source: "{#FileSourceLicense}"; DestName: "LICENSE.txt"; DestDir: "{code:GetPlugin3X64Dir}"; Components: main_far3_x64; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\LICENCE"; DestDir: "{code:GetPluginX86Dir}\PuTTY"; Components: main_x86 pageant puttygen; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\LICENCE"; DestDir: "{code:GetPluginX64Dir}\PuTTY"; Components: main_x64 pageant puttygen; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\putty.hlp"; DestDir: "{code:GetPluginX86Dir}\PuTTY"; Components: main_x86 pageant puttygen; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\putty.hlp"; DestDir: "{code:GetPluginX64Dir}\PuTTY"; Components: main_x64 pageant puttygen; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\pageant.exe"; DestDir: "{code:GetPluginX86Dir}\PuTTY"; Components: main_x86 pageant; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\pageant.exe"; DestDir: "{code:GetPluginX64Dir}\PuTTY"; Components: main_x64 pageant; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\puttygen.exe"; DestDir: "{code:GetPluginX86Dir}\PuTTY"; Components: main_x86 puttygen; Flags: ignoreversion
; Source: "{#PUTTY_SOURCE_DIR}\puttygen.exe"; DestDir: "{code:GetPluginX64Dir}\PuTTY"; Components: main_x64 puttygen; Flags: ignoreversion
[InstallDelete]
[Code]
var
InputDirsPage: TInputDirWizardPage;
function GetFar2X86InstallDir(): String;
var
InstallDir: String;
begin
if RegQueryStringValue(HKLM, 'Software\Far2', 'InstallDir', InstallDir) or
RegQueryStringValue(HKCU, 'Software\Far2', 'InstallDir', InstallDir) then
begin
Result := InstallDir;
end;
end;
function GetFar2X64InstallDir(): String;
var
InstallDir: String;
begin
if RegQueryStringValue(HKCU, 'Software\Far2', 'InstallDir_x64', InstallDir) or
RegQueryStringValue(HKLM, 'Software\Far2', 'InstallDir_x64', InstallDir) then
begin
Result := InstallDir;
end;
end;
function IsFar2X86Installed(): Boolean;
begin
Result := GetFar2X86InstallDir() <> '';
end;
function IsFar2X64Installed(): Boolean;
begin
Result := GetFar2X64InstallDir() <> '';
end;
function GetDefaultFar2X86Dir(): String;
var
InstallDir: String;
begin
InstallDir := GetFar2X86InstallDir();
if InstallDir <> '' then
begin
Result := AddBackslash(InstallDir) + 'Plugins\{#PluginSubDirName}';
end
else
begin
Result := ExpandConstant('{pf}\Far2\Plugins\{#PluginSubDirName}');
end;
end;
function GetDefaultFar2X64Dir(): String;
var
InstallDir: String;
begin
InstallDir := GetFar2X64InstallDir();
if InstallDir <> '' then
begin
Result := AddBackslash(InstallDir) + 'Plugins\{#PluginSubDirName}';
end
else
begin
Result := ExpandConstant('{pf}\Far2\Plugins\{#PluginSubDirName}');
end;
end;
function GetPlugin2X86Dir(Param: String): String;
begin
Result := InputDirsPage.Values[0];
end;
function GetPlugin2X64Dir(Param: String): String;
begin
Result := InputDirsPage.Values[1];
end;
function GetFar3X86InstallDir(): String;
var
InstallDir: String;
begin
if RegQueryStringValue(HKLM, 'Software\Far Manager', 'InstallDir', InstallDir) or
RegQueryStringValue(HKCU, 'Software\Far Manager', 'InstallDir', InstallDir) then
begin
Result := InstallDir;
end;
end;
function GetFar3X64InstallDir(): String;
var
InstallDir: String;
begin
if RegQueryStringValue(HKLM, 'Software\Far Manager', 'InstallDir_x64', InstallDir) or
RegQueryStringValue(HKCU, 'Software\Far Manager', 'InstallDir_x64', InstallDir) then
begin
Result := InstallDir;
end;
end;
function IsFar3X86Installed(): Boolean;
begin
Result := GetFar3X86InstallDir() <> '';
end;
function IsFar3X64Installed(): Boolean;
begin
Result := GetFar3X64InstallDir() <> '';
end;
function GetDefaultFar3X86Dir(): String;
var
InstallDir: String;
begin
InstallDir := GetFar3X86InstallDir();
if InstallDir <> '' then
begin
Result := AddBackslash(InstallDir) + 'Plugins\{#PluginSubDirName}';
end
else
begin
Result := ExpandConstant('{pf}\Far Manager\Plugins\{#PluginSubDirName}');
end;
end;
function GetDefaultFar3X64Dir(): String;
var
InstallDir: String;
begin
InstallDir := GetFar3X64InstallDir();
if InstallDir <> '' then
begin
Result := AddBackslash(InstallDir) + 'Plugins\{#PluginSubDirName}';
end
else
begin
Result := ExpandConstant('{pf}\Far Manager\Plugins\{#PluginSubDirName}');
end;
end;
function GetPlugin3X86Dir(Param: String): String;
begin
Result := InputDirsPage.Values[2];
end;
function GetPlugin3X64Dir(Param: String): String;
begin
Result := InputDirsPage.Values[3];
end;
procedure CreateTheWizardPage;
begin
// Input dirs
InputDirsPage := CreateInputDirPage(wpSelectComponents,
'Select plugin location', 'Where plugin should be installed?',
'Plugin will be installed in the following folder(s).'#13#10#13#10 +
'To continue, click Next. If you would like to select a different folder, click Browse.',
False, 'Plugin folder');
InputDirsPage.Add('Far2/x86 plugin location:');
InputDirsPage.Values[0] := GetDefaultFar2X86Dir();
InputDirsPage.Add('Far2/x64 plugin location:');
InputDirsPage.Values[1] := GetDefaultFar2X64Dir();
InputDirsPage.Add('Far3/x86 plugin location:');
InputDirsPage.Values[2] := GetDefaultFar3X86Dir();
InputDirsPage.Add('Far3/x64 plugin location:');
InputDirsPage.Values[3] := GetDefaultFar3X64Dir();
end;
procedure SetupInputDirs();
begin
InputDirsPage.Edits[0].Enabled := IsComponentSelected('main_far2_x86');
InputDirsPage.Buttons[0].Enabled := IsComponentSelected('main_far2_x86');
InputDirsPage.PromptLabels[0].Enabled := IsComponentSelected('main_far2_x86');
// InputDirsPage.Edits[1].Visible := IsWin64();
// InputDirsPage.Buttons[1].Visible := IsWin64();
// InputDirsPage.PromptLabels[1].Visible := IsWin64();
InputDirsPage.Edits[1].Enabled := IsComponentSelected('main_far2_x64');
InputDirsPage.Buttons[1].Enabled := IsComponentSelected('main_far2_x64');
InputDirsPage.PromptLabels[1].Enabled := IsComponentSelected('main_far2_x64');
InputDirsPage.Edits[2].Enabled := IsComponentSelected('main_far3_x86');
InputDirsPage.Buttons[2].Enabled := IsComponentSelected('main_far3_x86');
InputDirsPage.PromptLabels[2].Enabled := IsComponentSelected('main_far3_x86');
// InputDirsPage.Edits[3].Visible := IsWin64();
// InputDirsPage.Buttons[3].Visible := IsWin64();
// InputDirsPage.PromptLabels[3].Visible := IsWin64();
InputDirsPage.Edits[3].Enabled := IsComponentSelected('main_far3_x64');
InputDirsPage.Buttons[3].Enabled := IsComponentSelected('main_far3_x64');
InputDirsPage.PromptLabels[3].Enabled := IsComponentSelected('main_far3_x64');
end;
function NextButtonClick(CurPageID: Integer): Boolean;
begin
if CurPageID = wpWelcome then
begin
// SetupComponents();
end
else
if CurPageID = wpSelectComponents then
begin
SetupInputDirs();
end
else
if CurPageID = InputDirsPage.ID then
begin
WizardForm.DirEdit.Text := InputDirsPage.Values[0];
end;
Result := True;
end;
function BackButtonClick(CurPageID: Integer): Boolean;
begin
// MsgBox('CurPageID: ' + IntToStr(CurPageID), mbInformation, mb_Ok);
if CurPageID = InputDirsPage.ID then
begin
// SetupComponents();
end;
if CurPageID = wpReady then
begin
SetupInputDirs();
end;
Result := True;
end;
procedure InitializeWizard();
begin
// Custom wizard page
CreateTheWizardPage;
WizardForm.LicenseAcceptedRadio.Checked := True;
end;
|
/* fre:ac - free audio converter
* Copyright (C) 2001-2020 Robert Kausch <[email protected]>
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 2 of
* the License, or (at your option) any later version.
*
* THIS PACKAGE IS PROVIDED "AS IS" AND WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. */
#include <dialogs/config/configcomponent.h>
#include <config.h>
#include <resources.h>
#ifdef __WIN32__
# include <smooth/init.win32.h>
#endif
using namespace BoCA;
using namespace BoCA::AS;
freac::ConfigComponentDialog::ConfigComponentDialog(Component *component)
{
BoCA::Config *config = BoCA::Config::Get();
BoCA::I18n *i18n = BoCA::I18n::Get();
i18n->SetContext("Configuration");
layer = component->GetConfigurationLayer();
if (layer != NIL)
{
mainWnd = new Window(component->GetName(), Point(config->GetIntValue(Config::CategorySettingsID, Config::SettingsWindowPosXID, Config::SettingsWindowPosXDefault), config->GetIntValue(Config::CategorySettingsID, Config::SettingsWindowPosYID, Config::SettingsWindowPosYDefault)) + Point(60, 60), layer->GetSize() + Size(8, 73));
mainWnd->SetRightToLeft(i18n->IsActiveLanguageRightToLeft());
mainWnd_titlebar = new Titlebar(TB_CLOSEBUTTON);
divbar = new Divider(39, OR_HORZ | OR_BOTTOM);
btn_cancel = new Button(i18n->TranslateString("Cancel"), Point(175, 29), Size());
btn_cancel->onAction.Connect(&ConfigComponentDialog::Cancel, this);
btn_cancel->SetOrientation(OR_LOWERRIGHT);
btn_ok = new Button(i18n->TranslateString("OK"), btn_cancel->GetPosition() - Point(88, 0), Size());
btn_ok->onAction.Connect(&ConfigComponentDialog::OK, this);
btn_ok->SetOrientation(OR_LOWERRIGHT);
Add(mainWnd);
mainWnd->Add(mainWnd_titlebar);
mainWnd->Add(divbar);
mainWnd->Add(btn_ok);
mainWnd->Add(btn_cancel);
mainWnd->GetMainLayer()->Add(layer);
mainWnd->SetFlags(mainWnd->GetFlags() | WF_NOTASKBUTTON | WF_MODAL);
mainWnd->SetIcon(ImageLoader::Load(String(Config::Get()->resourcesPath).Append("icons/freac.png")));
#ifdef __WIN32__
mainWnd->SetIconDirect(LoadImageA(hInstance, MAKEINTRESOURCEA(IDI_ICON), IMAGE_ICON, 0, 0, LR_DEFAULTSIZE | LR_SHARED));
#endif
}
else
{
mainWnd = NIL;
mainWnd_titlebar = NIL;
btn_cancel = NIL;
btn_ok = NIL;
divbar = NIL;
}
}
freac::ConfigComponentDialog::~ConfigComponentDialog()
{
if (layer == NIL) return;
DeleteObject(mainWnd_titlebar);
DeleteObject(mainWnd);
DeleteObject(btn_ok);
DeleteObject(btn_cancel);
DeleteObject(divbar);
}
const Error &freac::ConfigComponentDialog::ShowDialog()
{
if (layer != NIL) mainWnd->WaitUntilClosed();
else error = Error();
return error;
}
Void freac::ConfigComponentDialog::OK()
{
if (layer->SaveSettings() == Error()) return;
mainWnd->Close();
}
Void freac::ConfigComponentDialog::Cancel()
{
mainWnd->Close();
}
|
Benign Childhood Epilepsy with CentroTemporal Spikes (BECTS), an extremely common type of childhood epilepsy, is traditionally assumed to have a benign course, but recent studies have shown that cognitive function, especially language, is often impaired in BECTS patients. However, it is not clear whether the seizures, the centrotemporal spikes (CTS), or other factors cause the negative cognitive consequences that may impact school performance and social interaction. BECTS patients have scattered seizures but very frequent CTS, and may be suffering with undiagnosed cognitive and language deficits. This suggests a causal role for CTS that has not yet been investigated in detail. This project will examine the impact of seizures and CTS on neurocognitive function in BECTS patients, at diagnosis and after one year. We will gather critical information regarding the effect of the antiepileptic medication levetiracetam on CTS, which will inform a future Phase III clinical trial aimed at eliminating CTS and improving long term outcome. This study will explore the interactions between CTS, seizures and neuropsychological outcomes using Functional MRI of language in order to decipher changes in neural circuitry that underlie language deficits found in children with BECTS. Using standardized neuropsychological testing and fMRI at the time of diagnosis, this study will first characterize the nature and incidence of language problems in children with BECTS, separating the effects of CTS and seizures. It is expected that children with BECTS will perform below normative standards on tests of language skill, accompanied by aberrations in the neural circuitry supporting language processing as tested with fMRI. These data will also make it possible to characterize which children with BECTS are most at risk for language problems, by taking into account contributing factors such as number of seizures, age of onset, and frequency and lateralization of CTS. The proposed exploratory clinical trial will also provide key information needed to properly design and conduct a future double blind Phase III randomized clinical trial (RCT) children aimed at improving language outcome through elimination of CTS. Using an open-label dose-ranging selection design and 1-year follow up, we will determine which dose of levetiracetam control seizures, eliminate CTS is well tolerated and should be used in the Phase III trial. We will also examine the extent of changes in language function and neural circuitry of language with 1-year follow-up neuropsychological testing and fMRI in LEV-treated and untreated BECTS compared to controls (which will document the natural history of neuropsychological function in untreated BECTS children and give additional information about the effect of levetiracetam). The future double blind RCT will compare levetiracetam to carbamazepine (the current standard of care that does not eliminate CTS) in BECTS. This future study would change clinical practice by demonstrating the need for AED treatment in all BECTS children to eliminate CTS, in turn improving long term language and cognitive outcome. PUBLIC HEALTH RELEVANCE: This project examines how seizures, and abnormal brain activity, affect language skill in children with Benign Childhood Epilepsy with Centro-Temporal Spikes (BECTS). BECTS is a common type of childhood epilepsy, and while BECTS patients stop having seizures by their late teenage years, many studies have shown that these children have language problems that may lead to academic and social difficulties. Using standardized language testing, monitoring of brain activity, and MRI brain imaging, this project aims to determine what particular combination of BECTS symptoms put children most at risk for language problems and what dose of the anti-epileptic medication levetiracetam may be helpful. Disclaimer: Please note that the following critiques were prepared by the reviewers prior to the Study Section meeting and are provided in an essentially unedited form. While there is opportunity for the reviewers to update or revise their written evaluation, based upon the group's discussion, there is no guarantee that individual critiques have been updated subsequent to the discussion at the meeting. Therefore, the critiques may not fully reflect the final opinions of the individual reviewers at the close of group discussion or the final majority opinion of the group. Thus the Resume and Summary of Discussion is the final word on what the reviewers actually considered critical at the meeting. |
Background {#Sec1}
==========
Hypoxia is common after stroke, and associated with poor outcomes. In this article, we have reviewed the physiology of oxygen transport, the cerebrovascular response to hypoxia and pathophysiology, incidence and aetiology behind hypoxia in stroke and its subsequent clinical consequences. We have then reviewed all randomised clinical trials looking at the use of supplemental oxygen therapy in acute stroke and made conclusions regarding current evidence and recommendations for clinical practice.
Oxygen physiology {#Sec2}
=================
The normal adult range of arterial oxygen pressure (PaO2) is 11.0--14.4 kPa and the normal range for arterial oxygen saturation (SaO2) is 95--98% \[[@CR1]\]. The term hypoxia refers to oxygen levels below normal. It includes both tissue (e.g. brain, myocardium) hypoxia and hypoxia in the blood (hypoxaemia). Tissue hypoxia is defined by the concentration of oxygen in blood and also tissue perfusion, whilst hypoxaemia is defined by the concentration of oxygen in inspired air and its transfer into the blood \[[@CR2]\].
Following inhalation oxygen is taken up in the lung capillaries via diffusion down an oxygen concentration gradient across the alveoli \[[@CR3], [@CR4]\]. Oxygen binds to the haemoglobin molecule, which can carry four oxygen molecules; each binding and changing the shape of the haemoglobin molecule and increasing its affinity for oxygen \[[@CR5]\]. A small amount of oxygen is also dissolved in plasma. This proportion increases in hyperoxia, when all haemoglobin is saturated \[[@CR6]\]. Oxygen dissociates from the haemoglobin molecule in the tissues owing to the relatively hypercapnic and acidic environment (the Bohr effect) \[[@CR3]\].
Oxygen is a vital substrate that supports virtually all metabolic processes. 90% of oxygen intake is engaged in the cytochrome C oxidase system in the mitochondria \[[@CR7]\] generating adenosine triphosphate (ATP), which acts as the main energy substrate within cells. A continuous supply of oxygen is required to secure a continuous supply of ATP maintaining sufficient energy for cerebral neuronal and cellular activity. This facilitates an efficient energy producing process making 38 molecules of ATP during aerobic respiration, equivalent to 1270 joules (J) energy, in comparison to two molecules of ATP (67 J of energy) during anaerobic respiration \[[@CR7], [@CR8]\].
The anoxic brain {#Sec3}
================
20% of all human oxygen consumption is utilised by the brain \[[@CR9]\]. The brain has no oxygen or glucose (the other important substrate in the ATP producing equation) stores. Thus complete disruption of cerebral blood flow very rapidly results in an anoxic, hypoglycaemic state, which via a variety of mechanisms ultimately leads to cell death. Excitatory neurotransmitters, such as glutamate, bind to a variety of receptors and allow for an influx of calcium ions that help formulate the chemical signal for depolarisation \[[@CR10], [@CR11]\]. Normally the re-uptake of glutamate is an active energy-driven process. In the absence of ATP this process fails, resulting in an extracellular accumulation of glutamate, which continually stimulates receptors leading to a persistent influx of calcium ions \[[@CR12]\]. Furthermore, the Na+/Ca2+ ATP driven pump normally used to eliminate calcium fails, also due to a lack of ATP \[[@CR13]\]. The resultant high intracellular calcium triggers multiple cascades that ultimately lead to mitochondrial dysfunction and cell death. Furthermore, instead of producing ATP, glial cells have been shown to release ATP extracellularly \[[@CR11]\]. Aside from rendering this unusable by mitochondria, ATP also stimulates the P2X7 receptor, which again leads to significant calcium influx and ultimately cell death \[[@CR13]\]. The other major mechanism of cellular demise is via the formation of free radicals facilitated by the reduction of iron from its ferric (Fe3+) to its ferrous (Fe2+) form and the initiation of inflammatory cascades \[[@CR12]\].
Cerebral blood flow in hypoxia {#Sec4}
==============================
In normoxic states, cerebral blood flow is very tightly controlled by the partial pressure of carbon dioxide (PaCO~2~). Any hypocapnic state will result in vasoconstriction and reduction in regional cerebral blood flow and a hypercapnic state leads to the reverse with vasodilatation and an increase in cerebral blood flow. Cerebral blood flow is somewhat less responsive to changes in PaO~2~, which has the opposite effect to carbon dioxide; a hypoxic state causing cerebral vasodilatation with the aim of improving oxygen delivery and a hyperoxic state causing vasoconstriction \[[@CR14], [@CR15]\].
In a hypoxic state, whilst the vasodilatory response improves flow, the detection of hypoxia by peripheral chemoreceptors will in turn lead to an increase in respiratory drive, increasing arterial oxygen content. However, the consequence of this is also an increase in the clearance of carbon dioxide, which would theoretically cause vasoconstriction and reduced cerebral blood flow \[[@CR9]\]. It appears there is a threshold to which the hypoxic response predominates (and the carbon dioxide one attenuated) at a PaO~2~ of around 50--60 mmHg \[[@CR9], [@CR14]\]. Whilst the carbon dioxide mediated vascular response is mediated via a direct change in vessel wall pH \[[@CR15]\], the oxygen response appears to be mediated by the deoxygenated erythrocyte via a number of mechanisms; which include release of ATP and the subsequent actions of endothelial nitric oxide synthase on the vessel wall, reduction of nitrite to nitric oxide and the activity of S-nitrosohaemoglobin \[[@CR9]\].
The cerebral vascular response to hypoxia is not uniform. A study found that in an induced isocapnic hypoxic state increases in cerebral blood flow were most prominent in basal ganglia nuclei, the putamen, thalamus, nucleus accumbens and pallidum \[[@CR16]\]. Studies of blood flow in individual vessels have found that flow in the internal carotid artery is maintained during hypoxia and that vertebral artery flow is increased \[[@CR17]\]. This had led to the hypothesis that blood flow is increased in this region to preserve vital brainstem structures, or that possibly the posterior circulation vasculature is less susceptible to the effects of carbon dioxide for similar reasons.
Neurological effects of hypoxia {#Sec5}
===============================
The neurological consequences of hypoxia are dependent upon the speed of onset, the severity of hypoxia, and the level of tissue perfusion. Rapid decreases in PaO~2~, as in a cardiorespiratory arrest, can lead to permanent neurological damage within minutes. However, lower, less abrupt changes, can be tolerated if the decrease in oxygen occurs in a gradual manner, such as ascending at altitude, where individuals can acclimatise and develop tolerance to lower oxygen partial pressures or, (to a lesser degree), in chronic smokers. Initial clinical features include altered judgement, difficulty in completing complex tasks, and impairment in short term memory \[[@CR18], [@CR19]\], but in the longer term deficits can be more widespread and span physical and neuropsychological domains. Seizures occur in up to a third of individuals within a day of exposure to hypoxia, and are commonly partial complex or myoclonic in nature. Intractable forms of either of these types of seizure are associated with a poor prognosis \[[@CR20]\]. Cognitive impairment domains include amnesia, visuospatial deficits, frontal lobe symptoms, impairment of executive function, and impairments in language \[[@CR21]\]. These are covered in more detailed reviews on the subject \[[@CR22], [@CR23]\]. Involvement of the basal ganglia, a region particularly susceptible to hypoxic injury, can result in delayed Parkinsonism in older subjects, dystonia mainly in younger people, choreo-athetosis, and tremors \[[@CR20]\]. Varying degrees of unilateral or bilateral motor impairment may be observed depending on both the anatomical level and extent of corticospinal tract involvement. In very rare cases, the syndrome of delayed post-hypoxic leukoencephalopathy may occur weeks after a seemingly rapid recovery from the original insult. This condition is characterised by rapid deterioration in cognition, emergence of extra-pyramidal signs, and loss of executive function as a results of severe demyelination \[[@CR24]\]. The severity of leukoencephalopathy can be assessed by magnetic resonance imaging (MRI) \[[@CR20]\]. Electroencephalography, somatosensory evoked potentials and MRI can provide valuable information about the severity of hypoxic injury, but also aid in prognostication together with overall clinical state \[[@CR25]\].
Hypoxia in the context of a stroke {#Sec6}
==================================
There is no specific definition as to what constitutes hypoxia in an acute stroke, and it is therefore reasonable to assume that normal values for the general population apply.
Sulter and colleagues \[[@CR26]\] monitored 49 consecutive patients who presented with an acute stroke within 12 h duration using pulse oximetry for 48 h. Patients were considered hypoxic and treated with supplemental oxygen if saturations were below 96% for more than 5 min. This occurred in 63% \[[@CR31]\] of patients, with 28 of those returning to 'normal' oxygen saturations following administration of up to 5 L/min of oxygen. The remaining three required much higher concentrations. Factors associated with hypoxia in this group were stroke severity, presence of dysphagia, and older age. Roffe et al. \[[@CR27]\] recruited 118 patients (100 of whom had adequate measurements by pulse oximetry) and found that the mean daytime awake SO~2~ was 94.5 ± 1.7% in stroke patients and 95.8 ± 1.7% in healthy controls. Nocturnal saturations were reduced to 93.5 ± 1.9% in the stroke group and 94.3 ± 1.9% in controls. In the stroke group the average 4% oxygen desaturation index (ODI) (number of times per hour the saturation dipped more than 4% from baseline) was higher than in controls. At night almost a quarter of the stroke group had desaturations below 90%. The same group also looked further at the differences between day and night oxygen saturations \[[@CR28]\]. In stroke patients who were not hypoxic (defined as SaO~2~ less than 90%) during the day, baseline daytime saturations were measured between 9am and 9pm and nocturnal saturation between 10pm and 6am. In total 40 patients were recruited and in addition to SaO~2~, respiratory rate and sleep/awakeness was measured twice in each time period. The mean respiratory rate day vs. night was 20 and 18 breaths per minute respectively. The mean daytime SaO~2~ was 95.5% (87--98.6%) and 94.3% (80--98%) at night. There was a strong correlation between respiratory rate, SaO~2~ and the 4% ODI, making it clear that borderline daytime hypoxia could predict nocturnal hypoxic episodes. Comparisons in a later study were then made with matched controls overnight \[[@CR29]\]. In this study the mean nocturnal oxygen saturations were found to be 0.5% less than controls, with the lowest measured desaturation in this group of 79.4%, still almost 6% lower than the control group. The largest difference was in the percentage of patients with more than 10 desaturations per hour (42% stroke vs. 15% controls). Hand et al. \[[@CR30]\] performed a study looking at the feasibility of MRI as an imaging modality in hyperacute stroke assessment. One of the eligible 138 patients for the study could not be scanned owing to pulmonary oedema severe enough to cause considerable hypoxia. For a variety of reasons it was only possible to consistently measure oxygen saturations in 61 out of 85 patients. In those in whom saturations could reliably be measured, 11 out of 61 developed hypoxia (lowest 74%) and of those who received oxygen during the scan only two could be monitored successfully. This highlights not only the prevalence of hypoxia in acute stroke, but the logistical difficulties acute hypoxia may pose for assessment. Another study examined the effect of five different, but randomly ordered body positions, each for 10 min on the impact on oxygen saturation \[[@CR31]\]. Interestingly, lying on the left hand side reduced oxygen saturations, but only in those who hand a right hemiparesis. Those who were able to sit in a chair were able to achieve much higher mean SaO~2~, albeit suffering from more minor strokes. It was felt that a severe stroke, with a right hemiparesis and underlying chest disease were the greatest predictors of desaturation, but only when lying on the left side. A subsequent systematic review \[[@CR32]\] comprising of three randomised controlled trials (173 patients) and one case controlled trial (10 patients) found that body position only played a role in oxygen saturations if patients had underlying respiratory co-morbidities.
The risk of aspiration is well documented in acute stroke (see below), but independent of this the question as to whether feeding (oral or nasogastric) contributes to hypoxia has also been examined. Dutta et al. \[[@CR33]\] reported that nasogastric feeding caused no decrease in SaO~2~. A later study \[[@CR34]\] found a small but statistically non-significant trend towards hypoxia when tube fed, in particular in patients that were fed overnight. Rowat and colleagues looked at the impact of oral feeding on oxygen saturations, using hospitalised elderly patients and young healthy controls as comparators \[[@CR35]\]. The baseline SaO~2~ was lower in the stroke cohort than the other two, with a very small decrease in SaO~2~ with oral feeding in the stroke (0.1%) and the elderly groups. Nearly a quarter of stroke patients dropped SaO~2~ to less than 90% (16% elderly, 0% young), but this did not occur in close relation to the time of swallowing, and thus no immediate risk could be attributed to oral feeding.
There is relatively little research on the correlation between hypoxia and clinical outcome. Hypoxia has been shown to be an independent clinical risk factor for post stroke dementia \[[@CR36]\]. Rowat et al. \[[@CR37]\] found that hypoxic patients were more likely to have respiratory disease and this led to an increased mortality. A smaller study looked at the prevalence of hypoxia in patients undergoing rehabilitation and found no significant difference in mean SaO~2~ at baseline, in nocturnal SaO~2~, the lowest nocturnal SaO~2~ or in the 4% ODI \[[@CR38]\]. In conclusion, no association between SaO~2~ and functional outcome was found. Hypoxia has, however, been shown to correlate with the degree of white mater disease on MRI. White matter hyperintensity volumes were greatest in obstructive sleep apnoea (OSA) patients compared with non-OSA patients and more explicitly in hypoxic compared to non-hypoxic patients \[[@CR39]\].
Causes of hypoxia in acute stroke {#Sec7}
=================================
Pneumonia is a frequent complication of acute stroke. A recent consensus defined the term stroke-associated pneumonia (SAP) as a representation of a spectrum of lower respiratory tract disorders occurring within 7 days after the onset of stroke \[[@CR40]\]. The criteria were based on a modified version of the centre for disease control (CDC) criteria, with a probable SAP fulfilling all CDC criteria but not meeting typical chest radiography changes and definite SAP fulfilling all CDC criteria including typical chest X-ray changes. In addition the consensus group concluded that there was a limited role for C-reactive protein, white blood cell count and other inflammatory biomarkers in the diagnosis \[[@CR40]\]. A meta-analysis of 64 studies showed that the definition of stroke---associated pneumonias varied widely \[[@CR41]\].
The incidence of pneumonia post stroke has been reported to range between 1 and 44% \[[@CR42], [@CR43]\] and has been shown to increase mortality (threefold) and overall hospital care costs \[[@CR42]\]. Two recent studies have looked at the utility of prophylactic antibiotics to reduce pneumonia. The STROKE-INF study \[[@CR44]\] randomised patients with acute stroke and dysphagia to 7 days of prophylactic antibiotics (to be commenced within 48 h of stroke onset) or standard care and found no reduction in the incidence of pneumonia (OR 1.21, 95% CI 0.71--2.08, p = 0.489). The PASS study \[[@CR45]\] investigated the effects of prophylactic ceftriaxone and found that this did not affect functional outcome at 3 months. While there was a significant reduction in infections overall, there was no effect on the incidence of pneumonia (OR 0.67 95% CI 0.39--1.15, p = 0.18). Therefore, current evidence does not support the use of antibiotic prophylaxis to prevent pneumonia. There are several validated risk scores which can help the clinician to identify patients at high risk of stroke-associated pneumonia \[[@CR46]--[@CR48]\]. Given the considerable morbidity and mortality, and the lack of benefit from prophylactic treatment, highlighting patients at high risk to allow early identification and treatment of established infection is important in the care of stroke patients.
Aspiration is a frequent cause of pneumonia post stroke, especially in patients with dysphagia. Dysphagia is seen in up to 50% of ischaemic strokes \[[@CR49]\], although the reported incidence can vary between studies. Individuals suffering from dysphagia were three times more likely to develop pneumonia and this number increased to eleven times if they were shown to aspirate \[[@CR50]\]. Often aspiration occurs silently (reported in up to 40%), that is, with few or no clinical signs. The presence of either dysphagia or a subsequent pneumonia is predictors of a worse clinical outcome \[[@CR51]\]. An often neglected aspect of stroke treatment is oral care. Poor oral hygiene leads to proliferation of bacteria and debris in the oral cavity \[[@CR52]\], which are liable to be aspirated causing respiratory tract infection \[[@CR53]\]. This is particularly important in nasogastric tube fed patients in whom oral care can easily be missed.
Sleep apnoea is a common cause of intermittent nocturnal hypoxia after stroke, affecting up to 60% of patients \[[@CR54]\]. This condition has also been shown to be a risk factor for future stroke and stroke mortality, if not appropriately treated. A few small studies have shown that nocturnal continuous positive airway pressure ventilation is feasible \[[@CR55], [@CR56]\], and can improve wellbeing in some stroke patients with sleep apnoea during the acute and rehabilitation phase, but compliance with the intervention is poor, especially in patients with delirium or cognitive impairment \[[@CR57]\]. Obstructive sleep apnoea can cause or accentuate many traditional vascular risk factors, in particular hypertension \[[@CR58]\] and atrial fibrillation \[[@CR59]\], and has been shown to be an independent risk factor for stroke \[[@CR54], [@CR57], [@CR60]\]. A review of the cohort of the Wisconsin Sleep Study found a significant association between sleep disordered breathing and stroke prevalence, the more severe the indices of sleep apnoea, the greater the risk \[[@CR61]\].
Respiratory muscle function is also a potential cause of hypoxia either directly by associated muscle paralysis or as a result of a secondary infection. Several studies have shown (some in comparison to matched controls) a significant reduction in forced vital capacity, forced expiratory volume in one second, peak expiratory flow rate and maximal inspiratory and expiratory pressures \[[@CR62]--[@CR64]\], suggesting impairment in function of accessory respiratory muscles as well as the diaphragm. This may pave the way for treatment strategies aiming to improve respiratory muscle function \[[@CR65]\].
Less common stroke complications resulting in hypoxia include pulmonary embolism, which despite its low incidence in most reported series (around 1%), is associated with increased in hospital mortality (31.5 vs 12.7% in a review of over 11,000 patients in the Registry of the Canadian Stroke Network), length of stay and severity of disability \[[@CR66]\]. The risk of pulmonary embolism can persist for up to 4 weeks post stroke \[[@CR67]\]. A review of a relatively small cohort of cryptogenic stroke patients found a significant incidence of silent pulmonary embolism (37%), but did not comment as to whether or not this led to a resultant hypoxic state \[[@CR68]\]. Improvements in mechanical, pharmacological and therapy based regimes are the likely reason pulmonary embolism is now a relative rarity. Cardiac failure and very rarely neurogenic pulmonary oedema \[[@CR69], [@CR70]\] are among the other causes.
Oxygen therapy for acute stroke {#Sec8}
===============================
Oxygen treatment can be used to maintain normal oxygen saturation or to increase the oxygen saturation above normal in patients with acute stroke. The rationale for the latter is that blood with higher oxygen content may improve oxygen action in ischaemic brain areas \[[@CR2]\]. When considering oxygen treatment it is important to weigh up potential adverse effects against benefits.
Potential adverse effects of oxygen treatment after stroke {#Sec9}
----------------------------------------------------------
Oxygen treatment is not without side effects. Attachment to a wall delivery system as an inpatient restricts mobility in the acute phase and may represent an infection risk. In critical ill states or when bordering on the anaerobic threshold for exercise capacity, the body has several intrinsic systems to increase oxygen tension and deliver oxygen at the required rate in order to produce ATP and meet energy demands. One of the by-products of ATP formation is the formation of oxygen free-radical species, which, if not dealt with, can lead to cell apoptosis and developmental of tissue damage. In normal states the body has several intrinsic enzymes to neutralise free radicals by pairing them with so called donor electrons to form substances like oxygen or hydrogen peroxide which can then be efficiently removed. When high concentrations of oxygen are given this leads not only to increased oxygen delivery from red blood cells but also increased delivery via plasma. This then by-passes and overrides usual mechanism of clearance and is one the reasons tissue damage develops in inappropriately high concentrations of oxygen \[[@CR71]--[@CR73]\]. The cascade outlined above is only partially reversed during reperfusion, even though oxygen delivery has improved. Most of the clinical problems surrounding oxygen toxicity initially affect the lungs. High concentrations of oxygen may displace all nitrogen present in the alveoli and owing to the significant alveolar plasma gradient, the oxygen rapidly diffuses and dissolves into the plasma, effectively reducing the alveolar volume and leading to subsequent collapse. Hyperoxia may also impair mucilliary clearance and alter surfactant properties which may cause an 'adhesive collapse' \[[@CR73], [@CR74]\]. Neurological consequences outside of those described in the context of stroke include cerebral vasoconstriction, a by-product of excessive free radical formation, confusion, and seizures \[[@CR73]\]. Oxygen toxicity more often occurs during use of high concentrations of oxygen or in hyperbaric conditions. In the clinical setting a stroke patient is exposed to, these are highly unlikely scenarios to occur.
Recommendations from national and international stroke guidelines {#Sec10}
-----------------------------------------------------------------
A review of the most recent societal guidelines shows uniformity in the approach to oxygen therapy in acute ischaemic stroke. The Royal College of Physicians guidelines \[[@CR75]\] advise use of supplemental oxygen only if oxygen saturation drops below 95% and is not contraindicated, and recommends no supplemental oxygen for saturations of 95% or above. The European Stroke Organisation \[[@CR76]\] advises supplemental oxygen use for oxygen saturations of less than 95%. The American Heart Association/American Stroke Association Guidelines \[[@CR77]\] advise that in the pre-hospital setting, oxygen supplementation to maintain oxygen saturations above 94% is reasonable and recommended for suspected stroke patients and that on presentation to hospital saturations should be continually monitored to watch out for hypoxia. This guidance is based on the American Heart Association post cardiac arrest guidelines \[[@CR78]\] and thus the same advice applies to stroke patients. Again the guidelines do not support the use of hyperbaric oxygen therapy.
Randomised controlled trials of supplemental oxygen in acute stroke {#Sec11}
-------------------------------------------------------------------
A plausible solution to aid the correction of cerebral hypoxia in stroke would be to provide supplemental oxygen therapy in the acute phase, potentially helping to correct or prevent many of the catastrophic cerebral changes that may occur. To date 6 randomised controlled trials have tested this hypothesis. A quasi-randomised study of routine oxygen supplementation within the first 24 h of acute stroke by Ronning and Guldvog \[[@CR79]\] showed that routine oxygen treatment (3 L/min for 24 h) in unselected stroke patients did not reduce morbidity or mortality. Subgroup analyses suggested worse outcomes in patients with mild strokes treated with oxygen and a trend towards better outcomes in severe strokes (Scandinavian stroke scale score \<40), but the study was not large enough to identify with certainty those who are likely to derive benefit. Oxygen saturation before or during treatment was not reported and it is therefore impossible to determine whether or not oxygen was ineffective because it failed to improve oxygen saturation or because of a genuine lack of effect on the ischaemic brain. A small study (n = 16) delivered oxygen at a rate of 45 L/min for 8 h, commencing with 12 h of stroke onset. Perfusion-diffusion mismatch on MRI showed that cerebral blood volume and blood flow within ischaemic regions improved in the hyperoxia. Neurological deficit improved at 4 h (during treatment), 24 h and at 1 week. By 24 h MRI of the brain showed reperfusion and (asymptomatic) petechial haemorrhages in 50% of hyperoxia treated patients and 17% of controls (p = 0.06). No long-term clinical benefit was seen at 3 months \[[@CR80]\]. This study was too small to draw reliable conclusions, leading to a larger (unpublished) study by the same group (<http://www.clinicaltrials.gov/ct2/show/NCT00414726?term=singhal&rank=1>) which initially planned to enrol 240 patients, randomising to either room air or high flow oxygen (30--45 L/min for 8 h) within 9 h of acute stroke onset. After enrolment of 85 patients, the study was terminated early due to an imbalance of deaths favouring the control arm, though it is noted that the excess in mortality in the treatment group was not considered related to the treatment by an external blinded assessor. An Indian study \[[@CR81]\] enrolled 40 patients within 12 h of an acute anterior circulation ischaemic stroke and a National Institute Stroke Scale of more than 4 to receive either 10 L/min for 12 h via face mask in the treatment group versus room air or 2 L/min to keep oxygen saturation above 95%. There was no significant difference in NIHSS, modified Rankin or Barthel index scores between the two groups. There was also no statistically significant difference between DWI lesion volumes in either group, though there was a trend towards smaller lesions in the treatment group.
In the Stroke Oxygen Pilot study \[[@CR82]\], oxygen was given for 72 h and the dose was dependent on baseline oxygen saturation (2 L/min if the saturation was \>93%, 3 L/min if the saturation was 93% or less). Initial results showed that the treatment regime increased oxygen saturation by about 2% in the treatment arm and this was associated with a small, but significant improvement in neurological recovery at one week. At 6 months \[[@CR83]\] there was no statistically significant difference between the two groups, although there remained a small trend towards overall benefit with supplemental oxygen. This data led to the Stroke Oxygen Study (SO~2~S) \[[@CR84]\], in which 8003 patients within 24 h of hospital admission with acute stroke were randomized 1:1:1 to receive either continuous supplemental oxygen, supplemental oxygen only at night (9pm--7am) oxygen, or no supplemental oxygen treatment for 72 h. This study has completed recruitment and is expected to report in 2016.
Conclusion {#Sec12}
==========
Oxygen is a vital substrate to the continual function and survival of cerebral tissue. Rapid reduction in partial pressures can very rapidly lead to catastrophic and permanent cerebral injury and physical disability. Whilst evidence does not currently support the additional supplementation of oxygen to stroke patients, it remains important to prevent hypoxia in stroke patients by identifying and treating reversible causes rapidly. Results of the Stroke Oxygen Study will provide new evidence of whether prophylactic oxygen treatment can prevent neurological deterioration and improve recovery.
PF and CR both equally participated in the search of the literature and writing of the manuscript. Both authors read and approved the final manuscript.
Acknowledgements {#FPar1}
================
None.
Competing interests {#FPar2}
===================
The authors declare that they have no competing interests.
Consent for publication {#FPar3}
=======================
No individual patient information used.
|
Simon Cowell Just Let Slip Which X Factor Judges Are Paid The Most!
There has always been speculation about the pay packets of the panel but Simon has just added fuel to the fire.
When it comes to judges on the X Factor, it's only the best for Simon Cowell.
The talent show boss is no stranger to coughing up the cash either, with reports he was prepared to pay Mariah Carey £1 million to appear on the panel.
With just weeks to go until X Factor returns to our screens for its thirteenth series with Simon Cowell has shed light on just how much his co-judges are being paid and even let slip that some are paid more than others.
According to the SyCo label boss, Sharon Osbourne and Nicole Scherzinger and former judge Cheryl cost him the most money they paid favourably in comparison to fellow judge Louis Walsh, who is also set to reprise his role on the panel this year.
Simon believes paying his female stars more is a pioneering move and a stark contrast to the BBC, who received backlash last month after their highest paid stars were revealed to be men.
Speaking about his female co-stars, he told The Sun: “For once this is good news. Victory. Yeah, they definitely are [paid more]. I just don’t tell Louis.”
The revealing interview also shed light on X Factor USA, which ran for two years between 2010 and 2012, as Simon confirmed he paid Britney Spears a hefty fee to appear on the panel.
Speaking about the comparison between wages, Simon explained: “If they get the money, it doesn’t matter to me whether you’re a boy or a girl. But I would say we’ve probably paid girls more money than guys over the years.”
“The truth is, in showbusiness normal circumstances, you are paid by your worth and that’s just the way it goes." |
Q:
What is C#.net meaning in conjuction with terms like Javascript, HTML5, CSS etc?
I recently got an offer for a traineeship for C#.NET. However before being allowed in the traineeship I need to make a small program which displays my programming skills in "C#.net". I don't know what to do now. I've downloaded visual studio 2015 and when I open it I see lots of stuff like console application/windows application etc and even .asp.net applications for web.
In the traineeship document terms are used like " Object Oriëntated, Object Orientated Analysis and Design, UML, Database Design, SQL, XML, Scrum, Javascript, HTML5 CSS3, jQuery, Ajax, Design Pattern (MVC) and WCF.
I don't have a clue where to start! If they wanted ASP websites they could've explicated this right? Should I make them a keygen music mp3 player in a console application? Srs please help. I got 1 week for this.
A:
Usually when asked to perform such task with as vague description as possible, the recruiters want to see your creativity and general knowledge of the technology. You don't have write another Windows system, so it's entirely up to you on what you decide to write. Just make sure it will work and it will follow general coding guidelines and it should be okay :)
|
Effect of residual mercury content on creep in dental amalgams.
For most of the tested amalgams, the increased mercury content caused by delayed compaction increases the flow or creep. The amalgams that had high creep values when packed early were decidedly affected by the increase in mercury content caused by delay in compaction. Amalgams made with Dispersalloy, Tytin, Sybraloy, and New True Dentalloy are not as sensitive to the mercury content as are some of the others tested. Tests for creep may be related more to clinical practice if they are performed on specimens compacted three minutes after trituration rather than on specimens compacted immediately (a half minute) after trituration. In clinical practice, small amounts of amalgam should be mixed and used immediately after trituration. If the delay between trituration and compaction is longer than three minutes, additional mixes are required. We therefore conclude that, in making a large amalgam restoration, many small mixes have superior results over one large mix. |
Raw deep sequencing cannot be provided because these data are derived from patient samples. Because of the Minimum Necessary Requirement of the HIPAA Privacy Rule these data may not be deposited into a public repository. A Supporting Information File accompanying the submission contains the de-identified results and interpretations of all clinical NGS tests included in our analysis next to the results of single-gene testing of the same specimen.
Introduction {#sec001}
============
The advance of next-generation sequencing (NGS) is a cornerstone of a recent development in molecular pathology, variably referred to as "personalized," "precision," or "individualized" medicine. Much of the focus of clinical NGS has been on oncology, as there are clear diagnostic, prognostic, and therapeutic implications for a multitude of genomic mutations in both solid and liquid malignancies. For example, in non-small cell lung cancers, activating mutations of the *EGFR* gene predict therapeutic response to tyrosine kinase inhibitors (TKI) such as erlotinib, gefitinib, and afatinib \[[@pone.0152851.ref001]--[@pone.0152851.ref003]\]. The KRAS protein acts downstream of EGFR, and thus mutations of the *KRAS* gene predict resistance to TKI \[[@pone.0152851.ref002],[@pone.0152851.ref004]--[@pone.0152851.ref006]\]. In metastatic melanoma, *BRAF* V600 mutations predict response to dabrafenib, vemurafenib, and trametinib \[[@pone.0152851.ref007]\]. Mutations of the *FLT3* and *NPM1* genes affect the prognosis of karyotypically normal acute myeloid leukemia and aid in the decision whether or not to pursue hematopoietic stem cell transplantation \[[@pone.0152851.ref008]\]. In addition, activating mutations of *JAK2*, which encodes a tyrosine kinase essential for cytokine and growth factor signaling, are found in a large proportion of patients with myeloproliferative neoplasms \[[@pone.0152851.ref009]\]. Ruxolitinib is a JAK1/JAK2 inhibitor approved for the treatment of myelofibrosis \[[@pone.0152851.ref010]\], and additional JAK2 inhibitors are in clinical development \[[@pone.0152851.ref011]\].
Detection of mutations in *EGFR*, *KRAS*, *BRAF*, *FLT3*, *NPM1*, and *JAK2* is most commonly accomplished by targeted tests that are designed to detect one or at most a small number of mutations in a single gene. However, NGS is gaining momentum as a complementary test for a number of reasons. Firstly, clinical trials for targeted cancer therapies rely on detection of mutations that are frequently not covered by existing targeted tests. In contrast to the laborious and lengthy process of validating and implementing a new molecular assay testing for one or a few mutations, NGS greatly simplifies the task of providing coverage of one of more additional mutations of interest. Secondly, targeted tests can provide misleading results. For example, the widely used FDA-approved cobas® *EGFR* Mutation Test only detects exon 19 deletion and L858R mutations, which together only comprise the mutations found in 85% of *EGFR*-mutated lung cancers \[[@pone.0152851.ref012]\]. In a significant proportion of cases, this test fails to identify therapeutically targetable mutations. Thirdly, targeted tests may fail to detect the very mutation they are designed to detect. Our group has recently reported a striking failure of two separate single-gene tests for the *BRAF* gene to detect a V600E mutation in a melanoma specimen \[[@pone.0152851.ref013]\]. The mutation was clearly demonstrated by concurrent NGS analysis. Finally, as has recently become apparent, tumors frequently harbor mutations that are therapeutically targetable but are not typically seen in that tumor type. Due to its massively parallel nature, NGS is very well-suited for detecting mutations in unexpected genes. One study reported a three-fold increased yield of clinically actionable mutations with NGS as compared to traditional molecular approaches targeting mutation hotspots \[[@pone.0152851.ref014]\].
Multiple recent studies have investigated the potential utility of NGS for detection of clinically actionable cancer mutations with encouraging results \[[@pone.0152851.ref014]--[@pone.0152851.ref025]\]. With the exception of one study \[[@pone.0152851.ref021]\], all demonstrated excellent performance of NGS on various platforms as measured by detection of point mutations and small insertions and deletions (indels). In many cases, additional potentially important variants were uncovered by NGS. All of the aforementioned studies were designed to validate clinical NGS pipelines that were not yet in clinical practice. As a consequence, they enrolled selected samples from previously examined specimens. With the exception of one commercially-sponsored study \[[@pone.0152851.ref014]\], in all cases a very limited number of samples was re-examined (range 13--61), often from only a single tissue type. While these important contributions confirm the potential usefulness of clinical NGS, they do not address the important question whether a well-validated NGS pipeline performs at an acceptable level in day-to-day clinical practice. Here we present a summative analysis of mutation results and quality control metrics obtained during the first year (March 2013 through March 2014) of clinical solid and liquid malignancy NGS carried out at the Center for Personalized Diagnostics at the University of Pennsylvania Health System. More than 900 specimens were submitted and processed during this time frame. We report that using our validated molecular and bioinformatics pipeline \[[@pone.0152851.ref026]\] with pre-determined tumor percentage and DNA quality cutoffs, we achieved excellent NGS data quality as determined by virtually perfect concordance between NGS and targeted single-gene tests for various genes in a large number of solid and liquid malignancy specimens.
Materials and Methods {#sec002}
=====================
Specimen Characteristics and Processing {#sec003}
---------------------------------------
Over the course of the study duration, 938 liquid and solid tumor specimens were submitted to the Center for Personalized Diagnostics ([Table 1](#pone.0152851.t001){ref-type="table"}). Specimens were eligible for NGS if they passed the tumor percentage, DNA quality, and DNA quantity thresholds that had been determined at the time of the validation of the NGS assay, which preceded the study period. Briefly, specimens with \<10% tumor were not eligible for NGS, because sequencing of samples with lower tumor percentages frequently yielded changes that were represented in fewer than five unique reads, making it difficult to distinguish true variants from sequencing artifacts. For similar reasons, DNA quality and quantity were judged to be insufficient, and the specimen was ineligible for NGS, if the DNA concentration was \<1 ng/μL; the DNA concentration was \<5 ng/μL with \>20% DNA degraded; the DNA concentration was \<50 ng/μL with \>45% DNA degraded; or DNA degradation was \>60%. Degraded DNA was defined as the proportion of DNA under 1000 bp in length.
10.1371/journal.pone.0152851.t001
###### Characteristics of Specimens by Tumor Site.
{#pone.0152851.t001g}
Tumor site Number of specimens submitted for NGS Specimens with DNA quality or quantity inadequate for NGS analysis Number of "shared" specimens (i.e., results are available from both NGS and targeted tests)
------------------ --------------------------------------- -------------------------------------------------------------------- ---------------------------------------------------------------------------------------------
Lung 196 13 (6.6%) 101 (51.5%)
Brain 174 9 (5.2%) 6 (3.4%)
Bone Marrow 161 0 95 (59.0%)
Lymph Node 70 8 (11.4%) 32 (45.7%)
Peripheral blood 56 0 29 (51.8%)
Liver 36 4 (11.1%) 5 (13.9%)
Skin 23 2 (8.7%) 5 (21.7%)
Other 222 24 (10.8%) 31 (14.0%)
Tumor site is not necessarily tissue of origin. Please note that in contrast to solid tumor specimens, all liquid specimens (bone marrow and peripheral blood) were adequate for NGS processing.
To determine the tumor percentage and volume of solid tumors, hematoxylin- and eosin-stained tissue specimens were evaluated by an anatomic pathologist, and the region with the highest tumor burden was marked. Genomic DNA was extracted from fresh bone marrow or peripheral blood using the Gentra Puregene Cell Kit (Qiagen, Netherlands). For formalin-fixed, paraffin-embedded (FFPE) specimens, tissues were macro-dissected from 5 μM or 10μM slides. Scrapings were dewaxed with Qiagen Deparaffinization Solution and purified with Gentra Puregene Tissue reagents following the manufacturer's protocol (Qiagen, Netherlands). DNA quantification was performed using the Qubit Broad Range assay following manufacturer's protocols (Life Technologies, CA). Agilent Genomic TapeScreens were used following manufacturer's protocols to assess the degree of DNA degradation (Agilent, CA).
Targeted Molecular Testing {#sec004}
--------------------------
### *EGFR*, *KRAS*, and *BRAF* Assays {#sec005}
The mutational status of *EGFR* exons 19 and 21 was determined using a laboratory-developed test (LDT) as previously described \[[@pone.0152851.ref027]\]. Briefly, genomic DNA was extracted from FFPE tissue and amplified with primers covering two regions, one that is commonly deleted in exon 19, and a part of exon 21 that encompasses codon 858. The L858R missense mutation in exon 21 creates a new *Sau*96I cleavage site within exon 21. The amplification products were digested with *Sau*96I and then separated by capillary electrophoresis.
*KRAS* mutations in codons 12 and 13 were assayed using a LDT as previously described \[[@pone.0152851.ref028]\]. Briefly, genomic DNA was extracted and amplified using primers designed to detect point mutations, hybridized to target-specific capture probes, and subjected to a bead assay (Lumina, TX).
*BRAF* mutations were assayed by pyrosequencing of an amplified portion of the *BRAF* gene including codon 600, as previously described \[[@pone.0152851.ref029]\].
### *FLT3* Assay {#sec006}
DNA was extracted using the QIAamp DNA Blood Mini Kit (Qiagen, Netherlands). Mutation analysis of the *FLT3* gene was performed using multiplex PCR amplification with two sets of fluorescently labeled primers. For internal tandem duplication (ITD) detection, PCR was performed with the following primers: 5'-GCA ATT TAG GTA TGA AAG CCA GC-3' (forward) and 5'-CTT TCA GCA TTT TGA CGG CAA CC-3' (reverse); forward primers were labeled with 6-carboxyfluorescin (6-FAM), and reverse primers were labeled with VIC. An internal tandem duplication (ITD) was determined to be present if a product larger than the wild-type (329 bp) product was detected by capillary electrophoresis. Detection of the D835 mutation of *FLT3* (NM_004119.2: c.2503_2505) was based on the fact that this mutation abolishes an *Eco*RV cleavage site. PCR was performed with the following primers: 5'-GTA AAA CGA CGG CCA GCC GCC AGG AAC GTG CTT-3' (forward) and 5'-CAG GAA ACA GCT ATG ACG ATA TCA GCC TCA CAT TGC CCC-3' (reverse); forward primers were labeled with NED at the 5' end. After *Eco*RV digestion, PCR products were analyzed by capillary electrophoresis using a 3500xL Genetic Analyzer (Life Technologies, NY). A D835 point mutation was indicated by the presence of a 129 bp fragment.
### *NPM1* Assay {#sec007}
Total RNA was extracted using the QIAamp RNA Blood Mini Kit (Qiagen, Netherlands), reverse transcribed, and amplified in a multiplex PCR reaction using primers designed to detect common mutations in *NPM1* (NM_002520.4) using the Signature *NPM1* Mutations Assay (Asuragen, TX). Labeled PCR products were hybridized to target-specific capture probes covalently bound to fluorescent microspheres in a liquid bead array followed by analysis with a Luminex 100 (Luminex, TX). Interpretation was based on the mean fluorescence intensity (MFI) obtained from a minimum of 50 microspheres.
### *JAK2* Assay {#sec008}
Genomic DNA was isolated from leukocytes using the QIAamp DNA Blood Mini Kit (Qiagen, Netherlands) and amplified using real-time PCR with primers flanking *JAK2* codon 617. Allelic discrimination between the normal sequence and the *JAK2* V617F (NM_004972 c.1849G\>T) mutation was subsequently accomplished by simultaneous differential hybridization of two sequence-specific probes, each labeled with a different fluorescent marker (MutaScreen Assay, Qiagen, Netherlands).
Next-Generation Sequencing and Bioinformatic Analysis {#sec009}
-----------------------------------------------------
For solid tumors, target enrichment was performed with the TruSeq Amplicon Cancer Panel (Illumina, CA), a cancer gene panel consisting of 212 target amplicons covering mutation hotspots of 47 cancer genes. For hematologic malignancies, an in-house developed gene panel was utilized, which is composed of 382 amplicons covering 33 genes. For all successful sequencing runs, read depth was 250x at any given position, with 1000x mean coverage across the entire targeted sequence, and a Q30 at greater than 75% of reads. An in-house bioinformatics pipeline \[[@pone.0152851.ref026]\] was used to map reads, detect variants, and annotate them. Reads were de-multiplexed, mapped to the hg19 version of the human reference genome, filtered to remove off-target and poor-quality reads ([Fig 1](#pone.0152851.g001){ref-type="fig"}). Using custom scripts, four types of variants were extracted: single-nucleotide variants (SNVs), small indels, copy number variants, and large indels. Variants were then compared to an in-house developed knowledge base, which draws from publicly available sources such as PubMed, dbSNP database \[[@pone.0152851.ref030]\], COSMIC database \[[@pone.0152851.ref031]\], 1000 Genomes \[[@pone.0152851.ref032]\], and the Exome Variant Server ([http://evs.gs.washington.edu](http://evs.gs.washington.edu/)). Using this knowledge base, variants were classified into 1 of 5 categories: disease associated mutation (DAM), likely pathogenic mutation (LPM), variants of uncertain significance (VUS), likely benign (LB), or benign (B). DAMs include mutations previously reported and associated with disease, including gain-of-function mutations in oncogenes (e.g., the canonical *KRAS* G12D mutation) and truncating mutations in known tumor suppressor genes. LPMs were classified as variants that had some evidence of disease association, such as case reports, but are not well described otherwise. Variants were classified as VUS if they had not been previously reported either as a disease-associated mutation or as a normal variant on the Exome Variant Server, but whose pathogenicity could not be established with certainty. Variants were classified as LB if there was no report of association with disease and if they occurred in regions of the gene not predicted to have pathologic consequences. Variants noted on the clinical report, which are the ones included in this analysis, included the DAM, LPM and VUS (not LB or B). All reported variants were manually reviewed using the Integrative Genomics Viewer (IGV) \[[@pone.0152851.ref033]\] by at least two pathologists.
{#pone.0152851.g001}
Ethics Statement {#sec010}
----------------
Patient data were analyzed anonymously in accordance with institutional practice guidelines. The institutional review board of the University of Pennsylvania determined this study to be exempt.
Results {#sec011}
=======
Study Design and Specimen Characteristics {#sec012}
-----------------------------------------
The University of Pennsylvania Health System began routine clinical NGS of solid tumors and hematologic malignancies in February of 2013. During validation of our NGS pipeline, we established thresholds for acceptable tumor percentage (10%) and DNA quantity and quality (see [Methods](#sec002){ref-type="sec"} for details).
For a large number of specimens, clinicians ordered targeted single-gene tests and NGS analysis on the same specimen ([Table 1](#pone.0152851.t001){ref-type="table"}): this occurred frequently with pulmonary and hematological specimens, but relatively rarely with specimens derived from other sites such as brain. We reasoned that comparing results from targeted and NGS testing of all "shared" specimens (i.e. specimens that had been analyzed by both NGS and single-gene tests) would allow us to probe the robustness of our NGS pipeline. We therefore set out to compare NGS and targeted test results in specimens that underwent NGS analysis during the first year of operation of the NGS pipeline (March 1, 2013 through March 1, 2014). During this time, 938 specimens (717 solid and 221 hematologic) were submitted for NGS analysis. While the majority of solid tumor specimens were composed of \>50% tumor cells ([Fig 2](#pone.0152851.g002){ref-type="fig"}), a fraction of solid tumors was not tested due to low tumor percentage. The most common tumor sites were lung, brain, bone marrow, lymph nodes, and peripheral blood ([Table 1](#pone.0152851.t001){ref-type="table"}). A small fraction of solid tumor specimens could not be analyzed by NGS due to inadequate DNA quantity or quality (*n* = 60, 8.3%), however this was not an issue with peripheral blood and bone marrow specimens.
{#pone.0152851.g002}
Comparison of *EGFR* and *KRAS* Gene Mutations by NGS and Targeted Testing {#sec013}
--------------------------------------------------------------------------
We were particularly interested in the performance of *EGFR* testing in our NGS assay, because mutations in this gene may be therapeutically targetable, and because it is often challenging to analyze, as DNA degradation and low tumor percentage are frequently encountered in lung cancer specimens. Since *KRAS* mutations were frequently evaluated alongside *EGFR* in cases of lung cancers at our institution, we also wanted to compare the performance of both methods on this gene. The tumor percentages for all specimens for which targeted *EGFR* mutation analysis was reported during the study period (*n* = 283) are shown in [Fig 3](#pone.0152851.g003){ref-type="fig"}. Approximately 10% of the cases evaluated by targeted testing had a tumor percentage below the cutoff for NGS.
{#pone.0152851.g003}
We compared NGS and targeted testing in 139 specimens that had been tested for *EGFR* mutations ([Fig 4A](#pone.0152851.g004){ref-type="fig"}) and 138 that had been tested for *KRAS* mutations by both methods ([Fig 4B](#pone.0152851.g004){ref-type="fig"}). Among the shared specimens, all generated a result with the targeted single-gene methods. However, 15/139 (11%) of shared *EGFR*-tested and 13/138 (9%) of shared *KRAS*-tested specimens were excluded from NGS analysis due to insufficient DNA quality or quantity.
{#pone.0152851.g004}
In the remaining specimens, all mutations detected by the targeted assays were also detected by NGS. Conversely, NGS identified a number of mutations that the targeted tests were not designed to detect. For example, our targeted *EGFR* mutation test only covers deletions in exon 19 and the L858R mutation in exon 21. Similarly, the targeted *KRAS* test only detects mutations in codons 12 and 13. In 10 *EGFR* shared cases (6%), additional pathogenic mutations were detected by NGS. In two of these cases, the T790M mutation was found, which predicts resistance to TKI therapy \[[@pone.0152851.ref004]\]. Additionally, NGS detected *EGFR* amplification in five cases; the predictive value of this copy number alteration in the context of TKI therapy is currently unclear. In four *KRAS* shared cases (3%), NGS detected mutations in codon 61, which predict resistance to TKI therapy \[[@pone.0152851.ref034]\].
Comparison of *BRAF* Gene Mutations by NGS and Targeted Testing {#sec014}
---------------------------------------------------------------
The *BRAF* single-gene test was performed less frequently in parallel with solid tumor NGS than the *EGFR* or *KRAS* tests, because thyroid fine-needle aspiration samples, for which *BRAF* testing was frequently ordered, were not originally validated for the NGS assay. Of 224 specimens that were tested with targeted *BRAF* tests, 38 were also analyzed by NGS ([Fig 4C](#pone.0152851.g004){ref-type="fig"}). Among the shared specimens, all generated a result with the targeted *BRAF* test. In contrast, 8/38 shared cases (21%) could not be analyzed by NGS due to poor DNA quality or inadequate DNA quantity. All remaining shared specimens showed perfect concordance between NGS and targeted testing.
Comparison *FLT3*, *NPM1*, and *JAK2* Mutations by NGS and Targeted Testing {#sec015}
---------------------------------------------------------------------------
Of 221 hematologic specimens tested by NGS during the study period, 118 were also tested with the *FLT3*, and 98 with the *NPM1* targeted tests. In two cases, the targeted *FLT3* test detected an internal tandem duplication (ITD) that was not automatically called by the NGS analysis pipeline ([Fig 5A](#pone.0152851.g005){ref-type="fig"}). However, manual review of the sequencing data demonstrated ITD mutations at allele frequencies of 1.3% and 1.6% ([Fig 6A and 6C](#pone.0152851.g006){ref-type="fig"}, respectively). In one of these two cases, the hematologic malignancy NGS panel additionally detected a pathogenic *FLT3* D839G (c. 2516A\>G) mutation ([Fig 6B](#pone.0152851.g006){ref-type="fig"}); this mutation was not detected by the *FLT3* single-gene test that is designed to detect only ITDs and D835 mutations.
{#pone.0152851.g005}
{#pone.0152851.g006}
In the remainder of *FLT3* shared cases, and also in all *NPM1* shared cases ([Fig 5B](#pone.0152851.g005){ref-type="fig"}), NGS and targeted tests were concordant. Additionally, a small number of specimens (*n* = 8) that had been tested for *JAK2* mutations by both modalities were analyzed and showed complete concordance ([Fig 5C](#pone.0152851.g005){ref-type="fig"}).
Discussion {#sec016}
==========
In this study, we report the properties of solid and liquid malignancy specimens processed during the first year of clinical oncologic NGS performed within the University of Pennsylvania Health System. We found that when we adhered to two predetermined quality control metrics, i.e., tumor percentage and DNA quantity and quality, we achieved excellent NGS data as determined by virtually perfect concordance between NGS and targeted, single-gene testing. While a number of recent studies have confirmed the potential utility of clinical NGS for oncology \[[@pone.0152851.ref014]--[@pone.0152851.ref025]\], there have been none, to our knowledge, that have evaluated the quality of data generated during day-to-day practice at a clinical oncologic sequencing facility. Additionally, in contrast to previous validation studies, we examined a larger number of specimens from a greater variety of tissues, and our data is therefore less subject to sample selection bias and may also more accurately reflect the expected annual case volume and distribution of tissue types encountered at a major academic medical center.
Solid tumors and hematologic malignancy specimens differed considerably in their performance across the established quality control measures. We found that a sizable fraction of solid but not liquid specimens yielded DNA of insufficient quality or quantity for NGS testing. With respect to specimens tested for *EGFR* and *KRAS* (predominantly lung), this was likely largely due to formalin fixation, which degrades DNA through cross-linking as well as other less well understood mechanisms \[[@pone.0152851.ref035]\]. One potential approach to reduce the number of samples that are currently rejected from NGS analysis might be to determine the amplifiability of extracted genomic DNA, for example by using the human genomic DNA quantitation and quality control assay by Kapa Biosystems (Wilmington, MA).
Our study highlights the complementarity of NGS and targeted tests for mutation detection. In a number of instances, NGS detected clinically important mutations that were not captured by targeted assays. For example, the *EGFR* test specifically interrogates potential exon 19 deletions and L858R mutations, which constitute about 85% of EGFR mutations in lung cancers \[[@pone.0152851.ref012]\]. In 9 shared cases, *EGFR* mutations were found in different regions of the gene by the NGS assay ([Fig 4A](#pone.0152851.g004){ref-type="fig"}). Similarly, clinically important *KRAS* mutations occur in codons 12, 13, and 61, but only codons 12 and 13 were evaluated by the in-house *KRAS* single-gene test. In 4 shared cases, *KRAS* mutations in codon 61 were detected by NGS only.
Targeted assays generally outperformed NGS in specimens with low tumor percentage, DNA quantity, or quality. In fact, we identified actionable mutations by targeted analysis in multiple cases that were unable to be analyzed by NGS (data not shown). In two specimens, a *FLT3* ITD mutation, which was not automatically called by the NGS pipeline, was readily detected by the targeted assay. While *FLT3* ITDs can be challenging to detect by NGS due to the complex structure of the mutation \[[@pone.0152851.ref036]\], the problem in these two cases was that the allele frequency fell below the validated threshold for automatic detection of 4%. However, manual inspection of the *FLT3* exon 14 and the flanking intronic sequence using the Integrative Genomics Viewer (IGV) \[[@pone.0152851.ref033]\] clearly showed the presence of ITD mutations in both cases ([Fig 6A and 6C](#pone.0152851.g006){ref-type="fig"}). The detection of NGS for indel mutations, in contrast to single nucleotide variants, is not fundamentally limited by PCR artifacts and sequencing errors. Therefore, we validated our pipeline for the detection of *FLT3* ITDs with allele frequencies of 1%, and we altered the indel allele frequency calling threshold specifically for *FLT3* ITDs. Reanalysis of the two *FLT3* cases with updated parameters, which was part of the revalidation study, revealed the expected results. These findings highlight the importance of manual review of the sequencing data.
Low tumor percentage was also limiting in solid tumor cases. Approximately 10% of specimens submitted for *EGFR* mutation testing were found to contain less than 10% tumor ([Fig 3](#pone.0152851.g003){ref-type="fig"}), thereby failing tumor percentage requirements for NGS testing. All of these specimens generated a result with the targeted assay. It should be noted, however, that as NGS methodologies continue to mature, the ability of NGS to detect single nucleotide variants in specimens with lower tumor percentage will improve. Rare variant detection by NGS is hampered by the high rate of amplification and sequencing errors, which can approach 1% for single nucleotide variants \[[@pone.0152851.ref037]\]. Various approaches to increase analytic sensitivity for rare variants by NGS have recently been described, including barcoding of each DNA fragment before amplification \[[@pone.0152851.ref038]--[@pone.0152851.ref040]\], barcoding of both strands of each fragment \[[@pone.0152851.ref041]\], and generation of multiple linked tandem copies of each DNA fragment by rolling circle amplification \[[@pone.0152851.ref042]\]. In particular, the latter method has been shown to improve sensitivity of rare variant detection by more than 100-fold without introducing excessive computational inefficiency.
There are a number of limitations to this study. First, only genes for which both NGS analysis and single-gene tests are performed at our institution were included in the analysis. While the genes examined in this study currently represent the essential core of cancer gene testing, it is possible that NGS might function less reliably with certain other genes or specific mutations that were not assessed. Of note, our NGS pipeline produced excellent results for the challenging genes *EGFR* and *FLT3*. We therefore expect that most other genes covered by our cancer panels generate NGS data of similarly high quality. Second, not all specimens that were submitted for NGS analysis were also tested by single-gene methods. For example, only 3.4% of brain tumor specimens submitted for NGS were at the same time examined by targeted tests, and therefore our conclusions may not necessarily extend to all tumors at this time. Additionally, the specimens tested did not contain the entire spectrum of mutations that can be evaluated by our targeted tests. Finally, our findings may not be generalizable to other platforms, especially those that utilize more complex gene panels.
Recently issued recommendations for validation and quality control of clinical NGS data \[[@pone.0152851.ref043]\] include monitoring of quality metrics (e.g., sequencing quality scores, depth of coverage, uniformity of coverage, mapping quality), proficiency testing, and confirmation of actionable results by independent methods. Multiple studies that appeared after these recommendations were published have established that particularly for solid tumors, tumor percentage and DNA quality are important additional metrics \[[@pone.0152851.ref014],[@pone.0152851.ref022],[@pone.0152851.ref023]\], and we found this as well in our validation studies (not shown). Proficiency testing for cancer NGS is not yet available but is currently being developed by the College of American Pathologists (CAP).
A proposed requirement to confirm actionable mutations by independent molecular methods \[[@pone.0152851.ref043]\] has been called into question \[[@pone.0152851.ref023]\]. Since single-gene tests such as Sanger sequencing may not have inherently greater sensitivity than a well-scaled NGS pipeline \[[@pone.0152851.ref015],[@pone.0152851.ref044]\], verification by these methods might not improve the accuracy of test results. Accordingly, very recent guidelines by the College of American Pathologists leave the decision when and how to perform confirmatory testing of NGS results to the clinical laboratory \[[@pone.0152851.ref044]\]. Our *EGFR* single-gene test had greater analytical sensitivity than NGS, detecting mutations in samples with well under 10% tumor. However, our finding that within pre-defined tumor percentage and DNA quality cutoffs NGS showed perfect concordance confirms the notion that it is unnecessary to confirm each actionable mutation detected via NGS by a single-gene test. In addition, single-gene tests frequently do not cover important disease-associated mutations and in some instances fail to detect the very mutations they target \[[@pone.0152851.ref013]\].
Based on these considerations, we propose a workflow that integrates NGS as an adjunct diagnostic modality for solid and liquid neoplasms ([Fig 7](#pone.0152851.g007){ref-type="fig"}). The typical turn-around time of the NGS assay at the time of the study was around 7--10 days from receipt in the sequencing facility to the time the final report was signed out in the electronic medical record. Turnaround is generally faster for targeted tests, and thus it is advantageous to perform targeted tests, perhaps in addition to NGS, in clinically urgent situations. Specimens with low tumor percentage or DNA quantity or quality should be subjected to targeted tests that we found to be more analytically sensitive than NGS. On the other hand, when DNA quality and quantity is adequate and a turnaround time of 7--10 days is acceptable, NGS holds clear advantages, including increased clinical sensitivity within targeted genes of interest and additional information from other covered genes on the panel. In these cases, our data suggest that targeted tests may be safely omitted.
{#pone.0152851.g007}
Supporting Information {#sec017}
======================
###### Raw Data for Comparison Analysis.
(XLSX)
######
Click here for additional data file.
We thank Daniel Desloover for comments on the manuscript.
[^1]: **Competing Interests:**The authors have declared that no competing interests exist.
[^2]: Conceived and designed the experiments: MCH DBR SK CDW RDD JJDM. Performed the experiments: MCH SK. Analyzed the data: MCH SK. Contributed reagents/materials/analysis tools: MCH SK DL JZ CDW RDD JJDM. Wrote the paper: MCH SK JZ CDW RDD JJDM.
[^3]: Current address: BioReference Laboratories, Elmwood Park, New Jersey, United States of America
[^4]: Current address: Department of Pathology, Massachusetts General Hospital, Boston, Massachusetts, United States of America
[^5]: ‡ These authors also contributed equally to this work
|
Methanol-inducible gene expression and heterologous protein production in the methylotrophic yeast Candida boidinii.
Methylotrophic yeasts can obtain all of their required carbon and energy from methanol, a promising feedstock for biotechnological and chemical processes and a potential replacement for coal and petroleum. When these yeast cells are cultured in the presence of methanol, the enzymes involved in methanol metabolism are massively produced, indicating that the gene promoters of these enzymes are strong methanol-inducible promoters. Using these promoters, high-level heterologous gene expression systems have been developed in several methylotrophic yeast strains, including Pichia pastoris, Hansenula polymorpha, Pichia methanolica and Candida boidinii. In the present minireview we describe recent insights into the molecular basis of methanol-inducible gene expression in C. boidinii. In addition, the utility of C. boidinii gene expression systems for the production of various enzymes is also reviewed. |
, 736, 735?
-o + 738
What is the u'th term of -39, -128, -217, -306?
-89*u + 50
What is the q'th term of -1046, -2094, -3142, -4190, -5238?
-1048*q + 2
What is the b'th term of -1664, -1687, -1724, -1781, -1864, -1979, -2132, -2329?
-b**3 - b**2 - 13*b - 1649
What is the h'th term of 82, 165, 226, 253, 234, 157?
-2*h**3 + h**2 + 94*h - 11
What is the g'th term of -24, -179, -576, -1335, -2576, -4419, -6984, -10391?
-20*g**3 - g**2 - 12*g + 9
What is the p'th term of -156, -171, -186, -201, -216, -231?
-15*p - 141
What is the u'th term of 217, 225, 235, 247, 261, 277?
u**2 + 5*u + 211
What is the j'th term of -27, -26, -25, -24?
j - 28
What is the c'th term of 26, 46, 54, 44, 10, -54, -154, -296?
-c**3 + 27*c
What is the y'th term of -12, -25, -50, -93, -160, -257?
-y**3 - 6*y - 5
What is the h'th term of 2757, 2777, 2809, 2859, 2933, 3037, 3177, 3359?
h**3 + 13*h + 2743
What is the p'th term of 7, 31, 79, 157, 271, 427, 631, 889?
p**3 + 6*p**2 - p + 1
What is the f'th term of 231, 210, 189, 168, 147?
-21*f + 252
What is the d'th term of 36, 74, 112?
38*d - 2
What is the g'th term of -29, -35, -57, -107, -197, -339, -545?
-2*g**3 + 4*g**2 - 4*g - 27
What is the w'th term of -1277, -2553, -3829, -5105, -6381?
-1276*w - 1
What is the x'th term of 65, 119, 177, 239, 305?
2*x**2 + 48*x + 15
What is the j'th term of -6, -28, -52, -72, -82?
j**3 - 7*j**2 - 8*j + 8
What is the b'th term of -295, -593, -891, -1189?
-298*b + 3
What is the y'th term of -27574, -55147, -82720, -110293, -137866, -165439?
-27573*y - 1
What is the s'th term of 63, 62, 61, 60, 59, 58?
-s + 64
What is the w'th term of -89, -186, -293, -416, -561, -734?
-w**3 + w**2 - 93*w + 4
What is the m'th term of -309, -342, -365, -372, -357, -314, -237?
m**3 - m**2 - 37*m - 272
What is the o'th term of 290, 289, 290, 293, 298, 305, 314?
o**2 - 4*o + 293
What is the x'th term of -42, -77, -112?
-35*x - 7
What is the p'th term of 5, 29, 89, 203, 389, 665, 1049?
3*p**3 + 3*p - 1
What is the g'th term of -3409, -3418, -3439, -3478, -3541, -3634?
-g**3 - 2*g - 3406
What is the w'th term of 544, 542, 538, 532, 524, 514, 502?
-w**2 + w + 544
What is the g'th term of 211, 416, 615, 808, 995, 1176, 1351?
-3*g**2 + 214*g
What is the c'th term of -41, -97, -183, -293, -421, -561, -707?
c**3 - 21*c**2 - 21
What is the d'th term of 925, 1839, 2741, 3625, 4485, 5315, 6109, 6861?
-d**3 + 921*d + 5
What is the p'th term of 139, 278, 421, 568, 719, 874?
2*p**2 + 133*p + 4
What is the c'th term of -206, -202, -196, -188, -178, -166?
c**2 + c - 208
What is the d'th term of -20, -26, -36, -50, -68, -90?
-2*d**2 - 18
What is the k'th term of 2801, 5604, 8407?
2803*k - 2
What is the s'th term of 52, 180, 384, 658, 996, 1392?
-s**3 + 44*s**2 + 3*s + 6
What is the r'th term of 26, 71, 154, 293, 506, 811, 1226, 1769?
3*r**3 + r**2 + 21*r + 1
What is the s'th term of 15, 47, 107, 201, 335, 515, 747, 1037?
s**3 + 8*s**2 + s + 5
What is the w'th term of 8003, 7998, 7989, 7976, 7959?
-2*w**2 + w + 8004
What is the f'th term of -71, -135, -199, -263?
-64*f - 7
What is the v'th term of 470, 938, 1406, 1874, 2342?
468*v + 2
What is the b'th term of 100, 405, 912, 1621, 2532, 3645?
101*b**2 + 2*b - 3
What is the h'th term of 257, 515, 771, 1025, 1277, 1527?
-h**2 + 261*h - 3
What is the a'th term of -531, -525, -509, -477, -423, -341, -225, -69?
a**3 - a**2 + 2*a - 533
What is the w'th term of 345, 344, 343, 342, 341?
-w + 346
What is the v'th term of 2146, 2144, 2142, 2140, 2138?
-2*v + 2148
What is the s'th term of 468, 930, 1382, 1818, 2232?
-s**3 + s**2 + 466*s + 2
What is the l'th term of 697, 702, 711, 724, 741, 762?
2*l**2 - l + 696
What is the t'th term of 391, 365, 301, 181, -13?
-3*t**3 - t**2 - 2*t + 397
What is the r'th term of -50, -41, -42, -59, -98, -165?
-r**3 + r**2 + 13*r - 63
What is the l'th term of 41, 13, -41, -127, -251, -419?
-l**3 - 7*l**2 + 49
What is the q'th term of 9, 27, 51, 81?
3*q**2 + 9*q - 3
What is the f'th term of -84, -345, -780, -1389, -2172, -3129, -4260?
-87*f**2 + 3
What is the n'th term of 5, 11, 11, -1, -31, -85, -169, -289?
-n**3 + 3*n**2 + 4*n - 1
What is the m'th term of 2852, 2832, 2800, 2750, 2676, 2572, 2432, 2250?
-m**3 - 13*m + 2866
What is the n'th term of 21, -49, -225, -555, -1087?
-8*n**3 - 5*n**2 + n + 33
What is the z'th term of 5, 24, 53, 92, 141, 200, 269?
5*z**2 + 4*z - 4
What is the w'th term of 53, 208, 465, 824?
51*w**2 + 2*w
What is the g'th term of -41, -343, -1153, -2723, -5305, -9151, -14513?
-42*g**3 - 2*g**2 - 2*g + 5
What is the a'th term of -9473, -9470, -9465, -9458?
a**2 - 9474
What is the j'th term of -22, -100, -232, -412, -634, -892, -1180, -1492?
j**3 - 33*j**2 + 14*j - 4
What is the y'th term of 456, 457, 458?
y + 455
What is the m'th term of 14, 68, 162, 302, 494, 744, 1058, 1442?
m**3 + 14*m**2 + 5*m - 6
What is the d'th term of -27, -33, -63, -129, -243, -417?
-2*d**3 + 8*d - 33
What is the o'th term of 181, 390, 627, 898, 1209, 1566, 1975, 2442?
o**3 + 8*o**2 + 178*o - 6
What is the h'th term of -2592, -2591, -2590, -2589, -2588?
h - 2593
What is the r'th term of -35, -65, -103, -155, -227, -325, -455?
-r**3 + 2*r**2 - 29*r - 7
What is the t'th term of -13, -14, -15, -16, -17?
-t - 12
What is the i'th term of -20, -137, -464, -1109, -2180, -3785?
-18*i**3 + 3*i**2 - 5
What is the w'th term of 1, 21, 53, 97, 153, 221?
6*w**2 + 2*w - 7
What is the a'th term of 113, 118, 123?
5*a + 108
What is the z'th term of 120, 128, 148, 186, 248, 340?
z**3 + z + 118
What is the s'th term of 37, 174, 405, 730?
47*s**2 - 4*s - 6
What is the n'th term of -1, 46, 125, 236, 379, 554, 761?
16*n**2 - n - 16
What is the o'th term of -11, -72, -247, -596, -1179, -2056, -3287, -4932?
-10*o**3 + 3*o**2 - 4
What is the q'th term of -139, -547, -1227, -2179, -3403, -4899, -6667?
-136*q**2 - 3
What is the u'th term of -4180, -4183, -4186, -4189?
-3*u - 4177
What is the u'th term of -3, -17, -61, -153, -311, -553, -897, -1361?
-3*u**3 + 3*u**2 - 2*u - 1
What is the z'th term of 2, -29, -80, -151, -242, -353?
-10*z**2 - z + 13
What is the o'th term of -36, -21, -2, 21, 48, 79, 114?
2*o**2 + 9*o - 47
What is the u'th term of 23, 99, 225, 401, 627, 903, 1229?
25*u**2 + u - 3
What is the k'th term of 43, 66, 101, 154, 231?
k**3 + 16*k + 26
What is the g'th term of -311, -302, -281, -242, -179, -86, 43?
g**3 + 2*g - 314
What is the k'th term of -31608, -31610, -31612?
-2*k - 31606
What is the j'th term of 230, 206, 182?
-24*j + 254
What is the n'th term of 4, -2, -8?
-6*n + 10
What is the m'th term of 14, 51, 142, 311, 582, 979, 1526, 2247?
4*m**3 + 3*m**2 + 7
What is the x'th term of -97, -201, -327, -481, -669, -897?
-x**3 - 5*x**2 - 82*x - 9
What is the k'th term of -3780, -3640, -3490, -3324, -3136, -2920, -2670?
k**3 - k**2 + 136*k - 3916
What is the d'th term of 30, -29, -90, -153, -218, -285, -354?
-d**2 - 56*d + 87
What is the n'th term of -208, -205, -200, -193, -184, -173, -160?
n**2 - 209
What is the y'th term of -26535, -26531, -26525, -26517, -26507, -26495, -26481?
y**2 + y - 26537
What is the n'th term of 99, 185, 261, 327, 383, 429?
-5*n**2 + 101*n + 3
What is the m'th term of 3, 7, 11, 15, 19?
4*m - 1
What is the d'th term of 3, 20, 51, 102, 179, 288, 435, 626?
d**3 + d**2 + 7*d - 6
What is the t'th term of 2289, 2287, 2287, 2289?
t**2 - 5*t + 2293
What is the n'th term of 2229, 4463, 6697?
2234*n - 5
What is the l'th term of -15, -24, -45, -84, -147, -240, -369, -540?
-l**3 - 2*l - 12
What is the k'th term of -59, -64, -55, -26, 29, 116, 241, 410?
k**3 + k**2 - 15*k - 46
What is the h'th term of -99, -162, -223, -282, -339, -394?
h**2 - 66*h - 34
What is the o'th term of 26, 43, 48, 23, -50, -189?
-3*o**3 + 12*o**2 + 2*o + 15
What is the s'th term of 27, 34, 47, 66, 91, 122?
3*s**2 - 2*s + 26
What is the v'th term of -19, -48, -75, -100, -123, -144?
v**2 - 32*v + 12
What is the h'th term of 5728, 5727, 5726, 5725, 5724, 5723?
-h + 5729
What is the k'th term of -116, -229, -342?
-113*k - 3
What is the s'th term of -37, -23, -1, 35, 91, 173, 287, 439?
s**3 - 2*s**2 + 13*s - 49
What is the l'th term of -7, -62, -211, -502, -983, -1702, -2707, -4046?
-8*l**3 + l**2 - 2*l + 2
What is the l'th term of 89, 168, 237, 290, 321, 324?
-l**3 + l**2 + 83*l + 6
What |
Q:
HTML 5 input range-thumb disappeared after updating Chrome to version-49
I've themed HTML5 input range-thumb in one of my Client website using pseudo classes :after and :before and using the -webkit- prefix. And it was displaying all fine until I updated my Chrome browser (Desktop, Windows 7) to Version 49.0.2623.87 m.
Can anyone please suggest, what has changed here?
Thanks!
Here is the css I used for Chrome:
input.thickness {
-webkit-appearance: none;
float: left;
width: 72%;
margin-right: 20px;
margin-top: 8px;
margin-left: 0 /*for firefox*/;
padding: 0 /*for IE*/;
}
input.thickness:focus::-webkit-slider-runnable-track {
outline: none;
}
input.thickness::-webkit-slider-runnable-track {
width: 100%;
height: 8px;
background-color: #2f9de2;
border-radius: 4px;
}
input.thickness::-webkit-slider-thumb {
-webkit-appearance: none;
position: relative;
background: transparent;
width: 22px;
height: 12px;
margin-top: 8px;
}
input.thickness::-webkit-slider-thumb:after,
input.thickness::-webkit-slider-thumb:before {
bottom: 0;
left: 0;
border: solid transparent;
content: " ";
height: 0;
width: 0;
position: absolute;
pointer-events: none;
}
input.thickness::-webkit-slider-thumb:after {
border-color: rgba(136, 183, 213, 0);
border-bottom-color: #2f9de2;
border-width: 10px;
}
input.thickness::-webkit-slider-thumb:before {
border-color: rgba(194, 225, 245, 0);
border-bottom-color: #2f9de2;
border-width: 10px;
}
<input class="thickness" type="range" min="0" max="100" value="50" />
A:
This is intentional. It's also on par with Gecko's behaviour.
|
Affecting factors in second language learning.
The present study investigated the influence of sex, handedness, level in second language (L2) and Faculty choice on the performance of phonological, syntactical and semantic tasks in L2. Level in L2 and sex were the most affecting factors. Subjects who achieved higher scores on L2 tasks had strong second language aptitude skills since they were those who had obtained a professional degree in the second language. Females performed better than males in syntax and semantics which is explained by the general female superiority on verbal tasks based on differences in hemispheric specialization for language functions between the sexes. Handedness and Faculty choice on the part of the participants had an impact on our results but only when combined with other factors. |
1. Field of the Invention
This invention relates in general to biased magnetic recording, and in particular to a biased cross-field recording head having increased short wavelength recording effectiveness. |
Peculiarities of the course of bronchial asthma in patients with excessive body weight or obesity.
Introduction: Clinical studies that were devoted to the analysis of the asthma course during concomitant obesity or excessive body weight, demonstrated a number of typical features. Both asthma and obesity or overweight are diseases that form a persistent chronic inflammatory process in the body. The combination and mutual enhancement of the factors of chronic inflammation leads to a more severe clinical course of asthma and reduced control of the disease. The aim: The main goal of our study was to determine the peculiarities of the course of bronchial asthma of various degrees of severity in patients with excessive body weight or obesity. Materials and methods: Anamnesis and examination of 86 patients with a major diagnosis of bronchial asthma were performed. According to the body weight index, patients were divided into two groups: main and comparison, and 20 somatic-healthy patients who were included in the control group also participated in the study. Results and conclusions: The patients had upper respiratory tract diseases, namely rhinitis, sinusitis, bronchitis, and pneumonia. A different incidence rate of respiratory infections in a child was noted in patients, depending on the severity of the course. The patients in the main group took an antibiotic on an average 3-4 times a year, of whom patients with severe bronchial asthma took antibiotics 4-5 times a year. In the comparison group, the average level of antibiotic ingestion coincided with that of the control group, namely 1-1.5 times a year. The patients have a close direct correlation between the asthma test and the body mass index. 28.75% of the patients in the main group had no symptoms of allergy. Damp basements, rooms with lots of dust or outdoor work with high concentrations of dust or pollen have a negative effect on the patients with asthma. 81% of the patients in the main group did not adhere to the appointments of the doctor, it should be noted that these are patients with any course of asthma. |
Introduction {#s1}
============
All organisms live in environments that vary through time and such environmental heterogeneity can impose highly variable selection pressures on populations. In this situation, an allele may be beneficial during one environmental regime and subsequently deleterious during another. Such an allele would be subject to short bursts of directional selection, alternately being favored and disfavored. When this situation occurs in diploids, the heterozygote can have a higher geometric mean fitness than either homozygote and allelic variation at this locus could be maintained for long periods despite being subject to directional selection at any given time [@pgen.1004775-Gillespie1]--[@pgen.1004775-Hedrick1]. This situation is referred to as marginal overdominance and is a form of balancing selection.
There is substantial evidence for the maintenance of phenotypic and genetic variation by temporally variable selection in a variety of organisms. For instance, evolutionary response to rapid changes in selection pressures has been demonstrated for morphological and life-history traits in mammals [@pgen.1004775-Gershenson1], [@pgen.1004775-Grant1], birds [@pgen.1004775-Tarwater1]--[@pgen.1004775-Wall1], plants [@pgen.1004775-Brakefield1], invertebrates [@pgen.1004775-Hairston1]--[@pgen.1004775-RodriguezTrelles1], and others (reviewed in [@pgen.1004775-Bell1], [@pgen.1004775-Siepielski1]). Chromosomal inversions and allozyme alleles in a variety of drosophilids vary among seasons [@pgen.1004775-Dobzhansky1]--[@pgen.1004775-Ananina1] suggesting that these polymorphisms confer differential fitness in alternating seasons. Further, in some species of drosophilids, life-history [@pgen.1004775-Bouletreaumerle1], [@pgen.1004775-Schmidt1], morphological [@pgen.1004775-Stalker1], [@pgen.1004775-Tantawy1] and stress tolerance traits [@pgen.1004775-Miyo1], [@pgen.1004775-Dev1] also fluctuate seasonally suggesting that these traits respond to seasonal shifts in selection pressures.
Although theoretical models suggest that temporal variation in selection pressures can maintain fitness-related genetic variation in populations [@pgen.1004775-Gillespie1]--[@pgen.1004775-Hedrick1] and empirical evidence from a variety of species [@pgen.1004775-Gershenson1]--[@pgen.1004775-Dev1] demonstrates that variation in selection pressures over short time periods does alter phenotypes and allele frequencies, we still lack a basic understanding of many fundamental questions about the genetics and evolutionary history of alleles that undergo rapid adaptation in response to temporal variation in selection pressures. Specifically, we do not know how many loci respond to temporally variable selection within a population, the strength of selection at each locus, nor the effects of such strong selection on neutral genetic differentiation through time. We do not know whether adaptation at loci that respond to temporally variable selection is predictable nor do we know the relationship between loci that respond to temporally variable selection and spatially varying selection. Finally, it is unclear whether rapid adaptation to temporally variable selection pressures is primarily fueled by young alleles that constantly enter the population but cannot be maintained for long periods of time or, rather, by old alleles that have possibly been maintained by variable selection associated with environmental heterogeneity despite short bursts of strong directional selection.
To address these questions, we estimated allele frequencies genome-wide from samples of *D. melanogaster* individuals collected along a broad latitudinal cline in North America and in the spring and fall over three consecutive years in a single temperate orchard. We demonstrate that samples of flies collected in a single Pennsylvania orchard over the course of several years are as differentiated as populations separated by 5--10° latitude. We identify hundreds of polymorphisms that are subject to strong, temporally varying selection and argue that genetic draft [@pgen.1004775-Gillespie3] in the wake of rapid, multilocus adaptation is sufficient to explain the high degree of genetic turnover that we observe in this population over several years. We examine the genome-wide relationship between spatial and temporal variation in allele frequencies and find that spatial genetic differentiation, but not clinality *per se*, in allele frequency is a good predictor of temporal variation in allele frequency. Moreover, at SNPs subject to seasonal fluctuations in selection pressures, northern populations are more similar to spring populations than southern ones are. Next, we show that allele frequencies at SNPs subject to seasonal fluctuations in selection pressures become more 'spring-like' (i.e., they move towards the average spring frequency) immediately following a hard frost event and that seasonally variably SNPs tend to be associated with two seasonally variable phenotypes, chill coma recovery time and starvation tolerance. Finally, we demonstrate that some of the loci that respond to temporal variation in selection pressures are likely ancient, balanced polymorphisms that predate the split of *D. melanogaster* from its sister species, *D. simulans*. Taken together, our results are consistent with a model in which temporally variable selection maintains fitness-related genetic variation at hundreds of loci throughout the genome for millions of generations if not millions of years.
Results/Discussion {#s2}
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Genomic differentiation through time and space {#s2a}
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To test for the genomic signatures of balancing selection caused by seasonal fluctuations in selection pressures, we performed whole genome, pooled resequencing of samples of male flies collected in the spring and fall over three consecutive years (2009--2011) in a temperate, Pennsylvanian orchard. We contrast changes in allele frequencies through time with estimates of allele frequencies we made from five additional populations spanning Florida to Maine along the east coast of North America over a number of years (2003--2010) largely during periods of peak abundance of *D. melanogaster* ([Fig. 1A](#pgen-1004775-g001){ref-type="fig"}, [Table S1](#pgen.1004775.s008){ref-type="supplementary-material"}). From each population and time point, we sampled approximately 50--100 flies and resequenced each sample to average read depth of 20--200× coverage ([Table S1](#pgen.1004775.s008){ref-type="supplementary-material"}, and see [Text S1](#pgen.1004775.s011){ref-type="supplementary-material"}). Estimates of allele frequency using this sampling design have been shown to be highly accurate [@pgen.1004775-Gillespie3].
![Experimental design and genomic turnover through time and space.\
(A) Map of sampling locations in North America used in this study. Grey boxes represent individual samples from each locale. Genome-wide differentiation among spatially (B) and temporally (C) separated samples, measured as genome-wide average *F~ST~* (y-axis). Lines represent the predicted value of *F~ST~* based on the linear (A; y = a+bx) and non-linear (B; y = ab^X^) regression. Note: Pennsylvanian samples are not represented in (B) and the negative *F~ST~* in (B) results from the conservative correction of heterozygosity [@pgen.1004775-Rashkovetsky1], [@pgen.1004775-Turelli1]. In addition, please note that there are four estimates of pairwise *F~ST~* between the two replicate Maine and Florida samples (corresponding to a difference in latitude of 20°) and that there are two estimates of *F~ST~* between each of the remaining clinal populations and each Maine and Florida replicate sample. Error bars represent 95% confidence intervals based on 500 blocked bootstrap samples of ∼2000 SNPs.](pgen.1004775.g001){#pgen-1004775-g001}
As a point of departure and to provide context for understanding the magnitude of genetic variation through the seasons, we first examined genetic differentiation along the cline ([Fig. 1B](#pgen-1004775-g001){ref-type="fig"}, [Fig. S1A](#pgen.1004775.s001){ref-type="supplementary-material"}). We calculated genome-wide average *F~ST~* among pairs of populations (excluding Pennsylvanian populations; hereafter 'spatial *F~ST~*') as well as the proportion of SNPs where average spatial *F~ST~* between a pair of populations is greater than expected by chance conditional on our sampling design and assuming panmixia using allele frequency estimates of 500,000 common polymorphisms ([Table S1](#pgen.1004775.s008){ref-type="supplementary-material"}). Genome-wide average spatial *F~ST~* ([Fig. 1B](#pgen-1004775-g001){ref-type="fig"}) as well as the proportion of SNPs where spatial *F~ST~* is greater than expected by chance ([Fig. S1A](#pgen.1004775.s001){ref-type="supplementary-material"}) is positively correlated with geographic distance (*r* = 0.75; *p* = 7e-5), a pattern consistent with isolation by distance [@pgen.1004775-Wright1]. Pooled resequencing did identify polymorphisms in or near genes previously shown to be clinal in North American populations (see [Text S1](#pgen.1004775.s011){ref-type="supplementary-material"}) demonstrating that clines are stable over multiple years. This suggests that populations sampled along the cline represent resident populations, and further confirms that our pooled resequencing design gives accurate estimates of allele frequencies [@pgen.1004775-Zhu1].
Next, we calculated genome-wide average *F~ST~* between samples collected through time in the Pennsylvanian population ('temporal *F~ST~*') as well as the proportion of SNPs where average temporal *F~ST~* is greater than expected by chance given our sampling design and assuming no allele frequency change through time ([Fig. 1C](#pgen-1004775-g001){ref-type="fig"}, [Fig. S1B](#pgen.1004775.s001){ref-type="supplementary-material"}). Genome-wide average temporal *F~ST~* ([Fig. 1C](#pgen-1004775-g001){ref-type="fig"}) as well as the proportion of SNPs where the observed temporal *F~ST~* is greater than expected by chance ([Fig. S1B](#pgen.1004775.s001){ref-type="supplementary-material"}) increases with the difference in time between samples. The temporal *F~ST~* increases non-linearly with duration of time between samples (*slope* ~log-log~ = 0.59, *p* ~log-log\ slope = 1~ = 0.0004, *df* = 19). Genome-wide average temporal *F~ST~* appears to asymptote by ∼7 months, corresponding to the duration of time between fall samples and the subsequent spring sample. Remarkably, samples of the Pennsylvanian population collected one to three years apart are as differentiated as populations separated by 5--10° latitude, demonstrating high genetic turnover through time.
Identification and genomic features of seasonal SNPs {#s2b}
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We sought to identify alleles whose frequency consistently and repeatedly oscillated between spring and fall over three years with the assumption that these polymorphisms would be the most likely to be adaptively responding to selection pressures that oscillate between the seasons. We identified seasonally variable polymorphisms that had a large and recurrent deviation from spring to fall around the average frequency using a generalized linear model (GLM) of allele frequency change as a function of season (spring or fall) that took into account read depth and the number of sampled chromosomes (see [Materials and Methods](#s3){ref-type="sec"} for details).
Of the ∼500,000 common SNPs tested, we identified approximately 1750 sites that cycle approximately 20% in frequency between spring and fall at FDR less than 0.3 (hereafter 'seasonal SNPs'; [Fig. 2A](#pgen-1004775-g002){ref-type="fig"}, [Fig. S2A](#pgen.1004775.s002){ref-type="supplementary-material"}). Statistically significant changes in allele frequency of this magnitude at seasonal SNPs correspond to selection coefficients of 5--50% per locus per generation ([Fig. 2B](#pgen-1004775-g002){ref-type="fig"}, see [Materials and Methods](#s3){ref-type="sec"}), assuming 10 generations per summer or 1--2 generations per winter. Given the statistical power of our experiment ([Fig. 2B](#pgen-1004775-g002){ref-type="fig"}), we estimate there may be as many as 10 times as many sites that could cycle either directly in response to seasonally varying selection or could be linked to seasonal SNPs.
{ref-type="sec"} for the definition of *S*. (C) Enrichment (log~2~ odds ratio) of seasonal SNPs that are annotated for each class of genetic element relative to control polymorphisms. (D) Seasonal *F~ST~* surrounding seasonal SNPs decays to background levels by ∼500 bp. (E) Allele frequency estimates at seasonal SNPs outside any large, cosmopolitan inversion (non-inv) or within the cosmopolitian inversions (diamonds) during the spring (blue) or fall (red). Allele frequency estimates at SNPs perfectly linked to the inversion during the spring and fall are denoted by circles. Error bars (C) and confidence bands (D) represent 95% confidence intervals based on blocked bootstrap resampling.](pgen.1004775.g002){#pgen-1004775-g002}
Our rationale for focusing on the1750 seasonal SNPs at the FDR of 0.3 is that we are seeking to assess general molecular and evolutionary features of polymorphisms that may underlie rapid adaptive evolution in response to seasonal fluctuations in selection pressure. To assess these general features and enrichments, we require a sufficient number of true positive SNPs while maintaining as low a false positive rate as possible. Reducing FDR rates to lower values yielded an insufficient number of polymorphisms to assess enrichments with adequate precision (FDR of 10% yields 11 SNPs; FDR cutoff of 20% yields 200 SNPs).
We note that our estimation of ∼1750 seasonal SNPs and their associated FDR should only be taken as a rough estimate of the number of seasonally varying SNPs: variance in linkage disequilibrium through the genome, heterscedasticity due to possible demographic events, limited statistical, unbalanced sampling of flies and variance in read-depth among samples, and modeling assumptions will affect our ability to infer the exact number of seasonally varying SNPs. One way to address some of these issues (e.g., heteroscedasticity) is to model allele frequency change through time with generalized linear mixed-effect (GLMM) or general estimation equation (GEE) models that account, to varying degrees, for the structured, time-series nature of our data. Seasonal SNPs inferred with these models are highly congruent with seasonal SNPs inferred using a simple GLM ([Fig. S2D,E](#pgen.1004775.s002){ref-type="supplementary-material"}) and *q-q* plots of the distribution of *p*-values from GLM, GLMM and GEE models suggest that GLM and GLMM modeling strategies fit the bulk of the genome well, with GEE models appearing to be anti-conservative ([Fig. S2B,C](#pgen.1004775.s002){ref-type="supplementary-material"}). However, the identification of a statistical excess of seasonally oscillating SNPs by any modeling strategy will be subject to a number of assumptions that will almost certainly be violated in some way or another and such violations could possibly lead to an increased false-positive rate.
Because the false positive and false negative rates are inherently difficult to estimate, we adopt an empirical strategy to demonstrate that the seasonal SNPs identified though a simple GLM are not a random sample of SNPs but rather are enriched for true positive SNPs that directly underlie the adaptive response to seasonal fluctuations selection pressure. The identified seasonal SNPs are enriched for many signatures consistent with natural selection relative to control SNPs that are matched for several biologically and experimentally relevant parameters such as chromosome, recombination rate, allele frequency, and SNP quality coupled with a rigorous blocked-bootstrap procedure that accounts for the spatial distribution of seasonal SNPs along the chromosome (see [Materials and Methods](#s3){ref-type="sec"} and [Table S3](#pgen.1004775.s010){ref-type="supplementary-material"}). We now proceed to demonstrate these enrichments.
Seasonal SNPs are enriched among functional genetic elements. These polymorphisms are likely to be in genic (i.e., 3′ and 5′ UTR, synonymous and non-synonymous, and long-intron SNPs; *p* = 0.054) and coding regions (synonymous and non-synonymous; *p*\<0.002) and are enriched among synonymous (*p*\<0.002), non-synonymous (*p* = 0.002) and 3′ UTR (*p* = 0.024, [Fig. 2C](#pgen-1004775-g002){ref-type="fig"}) relative to control, putatively neutral polymorphisms in short-introns [@pgen.1004775-Lawrie1]. The *p*-values of the enrichment tests were calculated after controlling for the spatial distribution of seasonal SNPs along the chromosome using a block bootstrap procedure coupled with the identification of paired control SNPs matched for several key genomic features ([Table S3](#pgen.1004775.s010){ref-type="supplementary-material"}), such as recombination rate, average allele frequency in the Pennsylvanian orchard, chromosome, and SNP quality (see 'Block Bootstrap' section in [Materials and Methods](#s3){ref-type="sec"}). Enrichment of adaptively oscillating polymorphisms among these genetic elements, including synonymous sites, suggests that these SNPs may affect organismal form and function through modification of protein function, translation rates, or mRNA expression and stability [@pgen.1004775-Lawrie1], [@pgen.1004775-Pechmann1].
Next, we show that rapid shifts in allele frequency at seasonal SNPs perturb allele frequencies at nearby SNPs. Adaptively oscillating polymorphisms are in regions of elevated temporal *F~ST~* ([Fig. 2D](#pgen-1004775-g002){ref-type="fig"}) and the elevation of temporal *F~ST~* decays, on average, by ∼500 bp, consistent with patterns of linkage disequilibrium in *D. melanogaster* [@pgen.1004775-Mackay1]. Elevation of temporal *F~ST~* within 500 bp of seasonal SNPs could contribute to high levels of genome-wide average *F~ST~* through time ([Fig. 1C](#pgen-1004775-g001){ref-type="fig"}). However, excluding SNPs within 500 bp of seasonal SNPs did not change patterns of genome-wide differentiation through time suggesting that genome-wide patterns of *F~ST~* through time are not driven by the seasonal SNPs themselves nor the SNPs in their immediate vicinity ([Fig. S3](#pgen.1004775.s003){ref-type="supplementary-material"}).
Seasonal SNPs are spread throughout the genome ([Fig. 3A](#pgen-1004775-g003){ref-type="fig"}) and there is a 95% chance of finding at least one seasonal SNP per megabase of the euchromatic genome. This result suggests that seasonal SNPs are not exclusively concentrated in any single region (such as an inversion) nor distributed among a small number of regions (such as a limited number of genes). Although seasonal SNPs are distributed throughout the genome, their distribution is over-dispersed. To assess this, we calculated the number of seasonal SNPs per 1000 SNPs under investigation in non-overlapping windows of 1000 SNPs. If seasonal SNPs are homogeneously distributed throughout the genome, the rate of seasonal SNPs/1000 SNPs should follow a Poisson distribution with mean equal to the variance. After accounting for heterogeneity in recombination rate throughout the genome (see [Materials and Methods](#s3){ref-type="sec"}), we find that the variance in the rate of seasonal SNPs is ∼2.3 times greater than expected under a Poisson distribution (*p*\<10^−10^) implying that some regions have an excess of seasonal SNPs and some have a deficit of seasonal SNPs. The overdispersion of seasonal SNPs throughout the genome could be caused by several factors including variation in the density of functional elements, multiple functional and clustered seasonal SNPs, variance in the age of seasonal SNPs, or inversion status.
{ref-type="supplementary-material"}). (B). Enrichment (log~2~ odds ratio) of seasonal SNPs with spatial *F~ST~* greater than or equal to value on *x*-axis relative to control SNPs. (C) Enrichment (log~2~ odds ratio) of seasonal SNPs with --log~10~(spatial q-value) greater than or equal to value on *x*-axis relative to control SNPs. (D) Absolute difference between average spring (blue) and fall (red) frequencies in the Pennsylvanian population and frequency estimates along the cline. Confidence bands represent 95% confidence intervals based on blocked bootstrap resampling.](pgen.1004775.g003){#pgen-1004775-g003}
In general, we find no evidence that seasonal SNPs are enriched among large, cosmopolitan inversions segregating in North American populations (*p*\>0.05, [Fig. S4](#pgen.1004775.s004){ref-type="supplementary-material"}), with only one inversion, *In3R(Mo)*, marginally enriched for seasonal SNPs (*p* = 0.02, with *p* = 0.18 after Bonferroni correction for multiple testing). In addition, seasonal SNPs are significantly more common in the Pennsylvanian orchard population than polymorphisms perfectly linked [@pgen.1004775-Kapun1] to large cosmopolitan inversions ([Fig. 2E](#pgen-1004775-g002){ref-type="fig"}) and polymorphisms linked to inversions do not vary between seasons ([Fig. 2E](#pgen-1004775-g002){ref-type="fig"}, *p*\>0.05), including those linked to *In3R(Mo)*. Therefore, enrichment of seasonal SNPs within *In3R(Mo)*, if present, is most likely due to increased linkage disequilibrium caused by decreased recombination surrounding this inversion [@pgen.1004775-CorbettDetig1]. Taken together, these results indicate that the inversions themselves do not cycle seasonally in the Pennsylvanian population in any appreciable manner ([Fig. 2E](#pgen-1004775-g002){ref-type="fig"}) and suggests that adaptive evolution to seasonal variation in selection pressures may be highly polygenic.
Relationship between spatial and temporal variation in allele frequencies {#s2c}
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To test the hypothesis that spatially varying selection pressures along the latitudinal cline reflect seasonally varying selection pressures in the Pennsylvanian population, we examined the relationship between temporal and spatial variation in allele frequencies. To quantify spatial variation in allele frequency, we calculated two statistics. First, we estimated average pairwise *F~ST~* among all populations for each SNP ('spatial *F~ST~*'). Second, we estimated clinality for each SNP by calculating the per-SNP false discovery rate (FDR) of the relationship between allele frequency and latitude using a generalized linear model that takes into account read depth and the number of sampled chromosomes (hereafter 'clinal *q*-value'). Spatial *F~ST~* and clinal *q*-value are highly correlated (*r* = 0.63, *p*\<1e-10; [Fig. S5](#pgen.1004775.s005){ref-type="supplementary-material"}) demonstrating that most, but not all, spatial variation along the latitudinal cline is represented by monotonic changes in allele frequency between northern and southern populations.
We calculated the number of clinally varying polymorphisms (clinal *q*-value\<0.1) and the number of adaptively oscillating polymorphisms per common segregating SNP (average, North American MAF\>0.15) per megabase of the genome ([Fig. 3A](#pgen-1004775-g003){ref-type="fig"}). Approximately one out of every three common polymorphisms varies with latitude with FDR\<0.1 (i.e., clinal *q*-value\<0.1) whereas only one out of every three thousand polymorphisms varies predictably between seasons with seasonal FDR\<0.3 ([Fig. 3A](#pgen-1004775-g003){ref-type="fig"}). Although our ability to detect clinal SNPs at FDR\<0.1 is greater than our ability to detect seasonal SNPs at FDR\<0.3 (cf. [Fig. 2B](#pgen-1004775-g002){ref-type="fig"}, [Fig. S6](#pgen.1004775.s006){ref-type="supplementary-material"}), differences in power cannot explain the three order of magnitude difference in the number of detected clinal and seasonal SNPs (cf. [Fig. 2B](#pgen-1004775-g002){ref-type="fig"}, [Fig. S6](#pgen.1004775.s006){ref-type="supplementary-material"}).
Next, we formally tested whether seasonal SNPs are enriched among spatially varying SNPs. Spatially varying SNPs, as defined by spatial *F~ST~*, are more likely to be seasonal SNPs than expected by chance ([Fig. 3B](#pgen-1004775-g003){ref-type="fig"}), and the odds of this enrichment increases with increasing spatial differentiation. In contrast, we cannot reject the null hypothesis of no enrichment of seasonal SNPs among clinal SNPs as defined by clinal *q*-value ([Fig. 3C](#pgen-1004775-g003){ref-type="fig"}).
The observed differences in the enrichment of seasonal SNPs among SNPs with high spatial *F~ST~* and low clinal *q*-value may reflect aspects of our sampling design and differences in the evolutionary forces that shape allele frequencies through time and space. We sampled flies along the East Coast during different years and at different points of time relative to the progression of the growing season in each population ([Table S1](#pgen.1004775.s008){ref-type="supplementary-material"}). Thus, in each sampled clinal population, seasonal SNPs would be at different points in their adaptive trajectory. Consequently, seasonal SNPs would not likely have exceedingly low clinal *q*-values, a statistic which reflects the deviation of observed allele frequencies from the predicted value as estimated by a GLM. Rather, seasonal SNPs would likely be highly differentiated along the cline (i.e., have a large spatial *F~ST~*). SNPs with low clinal *q*-values, therefore, represent those SNPs that do not change in frequency between seasons and possibly reflect long-term demographic processes or adaptation to selection pressures that vary clinally, but not seasonally.
Because of the relationship between spatial differentiation and seasonal variation in allele frequencies ([Fig. 3B](#pgen-1004775-g003){ref-type="fig"}) and because of parallels between spatial and seasonal variation in climate, we hypothesized that northern populations should be more 'spring-like' and southern populations should be more 'fall-like' in allele frequencies at the seasonal SNPs. To test this hypothesis, we calculated the absolute difference in allele frequencies for each population sampled along the cline with the average spring and fall allele frequency estimates for the Pennsylvanian population for all seasonal SNPs. Indeed, allele frequency estimates at seasonal SNPs from high latitude populations are more similar to spring Pennsylvanian populations and those from low latitude are more similar to fall populations ([Fig. 3D](#pgen-1004775-g003){ref-type="fig"}) demonstrating that latitudinally varying selection pressures at least partially reflect seasonally varying selection pressures.
Immediate adaptive response to an acute frost event {#s2d}
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In the late fall of 2011, about two weeks after our 2011 fall sample was collected, a hard frost occurred in the Pennsylvanian orchard ([Fig. 4A](#pgen-1004775-g004){ref-type="fig"}). We were able to obtain a sample of *D. melanogaster* approximately one week after the frost and we estimated allele frequencies genome-wide from this sample. We hypothesized that allele frequencies at seasonal SNPs would predictably change following the frost event and would become more 'spring-like.' To test this hypothesis, we calculated the probability that post-frost allele frequencies at seasonal SNPs overshoot the long-term average allele frequency (i.e., become more 'spring-like'). We also estimated this probability for control polymorphisms, matched to adaptively oscillating polymorphisms by several characteristics ([Table S3](#pgen.1004775.s010){ref-type="supplementary-material"}) including, importantly, difference in allele frequency between the long-term average and the pre-frost allele frequency. This later control is essential given that some shift in the 'spring-like' direction is expected here simply by chance due to regression to the mean. The probability that seasonal SNPs overshoot the long-term average allele frequency is ∼43%, whereas only ∼35% of control polymorphisms overshoot the long-term average. This significant excess of adaptively oscillating polymorphisms that become more 'spring-like' following the frost event ([Fig. 4B](#pgen-1004775-g004){ref-type="fig"}; log~2~(OR) = 0.48, *p*\<0.002) suggests that these SNPs respond to acute changes in climate and that cold temperatures associated with winter is one selective force acting on this population shaping allele frequencies between seasons.
{#pgen-1004775-g004}
Association with seasonally variable phenotypes {#s2e}
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Chill-coma recovery time and starvation tolerance are two phenotypes that vary seasonally in drosophilid populations [@pgen.1004775-Gibert1]--[@pgen.1004775-Sisodia1]. Accordingly, we hypothesized that the winter-favored allele at seasonal SNPs would be associated with decreased chill-coma recovery time and increased starvation tolerance. To test this hypothesis, we used allele frequency data from previously published tail-based mapping of chill-coma recovery time and starvation tolerance [@pgen.1004775-Huang1]. We show that the winter favored allele at seasonal SNPs is more likely to be associated with fast chill coma recovery time than expected by chance across a range of GWAS *p*-values ([Fig. 5A](#pgen-1004775-g005){ref-type="fig"}). A similar analysis of starvation tolerance was equivocal but the general pattern is that the winter-adaptive allele is associated with increased starvation tolerance ([Fig. 5B](#pgen-1004775-g005){ref-type="fig"}).
{#pgen-1004775-g005}
Long-term balancing selection {#s2f}
-----------------------------
Balancing selection caused by variation in selection pressures through time can in principle maintain allelic variation at adaptively oscillating loci and elevate levels of neutral diversity surrounding these balanced polymorphisms. Thus, if seasonal variation in selection pressures promotes balanced polymorphisms we hypothesized that seasonal SNPs would be old and present in regions of elevated polymorphism.
We tested the hypothesis that seasonal SNPs are old by first examining their allele frequencies in a broad survey of African *D. melanogaster* populations [@pgen.1004775-Pool1]. Approximately 5% of seasonal SNPs are rare in Africa (MAF\<0.01), however these SNPs are not more likely to be rare in Africa than control polymorphisms (log~2~(odds ratio) = 0.96; *p* = 0.328). Interestingly, for seasonal SNPs where one allele is rare in Africa, the summer favored alleles are more likely to be rare in Africa than winter favored alleles (log~2~(odds ratio) = 0.475; *p* = 0.018). Because the vast majority of seasonal SNPs segregate in Africa, it appears that adaptation to temperate environments, and particularly winter conditions, relies primarily on old, standing genetic variation.
Balancing selection acts to maintain alleles at intermediate frequencies for long periods of time and, in some instances, can maintain polymorphism across species boundaries [@pgen.1004775-Klein1], [@pgen.1004775-Leffler1]. We examined whether seasonal SNPs showed signatures of long-term balancing selection by examining patterns of polymorphism surrounding orthologous regions in *D. simulans*, the sister species to *D. melanogaster*. We note that the following analyses are conservative because we underestimate *D. simulans* diversity given the small number (\<6) of *D. simulans* haplotypes used.
First, we demonstrate that seasonal SNPs are approximately 1.5 times more likely to be polymorphic and share the same two alleles identical by state in both species relative to control SNPs. This pattern is observed for all seasonal SNPs ([Fig. 6](#pgen-1004775-g006){ref-type="fig"}, *p*\<0.002) and for seasonal SNPs residing in genes ([Fig. 6](#pgen-1004775-g006){ref-type="fig"}, *p*\<0.002). The increased probability of shared polymorphism between *D. melanogaster* and *D. simulans* at seasonal SNPs could, in principle, be driven by an over-representation of synonymous, genic SNPs ([Fig. 2C](#pgen-1004775-g002){ref-type="fig"}). Unless synonymous SNPs are in four-fold degenerate positions, certain mutations may cause them to be non-synonymous thereby limiting the number of possible neutral allelic states and increasing the probability of shared polymorphism between species. However, adaptively oscillating SNPs that do not reside in synonymous sites are also more likely than expected by chance to be polymorphic and share the same two alleles by state in *D. melanogaster* and *D. simulans* ([Fig. 6](#pgen-1004775-g006){ref-type="fig"}, *p* = 0.014).
{#pgen-1004775-g006}
The co-occurrence of shared polymorphism between *D. melanogaster* and *D. simulans* could result from three evolutionary mechanisms. First, trans-specific polymorphisms could result from adaptive introgression. This scenario seems implausible given the high degree of pre- and post-zygotic isolating mechanisms between these two species [@pgen.1004775-Welbergen1], [@pgen.1004775-Sturtevant1]. Furthermore, if trans-specific polymorphisms resulted from recent adaptive introgression we would expect average pairwise divergence between *D. melanogaster* and *D. simulans* surrounding seasonal SNPs to be smaller than at control SNPs. However, there is no significant difference in estimates of divergence between seasonal and control SNPs (*p* = 0.7 for windows ±250 bp). Second, trans-specific polymorphisms could result from convergent adaptive evolution. Finally, trans-specific polymorphisms could be millions of years old [@pgen.1004775-Tamura1], predating the divergence of *D. melanogaster* from *D. simulans*. While we cannot differentiate these latter two mechanisms, we postulate that the most parsimonious explanation is that trans-specific seasonal SNPs predate the divergence of these two sister species.
Seasonally variable selection is required to generate genome-wide patterns of allele frequency change through time {#s2g}
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Despite empirical support for the conclusion that seasonal SNPs show many signatures consistent with adaptive response to seasonally variable selection, drift, caused by cyclic population booms and busts, or migration from neighboring demes are alternative mechanisms that could drastically perturb allele frequencies in the Pennsylvanian population and could generate some of the genome-wide patterns we observe. We address these possibilities here and conclude that neither cyclic changes in population size nor seasonal migration can plausibly explain the extent of genome-wide genetic differentiation through time, the observed number of seasonal SNPs, nor the enrichment of seasonal SNPs among many distinct genomic features (e.g., [Figs. 2](#pgen-1004775-g002){ref-type="fig"}--[6](#pgen-1004775-g006){ref-type="fig"}). At the same time, we also show through several simulation approaches that rapid adaptive evolution in response to seasonal fluctuations in selection pressure is sufficient to explain patterns of allele frequency change through time. Furthermore, we discuss how large-scale migration is internally inconsistent with certain aspects of our data. Taken together, we conclude that rapid adaptive evolution to seasonally variable selection is required to explain the patterns of allele frequency change through time at seasonal SNPs and at linked neutral loci that we observe in our dataset.
First, we assessed the possibility that extensive drift caused by population contraction every winter [@pgen.1004775-Knibb1], [@pgen.1004775-Band1], [@pgen.1004775-Ives1] could generate genome-wide patterns of genetic differentiation through time observed in our data. To do so, we conducted forward genetic simulations that model biologically plausible variation in population size and included loci that cycle in frequency due to variable selection pressures [@pgen.1004775-Messer1]. For these simulations, we modeled a 20 Mb chromosome with constant recombination rate of 2 cM/Mb, representing the genome-wide average recombination rate in *D. melanogaster* [@pgen.1004775-Comeron1]. We simulated population contraction to one of various minimum, 'overwintering' population sizes followed by exponential growth over 10 generations in the 'summer' to a fixed maximum population size. In these models, we included various numbers of loci that respond to seasonally varying selection. Selection coefficients for each locus were set such that allele frequencies at selected sites oscillated by ∼20%, between 60 and 40%, representing the average change in allele frequency we actually see between spring and fall at seasonal SNPs. Finally, we placed 500 neutral loci randomly along the simulated chromosome and measured *F~ST~* at these neutral loci between three 'spring' (i.e., first generation of population expansion) and 'fall' (last generation of population expansion) samples. See [Materials and Methods](#s3){ref-type="sec"} for more details these models.
In the absence of seasonal selection, these forward simulations suggest that overwintering *N~e~* would have to be exceedingly low (∼20; [Fig. 7A](#pgen-1004775-g007){ref-type="fig"}) to generate levels of *F~ST~* between spring and fall as high as we observe in our data (arrow in [Fig. 1C](#pgen-1004775-g001){ref-type="fig"}). However, with overwintering *N~e~* of 200 and 5--10 seasonally adaptive SNPs per chromosome arm, simulated *F~ST~* at neutral loci is on the order of 0.002 ([Fig. 7A](#pgen-1004775-g007){ref-type="fig"}), which we observe in our data (arrow in [Fig. 1C](#pgen-1004775-g001){ref-type="fig"}). While we do not know overwintering population size, we speculate it could be on the order of 200 flies or likely substantially larger [@pgen.1004775-Band1], [@pgen.1004775-Ives1] and conclude that at least 25--50 (5--10 per main chromosome arm) loci are sufficient to generate patterns of differentiation we observe through time. Note that increasing the overwintering population size requires concomitant increase in number of seasonally selected loci.
{#pgen-1004775-g007}
We regard overwintering population sizes of ∼20 flies to be inconsistent with certain aspects of our data and also implausible given what we know about the biology of the species. First, such a severe population contraction would result in reduction of genetic diversity, particularly for low frequency alleles. However, the observed allele frequency spectrum between fall and the following spring samples is similar and spring samples do not exhibit the expected loss of low frequency polymorphisms that would result from a population contraction to 20 individuals ([Fig. S7](#pgen.1004775.s007){ref-type="supplementary-material"}). Second, population contraction to 20 individuals would often lead to population extirpation in the Pennsylvanian orchard and would certainly lead to extirpation at localities further north that experience more severe winters. However, *D. melanogaster* are routinely collected in Northern orchards very early in the season [@pgen.1004775-Schmidt3] and are routinely found in populations at as far north as 45° (Schmidt pers. obs). Furthermore, certain rare alleles have persisted in northern *D. melanogaster* populations for upwards of 30 years [@pgen.1004775-Ives2] cf. [@pgen.1004775-Coyne1] and allele frequency clines are relatively stable over decadal scales [@pgen.1004775-Umina1] demonstrating that high latitude populations are not frequently extirpated and that overwintering bottlenecks cannot be so severe as our neutral simulations would require.
In our forward simulations, seasonally variable selection is sufficient to generate high levels of genome-wide genetic differentiation through time. In addition, our forward simulations are consistent with the increase of genome-wide average *F~ST~* through time excluding polymorphisms that are within 500 bp of seasonal SNPs ([Fig. S3](#pgen.1004775.s003){ref-type="supplementary-material"}). In our simulations, 500 neutral loci were placed randomly along a 20 Mb chromosome and were initially completely unlinked to selected loci. Therefore, the high levels of simulated *F~ST~* are a consequence of genetic draft acting over long physical distances with low to moderate linkage disequilibrium between neutral and selected polymorphisms. Our observation that genome-wide average *F~ST~* (excluding polymorphisms near seasonal SNPs, [Fig. S3](#pgen.1004775.s003){ref-type="supplementary-material"}) increases with time resembles our simulations suggesting that draft can perturb allele frequencies over long genetic distances.
We also note that long-range genetic draft, caused by rapid frequency shifts of ancient balanced alleles to seasonally variable selection would likely cause an asymptotic change in genome-wide temporal *F~ST~*, whereas a purely drift-based model would likely cause a linear increase in genome-wide *F~ST~* through time. Seasonal SNPs tend to be old and are therefore likely found on a diverse array of haplotypes. Therefore, the exact composition of haplotypes that rise and fall every seasonal cycle will be somewhat stochastic giving rise to a high genome-wide *F~ST~* over a duration of time less than ∼7 months (the duration of time between fall and the following spring). Among years, genome-wide average *F~ST~* would possibly plateau if local *N~e~* were large (as we suspect it is, see [Results and Discussion](#s2){ref-type="sec"}: The plausibility...), coupled with the effects of recombination, gene conversion, and low-level migration from neighboring demes or populations. Finally, we note that because seasonal SNPs likely exist on a diverse array of haplotypes we do not expect genome-wide average *F~ST~* to oscillate with a period corresponding to approximately 6--7 months. For such oscillations to occur, a large (i.e., much larger than we identify) number of loci would have to be repeatedly shifting between seasons.
Next, we explore the possibility that migration could drastically alter allele frequencies in the Pennsylvanian population and generate the large number of loci that vary repeatedly among seasons. First, we examined a simple but general demographic model where the Pennsylvanian orchard population becomes extirpated every year and recolonized from a refugium such as a southern population or a large, local site such as a compost pile. Either situation is plausible given the purportedly high rates of migration in North American *D. melanogaster* populations [@pgen.1004775-Coyne1], [@pgen.1004775-Berry1] and what little is known about the overwintering biology of high latitude *D. melanogaster* [@pgen.1004775-Ives2]. In our model, we envisioned a resident, refugial population with stable allele frequencies across years that colonizes the orchard population. In this model, the orchard would be colonized early in the season with a random subsample of flies from the refugium and would therefore have aberrant allele frequencies. As more migrants arrived to the orchard from the refugium, allele frequencies at the orchard would stabilize to that of the source population. In such a scenario, allele frequencies in spring samples could vary considerably and a small fraction of SNPs might, by chance, have the same aberrant allele frequencies year after year and would appear to cycle seasonally.
We calculated the expected number of SNPs that would cycle by chance alone as a function of the number of initial migrants ([Fig. 7B](#pgen-1004775-g007){ref-type="fig"}). For instance, if five migrants arrived at the orchard prior to our spring sample every year, approximately 1300 SNPs would cycle seasonally producing similar patterns to the observed change in allele frequency through time as at 'seasonal SNPs' ([Fig. 2A](#pgen-1004775-g002){ref-type="fig"}). However, if four migrants arrived at the orchard prior to our sampling, ∼2600 SNPs would vary repeatedly but if six migrants arrived, only ∼700 would. Although the expected number of sites that oscillate under this migration model with 5 migrants is approximately the number we observe, we note that the expected number is highly dependent on the exact number of migrants. It seems unlikely that exactly five flies would migrate from the refugium to the orchard before our first spring sample three times in a row. Therefore, the extreme sensitivity of the expected number of sites to the number of migrants makes this general demographic scenario implausible. We are therefore led to conclude that the simple migration model presented here is likely to be insufficient to explain changes in allele frequency through time in the Pennsylvanian orchard.
In addition to our conclusion that a simple model of recolonization of the orchard is insufficient to explain the number of seasonally variable loci we observe, our data are also inconsistent with large-scale migrations from adjacent populations. For instance, if a large-scale migration from the South to resident northern populations were to occur, we would expect that clinally varying SNPs should also vary seasonally. Such a pattern would be expected both if a large-scale migration occurred randomly or were genotype dependent. However, seasonal SNPs are apparently not enriched among clinally varying polymorphisms ([Fig. 3C](#pgen-1004775-g003){ref-type="fig"}). A similar logic would apply for an early season migration from the North followed by a subsequent, late season migration from the South. We also note that this dual migration model is biologically implausible. The relationship between latitude and the onset of spring would suggest that far northern populations would be quite small in the early part of the growing season and the subsequent probability of emigration to southern locales would be low. Therefore, we conclude that large-scale migration does not play a major role shaping seasonal variation in allele frequencies in the Pennsylvanian orchard. Furthermore, even if seasonal SNPs were enriched among clinally varying polymorphisms (which they do not appear to be), adaptation to seasonally variable selection would need to be invoked in order to explain the yearly shift in allele frequencies every winter.
Taken together, the models presented here demonstrate that seasonal boom-bust or migration-based scenarios are insufficient to explain allele frequency change through time in the Pennsylvanian population. While temperate populations of *D. melanogaster* clearly undergo cyclic population booms and busts due to changes in climate associated with the season, the extent of these population contractions necessary to generate the patterns of genetic variation through time that we observe would be too extreme to allow for stable population persistence. Similarly, the Pennsylvanian population certainly exists as a part of a complex metapopulation and experiences immigration and emigration. However, analysis of a simple demographic model of population recolonization during the spring is also insufficient to explain the patterns of allele frequency change through time that we observe and our data are internally inconsistent with a model of large-scale migration from neighboring populations.
Finally, we point out that the boom-bust and recolonization models we presented here undoubtedly are oversimplifications and that there are other, more complex demographic models that we have not explored. Nonetheless, any stochastic demographic event would affect SNPs throughout the genome with equal probability. Many aspects of our data clearly show that seasonal SNPs are not a random set of common SNPs but rather show signatures consistent with both functional effect and long-term balancing selection such as enrichment in specific classes of genetic elements, association with seasonally variable phenotypes and predictable and virtually instantaneous shifts in allele frequency in response to frost. Therefore, while we cannot conclusively rule out the possibility that demographic events affect the temporal dynamics of allele frequencies at seasonal- and non-seasonal SNPs in the Pennsylvanian population, these demographic events are most likely coupled with adaptive evolution in response to temporally varying selection pressures.
The plausibility of seasonally variable selection {#s2h}
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We have previously argued that adaptive response to seasonally fluctuating selection at no less than 25--50 loci is necessary to generate the high levels of genome-wide genetic differentiation through time observed in the Pennsylvanian population. Next, we considered the plausibility of such strong selection and estimated the upper bound of the number of loci that could independently respond to seasonally variable selection. To do so, we modeled independent selection at 1--10,000 simulated seasonal SNPs whose allele frequency change was drawn from the observed allele frequency change at seasonal SNPs. Using a simple Poisson model (see [Materials and Methods](#s3){ref-type="sec"}), we estimated the minimum fall census size required for that number of loci to shift in allele frequency during one or two rounds of truncation selection. Using these models, we sought to estimate the most likely number of seasonal SNPs that could independently respond to seasonally variable selection by contrasting model-based estimates of population size with our best estimates of population size in the field.
Although fall census size of *D. melanogaster* in the focal Pennsylvanian population is unknown, some estimates of drosophilid population size have been made. Global population size of *D. melanogaster* is likely to be extremely large, greater than 10^8^ [@pgen.1004775-Karasov1]. However, estimates of local population size made from mark-release-recapture methods report census sizes on the order of 10^4^ to 10^5^ [@pgen.1004775-Mckenzie1]--[@pgen.1004775-Powell1]), with considerable variation among seasons, years and locales. *D. melanogaster* samples from orchards and vineyards often exceed 10^4^ flies [@pgen.1004775-Gravot1], [@pgen.1004775-Bastide1] and thousands of flies can easily be collected over large compost piles (Bergland pers. obs.). Therefore, we speculate that census size of temperate *D. melanogaster* populations at any locale is a function of the local ecology (e.g., amount of windfall fruit, number and size of compost piles, humidity) and given the favorable conditions in the focal Pennsylvanian orchard (Schmidt pers. obs.), large census sizes of more than 10^5^ are conceivable. If fall census size in the Pennsylvanian population is on the order of 10^5^, our truncation selection model suggests that no more than several hundred (200--700, [Fig. 7C](#pgen-1004775-g007){ref-type="fig"}) seasonal SNPs could respond to seasonally varying selection independently. We note that increasing the number of generations of winter-like selection pressures or the fall census size would lead to a concomitant increase in the number of seasonally selected loci that could independently respond to seasonally varying selection pressures.
Our survey of temporal changes in allele frequency identified 1750 seasonal SNPs that cycle significantly by ∼20% between seasons at FDR of 0.3. Unless local census size in the Pennsylvanian population were unrealistically large -- on the order of 10^10^ or 10^20^ -- it is unlikely that all of these loci respond to selection independently. Our model suggests, however, that a large fraction, on the order of 200--700 could vary independently in every cycle. One explanation for cycling in the remaining SNPs is linkage with loci responding to seasonally variable selection. It is possible that this linkage is generated either stochastically and neutrally or, alternatively, by selective processes such as assortative mating [@pgen.1004775-Kirkpatrick1] or epistatic selection [@pgen.1004775-Lewontin1], [@pgen.1004775-Giesel1]. For instance, if winter adapted flies were more likely to mate with other winter adapted flies during the summer, winter adapted alleles may become coupled and linkage disequilibrium between these alleles could increase. Similarly, certain forms of epistatic interactions could also generate linkage disequilibrium between seasonal SNPs if, for instance, couplings of winter and summer favored alleles at multiple loci were particularly deleterious relative to winter-winter or summer-summer combinations. The net effect of selective mechanisms that promote positive linkage disequilibrium between seasonal SNPs is that the effective number of 'independently' seasonally selected loci decreases. If seasonal SNPs are in linkage disequilibrium due to selective processes, it would imply that more than 200--700 seasonal SNPs contribute to organismal form and function and modify fitness during the summer and winter.
Conclusions -- Summary {#s2i}
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Herein, we present results from population based resequencing of samples of flies collected along a latitudinal cline in North America and over three years during the spring and fall in a Pennsylvanian orchard. We identify repeatable and dramatic changes in allele frequencies through time at hundreds of polymorphisms spread throughout the genome. Response to strong selection at these seasonal SNPs likely drives genetic differentiation through time at linked, neutral polymorphisms. This process leads to genome-wide differentiation between samples collected several years apart comparable to populations separated by 5--10° latitude. Seasonal SNPs are likely to be functional as they show enrichment at functional sites, vary predictably among populations sampled along the cline, respond immediately to a hard frost event, and are associated with phenotypes previously shown to vary seasonally in temperate *D. melanogaster* populations. Finally, our results suggest that some adaptively oscillating SNPs are possibly millions of years old, predating the split of *D. melanogaster* from its sister species *D. simulans*. Taken together, our results provide the first genomic picture of balancing selection caused by temporal fluctuations in selection pressures and provide novel insight into the biology of marginal overdominance.
Conclusions -- Functional properties of adaptively oscillating polymorphisms {#s2j}
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Temperate populations of *D. melanogaster* are exposed to high levels of environmental heterogeneity among seasons due to changes in various aspects of the environment including temperature, humidity, and nutritional quality and quantity. These shifts in the environment are primary determinants of cyclic population booms and busts [@pgen.1004775-Ives2], [@pgen.1004775-Mckenzie1], [@pgen.1004775-McInnis1] and impose strong temporally and spatially variable selection. Intuition, theoretical models [@pgen.1004775-Lewontin2], laboratory experimentation [@pgen.1004775-Schmidt1], and inference from patterns of clinal variation [@pgen.1004775-Schmidt4]--[@pgen.1004775-Arthur1] and seasonal variation in morphological, behavioral and life-history traits suggest that alternate seasons favor differing life-history strategies. In general, populations exposed to more harsh conditions such as those from Northern locales or those collected early in the season are larger [@pgen.1004775-James1], [@pgen.1004775-Robinson1], more stress tolerant [@pgen.1004775-Karan1]--[@pgen.1004775-Parkash1], [@pgen.1004775-Arthur1], longer lived [@pgen.1004775-Schmidt5], and are less fecund [@pgen.1004775-Schmidt5], [@pgen.1004775-Lazzaro1] than those collected in Southern locales or during the fall. The general picture that emerges, therefore, is that in temperate populations winter conditions select for hardier but less fecund individuals whereas summer selects for high reproductive output at the cost of somatic maintenance. Nonetheless, there is surprisingly little evidence directly linking adaptive differentiation between seasonally favored genetic polymorphisms, phenotypes and environmental perturbations (but see [@pgen.1004775-Schmidt1]). Herein we present several key results that link seasonal and spatial patterns of genotypic and phenotypic variation with environmental perturbations.
First, our data suggest that that acute bouts of cold temperature elicit adaptive response at seasonally oscillating polymorphisms ([Fig. 4](#pgen-1004775-g004){ref-type="fig"}). Heretofore, the specific environmental factors altering allele frequencies through time and space among dipteran species has generally remained elusive largely stemming from the fact that many aspects of the environment co-vary over temporal and spatial scales. Here we show that acute exposure to sub-freezing temperatures in the field shifts allele frequencies in a spring like direction at seasonal SNPs but not at control polymorphisms, thereby suggesting that sharp modulation of temperature can act as a selective force in the field. While post-frost allele frequencies at seasonal SNPs move in a 'spring-like' direction, they do not reach average spring allele frequencies. This suggests that multiple frost events, long-term exposure to cold temperatures or other selective factors linked to winter conditions such as starvation also impose strong selection in temperate populations.
Next, we demonstrate that environmental differences among populations predict, to a certain extent, changes in allele frequency at seasonal SNPs. Environmental factors that vary over seasonal time scales also vary with latitude. This fact has facilitated studies that substitute space for time and has led to a paradigm in many aspects of contemporary research in drosophilid evolutionary ecology of examining phenotypic and genetic differentiation along latitudinal (and altitudinal) clines as a proxy for studying adaptation to temperate environments [@pgen.1004775-Singh1]. Using allele frequency estimates that we made from populations sampled along the North American latitudinal cline, we demonstrate that southern populations are more 'fall-like' at seasonal SNPs whereas northern populations are more 'spring-like' ([Fig. 3D](#pgen-1004775-g003){ref-type="fig"}). Northern populations experience more severe winters and have shorter growing seasons; therefore, we speculate that the changes in allele frequency at adaptively oscillating polymorphisms along the cline is because (1) the summer favored allele would be at lower frequency due to stronger selection during the winter and (2) the summer favored allele would not rise in frequency as much during the summer because of the shorter growing season. The converse would be the case for Southern populations.
Finally, we relate seasonally variable SNPs with ecologically relevant phenotypic variation. Previous studies have demonstrated that two important stress tolerance traits, chill coma recovery time and starvation resistance vary in predictable ways among temperate populations of *D. melanogaster*. Northern populations tend to have fast chill coma recovery time [@pgen.1004775-Ayrinhac1]--[@pgen.1004775-Overgaard1] recapitulating deeper phylogenetic patterns among drosophilids originating from temperate and tropical locales [@pgen.1004775-Gibert1]. Evidence for latitudinal variation in starvation tolerance is more equivocal with low latitude populations of *D. melanogaster* being more starvation tolerant in some studies but not significantly so in others [@pgen.1004775-Karan1], [@pgen.1004775-Gilchrist1] and closely related species showing equally ambiguous patterns [@pgen.1004775-Schmidt2], [@pgen.1004775-Hoffmann2], [@pgen.1004775-Gilchrist1]. However, diapause-competent genotypes that are at high frequency in Northern populations and in the spring show increased starvation tolerance [@pgen.1004775-Schmidt2] suggesting that spatial and temporal differentiation in starvation tolerance may be parallel in the context of specific polymorphisms. Nonetheless, because selection pressures along latitudinal clines are generally parallel with seasonal selection pressures (e.g., [Fig. 3D](#pgen-1004775-g003){ref-type="fig"}) we reasoned that winter adapted alleles at seasonal SNPs would be associated with fast chill coma recovery time and increased starvation tolerance.
We show that winter adapted alleles at seasonal SNPs are likely to be associated with fast chill coma recovery time and, to a lesser extent, starvation tolerance ([Fig. 5](#pgen-1004775-g005){ref-type="fig"}). The strength of the relationship between seasonal SNPs with these two phenotypes likely differs for many reasons, including intrinsic differences in the statistical power and the complex genetic architecture of these traits. Nonetheless, the fact that seasonal SNPs are associated with chill coma recovery and starvation tolerance in the predicted direction given our prior knowledge of seasonal variation in these two traits strongly suggests that seasonal SNPs are functional and affect seasonally dependent fitness via stress tolerance traits. In addition, the concordance between seasonal SNPs and SNPs moderately associated with chill coma recovery time and starvation tolerance suggests that the intermediate frequency SNPs that we are investigating here have small effects on phenotype but nonetheless have large effects on average population fitness.
Taken together, our analysis has linked adaptive oscillations at hundreds of polymorphisms in *D. melanogaster* to specific and persistent differences in climate and to phenotypes known to be under diversifying selection through time and space. Our results support the hypothesis that stress tolerance traits are favored during the winter and disfavored during the summer. Stress tolerance traits such as chill coma recovery time and starvation tolerance often have negative genetic correlations with reproductive output [@pgen.1004775-Schmidt2], [@pgen.1004775-Ayroles1] or development time [@pgen.1004775-Reynolds1], two phenotypes that would be favored during exponential growth during the summer. Therefore, it is likely that a subset of seasonal SNPs directly contribute to a tradeoff between stress tolerance and reproductive output.
Because *D. melanogaster* originated in sub-Saharan Africa and colonized the world in the wake of human migration 200--10,000 years ago [@pgen.1004775-David1] it has been hypothesized [@pgen.1004775-Sezgin1] that phenotypes favored during the winter are derived whereas those favored during the summer are ancestral with respect to tropical, African populations. Although we show that the vast majority of seasonal SNPs are common in Africa, a small set (∼5%) are rare, segregating at less than 1%. Somewhat surprisingly, summer favored alleles are more likely to be rare in Africa than winter favored alleles (see [Results and Discussion](#s2){ref-type="sec"}: Long term...) suggesting that some environmental aspects of summer in temperate orchards are new for *D. melanogaster*. Consistent with the observation that flies sampled at low latitudes are likely subject to intense intra- and inter-specific competition [@pgen.1004775-James1], we speculate that the cornucopia of rotten fruit during the summer in mid- to high-latitude locales coupled with decreased inter-specific competition is a novel environment for *D. melanogaster* that has allowed formerly rare alleles associated with increased reproductive output to flourish.
Conclusions -- Long-term, polygenic balancing selection, and ecological generality {#s2k}
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Herein, we present several lines of evidence demonstrating that hundreds of loci adaptively respond to seasonal fluctuations in the environment. Despite (or because of) the fact that these loci promote rapid adaptive evolution, many have remained polymorphic for millions of generations within *D. melanogaster* and some possibly predate the divergence of *D. melanogaster* and *D. simulans* ∼5 million years ago. Taken together, these observations suggest that alleles at these loci have may have been maintained by environmental heterogeneity for exceptionally long periods of time. Long-term balancing selection is typically regarded as an evolutionary oddity, found predominantly in the genetic systems regulating host-pathogen interactions, self-incompatibility, and sex-determination [@pgen.1004775-Klein1], [@pgen.1004775-Langley1]. Herein, we provide evidence that environmental heterogeneity might promote long-term balanced polymorphisms at hundreds of loci that affect quantitative, stress tolerance traits.
Theory predicts that temporal variation in selection coefficients can maintain adaptive genetic variation for long periods of time when certain genetic and ecological conditions are met. Classic models suggest that the adaptive variation can be maintained in populations because of temporal shifts in selection pressure only when the heterozygote has a higher geometric mean fitness than either homozygote [@pgen.1004775-Gillespie1]. Such conditions are necessary for both finite and infinite populations and, moreover, in finite populations the persistence time of adaptive polymorphisms may be shorter than for neutral ones [@pgen.1004775-Hedrick1]. However, alternative models have demonstrated that overlapping generations [@pgen.1004775-Ellner2], the combination of spatial and temporal variation in selection pressures [@pgen.1004775-Ewing1], habitat fidelity [@pgen.1004775-GarciaDorado1], [@pgen.1004775-Hedrick2], and multiple liked loci subject to temporally variable selection [@pgen.1004775-Korol1] will increase the persistence time of balanced polymorphisms maintained by environmental heterogeneity.
Each of these conditions are met in for *D. melanogaster*. First, flies are highly fecund [@pgen.1004775-Bergland1], iteroparous insects with generation time a fraction of lifespan [@pgen.1004775-Schmidt4], [@pgen.1004775-Schmidt5]. Therefore natural populations are likely to be highly age structured which will prevent the loss of balanced alleles during alternate seasons. Second, spatial selection pressures vary on the order of meters to kilometers [@pgen.1004775-McKechnie1], [@pgen.1004775-Rashkovetsky1], all well within the dispersal radius of flies [@pgen.1004775-McInnis1]. In addition, flies often return to the substrate they were collected on [@pgen.1004775-Turelli1], [@pgen.1004775-Hoffmann3] and flies collected within a locale show signatures of population structure on the order of tens of meters [@pgen.1004775-Wallace1], [@pgen.1004775-Oshima1]. Therefore, low to moderate levels of migration between demes separated by various distances [@pgen.1004775-Coyne1], [@pgen.1004775-Berry1], [@pgen.1004775-McInnis1] and environmental heterogeneity over small spatial scales may help mitigate the loss of balanced polymorphisms in any one orchard. Finally, our study identified hundreds of adaptively oscillating polymorphisms. Although the vast majority of these polymorphisms are unlinked due to the large physical distance between them, there is evidence of heterogeneity in the abundance of seasonal SNPs throughout the genome suggesting that some might be in partial linkage disequilibrium. Some models [@pgen.1004775-Korol1] have suggested that linkage between polymorphisms subject to temporally variable selection can allow for long-term persistence of both alleles at multiple sites. Taken together, we suspect *D. melanogaster* satisfies several key features required for the long-term maintenance of balanced polymorphisms due to temporal (and spatial) variation in selection pressures. Nonetheless, how do we account for the observation that these polymorphisms have been possibly maintained across different continents with clear differences in climate and between species with different ecologies [@pgen.1004775-Capy1]?
The long-term persistence of these adaptively oscillating polymorphisms across populations, continents, and species suggests that these polymorphisms contribute to short-term and local adaptation in response to very generalized environmental conditions. This is in contrast to the hypothesis [@pgen.1004775-Ginzburg1] that adaptation to temperate environments in *D. melanogaster* was largely in response to novel environments, exclusively associated with life in northern, temperate locales. Rather, we speculate that the selective pressures associated with seasons in temperate environments are merely manifestations of general selective pressures resulting from cyclic population booms and busts. That is, during times of plenty, such as during the summer in temperate locales, populations rapidly expand and alleles that confer increased reproductive output or faster time to sexual maturity are strongly favored. Likewise, when population size contracts due to biotic and abiotic stressors such as those experienced during winter, alleles that confer increased stress resistance are favored.
Cyclic population booms and busts are almost certainly a perennial feature of *D. melanogaster* populations, are a likely common occurrence in highly fecund species that exploit ephemeral resources, and may be an inherent property of most species in general [@pgen.1004775-Ginzburg1]. If true, we speculate that such species may harbor alleles that promote reproductive fitness during population growth (at the cost of somatic maintenance) and increase stress tolerance (at the cost of reproductive growth) during population contraction. Such balanced polymorphisms may be particularly common for species whose population cycles are decoupled from predictable environmental cues (e.g., photoperiod) but are rather linked to stochastic changes in resource abundance. For species such as these, including many microorganisms and invertebrates, balanced polymorphisms maintained by environmental heterogeneity through time and space may be the norm rather than the exception.
Materials and Methods {#s3}
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Fly collections {#s3a}
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We resequenced samples of *D. melanogaster* from populations sampled over several years (2003--2010) largely during periods of peak abundance along a broad latitudinal cline in North America and during multiple time points over three consecutive years (2009 to 2011) at the Linvilla Orchard in Media, PA (39.9°N, 75.4°W). From each locality and sampling period, we collected ∼50--200 *D. melanogaster* largely by aspiration from individual fruits or baiting at strawberry fields and apple and peach orchards, established isofemale lines and collected male progeny at generation 1--5 for sequencing. One male progeny per isofemale line per population was pooled together to generate template DNA for high throughput sequencing ([Table S1](#pgen.1004775.s008){ref-type="supplementary-material"}). The only two exceptions are the second replicate sample from Maine which was derived from wild-caught males and the sample from North Carolina which was sampled from the Drosophila Genetic Reference Panel (DGRP) inbred lines. For the DGRP population, we resequenced a pooled sample consisting of one male from each of 92 DGRP strains and used allele frequency estimates from pooled samples when estimating clinality (see [@pgen.1004775-Wright1] for more information on this sample and [@pgen.1004775-Mackay1] for more information on this population). Note, there is evidence that two samples (Florida replicate 2 and post-frost Pennsylvania) show low levels of contamination with the sister species *D. simulans* (i.e., ∼ one wild caught *D. simulans* was accidentally included in our pooled sample). However, we have no evidence that the low level of contamination in two samples affects our results in any way (see [Text S1](#pgen.1004775.s011){ref-type="supplementary-material"}).
Sample preparation, sequencing, and bioinformatics of pooled samples {#s3b}
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DNA libraries were prepared for sequencing on the Illumina HiSeq2000 platform. To generate these libraries, we homogenized whole, male flies in 200 µL lysis buffer (100 mM Tris-Cl, 100 mM EDTA, 100 mM NaCL, 0.5% SDS) using a motorized pestle grinder. An additional 200 µL of lysis buffer was added to each sample and the homogenate was incubated at 65°C for 30 minutes. After lysis, we added 800 µL of 2 parts 5M potassium acetate, 5 parts 6M lithium chloride solution and incubated on ice for 15 minutes to precipitate proteins. The homogenate was centrifuged for at 12 K rotations per minute (RPM) for 15 minutes at room temperature, 1 mL supernatant was transferred to a new tube, and the sample was centrifuged again at 12K RPM for 15 minutes at room temperature. To precipitate DNA, we added 800 µL of isopropanol and centrifuged the sample at 12K RPM for 15 minutes. The supernatant was discarded and the DNA pellet was washed with 70% ethanol and centrifuged at 14K RPM for 10 minutes, washed with ethanol again and centrifuged once more. The ethanol was removed and the pellet was allowed to dry at room temperature. We resuspended the pellet in 100 µL TE buffer.
DNA was prepared for Illumina sequencing by shearing, end-repair and ligation. To do so, 50 µL of DNA was mixed with an additional 50 µL of TE and this DNA was sheared to ∼500 bp using a Covaris machine. DNA was eluted to 30 µL using a QIAGEN PCR-purification kit (product number 28104). We performed end repair by incubating each sample of DNA with 5 µL T4 DNA ligation buffer (New England Biolabs \[NEB\] product number B0202S), 4 µL of 10 mM dNTPs, 2.5 µL T4 DNA polymerase (NEB product number M0203S), 0.5 µL Klenow large fragment (NEB product number M0210S), 2.5 µL T4 PNK (NEB product number M0201S), and 5.5 µL nuclease free water for 30 minutes at 20°C. Following incubation, DNA was purified using a QIAGEN PCR-clean up kit. Next, we performed dATP addition by incubating 32 µL of DNA with 5 µL 10× NEBuffer 2 (NEB product number B7002S), 1 µL 10 mM dATP, 3 µL Klenow Exo-minus (NEB product number M0212S), and 9 µL nuclease free water at 37°C for 30 minutes. Following incubation, DNA was purified using a QIAGEN MinElute kit (product number 28004) to a final volume of 11 µL. Sequencing adapters (custom synthesized by IDT) were ligated to DNA using T/A ligation by incubating 10 µL DNA with 2 µL T4 DNA ligation buffer, 1 µL T4 ligase (NEB product number M020S), 40 µL of 40 µM pre-annealed adapter mix and 6 µL nuclease free water for 15 minutes at 20°C followed by 65°C at 10 minutes to deactivate the DNA ligase.
Finally, we performed size-selection and PCR amplification as a final step to prepare DNA sequencing libraries. Immediately following ligation, DNA was loaded into a 2%, pre-cast SizeSelect E-Gel (Life Technologies product number G661002) and run along side a 100 bp ladder. DNA at ∼500 bp was removed from the gel into a volume of ∼15 µL nuclease free water. To amplify ligated DNA, we performed two replicate PCR reactions for each sample where we used 7.5 µL template DNA, 0.25 µL of 100 µM forward and reverse primers (custom synthesized by IDT), 0.5 µL 10 mM dNTPs, 4 µL 5× High-Fidelity buffer (NEB product number B0518S), 0.5 µL Phusion High-Fidelity DNA polymerase (NEB product number M0530S), and 5 µL nuclease free water. Note, the use of two replicate PCR reactions and a high volume of template DNA was meant to prevent PCR-jackpotting. PCR was performed by 30 sections of initial denaturation at 98°C followed by 11 rounds of 10 seconds denaturation (98°C), 30 seconds annealing (65°C), 30 seconds elongation (72°C), followed by a final elongation at 72°C for 5 minutes. DNA was purified using a QIAGEN PCR-cleanup kit.
Following PCR, DNA was quantified on a Life Technologies Qubit spectrophotometer as well as with a Agilent Bioanalyzer. Libraries were diluted to the appropriate concentration and sent to the Sequencing Service Center at the Stanford Center Genomics and Personalized Medicine for sequencing on the HiSeq 2000 platform.
Raw, paired-end 100 bp sequence reads were mapped to the *D. melanogaster* reference genome version 5.39 using *bwa* version 0.5.9-r16 [@pgen.1004775-Li1] allowing for a maximum insert size of 800 bp and no more than 10 mismatches per 100 bp. PCR duplicates (∼5% per library) were removed using *samtools* version 0.1.18 [@pgen.1004775-Li2] and local realignment around indels was performed using GATK version 1.4--25 [@pgen.1004775-McKenna1]. We mapped SNPs and short indels (i.e., those occurring within the sequence reads) using CRISP [@pgen.1004775-Bansal1], excluding reads with base or mapping quality below 10. SNPs mapping to repetitive regions such as microsatellites and transposable elements, identified in the standard RepeatMasker library for *D. melanogaster* (obtained from <http://genome.ucsc.edu>) were excluded from analysis as were SNPs within 5 bp of polymorphic indels. SNPs with average minor allele frequency across all populations less than 15%, with minimum per-population coverage less than 10× or maximum per-population coverage greater than 400× were removed from analysis. Finally, to ensure that the examined SNPs were not artifacts of our pooled resequencing, we removed any SNP not present in the SNP tables provided by freeze 2 of the DGRP [@pgen.1004775-Mackay1] (<http://www.hgsc.bcm.tmc.edu/projects/dgrp/>). The inclusion of reads with read and mapping qualities greater than 10 (rather than greater than 20) is justified because we are restricting our analysis to common SNPs that have been previously identified in the DGRP. Of the 1,500,000 SNPs initially identified, ∼500,000 SNPs remained after applying these filters ([Table S2](#pgen.1004775.s009){ref-type="supplementary-material"}). SNPs were annotated using SNPeff version 2.0.5 [@pgen.1004775-Cingolani1]. Short intron annotations were taken from [@pgen.1004775-Lawrie1]. An annotated VCF file with allele frequency calls, genic annotations, and seaonsal/clinal p- and q-values is avaible on DataDryad (doi:10.5061/dryad.v883p). Raw sequence data are available from NCBI SRA (BioProject accession PRJNA256231, and see [Table S1](#pgen.1004775.s008){ref-type="supplementary-material"} for accession numbers of individual libraries).
*F~ST~* estimates {#s3c}
-----------------
To estimate average differentiation between populations or between samples collected trough time, we calculated genome-wide average (mean) *F~ST~* between pairs of populations. *F~ST~* was calculated as,where *H~total~* is the expected heterozygosity between two populations under panmixia and *H~with~* is the heterozygosity averaged between the two populations. Estimates of heterozygosity were corrected for read depth and number of sampled chromosomes by the factor,where,and where *N~chr~* is the number of sampled chromosomes and *N~rd~* is the number of reads at any site [@pgen.1004775-Nei1]--[@pgen.1004775-Feder1].
We performed a parametric permutation analysis to calculate the expected, genome-wide average *F~ST~* between pairs of populations under the null hypothesis of panmixia (spatial) or no allele frequency change through time (temporal) conditional on our experimental sampling design. To do so, we calculated the average allele frequency between any two pairs of populations or samples and randomly generated two estimates of allele frequency conditional on the average allele frequency, the number of reads at that site and the number of chromosomes sampled.
To calculate the proportion of SNPs where observed *F~ST~* is greater than expected by chance, we generated 500 block bootstrap samples of ∼2300 SNPs, where one SNP was drawn per 50 kb interval. The proportion of SNPs where the observed *F~ST~* distribution is greater than expected by chance is thus,with standard deviation,where *i* refers to the *i^th^* SNP from *j^th^* block bootstrap sample.
Identification of seasonally and clinally varying polymorphisms {#s3d}
---------------------------------------------------------------
To identify clinally varying and seasonally oscillating polymorphisms, we used generalized linear models implemented in R 2.10 [@pgen.1004775-R1] with binomial error structure and weights proportional to the number of reads sampled at a site and the number of chromosomes sampled (see above, *N~eff~*). To identify clinal polymorphisms, we regressed allele frequency at each site (excluding all Pennsylvanian samples) on latitude ([Table S1](#pgen.1004775.s008){ref-type="supplementary-material"}) according to the form,where *y~i~* is the observed allele frequencies of the *i^th^* SNP and *ε~i~* is the binomial error given the number of effective reads (see above) at the *i^th^* SNP. To identify seasonally oscillating polymorphisms, we regressed allele frequency for the three sets of spring and fall samples on a binary variable corresponding to *spring* or *fall* according to the form,In addition, we modeled allele frequency change through time using generalized linear mixed models (GLMM) implemented in the *lme4* R package [@pgen.1004775-Bates1] and generalized estimation equations (GEE) implemented in the *geepack* R package [@pgen.1004775-Hjsgaard1]. We fit GLMMs with the model,where *(1\|population~i~)* corresponds to the random effect of population *j* and *ε~i~* corresponds to the binomial error. We fit GEEs with the model,where *population~j~* corresponds to the population level strata and *ε~i~* corresponds to the binomial error fit with an autoregressive order one correlation structure. *q-q* plots ([Fig. S2](#pgen.1004775.s002){ref-type="supplementary-material"}) demonstrate that these models (clinal and seasonal) fit the bulk of the data adequately, with the exception of the seasonal GEE model which appears to be exceedingly anti-conservative. The false discovery rate was estimated using the Benjamini & Hochberg procedure [@pgen.1004775-Benjamini1].
For seasonal SNPs, we estimated the cumulative selection coefficient as,where *f~Sp~* is the average allele frequency at seasonal SNPs in the spring and *f~Fall~* is the average allele frequency at seasonal SNPs in the fall. This estimation of S is derived from a basic model of logistic growth of a beneficial allele [@pgen.1004775-Ewens1], namely,Because we do not know the specific values of heterozygosity (*h*) nor the number of generations of selections during each season (*t*), we calculate *S* as the product of *s, h*, and *t*.
Modeling the distribution of seasonal SNPs throughout the genome {#s3e}
----------------------------------------------------------------
We sought to test whether seasonal SNPs were homogeneously distributed throughout the genome. To do so, we grouped the genome into bins of 1000 non-overlapping SNPs (utilizing the ∼500,000 SNPs under investigation). For each window, we calculated the number of seasonal SNPs. The number of seasonal SNPs is Poisson distributed and we examined whether the observed distribution is over-dispersed after correcting for variation in rates of recombination within chromosomes and between the autosomes and X-chromsome. To do so, we fit the generalized linear model,where *n* is the count of seasonal SNPs per 1000 SNPs, *chrType* is the binary classification of autosome or X-chromosome, and *rec* is the average recombination rate estimated in [@pgen.1004775-Comeron1], and *ε* is the Poisson distributed error. To explicitly test if the number of seasonal SNPs is overdispersed, we used the *dispersiontest* function in the R package *AER* [@pgen.1004775-Kleiber1].
Control polymorphisms and the block bootstrap {#s3f}
---------------------------------------------
Throughout our analysis, we contrasted seasonal SNPs with control polymorphisms ([Figs. 2](#pgen-1004775-g002){ref-type="fig"}--[6](#pgen-1004775-g006){ref-type="fig"}). For these analyses, we identified 500 sets of control polymorphisms matched to each seasonal SNP. For each test described in the results, control polymorphisms were identified based on different sets of characteristics that have been shown, or could plausibly, influence the parameter we sought to investigate. In general, we matched seasonal SNPs to control SNPs by chromosome, recombination rate, and allele frequency in either Pennsylvania, North Carolina, North America, and/or Africa. The choice of which population to match allele frequencies was determined by the specific test. These three parameters (chromosome, recombination rate, allele frequency) correspond with many important evolutionary processes as well as genetic patterns (e.g., [@pgen.1004775-Begun1]) and therefore control SNPs will be matched to seasonal SNPs with respect to long-term evolutionary history, gene-density, and background levels of genetic variation. In general, we used as many parameters as possible while still identifying a sufficient number of control SNPs for each test and a full list of the matched characters for each test are listed in [Table S3](#pgen.1004775.s010){ref-type="supplementary-material"}. For continuous characters, such as allele frequency, we typically rounded values so that a sufficient number of unique control sites could be identified. If no matched control SNPs were identified for a seasonal SNP, that seasonal SNP was removed from subsequent analyses.
In addition, we implemented a block-bootstrap procedure to ameliorate positive dependence of our test-statistics due to linkage disequilbrium between seasonal SNPs. We generated 500 sets of seasonal SNPs where one seasonal SNP was sampled from each 50 kb consecutive interval of the genome. This block-bootstrap yielded ∼850 SNPs that were spaced approximately every 50 Kb.
Estimates of expected values (E) of test statistics \[e.g. log~2~-odds-ratios ([Fig. 2C](#pgen-1004775-g002){ref-type="fig"}, [3B--C](#pgen-1004775-g003){ref-type="fig"}, [6A](#pgen-1004775-g006){ref-type="fig"}), *F~ST~* ([Fig. 2D](#pgen-1004775-g002){ref-type="fig"}), probability ([Fig. 4B](#pgen-1004775-g004){ref-type="fig"})\] and standard deviations (SD) about those expected values were calculated as, where *i* refers to control bootstrap set *i* and *j* refers to block bootstrap set *j* of any test-statistic, *TS*.
Power calculations {#s3g}
------------------
To calculate statistical power of our experiment and to estimate the expected number of SNPs that are likely to vary repeatedly between seasons and along the cline we used Monte Carlo simulations based on the observed changes in allele frequency between spring and fall at seasonal SNPs or Maine and Florida at clinal SNPs. We calculated statistical power to detect seasonal SNPs as the probability of rejecting the null hypothesis of no repeatable change in allele frequency between spring and fall over three years given our sampling effort (e.g., number of chromosomes from nature and distribution of read depths in our Pennsylvanian samples) at α\<∼1e-5, corresponding to observed seasonal q-value of 0.3, conditional on *S*, the cumulative change in allele frequency between seasons calculated from the logistic function. Similarly, we calculated statistical power to detect clinal SNPs as the probability of rejecting the null hypothesis of no change in allele frequency with latitude given our sampling effort at α\<0.02, corresponding to the observed clinal q-value of 0.1, conditional on beta, the slope of the relationship between allele frequency and latitude. The expected number of seasonally (clinally) varying SNPs is then, the number of observed seasonal (clinal) SNPs at a particular value of S (beta) divided by the power to detect a seasonal (clinal) SNP at a selection coefficient S (beta).
Comparison with D. simulans {#s3h}
---------------------------
To estimate the extent of trans-specific polymorphism between *D. melanogaster* and *D. simulans*, we used *D. simulans* haplotype data available from the DPGP [@pgen.1004775-Begun2] (<http://www.dpgp.org/>). First, we remapped raw shot-gun sequences of each *D. simulans* strain (GenBank accessions AASS00000000 - AASW00000000) to the latest release of the *D. simulans* reference genome [@pgen.1004775-Hu1] with *bwa* version 0.5.9-r16 using the *bwa-sw* method.
To convert the genomic coordinate system of the new *D. simulans* genome to the *D. melanogaster* genome, we generated a lift-over file using *lastz* [@pgen.1004775-Harris1] and components of the UCSC genome-browser toolkit [@pgen.1004775-Kent1]. Gap parameters corresponded to those used to generate the lift-over file between the first generation *D. simulans* genome and the *D. melanogaster* genome (<http://hgdownload.soe.ucsc.edu/goldenPath/dm3/vsDroSim1/>). The lift-over file to translate the coordinate system of the second generation *D. simulans* genome to the *D. melanogaster* version 5 genome is available on Data Dryad (doi:10.5061/dryad.v883p).
We calculated average pairwise distance between *D. melanogaster* and *D. simulans* haplotypes at seasonal SNPs that were polymorphic in both species and shared the same two alleles by state. We calculated average pairwise distance at two windows surrounding seasonal SNPs, ±1--250 bp. Note, we excluded the focal, seasonal SNP. Pairwise distance calculations were performed using the *ape* [@pgen.1004775-Paradis1] package in R.
Forward genetic simulations {#s3i}
---------------------------
To simulate genome-wide allele frequency change due to cyclic changes in population size and selection at seasonally adaptive polymorphisms, we used a modified version of the forward genetic simulation software SLiM [@pgen.1004775-Messer1]. Source code for the modified version of SLiM is available upon request. In these simulations, we modeled a 20 Mb chromosome with constant recombination rate of 2 cM/Mb. For all simulations, we seeded the chromosome with 500 neutral mutations randomly placed along the chromosome all starting at 50% initial allele frequency and in complete linkage equilibrium. The number of loci under selection varied between 0 and 30 and loci under temporally heterogeneous selection were placed equidistantly along the chromosome. Selection coefficients for each selected locus were set to produce adaptive oscillations between 40 and 60% frequency every 2 (simulated 'winter') and 10 (simulated 'summer') generations. Genotypic state was assigned randomly to each simulated diploid genome at each selected locus. Population size varied over the course of each simulation. Populations grew exponentially each 'summer' to a maximum population size of 10^5^ over 10 generations. Population size instantaneously crashed at the start of winter to between 5 and 10^4^ individuals and was held constant for two generations. Simulations were run for 100 generations and *F~ST~* was estimated from the last three summer-winter cycles.
Truncation selection model {#s3j}
--------------------------
To estimate the upper bound of the number of loci that could plausibly respond to seasonally variable selection, we modeled a simple truncation selection scenario. For these models we calculated the expected number of winter adaptive alleles in the fall and the spring as the sum of average allele frequencies of the winter alleles in our fall and spring samples. If the oscillating alleles segregate independently, the variance in the number of winter alleles at any given time follows a Poisson distribution with mean and variance equal to the expected number of winter alleles. Therefore, the proportion of the population in the selected tail over winter is the probability of sampling the expected number of winter alleles in the spring from a Poisson distribution with mean equal to the number of winter alleles in the fall. To vary the number of independently oscillating polymorphisms in the spring and fall, we sub-sampled the number of oscillating polymorphisms 500 times for a range of values.
Supporting Information {#s4}
======================
######
Genomic turnover through space and time -- average *F~ST~*. Proportion of SNPs where average *F~ST~* among populations sampled along the cline (A) and through time (B) is greater than expected by chance conditional on our sampling design and panmixia among spatially separated populations or no allele frequency change through time, respectively. Lines represent the predicted values of Prop(Fst~Obs~\>Fst~Exp~) for the (A) linear relationship between Prop(Fst~Obs~\>Fst~Exp~) and difference latitude and (B) from non-linear relationship (y = ab^X^) between Prop(Fst~Obs~\>Fst~Exp~) and difference in months. Points represent mean *F~ST~*, error bars represent 95% confidence intervals based on blocked-bootstrap resampling.
(TIF)
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Click here for additional data file.
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*q-q* plots and congruence of GLM, GLMM and GEE models. (A--C) Standard q-q plots of *p-values* of GLM, GLMM and GEE models, respectively. q-q plots show that GLM and GLMM models fit the bulk of the genome well whereas GEE models appear to be anti-conservative. (D) log~2~(odds-ratio) that the top 1750 seasonal SNPs identified with the GLM model are among the top 1750 seasonal SNPs identified with the GLMM model. (E) log~2~(odds-ratio) that the top 1750 seasonal SNPs identified with the GLM model are among the top 1750 seasonal SNPs identified with the GEE model.
(TIF)
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Click here for additional data file.
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Genomic turnover through time excluding SNPs within 1 Kb of seasonal SNPs. (A) Genome-wide average *F~ST~* between samples of flies collected through time, excluding SNPs within 1 Kb of seasonal SNPs. (B) Proportion of SNPs where *F~ST~* between pairs of samples collected through time is greater than expected by chance given the null hypothesis of no allele frequency change through time and our sampling design. Solid line represents predicted relationship between genome-wide *F~ST~* and time excluding SNPs within 1 Kb; dashed line represents predicted relationship between genome-wide *F~ST~* for all common SNPs and time. The similarity between the solid and dashed line demonstrates that SNPs near seasonal SNPs are not driving genome-wide patterns of *F~ST~* through time. Lines represent the predicted values of Fst (A) and Prop(Fst~Obs~\>Fst~Exp~) (B) from non-linear regression (y = ab^X^). Points represent mean *F~ST~*, error bars represent 95% confidence intervals based on blocked-bootstrap resampling.
(TIF)
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Click here for additional data file.
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Enrichment among cosmopolitan inversions. Log~2~ odds ratio that seasonal SNPs are enriched among the large cosmopolitan inversions relative to control polymorphisms. Inversion breakpoints are defined as ±2.5 Mb from the proximal or distal breakpoints. Error bars represent 95% confidence intervals based on blocked bootstrap resampling.
(TIF)
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Spatial *F~ST~* and clinal *q*-value. Scatter plot of the relationship between spatial *F~ST~* (x-axis) and --log~10~(clinal *q*-value). Colors of the hexagons represent the density of points in that interval.
(TIF)
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Click here for additional data file.
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Power to detect clinal SNPs. Power to detect clinal SNPs (black line) is moderate and we estimate that we have identified ∼50% (red line) of all SNPs that change in frequency monotonically with latitude (black line).
(TIF)
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Click here for additional data file.
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Site frequency spectrum of seasonal samples. Unfolded site frequency spectrum of spring (blue) and fall (red) samples from 2009--2010 (A) and 2010--2011 (B). Solid lines represent observed site frequency spectra, dashed lines represent simulated spring site frequency spectra conditional on one generation of bottleneck to 20 individuals and dotted lines represent simulated spring site frequency spectra conditional on two generations of bottleneck to 20 individuals. The increase in low frequency alleles in the spring 2010 sample (B, blue line) is due to the high coverage of this library. Site frequency spectra only included SNPs with allele frequencies greater than 2/(read depth) or less than 1--2/(read depth) to account for sequencing errors.
(TIF)
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Click here for additional data file.
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Population sampling locales.
(DOCX)
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Click here for additional data file.
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Basic SNP statistics.
(DOCX)
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Click here for additional data file.
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Table of control characteristics.
(DOCX)
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Click here for additional data file.
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Assessing the possibility of contamination with wild caught D. simulans. Discussion of previously identified clinal polymorphisms in relation to clinal resequencing described here.
(DOCX)
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Click here for additional data file.
We thank the members of the Petrov and Schmidt labs for useful discussion and comments on previous versions of this manuscript. We also thank nine anonymous reviewers, Daniel Bolnick, and Hopi Hoekstra whose comments substantially improved the quality of this manuscript.
[^1]: The authors have declared that no competing interests exist.
[^2]: Conceived and designed the experiments: AOB ELB KRO PSS DAP. Analyzed the data: AOB PSS DAP. Contributed reagents/materials/analysis tools: AOB ELB KRO PSS. Wrote the paper: AOB PSS DAP.
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IFUP-TH 2013/21
1.4truecm
[**Background Field Method,**]{}
.5truecm
[**Batalin-Vilkovisky Formalism And**]{}
.5truecm
[**Parametric Completeness Of Renormalization**]{}
1truecm
*Damiano Anselmi* .2truecm
*Dipartimento di Fisica “Enrico Fermi”, Università di Pisa,*
*and INFN, Sezione di Pisa,*
*Largo B. Pontecorvo 3, I-56127 Pisa, Italy,*
.2truecm
[email protected]
1.5truecm
**Abstract**
We investigate the background field method with the Batalin-Vilkovisky formalism, to generalize known results, study the parametric completeness of general gauge theories and achieve a better understanding of several properties. In particular, we study renormalization and gauge dependence to all orders. Switching between the background field approach and the usual approach by means of canonical transformations, we prove parametric completeness without making use of cohomological theorems; namely we show that if the starting classical action is sufficiently general all divergences can be subtracted by means of parameter redefinitions and canonical transformations. Our approach applies to renormalizable and nonrenormalizable theories that are manifestly free of gauge anomalies and satisfy the following assumptions: the gauge algebra is irreducible and closes off shell, the gauge transformations are linear functions of the fields, and closure is field independent. Yang-Mills theories and quantum gravity in arbitrary dimensions are included, as well as effective and higher-derivative versions of them, but several other theories, such as supergravity, are left out.
1truecm
Introduction
============
The background field method [@dewitt; @abbott] is a convenient tool to quantize gauge theories and make explicit calculations, particularly when it is used in combination with the dimensional-regularization technique. It amounts to choosing a nonstandard gauge fixing in the conventional approach and, among its virtues, it keeps the gauge transformations intact under renormalization. However, it takes advantage of properties that only particular classes of theories have.
The Batalin-Vilkovisky formalism [@bata] is also useful for quantizing general gauge theories, especially because it collects all ingredients of infinitesimal gauge symmetries in a single identity, the master equation, which remains intact through renormalization, at least in the absence of gauge anomalies.
Merging the background field method with the Batalin-Vilkovisky formalism is not only an interesting theoretical subject *per se*, but can also offer a better understanding of known results, make us appreciate aspects that have been overlooked, generalize the validity of crucial theorems about the quantization of gauge theories and renormalization, and help us address open problems. For example, an important issue concerns the generality of the background field method. It would be nice to formulate a unique treatment for all gauge theories, renormalizable and nonrenormalizable, unitary and higher derivative, with irreducible or reducible gauge algebras that close off shell or only on shell. However, we will see that at this stage it is not possible to achieve that goal, due to some intrinsic features of the background field method.
Another important issue that we want to emphasize more than has been done so far is the problem of *parametric completeness* in general gauge theories [@regnocoho]. To ensure renormalization-group (RG) invariance, all divergences must be subtracted by redefining parameters and making canonical transformations. When a theory contains all independent parameters necessary to achieve this goal, we say that it is parametrically complete. The RG-invariant renormalization of divergences may require the introduction of missing Lagrangian terms, multiplied by new physical constants, or even deform the symmetry algebra in nontrivial ways. However, in nonrenormalizable theories such as quantum gravity and supergravity it is not obvious that the action can indeed be adjusted to achieve parametric completeness. One way to deal with this problem is to classify the whole cohomology of invariants and hope that the solution satisfies suitable properties. This method requires lengthy technical proofs that must be done case by case [@coho], and therefore lacks generality. Another way is to let renormalization build the new invariants automatically, as shown in ref. [@regnocoho], with an algorithm that is able to iteratively extend the classical action converting divergences into finite counterterms. However, that procedure is mainly a theoretical tool, because although very general and conceptually minimal, it is practically unaffordable. Among the other things, it leaves the possibility that renormalization may dynamically deform the gauge symmetry in physically observable ways. A third possibility is the one we are going to treat here, taking advantage of the background field method. Where it applies, it makes cohomological classifications unnecessary and excludes that renormalization may dynamically deform the symmetry in observable ways. Because of the intrinsic properties of the background field method, the approach of this paper, although general enough, is not exhaustive. It is general enough because it includes the gauge symmetries we need for physical applications, namely Abelian and non-Abelian Yang-Mills symmetries, local Lorentz symmetry and invariance under general changes of coordinates. At the same time, it is not exhaustive because it excludes other potentially interesting symmetries, such as local supersymmetry.
To be precise, our results hold for every gauge symmetry that satisfies the following properties: the algebra of gauge transformations ($i$) closes off shell and ($ii$) is irreducible; moreover ($iii$) there exists a choice of field variables where the gauge transformations $\delta _{\Lambda }\phi $ of the physical fields $\phi $ are linear functions of $\phi $ and the closure $[\delta _{\Lambda
},\delta _{\Sigma }]=\delta _{[\Lambda ,\Sigma ]}$ of the algebra is $\phi $ independent. We expect that with some technical work it will be possible to extend our results to theories that do not satisfy assumption ($ii$), but our impression is that removing assumptions ($i$) and ($iii$) will be much harder, if not impossible.
In this paper we also assume that the theory is manifestly free of gauge anomalies. Our results apply to renormalizable and nonrenormalizable theories that satisfy the assumptions listed so far, among which are QED, Yang-Mills theories, quantum gravity and Lorentz-violating gauge theories [@lvgauge], as well as effective [@weinberg], higher-derivative [@stelle] and nonlocal [@tombola] versions of such theories, in arbitrary dimensions, and extensions obtained including any set of composite fields. We recall that Stelle’s proof [@stelle] that higher-derivative quantum gravity is renormalizable was incomplete, because it assumed without proof a generalization of the Kluberg-Stern–Zuber conjecture [@kluberg] for the cohomological problem satisfied by counterterms. Even the cohomological analysis of refs. [@coho] does not directly apply to higher-derivative quantum gravity, because the field equations of higher-derivative theories are not equal to perturbative corrections of the ordinary field equations. These remarks show that our results are quite powerful, because they overcome a number of difficulties that otherwise need to be addressed case by case.
Strictly speaking, our results, in their present form, do not apply to chiral theories, such as the Standard Model coupled to quantum gravity, where the cancellation of anomalies is not manifest. Nevertheless, since all other assumptions we have made concern just the forms of gauge symmetries, not the forms of classical actions, nor the limits around which perturbative expansions are defined, we expect that our results can be extended to all theories involving the Standard Model or Lorentz-violating extensions of it [@kostelecky; @LVSM]. However, to make derivations more easily understandable it is customary to first make proofs in the framework where gauge anomalies are manifestly absent, and later extend the results by means of the Adler-Bardeen theorem [@adlerbardeen]. We follow the tradition on this, and plan to devote a separate investigation to anomaly cancellation.
Although some of our results are better understandings or generalizations of known properties, we do include them for the sake of clarity and self-consistence. We think that our formalism offers insight on the issues mentioned above and gives a more satisfactory picture. In particular, the fact that background field method makes cohomological classifications unnecessary is something that apparently has not been appreciated enough so far. Moreover, our approach points out the limits of applicability of the background field method.
To achieve parametric completeness we proceed in four basic steps. First, we study renormalization to all orders subtracting divergences “as they come”, which means without worrying whether the theory contains enough independent parameters for RG invariance or not. Second, we study how the renormalized action and the renormalized $\Gamma $ functional depend on the gauge fixing, and work out how the renormalization algorithm maps a canonical transformation of the classical theory into a canonical transformation of the renormalized theory. Third, we renormalize the canonical transformation that continuously interpolates between the background field approach and the conventional approach. Fourth, comparing the two approaches we show that if the classical action $S_{c}(\phi ,\lambda )$ contains all gauge invariant terms determined by the starting gauge symmetry, then there exists a canonical transformation $\Phi ,K\rightarrow \hat{\Phi},\hat{K}$ such that $$S_{R\hspace{0.01in}\text{min}}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)=S_{c}(\hat{\phi}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\tau (\lambda ))-\int R^{\alpha }(\hat{\phi}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{C})\hat{K}_{\alpha }, \label{key0}$$ where $S_{R\hspace{0.01in}\text{min}}$ is the renormalized action with the gauge-fixing sector switched off, $\Phi ^{\alpha }=\{\phi ,C\}$ are the fields ($C$ being the ghosts), $K_{\alpha }$ are the sources for the $\Phi^{\alpha}$ transformations $R^{\alpha }(\Phi )$, ${\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }$ are the background fields, $\lambda $ are the physical couplings and $\tau (\lambda )$ are $\lambda $ redefinitions. Identity (\[key0\]) shows that all divergences can be renormalized by means of parameter redefinitions and canonical transformations, which proves parametric completeness. Power counting may or may not restrict the form of $S_{c}(\phi ,\lambda )$.
Basically, under the assumptions we have made the background transformations do not renormalize, and the quantum fields $\phi $ can be switched off and then restored from their background partners ${\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }$. Nevertheless, the restoration works only up to a canonical transformation, which gives (\[key0\]). The story is a bit more complicated than this, but this simplified version is enough to appreciate the main point. However, when the assumptions we have made do not hold, the argument fails, which shows how peculiar the background field method is. Besides giving explicit examples where the construction works, we address some problems that arise when the assumptions listed above are not satisfied.
A somewhat different approach to the background field method in the framework of the Batalin-Vilkovisky formalism exists in the literature. In refs. [@quadri] Binosi and Quadri considered the most general variation $\delta {\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }=\Omega $ of the background gauge field ${\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }$ in Yang-Mills theory, and obtained a modified Batalin-Vilkovisky master equation that controls how the functional $\Gamma $ depends on ${\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }
$. Instead, here we introduce background copies of both physical fields and ghosts, which allows us to split the symmetry transformations into “quantum transformations” and “background transformations”. The master equation is split into the three identities (\[treide\]), which control invariances under the two types of transformations.
The paper is organized as follows. In section 2 we formulate our approach and derive its basic properties, emphasizing the assumptions we make and why they are necessary. In section 3 we renormalize divergences to all orders, subtracting them “as they come”. In section 4 we derive the basic differential equations of gauge dependence and integrate them, which allows us to show how a renormalized canonical transformation emerges from its tree-level limit. In section 5 we derive (\[key0\]) and prove parametric completeness. In section 6 we give two examples, non-Abelian Yang-Mills theory and quantum gravity. In section 7 we make remarks about parametric completeness and recapitulate where we stand now on this issue. Section 8 contains our conclusions, while the appendix collects several theorems and identities that are used in the paper.
We use the dimensional-regularization technique and the minimal subtraction scheme. Recall that the functional integration measure is invariant with respect to perturbatively local changes of field variables. Averages $\langle \cdots \rangle $ always denote the sums of *connected* Feynman diagrams. We use the Euclidean notation in theoretical derivations and switch to Minkowski spacetime in the examples.
Background field method and Batalin-Vilkovisky formalism
========================================================
In this section we formulate our approach to the background field method with the Batalin-Vilkovisky formalism. To better appreciate the arguments given below it may be useful to jump back and forth between this section and section 6, where explicit examples are given.
If the gauge algebra closes off shell, there exists a canonical transformation that makes the solution $S(\Phi ,K)$ of the master equation $(S,S)=0$ depend linearly on the sources $K$. We write $$S(\Phi ,K)=\mathcal{S}(\Phi )-\int R^{\alpha }(\Phi )K_{\alpha }.
\label{solp}$$ The fields $\Phi ^{\alpha }=\{\phi ^{i},C^{I},\bar{C}^{I},B^{I}\}$ are made of physical fields $\phi ^{i}$, ghosts $C^{I}$ (possibly including ghosts of ghosts and so on), antighosts $\bar{C}^{I}$ and Lagrange multipliers $B^{I}$ for the gauge fixing. Moreover, $K_{\alpha }=\{K_{\phi
}^{i},K_{C}^{I},K_{\bar{C}}^{I},K_{B}^{I}\}$ are the sources associated with the symmetry transformations $R^{\alpha}(\Phi)$ of the fields $\Phi ^{\alpha }$, while $$\mathcal{S}(\Phi )=S_{c}(\phi )+(S,\Psi )$$ is the sum of the classical action $S_{c}(\phi )$ plus the gauge fixing, which is expressed as the antiparenthesis of $S$ with a $K$-independent gauge fermion $\Psi (\Phi )$. We recall that the antiparentheses are defined as $$(X,Y)=\int \left\{ \frac{\delta _{r}X}{\delta \Phi ^{\alpha }}\frac{\delta
_{l}Y}{\delta K_{\alpha }}-\frac{\delta _{r}X}{\delta K_{\alpha }}\frac{\delta _{l}Y}{\delta \Phi ^{\alpha }}\right\} ,$$ where the summation over the index $\alpha $ is understood. The integral is over spacetime points associated with repeated indices.
The non-gauge-fixed action $$S_{\text{min}}(\Phi ,K)=S_{c}(\phi )-\int R_{\phi }^{i}(\phi ,C)K_{\phi
}^{i}-\int R_{C}^{I}(\phi ,C)K_{C}^{I}, \label{smin}$$ obtained by dropping antighosts, Lagrange multipliers and their sources, also solves the master equation, and is called the minimal solution. Antighosts $\bar{C}$ and Lagrange multipliers $B$ form trivial gauge systems, and typically enter (\[solp\]) by means of the gauge fixing $(S,\Psi )$ and a contribution $$\Delta S_{\text{nm}}=-\int B^{I}K_{\bar{C}}^{I}, \label{esto}$$ to $-\int R^{\alpha }K_{\alpha }$.
Let $\mathcal{R}^{\alpha }(\Phi ,C)$ denote the transformations the fields $\Phi ^{\alpha }$ would have if they were matter fields. Each function $\mathcal{R}^{\alpha }(\Phi ,C)$ is a bilinear form of $\Phi ^{\alpha }$ and $C$. Sometimes, to be more explicit, we also use the notation $\mathcal{R}_{\bar{C}}^{I}(\bar{C},C)$ and $\mathcal{R}_{B}^{I}(B,C)$ for $\bar{C}$ and $B$, respectively. It is often convenient to replace (\[esto\]) with the alternative nonminimal extension $$\Delta S_{\text{nm}}^{\prime }=-\int \left( B^{I}+\mathcal{R}_{\bar{C}}^{I}(\bar{C},C)\right) K_{\bar{C}}^{I}-\int \mathcal{R}_{B}^{I}(B,C)K_{B}^{I}.
\label{estobar}$$ For example, in Yang-Mills theories we have $$\Delta S_{\text{nm}}^{\prime }=-\int \left( B^{a}-gf^{abc}C^{b}\bar{C}^{c}\right) K_{\bar{C}}^{a}+g\int f^{abc}C^{b}B^{c}K_{B}^{a}$$ and in quantum gravity $$\Delta S_{\text{nm}}^{\prime }=-\int \left( B_{\mu }+\bar{C}_{\rho }\partial
_{\mu }C^{\rho }-C^{\rho }\partial _{\rho }\bar{C}_{\mu }\right) K_{\bar{C}}^{\mu }+\int \left( B_{\rho }\partial _{\mu }C^{\rho }+C^{\rho }\partial
_{\rho }B_{\mu }\right) K_{B}^{\mu }, \label{nmqg}$$ where $C^{\mu }$ are the ghosts of diffeomorphisms.
Observe that (\[estobar\]) can be obtained from (\[esto\]) making the canonical transformation generated by $$F_{\text{nm}}(\Phi ,K^{\prime })=\int \Phi ^{\alpha }K_{\alpha }^{\prime
}+\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},C)K_{B}^{I\hspace{0.01in}\prime }.$$ Requiring that $F_{\text{nm}}$ indeed give (\[estobar\]) we get the identities $$\mathcal{R}_{B}^{I}(B,C)=-\int B^{J}\frac{\delta _{l}}{\delta \bar{C}^{J}}\mathcal{R}_{\bar{C}}^{I}(\bar{C},C),\qquad \int \left( R_{C}^{J}\frac{\delta _{l}}{\delta C^{J}}+\mathcal{R}_{\bar{C}}^{J}(\bar{C},C)\frac{\delta
_{l}}{\delta \bar{C}^{J}}\right) \mathcal{R}_{\bar{C}}^{I}(\bar{C},C)=0,
\label{iddo}$$ which can be easily checked both for Yang-Mills theories and gravity. In this paper the notation $R^{\alpha }(\Phi )$ refers to the field transformations of (\[smin\]) plus those of the nonminimal extension (\[esto\]), while $\bar{R}^{\alpha }(\Phi )$ refers to the transformations of (\[smin\]) plus (\[estobar\]).
Background field action
-----------------------
To apply the background field method, we start from the gauge invariance of the classical action $S_{c}(\phi )$, $$\int R_{c}^{i}(\phi ,\Lambda )\frac{\delta _{l}S_{c}(\phi )}{\delta \phi ^{i}}=0, \label{lif}$$ where $\Lambda $ are the arbitrary functions that parametrize the gauge transformations $\delta \phi ^{i}=R_{c}^{i}$. Shifting the fields $\phi $ by background fields ${\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }$, and introducing arbitrary background functions ${\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu }$ we can write the identity $$\int \left[ R_{c}^{i}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\Lambda )+X^{i}\right] \frac{\delta _{l}S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })}{\delta \phi ^{i}}+\int \left[
R_{c}^{i}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu })-X^{i}\right] \frac{\delta _{l}S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i}}=0,$$ which is true for arbitrary functions $X^{i}$. If we choose $$X^{i}=R_{c}^{i}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu })-R_{c}^{i}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu }),$$ the transformations of the background fields contain only background fields and coincide with $R_{c}^{i}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu })$. We find $$\int \left[ R_{c}^{i}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\Lambda +{\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu })-R_{c}^{i}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu })\right] \frac{\delta
_{l}S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })}{\delta \phi ^{i}}+\int R_{c}^{i}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu })\frac{\delta _{l}S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i}}=0. \label{bas}$$
Thus, denoting background quantities by means of an underlining, we are led to consider the action $$S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })-\int R^{\alpha }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })K_{\alpha }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })({\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }-K_{\alpha }), \label{sback}$$ which solves the master equation $\llbracket S,S\rrbracket =0$, where the antiparentheses are defined as $$\llbracket X,Y\rrbracket =\int \left\{ \frac{\delta _{r}X}{\delta \Phi
^{\alpha }}\frac{\delta _{l}Y}{\delta K_{\alpha }}+\frac{\delta _{r}X}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}\frac{\delta _{l}Y}{\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }}-\frac{\delta _{r}X}{\delta K_{\alpha }}\frac{\delta _{l}Y}{\delta \Phi ^{\alpha }}-\frac{\delta _{r}X}{\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }}\frac{\delta _{l}Y}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}\right\} .$$
More directly, if $S(\Phi ,K)=S_{c}(\phi )-\int R^{\alpha }(\Phi )K_{\alpha
} $ solves $(S,S)=0$, the background field can be introduced with a canonical transformation. Start from the action $$S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=S_{c}(\phi )-\int R^{\alpha
}(\Phi )K_{\alpha }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha
}, \label{sback0}$$ which obviously satisfies two master equations, one in the variables $\Phi
,K $ and the other one in the variables ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$. [*A fortiori*]{}, it also satisfies $\llbracket S,S\rrbracket =0$. Relabeling fields and sources with primes and making the canonical transformation generated by the functional $$F_{\text{b}}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime
})=\int (\Phi ^{\alpha }+{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha })K_{\alpha }^{\prime
}+\int {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime },
\label{casbac}$$ we obtain (\[sback\]), and clearly preserve $\llbracket S,S\rrbracket =0$.
The shift ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ is called background field, while $\Phi $ is called quantum field. We also have quantum sources $K$ and background sources ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$. Finally, we have background transformations, those described by the background ghosts ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ or the functions ${\mkern2mu\underline{\mkern-2mu\smash{\Lambda }\mkern-2mu}\mkern2mu }$ in (\[bas\]), and quantum transformations, those described by the quantum ghosts $C$ and (\[esto\]) or the functions $\Lambda $ in (\[bas\]).
The action (\[sback\]) is not the most convenient one to study renormalization. It is fine in the minimal sector (the one with antighosts and Lagrange multipliers switched off), but not in the nonminimal one. Now we describe the improvements we need to make.
#### Non-minimal sector
So far we have introduced background copies of all fields. Nevertheless, strictly speaking we do not need to introduce copies of the antighosts $\bar{C}$ and the Lagrange multipliers $B$, since we do not need to gauge-fix the background. Thus we drop ${\mkern2mu\underline{\mkern-2mu\smash{\bar{C}}\mkern-2mu}\mkern2mu }$, ${\mkern2mu\underline{\mkern-2mu\smash{B}\mkern-2mu}\mkern2mu }$ and their sources from now on, and define ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }=\{{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{I},0,0\}$, ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }=\{{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\phi }^{i},{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C}^{I},0,0\}$. Observe that then we have $R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })=\bar{R}^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })=\{R_{\phi }^{i}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }),R_{C}^{I}({\mkern2mu\underline{\mkern-2mu\smash{\Phi
}\mkern-2mu}\mkern2mu }),0,0\}$.
Let us compare the nonminimal sectors (\[esto\]) and (\[estobar\]). If we choose (\[esto\]), $\bar{C}$ and $B$ do not transform under background transformations. Since (\[esto\]) are the only terms that contain $K_{\bar{C}}$, they do not contribute to one-particle irreducible diagrams and do not receive radiative corrections. Moreover, $K_{B}$ does not appear in the action. Instead, if we choose the nonminimal sector (\[estobar\]), namely if we start from $$S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=S_{c}(\phi )-\int \bar{R}^{\alpha
}(\Phi )K_{\alpha }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha
} \label{sback1}$$ instead of (\[sback0\]), the transformation (\[casbac\]) gives the action $$S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })-\int (\bar{R}^{\alpha }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })-\bar{R}^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }))K_{\alpha }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }. \label{sback2}$$ In particular, using the linearity of $\mathcal{R}_{\bar{C}}^{I}$ and $\mathcal{R}_{B}^{I}$ in $C$, we see that (\[estobar\]) is turned into itself plus $$-\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{\bar{C}}^{I}-\int
\mathcal{R}_{B}^{I}(B,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{I}. \label{bacca}$$ Because of these new terms, $\bar{C}$ and $B$ now transform as ordinary matter fields under background transformations. This is the correct background transformation law we need for them. On the other hand, the nonminimal sector (\[estobar\]) also generates nontrivial quantum transformations for $\bar{C}$ and $B$, which are renormalized and complicate our derivations.
It would be better to have (\[estobar\]) in the background sector and (\[esto\]) in the nonbackground sector. To achieve this goal, we make the canonical transformation generated by $$F_{\text{nm}}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\int \Phi ^{\alpha }K_{\alpha }^{\prime }+\int {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{I\hspace{0.01in}\prime } \label{casbacca}$$ on (\[sback\]). Using (\[iddo\]) again, the result is $$\begin{aligned}
S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }) &=&S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })-\int (R^{\alpha }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })-R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }))K_{\alpha } \nonumber \\
&&-\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{\bar{C}}^{I}-\int
\mathcal{R}_{B}^{I}(B,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{I}-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }. \label{sbacca}\end{aligned}$$ This is the background field action we are going to work with. It is straightforward to check that (\[sbacca\]) satisfies $\llbracket S,S\rrbracket =0$.
#### Separating the background and quantum sectors
Now we separate the background sector from the quantum sector. To do this properly we need to make further assumptions.
First, we assume that there exists a choice of field variables where the functions $R^{\alpha }(\Phi )$ are at most quadratic in $\Phi $. We call it *linearity assumption*. It is equivalent to assume that the gauge transformations $\delta _{\Lambda
}\phi ^{i}=R_{c}^{i}(\phi ,\Lambda )$ of (\[lif\]) are linear functions of the fields $\phi $ and closure is expressed by $\phi $-independent identities $[\delta _{\Lambda },\delta _{\Sigma }]=\delta _{[\Lambda ,\Sigma
]}$. The linearity assumption is satisfied by all gauge symmetries of physical interest, such as those of QED, non-Abelian Yang-Mills theory, quantum gravity and the Standard Model. On the other hand, it is not satisfied by other important symmetries, among which is supergravity, where the gauge transformations either close only on shell or are not linear in the fields.
Second, we assume that the gauge algebra is irreducible, which ensures that the set $\Phi $ contains only ghosts and not ghosts of ghosts.
Under these assumptions, we make the canonical transformation generated by $$F_{\tau }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\int
\Phi ^{\alpha }K_{\alpha }^{\prime }+\int {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+(\tau -1)\int {\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{I}{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C}^{I\hspace{0.01in}\prime } \label{backghost}$$ on the action (\[sbacca\]). This transformation amounts to rescaling the background ghosts ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{I}$ by a factor $\tau $ and their sources ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C}^{I}$ by a factor $1/\tau $. Since we do not have background antighosts, (\[backghost\]) is the background-ghost-number transformation combined with a rescaling of the background sources.
The action (\[sbacca\]) is not invariant under (\[backghost\]). Using the linearity assumption it is easy to check that the transformed action $S_{\tau }$ is linear in $\tau $. Writing $S_{\tau }=\hat{S}+\tau \bar{S}$ we can split the total action $S$ into the sum $\hat{S}+\bar{S}$ of a *quantum action* $\hat{S}$ and a *background action* $\bar{S}$.
Precisely, the quantum action $\hat{S}$ does not depend on the background sources ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$ and the background ghosts ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$, but only on the background copies ${\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }$ of the physical fields. We have $$\hat{S}=\hat{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)=S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })-\int R^{\alpha }(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },C,\bar{C},B)K_{\alpha }.
\label{deco}$$ Note that, in spite of the notation, the functions $R^{\alpha }(\Phi )$ are actually $\bar{C}$ independent. Moreover, we find $$\bar{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=-\int \mathcal{R}^{\alpha
}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{\alpha }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }, \label{sbar}$$ where, for $\phi $ and $C$, $$\mathcal{R}^{\alpha }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })=R^{\alpha }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi
}\mkern-2mu}\mkern2mu })-R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })-R^{\alpha }(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },C,\bar{C},B). \label{batra}$$ These functions transform $\phi $ and $C$ as if they were matter fields and are of course linear in $\Phi $ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$. Note that formula (\[batra\]) does not hold for antighosts and Lagrange multipliers. In the end all quantum fields transform as matter fields under background transformations.
The master equation $\llbracket S,S\rrbracket =0$ decomposes into the three identities $$\llbracket \hat{S},\hat{S}\rrbracket =\llbracket \hat{S},\bar{S}\rrbracket =\llbracket \bar{S},\bar{S}\rrbracket =0, \label{treide}$$ which we call *background field master equations*.
The quantum transformations are described by $\hat{S}$ and the background ones are described by $\bar{S}$. Background fields are inert under quantum transformations, because $\llbracket \hat{S},{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }\rrbracket =0$. Note that $$\llbracket \hat{S},\llbracket \bar{S},X\rrbracket \rrbracket +\llbracket
\bar{S},\llbracket \hat{S},X\rrbracket \rrbracket =0, \label{uso}$$ where $X$ is an arbitrary local functional. This property follows from the Jacobi identity of the antiparentheses and $\llbracket \hat{S},\bar{S}\rrbracket =0$, and states that background and quantum transformations commute.
#### Gauge-fixing
Now we come to the gauge fixing. In the usual approach, the theory is typically gauge-fixed by means of a canonical transformation that amounts to replacing the action $S$ by$\ S+(S,\Psi )$, where $\Psi $ is a local functional of ghost number $-1$ and depends only on the fields $\Phi $. Using the background field method it is convenient to search for a ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$-independent gauge-fixing functional $\Psi (\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })$ that is also invariant under background transformations, namely such that $$\llbracket \bar{S},\Psi \rrbracket =0. \label{backgf}$$ Then we fix the gauge with the usual procedure, namely we make a canonical transformation generated by $$F_{\text{gf}}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime
})=\int \ \Phi ^{\alpha }K_{\alpha }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+\Psi (\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }).
\label{backgfgen}$$ Because of (\[backgf\]) the gauge-fixed action reads $$S_{\text{gf}}=\hat{S}+\bar{S}+\llbracket \hat{S},\Psi \rrbracket .
\label{fgback}$$ Defining $\hat{S}_{\text{gf}}=\hat{S}+\llbracket \hat{S},\Psi \rrbracket $, identities (\[treide\]), (\[uso\]) and (\[backgf\]) give $\llbracket
\hat{S}_{\text{gf}},\hat{S}_{\text{gf}}\rrbracket =\llbracket
\hat{S}_{\text{gf}},\bar{S}\rrbracket =0$, so it is just like gauge-fixing $\hat{S}$. Since both $\hat{S}$ and $\Psi $ are ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independent, $\hat{S}_{\text{gf}}$ is also ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independent. Observe that the canonical transformations (\[backghost\]) and (\[backgfgen\]) commute; therefore we can safely apply the transformation (\[backghost\]) to the gauge-fixed action. A gauge fixing satisfying (\[backgf\]) is called *background-preserving gauge fixing*.
In some derivations of this paper the background field master equations (\[treide\]) are violated in intermediate steps; therefore we need to prove properties that hold more generally. Specifically, consider an action $$S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\hat{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)+\bar{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }), \label{assu}$$ equal to the sum of a ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$- and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$-independent “quantum action” $\hat{S}$, plus a “background action” $\bar{S}$ that satisfies the following requirements: ($i$) it is a linear function of the quantum fields $\Phi $, ($ii$) it gets multiplied by $\tau $ when applying the canonical transformation (\[backghost\]), and ($iii$) $\delta _{l}\bar{S}/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi $ independent. In particular, requirement ($ii$) implies that $\bar{S}$ vanishes at ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }=0$. Since $\bar{S}$ is a linear function of $\Phi $, it does not contribute to one-particle irreducible diagrams. Since $\hat{S}$ does not depend on ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$, while $\bar{S}$ vanishes at ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }=0$, $\bar{S}$ receives no radiative corrections. Thus the $\Gamma$ functional associated with the action (\[assu\]) satisfies $$\Gamma (\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\hat{\Gamma}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)+\bar{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }).
\label{becco}$$ Moreover, thanks to theorem \[thb\] of the appendix we have the general identity $$\llbracket \Gamma ,\Gamma \rrbracket =\langle \llbracket S,S\rrbracket \rangle , \label{univ}$$ under the sole assumption that $\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi $ independent.
Applying the canonical transformation (\[backghost\]) to $\Gamma $ we find $\Gamma _{\tau }=\hat{\Gamma}+\tau \bar{S}$, so (\[univ\]) gives the identities $$\llbracket \hat{\Gamma},\hat{\Gamma}\rrbracket =\langle \llbracket \hat{S},\hat{S}\rrbracket \rangle ,\qquad \llbracket \bar{S},\hat{\Gamma}\rrbracket =\langle \llbracket \bar{S},\hat{S}\rrbracket \rangle . \label{give}$$ When $\llbracket S,S\rrbracket =0$ we have $$\llbracket \Gamma ,\Gamma \rrbracket =\llbracket \hat{\Gamma},\hat{\Gamma}\rrbracket =\llbracket \bar{S},\hat{\Gamma}\rrbracket =0. \label{msb}$$
Observe that, thanks to the linearity assumption, an $\bar{S}$ equal to (\[sbar\]) satisfies the requirements of formula (\[assu\]).
Now we give details about the background-preserving gauge fixing we pick for the action (\[sbacca\]). It is convenient to choose gauge-fixing functions $G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi ^{i}$ that are linear in the quantum fields $\phi $, where $G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )$ may contain derivative operators. Precisely, we choose the gauge fermion $$\Psi (\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })=\int \bar{C}^{I}G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi ^{i}, \label{psiback}$$ and assume that it satisfies (\[backgf\]). A more common choice would be (see (\[seeym\]) for Yang-Mills theory) $$\Psi (\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })=\int \bar{C}^{I}\left( G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi
}\mkern-2mu}\mkern2mu },\partial )\phi ^{i}+\xi _{IJ}B^{J}\right) ,$$ where $\xi _{IJ}$ are gauge-fixing parameters. In this case, when we integrate the $B$ fields out the expressions $G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi ^{i}$ get squared. However, (\[psiback\]) is better for our purposes, because it makes the canonical transformations (\[casbacca\]) and (\[backgfgen\]) commute with each other. We call the choice (\[psiback\]) *regular Landau gauge*. The gauge-field propagators coincide with the ones of the Landau gauge. Nevertheless, while the usual Landau gauge (with no $B$’s around) is singular, here gauge fields are part of multiplets that include the $B$’s, therefore (\[psiback\]) is regular.
In the regular Landau gauge, using (\[backgf\]) and applying (\[backgfgen\]) to (\[sbacca\]) we find $$S_{\text{gf}}=\hat{S}_{\text{gf}}+\bar{S}=S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })-\int R^{\alpha }(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },C,\bar{C},B)\tilde{K}_{\alpha
}-\int \mathcal{R}^{\alpha }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{\alpha }-\int R^{\alpha
}({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }, \label{sbaccagf}$$ where the tilde sources $\tilde{K}_{\alpha }$ coincide with $K_{\alpha }$ apart from $\tilde{K}_{\phi }^{i}$ and $\tilde{K}_{\bar{C}}^{I}$, which are $$\tilde{K}_{\phi }^{i}=K_{\phi }^{i}-\bar{C}^{I}G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },-\overleftarrow{\partial }),\qquad \tilde{K}_{\bar{C}}^{I}=K_{\bar{C}}^{I}-G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi ^{i}. \label{chif}$$
Recalling that the functions $R^{\alpha }(\Phi )$ are $\bar{C}$ independent, we see that $\hat{S}_{\text{gf}}$ does not depend on $K_{\phi }^{i}$ and $\bar{C}$ separately, but only through the combination $\tilde{K}_{\phi }^{i}$. Every one-particle irreducible diagram with $\bar{C}^{I}$ external legs actually factorizes a $-\bar{C}^{I}G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },-\overleftarrow{\partial })$ on those legs. Replacing one or more such objects with $K_{\phi
}^{i}$s, we obtain other contributing diagrams. Conversely, replacing one or more $K_{\phi }^{i}$-external legs with $-\bar{C}^{I}G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },-\overleftarrow{\partial })$ we also obtain contributing diagrams. Therefore, all radiative corrections, as well as the renormalized action $\hat{S}_{R}$ and the $\Gamma $ functionals $\hat{\Gamma}$ and $\hat{\Gamma}_{R}$ associated with the action (\[sbaccagf\]), do not depend on $K_{\phi }^{i}$ and $\bar{C}$ separately, but only through the combination $\tilde{K}_{\phi }^{i}$.
The only $B$-dependent terms of $\hat{S}_{\text{gf}}$, provided by $\llbracket S,\Psi \rrbracket $ and (\[esto\]), are $$\Delta S_{B}\equiv -\int B^{I}\tilde{K}_{\bar{C}}^{I}=\int B^{I}\left(
G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi ^{i}-K_{\bar{C}}^{I}\right) ,
\label{chio}$$ and are quadratic or linear in the quantum fields. For this reason, no one-particle irreducible diagrams can contain external $B$ legs, therefore $\Delta S_{B}$ is nonrenormalized and goes into $\hat{S}_{R}$, $\hat{\Gamma}$ and $\hat{\Gamma}_{R}$ unmodified.
We thus learn that using linear gauge-fixing functions we can set $\bar{C}=B=0$ and later restore the correct $\bar{C}$ and $B$ dependencies in $\hat{S}_{\text{gf}}$, $\hat{S}_{R}$, $\hat{\Gamma}$ and $\hat{\Gamma}_{R}$ just by replacing $K_{\phi }^{i}$ with $\tilde{K}_{\phi }^{i}$ and adding $\Delta S_{B}$.
From now on when no confusion can arise we drop the subscripts of $S_{\text{gf}}$ and $\hat{S}_{\text{gf}}$ and assume that the background field theory is gauge-fixed in the way just explained.
Background-preserving canonical transformations
-----------------------------------------------
It is useful to characterize the most general canonical transformations $\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }\rightarrow \Phi ^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\prime },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime }$ that preserve the background field master equations (\[treide\]) and the basic properties of $\hat{S}$ and $\bar{S}$.
By definition, all canonical transformations preserve the antiparentheses, so (\[treide\]) are turned into $$\llbracket \hat{S}^{\prime },\hat{S}^{\prime }\rrbracket ^{\prime }=\llbracket \hat{S}^{\prime },\bar{S}^{\prime }\rrbracket ^{\prime }=\llbracket \bar{S}^{\prime },\bar{S}^{\prime }\rrbracket ^{\prime }=0.
\label{tretre}$$ Moreover, $\hat{S}^{\prime }$ should be ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{\prime }$ independent, while $\bar{S}$ should be invariant, because it encodes the background transformations. This means $$\bar{S}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\bar{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }). \label{thesisback}$$
We prove that a canonical transformation defined by a generating functional of the form $$F(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\int \ \Phi
^{\alpha }K_{\alpha }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+Q(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime }),
\label{cannonaback}$$ where $Q$ is a ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime }$- and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$-independent local functional such that $$\llbracket \bar{S},Q(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)\rrbracket =0,
\label{assumback}$$ satisfies our requirements.
Since $Q$ is ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independent, the background fields and the sources ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C}$ do not transform: ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\prime }={\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$, ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C}^{\prime }={\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C}$. Moreover, the action $\hat{S}^{\prime }$ is clearly ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{\prime }$ independent, as desired, so we just need to prove (\[thesisback\]). For convenience, multiply $Q$ by a constant parameter $\zeta $ and consider the canonical transformations generated by $$F_{\zeta }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\int
\ \Phi ^{\alpha }K_{\alpha }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+\zeta Q(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime
}). \label{fg}$$ Given a functional $X(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })$ it is often useful to work with the tilde functional $$\tilde{X}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=X(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }),{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime
}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })). \label{tildedfback}$$ obtained by expressing the primed sources in terms of unprimed fields and sources. Assumption (\[assumback\]) tells us that $Q(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi
}\mkern-2mu}\mkern2mu },K)$ is invariant under background transformations. Since $\Phi ^{\alpha }$ and $K_{\beta }$ transform as matter fields under such transformations, it is clear that $\delta Q/\delta K_{\alpha }$ and $\delta Q/\delta \Phi
^{\beta }$ transform precisely like them, as well as $\Phi ^{\alpha \hspace{0.01in}\prime }$ and $K_{\beta }^{\prime }$. Moreover, we have $\llbracket
\bar{S},\tilde{Q}\rrbracket =0$ for every $\zeta $. Applying theorem \[theorem5\] to $\chi =\bar{S}$ we obtain $$\frac{\partial ^{\prime }\bar{S}^{\prime }}{\partial \zeta }=\frac{\partial
\bar{S}}{\delta \zeta }-\llbracket \bar{S},\tilde{Q}\rrbracket =\frac{\partial \bar{S}}{\delta \zeta }, \label{tocback}$$ where $\partial ^{\prime }/\partial \zeta $ is taken at constant primed variables and $\partial /\partial \zeta $ is taken at constant unprimed variables. If we treat the unprimed variables as $\zeta $ independent, and the primed variables as functions of them and $\zeta $, the right-hand side of (\[tocback\]) vanishes. Varying $\zeta $ from 0 to 1 we get $$\bar{S}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\bar{S}^{\prime
}(\Phi ^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\prime },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\bar{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }),$$ where now the relations among primed and unprimed variables are those specified by (\[cannonaback\]).
We call the canonical transformations just defined *background-preserving canonical transformations*. We stress once again that they do not just preserve the background field (${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\prime }={\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$), but also the background transformations ($\bar{S}^{\prime }=\bar{S}$) and the ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independence of $\hat{S}$. The gauge-fixing canonical transformation (\[backgfgen\]) is background preserving.
Canonical transformations may convert the sources $K$ into functions of both fields and sources. However, the sources are external, while the fields are integrated over. Thus, canonical transformations must be applied at the level of the action $S$, not at the levels of generating functionals. In the functional integral they must be meant as mere replacements of integrands. Nevertheless, we recall that there exists a way [@fieldcov; @masterf; @mastercan] to upgrade the formalism of quantum field theory and overcome these problems. The upgraded formalism allows us to implement canonical transformations as true changes of field variables in the functional integral, and closely track their effects inside generating functionals, as well as throughout the renormalization algorithm.
Renormalization
===============
In this section we give the basic algorithm to subtract divergences to all orders. As usual, we proceed by induction in the number of loops and use the dimensional-regularization technique and the minimal subtraction scheme. We assume that gauge anomalies are manifestly absent, i.e. that the background field master equations (\[treide\]) hold exactly at the regularized level. We first work on the classical action $S=\hat{S}+\bar{S}$ of (\[sbaccagf\]) and define a background-preserving subtraction algorithm. Then we generalize the results to non-background-preserving actions.
Call $S_{n}$ and $\Gamma _{n}$ the action and the $\Gamma $ functional renormalized up to $n$ loops included, with $S_{0}=S$, and write the loop expansion as $$\Gamma _{n}=\sum_{k=0}^{\infty }\hbar ^{n}\Gamma _{n}^{(k)}.$$ The inductive assumptions are that $S_{n}$ has the form (\[assu\]), with $\bar{S}$ given by (\[sbar\]), and $$\begin{aligned}
S_{n} &=&S+\text{poles},\qquad \Gamma _{n}^{(k)}<\infty ~~\forall k\leqslant
n, \label{assu1} \\
\llbracket S_{n},S_{n}\rrbracket &=&\mathcal{O}(\hbar ^{n+1}),\qquad \llbracket \bar{S},S_{n}\rrbracket =0, \label{assu2}\end{aligned}$$ where “poles” refers to the divergences of the dimensional regularization. Clearly, the assumptions (\[assu1\]) and (\[assu2\]) are satisfied for $n=0$.
Using formulas (\[give\]) and recalling that $\llbracket
S_{n},S_{n}\rrbracket $ is a local insertion of order $\mathcal{O}(\hbar
^{n+1})$, we have $$\llbracket \Gamma _{n},\Gamma _{n}\rrbracket =\langle \llbracket S_{n},S_{n}\rrbracket \rangle =\llbracket S_{n},S_{n}\rrbracket +\mathcal{O}(\hbar
^{n+2}),\qquad \llbracket \bar{S},\Gamma _{n}\rrbracket =\langle \llbracket
\bar{S},S_{n}\rrbracket \rangle =0. \label{gnback2}$$ By $\llbracket S,S\rrbracket =0$ and the first of (\[assu1\]), $\llbracket
S_{n},S_{n}\rrbracket $ is made of pure poles.
Now, take the order $\hbar ^{n+1}$ of equations (\[gnback2\]) and then their divergent parts. The second of (\[assu1\]) tells us that all subdivergences are subtracted away, so the order-$\hbar ^{n+1}$ divergent part $\Gamma _{n\text{ div}}^{(n+1)}$ of $\Gamma _{n}$ is a local functional. We obtain $$\llbracket S,\Gamma _{n\text{ div}}^{(n+1)}\rrbracket =\frac{1}{2}\llbracket S_{n},S_{n}\rrbracket +\mathcal{O}(\hbar ^{n+2}),\qquad \llbracket \bar{S},\Gamma _{n\text{ div}}^{(n+1)}\rrbracket =0. \label{gn2back}$$
Define $$S_{n+1}=S_{n}-\Gamma _{n\text{ div}}^{(n+1)}. \label{snp1back}$$ Since $S_{n}$ has the form (\[assu\]), $\Gamma _{n}$ has the form (\[becco\]), therefore both $\hat{\Gamma}_{n}$ and $\Gamma _{n\text{ div}}^{(n+1)}$ are ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independent, which ensures that $S_{n+1}$ has the form (\[assu\]) (with $\bar{S}$ given by (\[sbar\])). Moreover, the first inductive assumption of (\[assu1\]) is promoted to $S_{n+1}$. The diagrams constructed with the vertices of $S_{n+1} $ are the diagrams of $S_{n}$, plus new diagrams containing vertices of $-\Gamma _{n\text{ div}}^{(n+1)}$; therefore $$\Gamma _{n+1}^{(k)}=\Gamma _{n}^{(k)}<\infty ~~\forall k\leqslant n,\qquad
\Gamma _{n+1}^{(n+1)}=\Gamma _{n}^{(n+1)}-\Gamma _{n\text{ div}}^{(n+1)}<\infty ,$$ which promotes the second inductive assumption of (\[assu1\]) to $n+1$ loops. Finally, formulas (\[gn2back\]) and (\[snp1back\]) give $$\llbracket S_{n+1},S_{n+1}\rrbracket =\llbracket S_{n},S_{n}\rrbracket -2\llbracket S,\Gamma _{n\text{ div}}^{(n+1)}\rrbracket +\mathcal{O}(\hbar
^{n+2})=\mathcal{O}(\hbar ^{n+2}),\qquad \llbracket \bar{S},S_{n+1}\rrbracket =0,$$ so (\[assu2\]) are also promoted to $n+1$ loops.
We conclude that the renormalized action $S_{R}=S_{\infty }$ and the renormalized generating functional $\Gamma _{R}=\Gamma _{\infty }$ satisfy the background field master equations $$\llbracket S_{R},S_{R}\rrbracket =\llbracket \bar{S},S_{R}\rrbracket =0,\qquad \llbracket \Gamma _{R},\Gamma _{R}\rrbracket =\llbracket \bar{S},\Gamma _{R}\rrbracket =0. \label{finback}$$ For later convenience we write down the form of $S_{R}$, which is $$S_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)+\bar{S}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)-\int \mathcal{R}^{\alpha }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{\alpha }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }.
\label{sr1}$$
In the usual (non-background field) approach the results just derived hold if we just ignore background fields and sources, as well as background transformations, and use the standard parentheses $(X,Y)$ instead of $\llbracket X,Y\rrbracket $. Then the subtraction algorithm starts with a classical action $S(\Phi ,K)$ that satisfies the usual master equation $(S,S)=0$ exactly at the regularized level and ends with a renormalized action $S_{R}(\Phi ,K)=S_{\infty }(\Phi ,K)$ and a renormalized generating functional $\Gamma _{R}(\Phi ,K)=\Gamma _{\infty }(\Phi ,K)$ that satisfy the usual master equations $(S_{R},S_{R})=(\Gamma _{R},\Gamma _{R})=0$.
In the presence of background fields ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ and background sources ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$, ignoring invariance under background transformations (encoded in the parentheses $\llbracket \bar{S},S\rrbracket $, $\llbracket \bar{S},S_{n}\rrbracket $, $\llbracket \bar{S},S_{R}\rrbracket
$ and similar ones for the $\Gamma $ functionals), we can generalize the results found above to any classical action $S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })$ that satisfies $\llbracket S,S\rrbracket =0$ at the regularized level and is such that $\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi $ independent. Indeed, these assumptions allow us to apply theorem \[thb\], instead of formulas (\[give\]), which is enough to go through the subtraction algorithm ignoring the parentheses $\llbracket \bar{S},X\rrbracket $. We have $\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }=\delta _{l}\Gamma /\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }=\delta
_{l}S_{n}/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ for every $n$. Thus, we conclude that a classical action $S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })$ that satisfies $\llbracket S,S\rrbracket =0$ at the regularized level and is such that $\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi $ independent gives a renormalized action $S_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })$ and a $\Gamma $ functional $\Gamma _{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })$ that satisfy $\llbracket S_{R},S_{R}\rrbracket =\llbracket \Gamma
_{R},\Gamma _{R}\rrbracket =0$ and $\delta _{l}S_{R}/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }=\delta _{l}\Gamma _{R}/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }=\delta
_{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$.
The renormalization algorithm of this section is a generalization to the background field method of the procedure first given in ref. [@lavrov]. Since it subtracts divergences just as they come, as emphasized by formula (\[snp1back\]), we use to call it “raw” subtraction [@regnocoho], to distinguish it from algorithms where divergences are subtracted away at each step by means of parameter redefinitions and canonical transformations. The raw subtraction does not ensure RG invariance [@regnocoho], because it subtracts divergent terms even when there is no (running) parameter associated with them. For the same reason, it tells us very little about parametric completeness.
In power-counting renormalizable theories the raw subtraction is satisfactory, since we can start from a classical action $S_{c}$ that already contains all gauge-invariant terms that are generated back by renormalization. Nevertheless, in nonrenormalizable theories, such as quantum gravity, effective field theories and nonrenormalizable extensions of the Standard Model, in principle renormalization can modify the symmetry transformations in physically observable ways (see ref. [@regnocoho] for a discussion about this possibility). In section 5 we prove that this actually does not happen under the assumptions we have made in this paper; namely when gauge anomalies are manifestly absent, the gauge algebra is irreducible and closes off shell, and $R^{\alpha }(\Phi )$ are quadratic functions of the fields $\Phi $. Precisely, renormalization affects the symmetry only by means of canonical transformations and parameter redefinitions. Then, to achieve parametric completeness it is sufficient to include all gauge-invariant terms in the classical action $S_{c}(\phi )$, as classified by the starting gauge symmetry. The background field method is crucial to prove this result without advocating involved cohomological classifications.
Gauge dependence
================
In this section we study the dependence on the gauge fixing and the renormalization of canonical transformations. We first derive the differential equations that govern gauge dependence; then we integrate them and finally use the outcome to describe the renormalized canonical transformation that switches between the background field approach and the conventional approach. These results will be useful in the next section to prove parametric completeness.
The parameters of a canonical transformation are associated with changes of field variables and changes of gauge fixing. For brevity we call all of them “gauge-fixing parameters” and denote them with $\xi $. Let (\[cannonaback\]) be a tree-level canonical transformation satisfying (\[assumback\]). We write $Q(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\xi )$ to emphasize the $\xi $ dependence of $Q$. We prove that for every gauge-fixing parameter $\xi $ there exists a local ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$- and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$-independent functional $Q_{R,\xi }$ such that $$Q_{R,\xi }=\widetilde{Q_{\xi }}+\mathcal{O}(\hbar )\text{-poles},\qquad
\langle Q_{R,\xi }\rangle <\infty , \label{babaoback}$$ and $$\frac{\partial S_{R}}{\partial \xi }=\llbracket S_{R},Q_{R,\xi }\rrbracket ,\qquad \llbracket \bar{S},Q_{R,\xi }\rrbracket =0,\qquad \frac{\partial
\Gamma _{R}}{\partial \xi }=\llbracket \Gamma _{R},\langle Q_{R,\xi }\rangle \rrbracket , \label{backgind}$$ where $Q_{\xi }=\partial Q/\partial \xi $, $\widetilde{Q_{\xi }}$ is defined as shown in (\[tildedfback\]) and the average is calculated with the action $S_{R}$. We call the first and last equations of the list (\[backgind\]) *differential equations of* *gauge dependence*. They ensure that renormalized functionals depend on gauge-fixing parameters in a cohomologically exact way. Later we integrate equations (\[backgind\]) and move every gauge dependence inside a (renormalized) canonical transformation. A consequence is that physical quantities are gauge independent.
We derive (\[backgind\]) proceeding inductively in the number of loops, as usual. The inductive assumption is that there exists a ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$- and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$-independent local functional $Q_{n,\xi }=\widetilde{Q_{\xi }}+\mathcal{O}(\hbar )$-poles such that $\langle Q_{n,\xi }\rangle $ is convergent up to the $n$th loop included (the average being calculated with the action $S_{n}$) and $$\frac{\partial S_{n}}{\partial \xi }=\llbracket S_{n},Q_{n,\xi }\rrbracket +\mathcal{O}(\hbar ^{n+1}),\qquad \llbracket \bar{S},Q_{n,\xi }\rrbracket =0.
\label{inda1back}$$ Applying the identity (\[thesis\]), which here holds with the parentheses $\llbracket X,Y\rrbracket $, we easily see that $Q_{0,\xi }=\widetilde{Q_{\xi
}}$ satisfies (\[inda1back\]) for $n=0$. Indeed, taking $\chi =S$ and noting that $\left. \partial S^{\prime }/\partial \xi \right| _{\Phi
^{\prime },K^{\prime }}=0$, since the parameter $\xi $ is absent before the transformation (a situation that we describe using primed variables), we get the first relation of (\[inda1back\]), without $\mathcal{O}(\hbar )$ corrections. Applying (\[thesis\]) to $\chi =\bar{S}$ and recalling that $\bar{S}$ is invariant, we get the second relation of (\[inda1back\]).
Let $Q_{n,\xi \hspace{0.01in}\text{div}}^{(n+1)}$ denote the $\mathcal{O}(\hbar ^{n+1})$ divergent part of $\langle Q_{n,\xi }\rangle $. The inductive assumption ensures that all subdivergences are subtracted away, so $Q_{n,\xi \hspace{0.01in}\text{div}}^{(n+1)}$ is local. Define $$Q_{n+1,\xi }=Q_{n,\xi }-Q_{n,\xi \hspace{0.01in}\text{div}}^{(n+1)}.
\label{refdback}$$ Clearly, $Q_{n+1,\xi }$ is ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independent and equal to $\widetilde{Q_{\xi }}+\mathcal{O}(\hbar )$-poles. Moreover, by construction $\langle Q_{n+1,\xi }\rangle $ is convergent up to the $(n+1)$-th loop included, where the average is calculated with the action $S_{n+1}$.
Now, corollary \[corolla\] tells us that $\llbracket
\bar{S},Q_{n,\xi }\rrbracket =0$ and $\llbracket
\bar{S},S_{n}\rrbracket =0$ imply $\llbracket
\bar{S},\langle Q_{n,\xi }\rangle \rrbracket =0$. Taking the $\mathcal{O}(\hbar ^{n+1})$ divergent part of this formula we obtain $\llbracket
\bar{S},Q_{n,\xi \hspace{0.01in}\text{div}}^{(n+1)}\rrbracket =0$; therefore the second formula of (\[inda1back\]) is promoted to $n+1$ loops.
Applying corollary \[cora\] to $\Gamma _{n}$ and $S_{n}$, with $X=Q_{n,\xi
}$, we have the identity $$\frac{\partial \Gamma _{n}}{\partial \xi }=\llbracket \Gamma _{n},\langle
Q_{n,\xi }\rangle \rrbracket +\left\langle \frac{\partial S_{n}}{\partial
\xi }-\llbracket S_{n},Q_{n,\xi }\rrbracket \right\rangle +\frac{1}{2}\left\langle \llbracket S_{n},S_{n}\rrbracket \hspace{0.01in}Q_{n,\xi
}\right\rangle _{\Gamma }, \label{provef}$$ where $\left\langle AB\right\rangle _{\Gamma }$ denotes the one-particle irreducible diagrams with one $A$ insertion and one $B$ insertion. Now, observe that if $A=\mathcal{O}(\hbar ^{n_{A}})$ and $B=\mathcal{O}(\hbar
^{n_{B}})$ then $\left\langle AB\right\rangle _{\Gamma }=\mathcal{O}(\hbar
^{n_{A}+n_{B}+1})$, since the $A,B$ insertions can be connected only by loops. Let us take the $\mathcal{O}(\hbar ^{n+1})$ divergent part of (\[provef\]). By the inductive assumption (\[assu2\]), the last term of (\[provef\]) can be neglected. By the inductive assumption (\[inda1back\]) we can drop the average in the second-to-last term. We thus get $$\frac{\partial \Gamma _{n\ \text{div}}^{(n+1)}}{\partial \xi }=\llbracket
\Gamma _{n\ \text{div}}^{(n+1)},Q_{0,\xi }\rrbracket +\llbracket
S,Q_{n,\xi \hspace{0.01in}\text{div}}^{(n+1)}\rrbracket +\frac{\partial S_{n}}{\partial \xi }-\llbracket
S_{n},Q_{n,\xi }\rrbracket +\mathcal{O}(\hbar ^{n+2}).$$ Using this fact, (\[snp1back\]) and (\[refdback\]) we obtain $$\frac{\partial S_{n+1}}{\partial \xi }=\llbracket S_{n+1},Q_{n+1,\xi }\rrbracket +\mathcal{O}(\hbar ^{n+2}), \label{sunpi}$$ which promotes the first inductive hypothesis of (\[inda1back\]) to order $\hbar ^{n+1}$. When $n$ is taken to infinity, the first two formulas of (\[backgind\]) follow, with $Q_{R,\xi }=Q_{\infty ,\xi }$. The third identity of (\[backgind\]) follows from the first one, using (\[provef\]) with $n=\infty $ and $\llbracket
\hat{S}_{R},\hat{S}_{R}\rrbracket =0$. This concludes the derivation of (\[backgind\]).
Integrating the differential equations of gauge dependence {#integrating}
----------------------------------------------------------
Now we integrate the first two equations of (\[backgind\]) and find the renormalized canonical transformation that corresponds to a tree-level transformation (\[cannonaback\]) satisfying (\[assumback\]). Specifically, we prove that
There exists a background-preserving canonical transformation $$F_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime },\xi )=\int
\ \Phi ^{A}K_{A}^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{A}{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{A}^{\prime }+Q_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\xi ),
\label{finalcanback}$$ where $Q_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\xi )=Q(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\xi )+\mathcal{O}(\hbar )$ is a ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$- and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$-independent local functional, such that the transformed action $S_{f}(\Phi ^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\prime },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=S_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu },\xi )$ is $\xi $ independent and invariant under background transformations: $$\frac{\partial S_{f}}{\partial \xi }=0,\qquad \llbracket \bar{S},S_{f}\rrbracket =0. \label{gindep2back}$$
*Proof*. To prove this statement we introduce a new parameter $\zeta $ multiplying the whole functional $Q$ of (\[cannonaback\]), as in (\[fg\]). We know that $\llbracket \bar{S},Q\rrbracket =0$ implies $\llbracket \bar{S},\tilde{Q}\rrbracket =0$. If we prove that the $\zeta $ dependence can be reabsorbed into a background-preserving canonical transformation we also prove the same result for every gauge-fixing parameter $\xi $ and also for all of them together. The differential equations of gauge dependence found above obviously apply with $\xi \rightarrow \zeta $.
Specifically, we show that the $\zeta $ dependence can be reabsorbed in a sequence of background-preserving canonical transformations $S_{R\hspace{0.01in}n}\rightarrow S_{R\hspace{0.01in}n+1}$ (with $S_{R\hspace{0.01in}0}=S_{R}$), generated by $$F_{n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\int \
\Phi ^{A}K_{A}^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{A}{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{A}^{\prime }+H_{n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\zeta ), \label{fn}$$ where $H_{n}=\mathcal{O}(\hbar ^{n})$, and such that $$\frac{\partial S_{R\hspace{0.01in}n}}{\partial \zeta }=\llbracket S_{R\hspace{0.01in}n},T_{n}\rrbracket ,\qquad T_{n}=\mathcal{O}(\hbar ^{n}).
\label{tn}$$ The functionals $T_{n}$ and $H_{n}$ are determined by the recursive relations $$\begin{aligned}
T_{n+1}(\Phi ^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\zeta ) &=&T_{n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K,\zeta )-\widetilde{\frac{\partial H_{n}}{\partial \zeta }}, \label{d1} \\
H_{n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\zeta ) &=&\int_{0}^{\zeta }d\zeta
^{\prime }\hspace{0.01in}T_{n,n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime },\zeta
^{\prime }), \label{d2}\end{aligned}$$ with the initial conditions $$T_{0}=Q_{R,\zeta },\qquad H_{0}=\zeta Q.$$ In formula (\[d1\]) the tilde operation (\[tildedfback\]) on $\partial
H_{n}/\partial \zeta $ and the canonical transformation $\Phi ,K\rightarrow
\Phi ^{\prime },K^{\prime }$ are the ones defined by $F_{n}$. In formula (\[d2\]) $T_{n,n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime })$ denotes the contributions of order $\hbar ^{n}$ to $T_{n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K(\Phi
,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime }))$, the function $K(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime })$ also being determined by $F_{n}$. Note that for $n>0$ we have $T_{n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime
}))=T_{n}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K^{\prime })+\mathcal{O}(\hbar ^{n+1})$, therefore formula (\[d2\]), which determines $H_{n}$ (and so $F_{n}$), does not really need $F_{n}$ on the right-hand side. Finally, (\[d2\]) is self-consistent for $n=0$.
Formula (\[thesis\]) of the appendix describes how the dependence on parameters is modified by a canonical transformation. Applying it to (\[tn\]), we get $$\frac{\partial S_{R\hspace{0.01in}n+1}}{\partial \zeta }=\frac{\partial S_{R\hspace{0.01in}n}}{\partial \zeta }-\llbracket S_{R\hspace{0.01in}n},\widetilde{\frac{\partial H_{n}}{\partial \zeta }}\rrbracket =\llbracket S_{R\hspace{0.01in}n},T_{n}-\widetilde{\frac{\partial H_{n}}{\partial \zeta }}\rrbracket ,$$ whence (\[d1\]) follows. For $n=0$ the first formula of (\[babaoback\]) gives $T_{0}=\widetilde{Q}+\mathcal{O}(\hbar )$, therefore $T_{1}=\mathcal{O}(\hbar )$. Then (\[d2\]) gives $H_{1}=\mathcal{O}(\hbar )$. For $n>0$ the order $\hbar ^{n}$ of $T_{n+1}$ vanishes by formula (\[d2\]); therefore $T_{n+1}=\mathcal{O}(\hbar ^{n+1})$ and $H_{n+1}=\mathcal{O}(\hbar ^{n+1})$, as desired.
Consequently, $S_{f}\equiv S_{R\hspace{0.01in}\infty }$ is $\zeta $ independent, since (\[tn\]) implies $\partial S_{R\hspace{0.01in}\infty
}/\partial \zeta =0$. Observe that ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$ and ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independence is preserved at each step. Finally, all operations defined by (\[d1\]) and (\[d2\]) are background preserving. We conclude that the canonical transformation $F_{R}$ obtained composing the $F_{n}$s solves the problem.
Using (\[gindep2back\]) and (\[give\]) we conclude that in the new variables $$\frac{\partial \Gamma _{f}}{\partial \xi }=\left\langle \frac{\partial S_{f}}{\partial \xi }\right\rangle =0\qquad \llbracket \bar{S},\Gamma _{f}\rrbracket =0, \label{finalmenteback}$$ for all gauge-fixing parameters $\xi $.
Non-background-preserving canonical transformations
---------------------------------------------------
In the usual approach the results derived so far apply with straightforward modifications. It is sufficient to ignore the background fields and sources, as well as the background transformations, and use the standard parentheses $(X,Y)$ instead of $\llbracket X,Y\rrbracket $. Thus, given a tree-level canonical transformation generated by $$F(\Phi ,K^{\prime })=\int \ \Phi ^{\alpha }K_{\alpha }^{\prime }+Q(\Phi
,K^{\prime },\xi ), \label{f1}$$ there exists a local functional $Q_{R,\xi }$ satisfying (\[babaoback\]) such that $$\frac{\partial S_{R}}{\partial \xi }=(S_{R},Q_{R,\xi }),\qquad \frac{\partial \Gamma _{R}}{\partial \xi }=(\Gamma _{R},\langle Q_{R,\xi }\rangle
), \label{br}$$ and there exists a renormalized canonical transformation $$F_{R}(\Phi ,K^{\prime })=\int \ \Phi ^{A}K_{A}^{\prime }+Q_{R}(\Phi
,K^{\prime },\xi ), \label{f2}$$ where $Q_{R}(\Phi ,K^{\prime },\xi )=Q(\Phi ,K^{\prime },\xi )+\mathcal{O}(\hbar )$ is a local functional, such that the transformed action $S_{f
}(\Phi ^{\prime },K^{\prime })=S_{R}(\Phi ,K,\xi )$ is $\xi $ independent. Said differently, the entire $\xi $ dependence of $S_{R}$ is reabsorbed into the transformation: $$S_{R}(\Phi ,K,\xi )=S_{f}(\Phi ^{\prime }(\Phi ,K,\xi ),K^{\prime
}(\Phi ,K,\xi )).$$
In the presence of background fields ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ and background sources ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$, dropping assumption (\[assumback\]) and ignoring invariance under background transformations, encoded in the parentheses $\llbracket \bar{S},X\rrbracket $, the results found above can be easily generalized to any classical action $S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })$ that solves $\llbracket S,S\rrbracket =0$ and is such that $\delta
_{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi $ independent, and to any ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$-independent canonical transformation. Indeed, these assumptions are enough to apply theorem \[thb\] and corollary \[cora\], and go through the derivation ignoring the parentheses $\llbracket \bar{S},X\rrbracket $. The tree-level canonical transformation is described by a generating functional of the form $$F(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\int \ \Phi
^{\alpha }K_{\alpha }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+Q(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },K^{\prime
},\xi ). \label{fa1}$$ We still find the differential equations $$\frac{\partial S_{R}}{\partial \xi }=\llbracket S_{R},Q_{R,\xi }\rrbracket ,\qquad \frac{\partial \Gamma _{R}}{\partial \xi }=\llbracket \Gamma
_{R},\langle Q_{R,\xi }\rangle \rrbracket , \label{eqw}$$ where $Q_{R,\xi }$ satisfies (\[babaoback\]). When we integrate the first of these equations with the procedure defined above we build a renormalized canonical transformation $$F_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime },\xi )=\int
\ \Phi ^{\alpha}K_{\alpha}^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha}{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha}^{\prime }+Q_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },K^{\prime },\xi ),
\label{fra1}$$ where $Q_{R}=Q+\mathcal{O}(\hbar )$ is a local functional, such that the transformed action $S_{f}(\Phi ^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\prime },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=S_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu },\xi )$ is $\xi $ independent. The only difference is that now $Q_{R,\xi }$, $\langle
Q_{R,\xi }\rangle $, $T_{n}$, $H_{n}$ and $Q_{R}$ can depend on ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$, which does not disturb any of the arguments used in the derivation.
Canonical transformations in
-----------------------------
We have integrated the first equation of (\[eqw\]), and shown that the $\xi$ dependence can be reabsorbed in the canonical transformation (\[fra1\]) on the renormalized action $S_{R}$, which gives the $\xi$-independent action with $S_{\rm f}$. We know that the generating functional $\Gamma_{\rm f}$ of one-particle irreducible Green functions determined by $S_{\rm f}$ is $\xi$ independent. We can also prove that $\Gamma_{\rm f}$ can be obtained applying a (non-local) canonical transformation directly on $\Gamma_{R}$.
To achieve this goal we integrate the second equation of (\[eqw\]). The integration algorithm is the same as the one of subsection \[integrating\], with the difference that $Q_{R,\xi}$ is replaced by $\langle Q_{R,\xi}\rangle$. The canonical transformation on $\Gamma_{R}$ has a generating functional of the form $$F_{\Gamma}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime },\xi )=\int
\ \Phi ^{\alpha}K_{\alpha}^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha}{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha}^{\prime }+Q_{\Gamma}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },K^{\prime },\xi ),
\label{fra2}$$ where $Q_{\Gamma}=Q+{\cal O}(\hbar)$ (non-local) radiative corrections.
The result just obtained is actually more general, and proves that if $S$ is any action that solves the master equation (it can be the classical action, the renormalized action, or any other action) canonical transformations on $S$ correspond to canonical transformations on the $\Gamma$ functional determined by $S$. See [@quadri] for a different derivation of this result in Yang-Mills theory. Our line of reasoning can be recapitulated as follows: in the usual approach, ($i$) make a canonical transformation (\[f1\]) on $S$; ($ii$) derive the equations of gauge dependence for the action, which are $\partial S/\partial\xi=( S,Q_{\xi}) $; ($iii$) derive the equations of gauge dependence for the $\Gamma$ functional determined by $S$, which are $\partial \Gamma/\partial\xi=( \Gamma,\langle Q_{\xi}\rangle)$, and integrate them.
The property just mentioned may sound obvious, and is often taken for granted, but actually needed to be proved. The reason is that the canonical transformations we are talking about are not true changes of field variables inside functional integrals, but mere replacements of integrands [@fieldcov]. Therefore, we cannot automatically infer how a transformation on the action $S$ affects the generating functionals $Z$, $W=\ln Z$ and $\Gamma$, and need to make some additional effort to get where we want. We recall that to skip this kind of supplementary analysis we need to use the formalism of the master functional, explained in refs. [@masterf; @mastercan].
Application
-----------
An interesting application that illustrates the results of this section is the comparison between the renormalized action (\[sr1\]), which was obtained with the background field method and the raw subtraction procedure of section 3, and the renormalized action $S_{R}^{\prime }$ that can be obtained with the same raw subtraction in the usual non-background field approach.
The usual approach is retrieved by picking a gauge fermion $\Psi ^{\prime }$ that depends on $\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$, such as $$\Psi ^{\prime }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })=\int \bar{C}^{I}G^{Ii}(0,\partial
)(\phi ^{i}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i}). \label{gfno}$$ Making the canonical transformation generated by $$F_{\text{gf}}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime })=\int \ \Phi ^{\alpha }K_{\alpha }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+\Psi ^{\prime }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }) \label{backgfgen2}$$ on (\[sback\]) we find the classical action $$S^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\hat{S}^{\prime }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K)+\bar{S}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }), \label{sr2c}$$ where $$\hat{S}^{\prime }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K)=S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })-\int R^{\alpha }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })\bar{K}_{\alpha },\qquad \bar{S}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })({\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }-K_{\alpha }), \label{sr2gf}$$ and the barred sources $\bar{K}_{\alpha }$ coincide with $K_{\alpha }$ apart from $\bar{K}_{\phi }^{i}$ and $\bar{K}_{\bar{C}}^{I}$, which are $$\bar{K}_{\phi }^{i}=K_{\phi }^{i}-\bar{C}^{I}G^{Ii}(0,-\overleftarrow{\partial }),\qquad \bar{K}_{\bar{C}}^{I}=K_{\bar{C}}^{I}-G^{Ii}(0,\partial
)(\phi ^{i}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i}). \label{chif2}$$ Clearly, $\hat{S}^{\prime }$ is the gauge-fixed classical action of the usual approach, apart from the shift $\Phi \rightarrow \Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi
}\mkern-2mu}\mkern2mu }$.
The radiative corrections are generated only by $\hat{S}^{\prime }$ and do not affect $\bar{S}^{\prime }$. Indeed, $\hat{S}^{\prime }$ as well as the radiative corrections are unaffected by setting ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }=0$ and then shifting $\Phi $ back to $\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$, while $\bar{S}^{\prime }$ disappears doing this. Thus, $\bar{S}^{\prime }$ is nonrenormalized, and the renormalized action $S_{R}^{\prime }$ has the form $$S_{R}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\hat{S}_{R}^{\prime
}(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K)+\bar{S}^{\prime }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }). \label{sr2}$$
Now we compare the classical action (\[sbaccagf\]) of the background field method with the classical action (\[sr2c\]) of the usual approach. We recapitulate how they are obtained with the help of the following schemes: $$\begin{tabular}{cccccccccc}
(\ref{sback}) & $\stackrel{(\ref{casbacca})}{\mathrel{\scalebox{2.5}[1]{$\longrightarrow$}}}$ & (\ref{sbacca}) & $\stackrel{(\ref{backgfgen})}{\mathrel{\scalebox{2.5}[1]{$\longrightarrow$}}}$ & $S=$ (\ref{sbaccagf}) &
\qquad \qquad & (\ref{sback}) & $\stackrel{(\ref{backgfgen2})}{\mathrel{\scalebox{2.5}[1]{$ \longrightarrow$}}}$ & $S^{\prime }=$ (\ref
{sr2gf}). &
\end{tabular}$$ Above the arrows we have put references to the corresponding canonical transformations, which are (\[casbacca\]), (\[backgfgen\]) and (\[backgfgen2\]) and commute with one another. We can interpolate between the classical actions (\[sbaccagf\]) and (\[sr2gf\]) by means of a ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$-independent non-background-preserving canonical transformation generated by $$F_{\xi }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime },\xi
)=\int \ \Phi ^{\alpha }K_{\alpha }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+\xi \Delta \Psi +\xi \int
\mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{I\hspace{0.01in}\prime }. \label{ds}$$ where $\xi $ is a gauge-fixing parameter that varies from 0 to 1, and $$\Delta \Psi =\int \bar{C}^{I}\left( G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi
^{i}-G^{Ii}(0,\partial )(\phi ^{i}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i})\right) .$$
Precisely, start from the non-background field theory (\[sr2c\]), andtake its variables to be primed ones. We know that $\hat{S}^{\prime }$ depends on the combination $$\tilde{K}_{\phi }^{i\hspace{0.01in}\prime }=K_{\phi }^{i\hspace{0.01in}\prime }-\bar{C}^{I\hspace{0.01in}}G^{Ii}(0,-\overleftarrow{\partial }),
\label{kip}$$ and we have $\bar{C}^{I\hspace{0.01in}}=\bar{C}^{I\hspace{0.01in}\prime }$. Expressing the primed fields and sources in terms of the unprimed ones and $\xi $, we find the interpolating classical action $$S_{\xi }(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })-\int R^{\alpha }(\Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })\tilde{K}_{\alpha }(\xi
)-\xi \int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })\tilde{K}_{\bar{C}}^{I}(\xi )-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })({\mkern2mu\underline{\mkern-2mu\smash{\tilde{K}}\mkern-2mu}\mkern2mu }_{\alpha }(\xi )-\tilde{K}_{\alpha }(\xi )), \label{sx}$$ where $\tilde{K}_{C}^{I}(\xi )=K_{C}^{I}$, $$\tilde{K}_{\phi }^{i}(\xi )=K_{\phi }^{i}-\xi \bar{C}^{I\hspace{0.01in}}G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },-\overleftarrow{\partial })-(1-\xi )\bar{C}^{I\hspace{0.01in}}G^{Ii}(0,-\overleftarrow{\partial }), \label{convex}$$ while the other $\xi $-dependent tilde sources have expressions that we do not need to report here. It suffices to say that they are $K_{\phi }^{i}$ independent, such that $\delta _{r}S_{\xi }/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha
}=-R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })$, and linear in the quantum fields $\Phi $, apart from ${\mkern2mu\underline{\mkern-2mu\smash{\tilde{K}}\mkern-2mu}\mkern2mu }_{\phi }^{i}(\xi )$, which is quadratic. Thus the action $S_{\xi }$ and the transformation $F_{\xi }$ satisfy the assumptions that allow us to apply theorem \[thb\] and corollary \[cora\]. Actually, (\[ds\]) is of type (\[fa1\]); therefore we have the differential equations (\[eqw\]) and the renormalized canonical transformation (\[fra1\]).
We want to better characterize the renormalized version $F_{R}$ of $F_{\xi }$. We know that the derivative of the renormalized $\Gamma $ functional with respect to $\xi $ is governed by the renormalized version of the average $$\left\langle \widetilde{\frac{\partial F_{\xi }}{\partial \xi }}\right\rangle =\langle \Delta \Psi \rangle +\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{I}.$$ It is easy to see that $\langle \Delta \Psi \rangle $ is independent of ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$, $B$, $K_{\bar{C}}$ and $K_{B}$, since no one-particle irreducible diagrams with such external legs can be constructed. In particular, $K_{B}^{I\hspace{0.01in}\prime }=K_{B}^{I}$. Moreover, using the explicit form (\[sx\]) of the action $S_{\xi }$ and arguments similar to the ones that lead to formulas (\[chif\]), we easily see that $\langle
\Delta \Psi \rangle $ is equal to $\Delta \Psi $ plus a functional that does not depend on $K_{\phi }^{i}$ and $\bar{C}^{I}$ separately, but only on the convex combination (\[convex\]). Indeed, the $\bar{C}$-dependent terms of (\[sx\]) that do not fit into the combination (\[convex\]) are $K_{\phi }^{i}$ independent and at most quadratic in the quantum fields, so they cannot generate one-particle irreducible diagrams that have either $K_{\phi }^{i}$ or $\bar{C}$ on the external legs. Clearly, the renormalization of $\langle \Delta \Psi \rangle $ also satisfies the properties just stated for $\langle \Delta \Psi \rangle $.
Following the steps of the previous section we can integrate the $\xi $ derivative and reconstruct the full canonical transformation. However, formula (\[d2\]) shows that the integration over $\xi $ must be done by keeping fixed the unprimed fields $\Phi $ and the primed sources $K^{\prime
} $. When we do this for the zeroth canonical transformation $F_{0}$ of (\[fn\]), the combination $\tilde{K}_{\phi }^{i}(\xi )$ is turned into (\[kip\]), which is $\xi $ independent. Every other transformation $F_{n}$ of (\[fn\]) preserves the combination (\[kip\]), so the integrated canonical transformation does not depend on $K_{\phi }^{i}$ and $\bar{C}^{I}$ separately, but only on the combination $\tilde{K}_{\phi }^{i\hspace{0.01in}\prime }$, and the generating functional of the renormalized version $F_{R}$ of $F_{\xi }$ has the form $$F_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime },\xi )=\int
\ \Phi ^{\alpha }K_{\alpha }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }+\xi \Delta \Psi +\xi \int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{I\hspace{0.01in}\prime }+\Delta
F_{\xi }(\phi ,C,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },\tilde{K}_{\phi }^{\prime
},K_{C}^{\prime },\xi ). \label{fr}$$ Using this expression we can verify [*a posteriori*]{} that indeed $\tilde{K}_{\phi }^{i}(\xi )$ depends just on (\[kip\]), not on $K_{\phi }^{i\hspace{0.01in}\prime }$ and $\bar{C}^{I}$ separately. Moreover, (\[fr\]) implies $${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha \hspace{0.01in}\prime }={\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha},\qquad B^{I\hspace{0.01in}\prime }=B^{I}+\xi
\mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }),\qquad \bar{C}^{I\hspace{0.01in}\prime }=\bar{C}^{I},\qquad K_{B}^{I\hspace{0.01in}\prime }=K_{B}^{I}. \label{besid}$$
In the next section these results are used to achieve parametric completeness.
Renormalization and parametric completeness
===========================================
The raw renormalization algorithm of section 3 subtracts away divergences just as they come. It does not ensure, *per se*, RG invariance, for which it is necessary to prove parametric completeness, namely that all divergences can be subtracted by redefining parameters and making canonical transformations. We must show that we can include in the classical action all invariants that are generated back by renormalization, and associate an independent parameter with each of them. The purpose of this section is to show that the background field method allows us to prove parametric completeness in a rather straightforward way, making cohomological classifications unnecessary.
We want to relate the renormalized actions (\[sr1\]) and (\[sr2\]). From the arguments of the previous section we know that these two actions are related by the canonical transformation generated by (\[fr\]) at $\xi =1$. We have $$\hat{S}_{R}^{\prime }(\Phi ^{\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime })-\int
R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })({\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }^{\prime }-K_{\alpha
}^{\prime })=\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)-\int \mathcal{R}^{\alpha
}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{\alpha }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }. \label{ei}$$ From (\[fr\]) we find the transformation rules (\[besid\]) at $\xi =1$ and $$\phi ^{\prime }=\phi +\frac{\delta \Delta F}{\delta \tilde{K}_{\phi
}^{\prime }},\qquad K_{\bar{C}}^{I}=K_{\bar{C}}^{I\hspace{0.01in}\prime
}+G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi ^{i}-G^{Ii}(0,\partial )(\phi ^{i\hspace{0.01in}\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i})+\frac{\delta }{\delta \bar{C}^{I}}\int \mathcal{R}_{\bar{C}}^{J}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{J},
\label{beside}$$ where $\Delta F$ is $\Delta F_{\xi}$ at $\xi=1$. Here and below we sometimes understand indices when there is no loss of clarity. We want to express equation (\[ei\]) in terms of unprimed fields and primed sources, and then set $\phi =C={\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime }=0$. We denote this operation with a subscript 0. Keeping ${\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },\bar{C},B$ and $K^{\prime }$ as independent variables, we get $$\begin{aligned}
\hat{S}_{R}^{\prime }(\Phi _{0}^{\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime }) &=&\hat{S}_{R}(0,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0)-\int B^{I\prime }(K_{\bar{C}}^{I\hspace{0.01in}\prime }-G^{Ii}(0,\partial )(\phi _{0}^{i\hspace{0.01in}\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i})) \nonumber \\
&&-\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })\frac{\delta }{\delta \bar{C}^{I}}\int \mathcal{R}_{\bar{C}}^{J}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{J\hspace{0.01in}\prime }-\int R^{\alpha }({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })({\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha 0}+K_{\alpha }^{\prime }). \label{uio}\end{aligned}$$ To derive this formula we have used $$\hat{S}_{R}(\{0,0,\bar{C},B\},{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)=\hat{S}_{R}(0,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0)-\int B^{I}K_{\bar{C}}^{I}, \label{mina}$$ together with (\[iddo\]), (\[besid\]) and (\[beside\]). The reason why (\[mina\]) holds is that at $C=0$ there are no objects with positive ghost numbers inside the left-hand side of this equation; therefore we can drop every object that has a negative ghost number, which means $\bar{C}$ and all sources $K$ but $K_{\bar{C}}^{I}$. Since (\[chio\]) are the only $B$ and $K_{\bar{C}}^{I}$-dependent terms, and they are not renormalized, at $\phi =0$ we find (\[mina\]).
Now, consider the canonical transformation $\{{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },\bar{C},B\},\breve{K}\rightarrow \Phi ^{\prime \prime },K^{\prime }$ defined by the generating functional $$F(\{{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },\bar{C},B\},K^{\prime })=\int {\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }K_{\phi }^{\prime }+\int \ {\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }K_{C}^{\prime }+F_{R}(\{0,0,\bar{C},B\},{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },0,1). \label{for}$$ It gives the transformation rules $$\begin{aligned}
\Phi ^{\hspace{0.01in}\prime \prime } &=&{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }+\Phi _{0}^{\prime
},\qquad \breve{K}_{\phi }=K_{\phi }^{\prime }+{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\phi 0},\qquad
\breve{K}_{C}=K_{C}^{\prime }+{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C0}, \\
\breve{K}_{\bar{C}}^{I} &=&K_{\bar{C}}^{I\hspace{0.01in}\prime
}-G^{Ii}(0,\partial )\phi ^{i\hspace{0.01in}\prime \prime }+\frac{\delta }{\delta \bar{C}^{I}}\int \mathcal{R}_{\bar{C}}^{J}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })K_{B}^{J\hspace{0.01in}\prime },\qquad \breve{K}_{B}=K_{B}^{\prime },\end{aligned}$$ which turn formula (\[uio\]) into $$\begin{aligned}
\hat{S}_{R}^{\prime }(\Phi ^{\prime \prime },K^{\prime }) &=&\hat{S}_{R}(0,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0)-\int R_{\phi }^{i}({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })\breve{K}_{\phi
}^{i}-\int R_{C}^{I}({\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu })\breve{K}_{C}^{I} \nonumber \\
&&-\int B^{I}\breve{K}_{\bar{C}}^{I}-\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })\breve{K}_{\bar{C}}^{I}-\int \mathcal{R}_{B}^{I}(B,{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu })\breve{K}_{B}^{I}. \label{fin0}\end{aligned}$$
Note that $(\hat{S}_{R}^{\prime },\hat{S}_{R}^{\prime })=0$ is automatically satisfied by (\[fin0\]). Indeed, we know that $\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)$ is invariant under background transformations, and so is $\hat{S}_{R}(0,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0)$, because $\Phi $ and $K$ transform as matter fields.
We can classify $\hat{S}_{R}(0,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0)$ using its gauge invariance. Let $\mathcal{G}_{i}(\phi )$ denote a basis of gauge-invariant local functionals constructed with the physical fields $\phi $. Then $$\hat{S}_{R}(0,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0)=\sum_{i}\tau _{i}\mathcal{G}_{i}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }), \label{comple}$$ for suitable constants $\tau _{i}$.
Now we manipulate these results in several ways to make their consequences more explicit. To prepare the next discussion it is convenient to relabel $\{{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu },\bar{C},B\}$ as $\breve{\Phi}^{\alpha }$ and $K^{\prime }$ as $K^{\prime \prime }$. Then formulas (\[for\]) and (\[fin0\]) tell us that the canonical transformation $$F_{1}(\breve{\Phi},K^{\prime \prime })=\int \breve{\phi}K_{\phi }^{\prime
\prime }+\int \ \breve{C}K_{C}^{\prime \prime }+F_{R}(\{0,0,{\breve{\bar{C}}},\breve{B}\},\{\breve{\phi},\breve{C}\},K^{\prime \prime },0,1)
\label{forex}$$ is such that $$\hat{S}_{R}^{\prime }(\Phi ^{\prime \prime },K^{\prime \prime })=\hat{S}_{R}(0,\breve{\phi},0)-\int \bar{R}^{\alpha }(\breve{\Phi})\breve{K}_{\alpha
}. \label{fin0ex}$$
#### Parametric completeness
Making the further canonical transformation $\breve{\Phi},\breve{K}\rightarrow \Phi ,K$ generated by $$F_{2}(\Phi ,\breve{K})=\int \Phi ^{\alpha }\breve{K}_{\alpha }+\int \bar{C}^{I}G^{Ii}(0,\partial )\phi ^{i}-\int \mathcal{R}_{\bar{C}}^{I}(\bar{C},C)\breve{K}_{B}^{I},$$ we get $$\hat{S}_{R}^{\prime }(\Phi ^{\prime \prime },K^{\prime \prime })=\hat{S}_{R}(0,\phi ,0)-\int R^{\alpha }(\Phi )\bar{K}_{\alpha }, \label{keynb}$$ where the barred sources are the ones of (\[chif2\]) at ${\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }=0$. If we start from the most general gauge-invariant classical action, $$S_{c}(\phi ,\lambda )\equiv \sum_{i}\lambda _{i}\mathcal{G}_{i}(\phi ),
\label{scgen}$$ where $\lambda _{i}$ are physical couplings (apart from normalization constants), identities (\[comple\]) and (\[keynb\]) give $$\hat{S}_{R}^{\prime }(\Phi ^{\prime \prime },K^{\prime \prime })=S_{c}(\phi
,\tau (\lambda ))-\int R^{\alpha }(\Phi )\bar{K}_{\alpha }. \label{kk}$$ This result proves parametric completeness in the usual approach, because it tells us that the renormalized action of the usual approach is equal to the classical action $\hat{S}^{\prime }(\Phi ,K)$ (check (\[sr2c\])-(\[sr2gf\]) at ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }={\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }=0$), apart from parameter redefinitions $\lambda \rightarrow \tau $ and a canonical transformation. In this derivation the role of the background field method is just to provide the key tool to prove the statement.
We can also describe parametric completeness in the background field approach. Making the canonical transformation $\breve{\Phi},\breve{K}\rightarrow \hat{\Phi},\hat{K}$ generated by $$F_{2}^{\prime }(\hat{\Phi},\breve{K})=\int \hat{\Phi}^{\alpha }\breve{K}_{\alpha }+\int {\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu }^{i}\breve{K}_{\phi }^{i}+\int {\hat{\bar{C}}}^{I}G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\hat{\phi}^{i}-\int \mathcal{R}_{\bar{C}}^{I}({\hat{\bar{C}}},\hat{C})\breve{K}_{B}^{I}, \label{cancan}$$ formula (\[fin0ex\]) becomes $$\hat{S}_{R}^{\prime }(\Phi ^{\prime \prime },K^{\prime \prime })=S_{c}(\hat{\phi}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\tau )-\int R^{\alpha }(\hat{\phi}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{C},{\hat{\bar{C}}},\hat{B})\widetilde{\hat{K}}_{\alpha }, \label{y0}$$ where the relations between tilde and nontilde sources are the hat versions of (\[chif\]). Next, we make a ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ translation on the left-hand side of (\[y0\]) applying the canonical transformation $\Phi
^{\prime \prime },K^{\prime \prime }$ $\rightarrow \Phi ^{\prime },K^{\prime
}$ generated by $$F_{3}(\Phi ^{\prime },K^{\prime \prime })=\int (\Phi ^{\alpha \hspace{0.01in}\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha })K_{\alpha }^{\prime \prime }.
\label{traslacan}$$ Doing so, $\hat{S}_{R}^{\prime }(\Phi ^{\prime \prime },K^{\prime \prime })$ is turned into $\hat{S}_{R}^{\prime }(\Phi ^{\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime })$.
At this point, we want to compare the result we have obtained with (\[ei\]). Recall that formula (\[ei\]) involves the canonical transformation (\[fr\]) at $\xi =1$. If we set ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\prime }=0$ we project that canonical transformation onto a canonical transformation $\Phi ,K\rightarrow
\Phi ^{\prime },K^{\prime }$ generated by $F_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime },0,1)$, where ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ is regarded as a spectator. Furthermore, it is convenient to set ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }=0$, because then formula (\[ei\]) turns into $$\hat{S}_{R}^{\prime }(\Phi ^{\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime })=\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K),$$ where now primed fields and sources are related to the unprimed ones by the canonical transformation generated by $F_{R}(\Phi ,\{{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0\},K^{\prime },0,1)$. Finally, recalling that $\hat{S}_{R}^{\prime }(\Phi
^{\prime \prime },K^{\prime \prime })=\hat{S}_{R}^{\prime }(\Phi ^{\prime }+{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K^{\prime })$ and using (\[y0\]) we get the key formula we wanted, namely $$\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },K)=S_{c}(\hat{\phi}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\tau (\lambda ))-\int R^{\alpha }(\hat{\phi}+{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{C},{\hat{\bar{C}}},\hat{B})\widetilde{\hat{K}}_{\alpha }. \label{key}$$ Observe that formula (\[key0\]) of the introduction is formula (\[key\]) with antighosts and Lagrange multipliers switched off. Checking (\[sbaccagf\]), formula (\[key\]) tells us that the renormalized background field action $\hat{S}_{R}$ is equal to the classical background field action $\hat{S}_{\text{gf}}$ up to parameter redefinitions $\lambda \rightarrow \tau $ and a canonical transformation. This proves parametric completeness in the background field approach.
The canonical transformation $\Phi ,K\rightarrow \hat{\Phi},\hat{K}$ involved in formula (\[key\]) is generated by the functional $\hat{F}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{K})$ obtained composing the transformations generated by $F_{R}(\Phi ,\{{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },0\},K^{\prime
},0,1)$, $F_{1}(\breve{\Phi},K^{\prime \prime })$, $F_{2}^{\prime }(\hat{\Phi},\breve{K})$ and $F_{3}(\Phi ^{\prime },K^{\prime \prime })$ of formulas (\[fr\]), (\[forex\]), (\[cancan\]) and (\[traslacan\]) (at ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }=0$). Working out the composition it is easy to prove that $${\hat{\bar{C}}}=\bar{C},\qquad \hat{B}=B,\qquad \hat{K}_{B}=K_{B},\qquad \hat{K}_{\bar{C}}^{I}-G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\hat{\phi}^{i}=K_{\bar{C}}^{I}-G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\partial )\phi ^{i},$$ and therefore $\hat{F}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{K})$ has the form $$\hat{F}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{K})=\int \Phi ^{\alpha }\hat{K}_{\alpha }+\Delta \hat{F}(\phi ,C,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{K}_{\phi }^{i}-{\hat{\bar{C}}}^{I}G^{Ii}({\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },-\overleftarrow{\partial }),\hat{K}_{C}), \label{frhat}$$ where $\Delta \hat{F}=\mathcal{O}(\hbar )$-poles.
Examples
========
In this section we give two examples, non-Abelian gauge field theories and quantum gravity, which are also useful to familiarize oneself with the notation and the tools used in the paper. We switch to Minkowski spacetime. The dimensional-regularization technique is understood.
Yang-Mills theory
-----------------
The first example is non-Abelian Yang-Mills theory with simple gauge group $G $ and structure constants $f^{abc}$, coupled to fermions $\psi ^{i}$ in some representation described by anti-Hermitian matrices $T_{ij}^{a}$. The classical action $S_{c}(\phi )$ can be restricted by power counting, or enlarged to include all invariants of (\[scgen\]). The nonminimal non-gauge-fixed action $S$ is the sum $\hat{S}+\bar{S}$ of (\[deco\]) and (\[sbar\]). We find $$\begin{aligned}
\hat{S} &=&S_{c}(\phi +{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu })+\int \hspace{0.01in}\left[ g(\bar{\psi}^{i}+{\mkern2mu\underline{\mkern-2mu\smash{\bar{\psi}}\mkern-2mu}\mkern2mu }^{i})T_{ij}^{a}C^{a}K_{\psi }^{j}+g\bar{K}_{\psi
}^{i}T_{ij}^{a}C^{a}(\psi ^{j}+{\mkern2mu\underline{\mkern-2mu\smash{\psi }\mkern-2mu}\mkern2mu }^{j})\right] \\
&&-\int \hspace{0.01in}\left[ ({\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }_{\mu }C^{a}+gf^{abc}A_{\mu
}^{b}C^{c})K^{\mu a}-\frac{1}{2}gf^{abc}C^{b}C^{c}K_{C}^{a}+B^{a}K_{\bar{C}}^{a}\right] ,\end{aligned}$$ and $$\begin{aligned}
\bar{S} &=&gf^{abc}\int \hspace{0.01in}{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{b}(A_{\mu }^{c}K^{\mu
a}+C^{c}K_{C}^{a}+\bar{C}^{c}K_{\bar{C}}^{a}+B^{c}K_{B}^{a})+g\int \hspace{0.01in}\left[ \bar{\psi}^{i}T_{ij}^{a}{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{a}K_{\psi }^{j}+\bar{K}_{\psi
}^{i}T_{ij}^{a}{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{a}\psi ^{j}\right] \nonumber \\
&&-\int \hspace{0.01in}\left[ ({\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }_{\mu }{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{a}){\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }^{\mu a}-\frac{1}{2}gf^{abc}{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{b}{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{c}{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{C}^{a}-g{\mkern2mu\underline{\mkern-2mu\smash{\bar{\psi}}\mkern-2mu}\mkern2mu }^{i}T_{ij}^{a}{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{a}{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\psi }^{j}-g{\mkern2mu\underline{\mkern-2mu\smash{\bar{K}}\mkern-2mu}\mkern2mu }_{\psi }^{i}T_{ij}^{a}{\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }^{a}{\mkern2mu\underline{\mkern-2mu\smash{\psi }\mkern-2mu}\mkern2mu }^{j}\right] . \label{sbary}\end{aligned}$$ The covariant derivative ${\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }_{\mu }$ is the background one; for example ${\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }_{\mu }\Lambda ^{a}=\partial _{\mu }\Lambda
^{a}+gf^{abc}{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }_{\mu }^{b}\Lambda ^{c}$. The first line of (\[sbary\]) shows that all quantum fields transform as matter fields under background transformations. It is easy to check that $\hat{S}$ and $\bar{S}$ satisfy $\llbracket \hat{S},\hat{S}\rrbracket =\llbracket \hat{S},\bar{S}\rrbracket =\llbracket \bar{S},\bar{S}\rrbracket =0$.
A common background-preserving gauge fermion is $$\Psi =\int \bar{C}^{a}\left( -\frac{\lambda }{2}B^{a}+{\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu
}A_{\mu }^{a}\right) , \label{seeym}$$ and the gauge-fixed action $\hat{S}_{\text{gf}}=\hat{S}+\llbracket \hat{S},\Psi \rrbracket $ reads $$\hat{S}_{\text{gf}}=\hat{S}-\frac{\lambda }{2}\int (B^{a})^{2}+\int B^{a}{\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu }A_{\mu }^{a}-\int \bar{C}^{a}{\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu }({\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }_{\mu }C^{a}+gf^{abc}A_{\mu }^{b}C^{c}).$$ Since the gauge fixing is linear in the quantum fields, the action $\hat{S}$ depends on the combination $K_{\mu }^{a}+{\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }_{\mu }\bar{C}^{a}$ and not on $K_{\mu }^{a}$ and $\bar{C}^{a}$ separately. From now on we switch matter fields off, for simplicity, and set $\lambda =0$.
We describe renormalization using the approach of this paper. First we concentrate on the standard power-counting renormalizable case, where $$S_{c}(A,g)=-\frac{1}{4}\int F_{\mu \nu }^{a}(A,g)F^{\mu \nu \hspace{0.01in}a}(A,g),\qquad \qquad F_{\mu \nu }^{a}(A,g)=\partial _{\mu }A_{\nu
}^{a}-\partial _{\nu }A_{\mu }^{a}+gf^{abc}A_{\mu }^{b}A_{\nu }^{c}.$$ The key formula (\[key\]) gives $$\begin{aligned}
\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },K) &=&-\frac{Z}{4}\int F_{\mu \nu }^{a}(\hat{A}+{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },g)F^{\mu \nu \hspace{0.01in}a}(\hat{A}+{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },g)+\int \hat{B}^{a}{\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu }\hat{A}_{\mu }^{a}-\int \hat{B}^{a}\hat{K}_{\bar{C}}^{a} \nonumber \\
&&+\int \hspace{0.01in}(\hat{K}^{\mu a}+{\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu }{\hat{\bar{C}}}^{a})({\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }_{\mu }\hat{C}^{a}+gf^{abc}\hat{A}_{\mu }^{b}\hat{C}^{c})+\frac{1}{2}gf^{abc}\int \hat{C}^{b}\hat{C}^{c}\hat{K}_{C}^{a}, \label{sat}\end{aligned}$$ where $Z$ is a renormalization constant. The most general canonical transformation $\Phi ,K\rightarrow \hat{\Phi},\hat{K}$ that is compatible with power counting, global gauge invariance and ghost number conservation can be easily written down. Introducing unknown constants where necessary, we find that its generating functional has the form $$\begin{aligned}
\hat{F}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },\hat{K}) &=&\int (Z_{A}^{1/2}A_{\mu }^{a}+{\mkern2mu\underline{\mkern-2mu\smash{Z}\mkern-2mu}\mkern2mu }_{A}^{1/2}{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }_{\mu }^{a})\hat{K}^{\mu a}+\int
Z_{C}^{1/2}C^{a}\hat{K}_{C}^{a}+\int Z_{\bar{C}}^{1/2}\bar{C}^{a}\hat{K}_{\bar{C}}^{a} \\
&&+\int (Z_{B}^{1/2}B^{a}+\alpha {\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu }A_{\mu }^{a}+\beta
\partial ^{\mu }{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }_{\mu }^{a}+\gamma gf^{abc}{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }^{\mu
b}A_{\mu }^{c}+\delta gf^{abc}\bar{C}^{b}C^{c})\hat{K}_{B}^{a} \\
&&+\int \bar{C}^{a}(\zeta B^{a}+\xi {\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu }A_{\mu }^{a}+\eta
\partial ^{\mu }{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }_{\mu }^{a}+\theta gf^{abc}{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }^{\mu
b}A_{\mu }^{c}+\chi gf^{abc}\bar{C}^{b}C^{c}) \\
&&+\int \sigma \hat{K}_{\bar{C}}^{a}\hat{K}_{B}^{a}+\int \tau gf^{abc}C^{a}\hat{K}_{B}^{b}\hat{K}_{B}^{c}.\end{aligned}$$ Inserting it in (\[sat\]) and using the nonrenormalization of the $B$ and $K_{\bar{C}}$-dependent terms, we find $a=\beta =\gamma =\delta =\zeta
=\theta =\chi =\sigma =\tau =0$ and $$\xi =1-Z_{\bar{C}}^{1/2}Z_{A}^{1/2},\qquad \eta =-Z_{\bar{C}}^{1/2}{\mkern2mu\underline{\mkern-2mu\smash{Z}\mkern-2mu}\mkern2mu }_{A}^{1/2},\qquad Z_{B}=Z_{\bar{C}}. \label{zeta}$$ It is easy to check that $Z_{\bar{C}}$ disappears from the right-hand side of (\[sat\]), so we can set $Z_{\bar{C}}=1$. Furthermore, we know that $\hat{S}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },K)$ is invariant under background transformations ($\llbracket \hat{S}_{R},\bar{S}\rrbracket =0$), which requires ${\mkern2mu\underline{\mkern-2mu\smash{Z}\mkern-2mu}\mkern2mu }_{A}=0$. Finally, the canonical transformation just reads $$\hat{F}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },\hat{K})=\int Z_{A}^{1/2}A_{\mu }^{a}\hat{K}^{\mu a}+\int Z_{C}^{1/2}C^{a}\hat{K}_{C}^{a}+\int \bar{C}^{a}\hat{K}_{\bar{C}}^{a}+\int B^{a}\hat{K}_{B}^{a}+(1-Z_{A}^{1/2})\int \bar{C}^{a}({\mkern2mu\underline{\mkern-2mu\smash{D}\mkern-2mu}\mkern2mu }^{\mu }A_{\mu }^{a}),$$ which contains the right number of independent renormalization constants and is of the form (\[frhat\]).
Defining $Z_{g}=Z^{-1/2}$ and $Z_{A}^{\prime }=ZZ_{A}$ we can describe renormalization in a more standard way. Writing $$\hat{S}_{R}(0,\hat{A}+{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },0)=-\frac{1}{4}\int F_{\mu \nu
}^{a}(Z_{A}^{\prime \hspace{0.01in}1/2}A+Z_{g}^{-1}{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },gZ_{g})F^{\mu \nu \hspace{0.01in}a}(Z_{A}^{\prime \hspace{0.01in}1/2}A+Z_{g}^{-1}{\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu },gZ_{g}),$$ we see that $Z_{g}$ is the usual gauge-coupling renormalization constant, while $Z_{A}^{\prime }$ and $Z_{g}^{-2}$ are the wave-function renormalization constants of the quantum gauge field $A$ and the background gauge field ${\mkern2mu\underline{\mkern-2mu\smash{A}\mkern-2mu}\mkern2mu }$, respectively. We remark that the local divergent canonical transformation $\Phi ,K\rightarrow \hat{\Phi},\hat{K}$ corresponds to a highly nontrivial, convergent but non-local canonical transformation at the level of the $\Gamma $ functional.
If the theory is not power-counting renormalizable, then we need to consider the most general classical action, equal to the right-hand side of (\[scgen\]). Counterterms include vertices with arbitrary numbers of external $\Phi $ and $K$ legs. Nevertheless, the key formula (\[key\]) ensures that the renormalized action $\hat{S}_{R}$ remains exactly the same, up to parameter redefinitions and a canonical transformation. The only difference is that now even the canonical transformation $\hat{F}_{R}(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\phi }\mkern-2mu}\mkern2mu },\hat{K})$ of (\[frhat\]) becomes nonpolynomial and highly nontrivial.
Quantum gravity
---------------
Having written detailed formulas for Yang-Mills theory, in the case of quantum gravity we can just outline the key ingredients. In particular, we stress that the linearity assumption is satisfied both in the first-order and second-order formalisms, both using the metric $g_{\mu \nu }$ and the vielbein $e_{\mu }^{a}$. For example, using the second-order formalism and the vielbein, the symmetry transformations are encoded in the expressions $$\begin{aligned}
-\int R^{\alpha }(\Phi )K_{\alpha } &=&\int (e_{\rho }^{a}\partial _{\mu
}C^{\rho }+C^{\rho }\partial _{\rho }e_{\mu }^{a}+C^{ab}e_{\mu b})K_{a}^{\mu
}+\int C^{\rho }(\partial _{\rho }C^{\mu })K_{\mu }^{C} \\
&&+\int (C^{ac}\eta _{cd}C^{db}+C^{\rho }\partial _{\rho
}C^{ab})K_{ab}^{C}-\int B_{\mu }K_{\bar{C}}^{\mu }-\int B_{ab}K_{\bar{C}}^{ab}, \\
-\int \bar{R}^{\alpha }(\Phi )K_{\alpha } &=&-\int R^{\alpha }(\Phi
)K_{\alpha }-\int (\bar{C}_{\rho }\partial _{\mu }C^{\rho }-C^{\rho
}\partial _{\rho }\bar{C}_{\mu })K_{\bar{C}}^{\mu }+\int \left( B_{\rho
}\partial _{\mu }C^{\rho }+C^{\rho }\partial _{\rho }B_{\mu }\right)
K_{B}^{\mu },\end{aligned}$$ in the minimal and nonminimal cases, respectively, where $C^{\mu }$ are the ghosts of diffeomorphisms, $C^{ab}$ are the Lorentz ghosts and $\eta _{ab}$ is the flat-space metric. We see that both $R^{\alpha }(\Phi )$ and $\bar{R}^{\alpha }(\Phi )$ are at most quadratic in $\Phi $. Matter fields are also fine, since vectors $A_{\mu }$, fermions $\psi $ and scalars $\varphi $ contribute with $$\begin{aligned}
&&-\int (\partial _{\mu }C^{a}+gf^{abc}A_{\mu }^{b}C^{c}-C^{\rho }\partial
_{\rho }A_{\mu }^{a}-A_{\rho }^{a}\partial _{\mu }C^{\rho })K_{A}^{\mu
a}+\int \left( C^{\rho }\partial _{\mu }C^{a}+\frac{1}{2}gf^{abc}C^{b}C^{c}\right) K_{C}^{a} \\
&&\qquad +\int C^{\rho }(\partial _{\rho }\varphi )K_{\varphi }+\int C^{\rho
}(\partial _{\rho }\bar{\psi})K_{\psi }-\frac{i}{4}\int \bar{\psi}\sigma
^{ab}C_{ab}K_{\psi }+\int K_{\bar{\psi}}C^{\rho }(\partial _{\rho }\psi )-\frac{i}{4}\int K_{\bar{\psi}}\sigma ^{ab}C_{ab}\psi ,\end{aligned}$$ where $\sigma ^{ab}=i[\gamma ^{a},\gamma ^{b}]/2$. Expanding around flat space, common linear gauge-fixing conditions for diffeomorphisms and local Lorentz symmetry are $\eta ^{\mu \nu }\partial _{\mu }e_{\nu }^{a}=\xi \eta ^{a\mu
}\partial _{\mu }e_{\nu }^{b}\delta _{b}^{\nu }$, $e_{\mu }^{a}=e_{\nu
}^{b}\eta _{b\mu }\eta ^{\nu a}$, respectively.
In the first-order formalism we just need to add the transformation of the spin connection $\omega _{\mu }^{ab}$, encoded in $$\int (C^{\rho }\partial _{\rho }\omega _{\mu }^{ab}+\omega _{\rho
}^{ab}\partial _{\mu }C^{\rho }-\partial _{\mu }C^{ab}+C^{ac}\eta
_{cd}\omega _{\mu }^{db}-\omega _{\mu }^{ac}\eta _{cd}C^{db})K_{ab}^{\mu }.$$ Moreover, in this case we can also gauge-fix local Lorentz symmetry with the linear gauge-fixing condition $\eta ^{\mu \nu }\partial _{\mu }\omega _{\nu }^{ab}=0$, instead of $e_{\mu }^{a}=e_{\nu }^{b}\eta _{b\mu }\eta ^{\nu a}$.
We see that all gauge symmetries that are known to have physical interest satisfy the linearity assumption, together with irreducibility and off-shell closure. On the other hand, more speculative symmetries (such as local supersymmetry) do not satisfy those assumptions in an obvious way. When auxiliary fields are introduced to achieve off-shell closure, some symmetry transformations (typically, those of auxiliary fields) are nonlinear [@superg]. The relevance of this issue is already known in the literature. For example, in ref. [@superspace] it is explained that in supersymmetric theories the standard background field method cannot be applied, precisely because the symmetry transformations are nonlinear. It is argued that the linearity assumption is tied to the linear splitting $\Phi
\rightarrow \Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ between quantum fields $\Phi $ and background fields ${\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$, and that the problem of supersymmetric theories can be avoided with a nonlinear splitting of the form $\Phi \rightarrow \Phi +{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ $+$ nonlinear corrections. Perhaps it is possible to generalize the results of this paper to supergravity following those guidelines. From our viewpoint, the crucial property is that the background transformations of the quantum fields are linear in the quantum fields themselves, because then they do not renormalize.
An alternative strategy, not bound to supersymmetric theories, is that of introducing (possibly infinitely many) auxiliary fields, replacing every nonlinear term appearing in the symmetry transformations with a new field $N $, and then proceeding similarly with the $N$ transformations and the closure relations, till all functions $R^{\alpha }$ are at most quadratic. The natural framework for this kind of job is the one of refs. [@fieldcov; @masterf; @mastercan], where the fields $N$ are dual to the sources $L$ coupled to composite fields. Using that approach the Batalin-Vilkovisky formalism can be extended to the composite-field sector of the theory and all perturbative canonical transformations can be studied as true changes of field variables in the functional integral, instead of mere replacements of integrands. For reasons of space, though, we cannot pursue this strategy here.
The quest for parametric completeness: Where we stand now
=========================================================
In this section we make remarks about the problem of parametric completeness in general gauge theories and recapitulate where we stand now on this issue. To begin with, consider non-Abelian Yang-Mills theory as a deformation of its Abelian limit. The minimal solution $S(g)$ of the master equation $(S(g),S(g))=0$ reads $$S(g)=-\frac{1}{4}\int F_{\mu \nu }^{a}F^{\mu \nu \hspace{0.01in}a}+\int
K^{\mu a}\partial _{\mu }C^{a}+gf^{abc}\int \left( K^{\mu a}A_{\mu
}^{b}+\frac{1}{2}K_{C}^{a}C^{b}\right) C^{c}.$$ Differentiating the master equation with respect to $g$ and setting $g=0$, we find $$(S,S)=0,\qquad (S,\omega )=0,\qquad S=S(0),\qquad \omega =\left. \frac{\mathrm{d}S(g)}{\mathrm{d}g}\right| _{g=0}.$$ On the other hand, we can easily prove that there exists no local functional $\chi $ such that $\omega =(S,\chi )$. Thus, we can say that $\omega $ is a nontrivial solution of the cohomological problem associated with an Abelian Yang-Mills theory that contains a suitable number of photons [@regnocoho]. Nevertheless, renormalization cannot turn $\omega $ on as a counterterm, because $S(0)$ is a free field theory. Even if we couple the theory to gravity and assume that massive fermions are present (which allows us to construct dimensionless parameters multiplying masses with the Newton constant), radiative corrections cannot dynamically “un-Abelian-ize” the theory, namely convert an Abelian theory into a non-Abelian one. One way to prove this fact is to note that the dependence on gauge fields is even at $g=0$, but not at $g\neq 0$. The point is, however, that cohomology *per se* is unable to prove it. Other properties must be advocated, such as the discrete symmetry just mentioned. In general, we cannot rely on cohomology only, and the possibility that gauge symmetries may be dynamically deformed in nontrivial and observable ways remains open.
In ref. [@regnocoho] the issue of parametric completeness was studied in general terms. In that approach, which applies to all theories that are manifestly free of gauge anomalies, renormalization triggers an automatic parametric extension till the classical action becomes parametrically complete. The results of ref. [@regnocoho] leave the door open to dynamically induced nontrivial deformations of the gauge symmetry. Instead, the results found here close that door in all cases where they apply, which means manifestly nonanomalous irreducible gauge symmetries that close off shell and satisfy the linearity assumption. The reason is – we stress it again – that by formulas (\[kk\]) and (\[key\]) all dynamically induced deformations can be organized into parameter redefinitions and canonical transformations. As far as we know now, gauge symmetries can still be dynamically deformed in observable ways in theories that do not satisfy the assumptions of this paper. Supergravities are natural candidates to provide explicit examples.
Conclusions
===========
The background field method and the Batalin-Vilkovisky formalism are convenient tools to quantize general gauge field theories. In this paper we have merged the two to rephrase and generalize known results about renormalization, and to study parametric completeness. Our approach applies when gauge anomalies are manifestly absent, the gauge algebra is irreducible and closes off shell, the gauge transformations are linear functions of the fields, and closure is field independent. These assumptions are sufficient to include the gauge symmetries we need for physical applications, such as Abelian and non-Abelian Yang-Mills symmetries, local Lorentz symmetry and general changes of coordinates, but exclude other potentially interesting symmetries, such as local supersymmetry. Both renormalizable and nonrenormalizable theories are covered, such as QED, non-Abelian Yang-Mills theories, quantum gravity and Lorentz-violating gauge theories, as well as effective and higher-derivative models, in arbitrary dimensions, and also extensions obtained adding any set of composite fields. At the same time, chiral theories, and therefore the Standard Model, possibly coupled with quantum gravity, require the analysis of anomaly cancellation and the Adler-Bardeen theorem, which we postpone to a future investigation. The fact that supergravities are left out from the start, on the other hand, suggests that there should exist either a no-go theorem or a more advanced framework. At any rate, we are convinced that our formalism is helpful to understand several properties better and address unsolved problems.
We have studied gauge dependence in detail, and renormalized the canonical transformation that continuously interpolates between the background field approach and the usual approach. Relating the two approaches, we have proved parametric completeness without making use of cohomological classifications. The outcome is that in all theories that satisfy our assumptions renormalization cannot hide any surprises; namely the gauge symmetry remains essentially the same throughout the quantization process. In the theories that do not satisfy our assumptions, instead, the gauge symmetry could be dynamically deformed in physically observable ways. It would be remarkable if we discovered explicit examples of theories where this sort of “dynamical creation” of gauge symmetries actually takes place.
12truept [**Acknowledgments**]{}
2truept
The investigation of this paper was carried out as part of a program to complete the book [@webbook], which will be available at [`Renormalization.com`](http://renormalization.com) once completed.
Appendix
========
In this appendix we prove several theorems and identities that are used in the paper. We use the Euclidean notation and the dimensional-regularization technique, which guarantees, in particular, that the functional integration measure is invariant under perturbatively local changes of field variables. The generating functionals $Z$ and $W$ are defined from $$Z(J,K,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })=\int [\mathrm{d}\Phi ]\hspace{0.01in}\exp (-S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })+\int \Phi ^{\alpha
}J_{\alpha })=\exp W(J,K,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }), \label{defa}$$ and $\Gamma (\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })$ $=-W+\int \Phi
^{\alpha }J_{\alpha }$ is the $W$ Legendre transform. Averages denote the sums of connected diagrams (e.g. $\langle A(x)B(y)\rangle =\langle
A(x)B(y)\rangle _{\text{nc}}-\langle A(x)\rangle \langle B(y)\rangle $, where $\langle A(x)B(y)\rangle _{\text{nc}}$ includes disconnected diagrams). Moreover, the average $\langle X\rangle $ of a local functional $X $ can be viewed as a functional of $\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }
$ (in which case it collects one-particle irreducible diagrams) or a functional of $J,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$. When we need to distinguish the two options we specify whether $\Phi $ or $J$ are kept constant in functional derivatives. First we work in the usual (non-background field) framework; then we generalize the results to the background field method.
To begin with, we recall a property that is true even when the action $S(\Phi ,K)$ does not satisfy the master equation.
The identity $(\Gamma ,\Gamma )=\langle (S,S)\rangle $ holds. \[th0\]
*Proof*. Applying the change of field variables $$\Phi ^{\alpha }\rightarrow \Phi ^{\alpha }+\theta (S,\Phi ^{\alpha })
\label{chv}$$ to (\[defa\]), where $\theta $ is a constant anticommuting parameter, we obtain $$\theta \int \left\langle \frac{\delta _{r}S}{\delta K_{\alpha }}\frac{\delta
_{l}S}{\delta \Phi ^{\alpha }}\right\rangle -\theta \int \left\langle \frac{\delta _{r}S}{\delta K_{\alpha }}\right\rangle J_{\alpha }=0,$$ whence $$\frac{1}{2}\langle (S,S)\rangle =-\int \left\langle \frac{\delta _{r}S}{\delta K_{\alpha }}\frac{\delta _{l}S}{\delta \Phi ^{\alpha }}\right\rangle
=-\int \left\langle \frac{\delta _{r}S}{\delta K_{\alpha }}\right\rangle
J_{\alpha }=\int \frac{\delta _{r}W}{\delta K_{\alpha }}\frac{\delta
_{l}\Gamma }{\delta \Phi ^{\alpha }}=-\int \frac{\delta _{r}\Gamma }{\delta
K_{\alpha }}\frac{\delta _{l}\Gamma }{\delta \Phi ^{\alpha }}=\frac{1}{2}(\Gamma ,\Gamma ).$$
Now we prove results for an action $S$ that satisfies the master equation $(S,S)=0$.
If $(S,S)=0$ then $(\Gamma ,\langle X\rangle )=\langle (S,X)\rangle $ for every local functional $X$. \[theorem2\]
*Proof*. Applying the change of field variables (\[chv\]) to $$\langle X\rangle =\frac{1}{Z(J,K)}\int [\mathrm{d}\Phi ]\hspace{0.01in}X\exp
(-S+\int \Phi ^{\alpha }J_{\alpha }),$$ and using $(S,S)=0$ we obtain $$\int \left\langle \frac{\delta _{r}S}{\delta K_{\alpha }}\frac{\delta _{l}X}{\delta \Phi ^{\alpha }}\right\rangle =(-1)^{\varepsilon _{X}+1}\int
\left\langle X\frac{\delta _{r}S}{\delta K_{\alpha }}\right\rangle \frac{\delta _{l}\Gamma }{\delta \Phi ^{\alpha }}, \label{r1}$$ where $\varepsilon _{X}$ denotes the statistics of the functional $X$ (equal to 0 if $X$ is bosonic, 1 if it is fermionic, modulo 2). Moreover, we also have $$\int \left\langle \frac{\delta _{r}S}{\delta \Phi ^{\alpha }}\frac{\delta
_{l}X}{\delta K_{\alpha }}\right\rangle =\int \frac{\delta _{r}\Gamma }{\delta \Phi ^{\alpha }}\left\langle \frac{\delta _{l}X}{\delta K_{\alpha }}\right\rangle , \label{r2}$$ which can be proved starting from the expression on the left-hand side and integrating by parts. In the derivation we use the fact that since $X$ is local, $\delta _{r}\delta _{l}X/(\delta \Phi ^{\alpha }\delta K_{\alpha })$ is set to zero by the dimensional regularization, which kills the $\delta
(0) $s and their derivatives.
Next, straightforward differentiations give $$\begin{aligned}
\left. \frac{\delta _{l}\langle X\rangle }{\delta K_{\alpha }}\right| _{J}
&=&\left\langle \frac{\delta _{l}X}{\delta K_{\alpha }}\right\rangle
-\left\langle \frac{\delta _{l}S}{\delta K_{\alpha }}X\right\rangle
\label{r3} \\
&=&\left. \frac{\delta _{l}\langle X\rangle }{\delta K_{\alpha }}\right|
_{\Phi }-\int \left. \frac{\delta _{l}J_{\beta }}{\delta K_{\alpha }}\right|
_{\Phi }\left. \frac{\delta _{l}\langle X\rangle }{\delta J_{\beta }}\right|
_{K}. \label{r4}\end{aligned}$$ At this point, using (\[r1\])-(\[r4\]) and $(J_{\alpha},\Gamma )=0$ (which can be proved by differentiating $(\Gamma ,\Gamma )=0$ with respect to $\Phi
^{\alpha}$), we derive $(\Gamma ,\langle X\rangle )=\langle (S,X)\rangle $.
If $(S,S)=0$ and $$\frac{\partial S}{\partial \xi }=(S,X), \label{bbug}$$ where $X$ is a local functional and $\xi $ is a parameter, then $$\frac{\partial \Gamma }{\partial \xi }=(\Gamma ,\langle X\rangle ).
\label{pprove}$$ \[bbugc\]
*Proof*. Using theorem \[theorem2\] we have $$\frac{\partial \Gamma }{\partial \xi }=-\frac{\partial W}{\partial \xi }=\langle \frac{\partial S}{\partial \xi }\rangle =\langle (S,X)\rangle
=(\Gamma ,\langle X\rangle ).$$
Now we derive results that hold even when $S$ does not satisfy the master equation.
\[blabla\]The identity $$(\Gamma ,\langle X\rangle )=\langle (S,X)\rangle -\frac{1}{2}\langle
(S,S)X\rangle _{\Gamma } \label{prove0}$$ holds, where $X$ is a generic local functional and $\langle AB\cdots
Z\rangle _{\Gamma }$ denotes the set of connected, one-particle irreducible diagrams with one insertion of $A$, $B$, $\ldots Z$.
This theorem is a generalization of theorem \[theorem2\]. It is proved by repeating the derivation without using $\left( S,S\right) =0$. First, observe that formula (\[r1\]) generalizes to $$\int \left\langle \frac{\delta _{r}S}{\delta K_{\alpha }}\frac{\delta _{l}X}{\delta \Phi ^{\alpha }}\right\rangle =(-1)^{\varepsilon _{X}+1}\int
\left\langle X\frac{\delta _{r}S}{\delta K_{\alpha }}\right\rangle \frac{\delta _{l}\Gamma }{\delta \Phi ^{\alpha }}-\frac{1}{2}\langle (S,S)X\rangle
. \label{r11}$$ On the other hand, formula (\[r2\]) remains the same, as well as (\[r3\]) and (\[r4\]). We have $$\left( \Gamma ,\langle X\rangle \right) =\langle (S,X)\rangle -\frac{1}{2}\langle (S,S)X\rangle +\int \frac{\delta _{r}\Gamma }{\delta \Phi ^{\alpha }}\left. \frac{\delta _{l}J_{\beta }}{\delta K_{\alpha }}\right| _{\Phi
}\left. \frac{\delta _{l}\langle X\rangle }{\delta J_{\beta }}\right|
_{K}-\int \frac{\delta _{r}\Gamma }{\delta K_{\alpha }}\left. \frac{\delta
_{l}\langle X\rangle }{\delta \Phi ^{\alpha }}\right| _{K}.$$ Differentiating $(\Gamma ,\Gamma )$ with respect to $\Phi ^{\alpha}$ we get $$\frac{1}{2}\frac{\delta _{r}(\Gamma ,\Gamma )}{\delta \Phi ^{\alpha}}=\frac{1}{2}\frac{\delta _{l}(\Gamma ,\Gamma )}{\delta \Phi ^{\alpha}}=(J_{\alpha },\Gamma
)=(-1)^{\varepsilon _{\alpha }}(\Gamma ,J_{\alpha }),$$ where $\varepsilon _{\alpha }$ is the statistics of $\Phi ^{\alpha }$. Using $(\Gamma ,\Gamma )=\langle (S,S)\rangle $ we finally obtain $$\left( \Gamma ,\langle X\rangle \right) =\langle (S,X)\rangle -\frac{1}{2}\langle (S,S)X\rangle +\frac{1}{2}\int (-1)^{\varepsilon _{\alpha }}\frac{\delta _{r}\langle (S,S)\rangle }{\delta \Phi ^{\alpha }}\left. \frac{\delta
_{l}\langle X\rangle }{\delta J_{\alpha }}\right| _{K}. \label{allo}$$
The set of irreducible diagrams contained in $\langle A\hspace{0.01in}B\rangle $, where $A$ and $B$ are local functionals, is given by the formula $$\langle A\hspace{0.01in}B\rangle _{\Gamma }=\langle AB\rangle -\{\langle
A\rangle ,\langle B\rangle \}, \label{oo}$$ where $\{X,Y\}$ are the “mixed brackets” [@BV2] $$\{X,Y\}\equiv \int \frac{\delta _{r}X}{\delta \Phi ^{\alpha }}\langle \Phi
^{\alpha }\Phi ^{\beta }\rangle \frac{\delta _{l}Y}{\delta \Phi ^{\beta }}=\int \frac{\delta _{r}X}{\delta \Phi ^{\alpha }}\frac{\delta _{r}\delta
_{r}W}{\delta J_{\beta }\delta J_{\alpha }}\frac{\delta _{l}Y}{\delta \Phi
^{\beta }}=\int \left. \frac{\delta _{r}X}{\delta J_{\alpha }}\right| _{K}\frac{\delta _{l}Y}{\delta \Phi ^{\alpha }}, \label{mixed brackets}$$ $X$ and $Y$ being functionals of $\Phi $ and $K$. Indeed, $\{\langle
A\rangle ,\langle B\rangle \}$ is precisely the set of diagrams in which the $A$ and $B$ insertions are connected in a one-particle reducible way. Thus, formula (\[allo\]) coincides with (\[prove0\]).
Using (\[prove0\]) we also have the identity $$\frac{\partial \Gamma }{\partial \xi }-\left( \Gamma ,\langle X\rangle
\right) =\left\langle \frac{\partial S}{\partial \xi }-\left( S,X\right)
\right\rangle +\frac{1}{2}\left\langle \left( S,S\right) \hspace{0.01in}X\right\rangle _{\Gamma }, \label{provee}$$ which generalizes corollary \[bbugc\].
Now we switch to the background field method. We begin by generalizing theorem \[th0\].
If the action $S(\Phi ,{\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu },K,{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu })$ is such that $\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi $ independent, the identity $$\llbracket \Gamma ,\Gamma \rrbracket =\langle \llbracket S,S\rrbracket \rangle$$ holds. \[thb\]
*Proof*. Since $\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi
$ independent we have $\delta _{l}\Gamma /\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha
}=\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$. Using theorem \[th0\] we find $$\llbracket \Gamma ,\Gamma \rrbracket =(\Gamma ,\Gamma )+2\int \frac{\delta
_{r}\Gamma }{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}\frac{\delta _{l}\Gamma }{\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }}=\langle (S,S)\rangle +2\int \langle \frac{\delta _{r}S}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}\rangle \frac{\delta _{l}S}{\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }}=\langle (S,S)\rangle +2\int \langle \frac{\delta _{r}S}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}\frac{\delta _{l}S}{\delta
{\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }}\rangle =\langle \llbracket S,S\rrbracket \rangle .$$
Next, we mention the useful identity $$\left. \frac{\delta _{l}\langle X\rangle }{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}\right| _{\Phi }=\left\langle \frac{\delta _{l}X}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}\right\rangle -\left\langle \frac{\delta _{l}S}{\delta {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }^{\alpha }}X\right\rangle _{\Gamma }, \label{dera}$$ which holds for every local functional $X$. It can be proved by taking (\[r3\])–(\[r4\]) with $K\rightarrow {\mkern2mu\underline{\mkern-2mu\smash{\Phi }\mkern-2mu}\mkern2mu }$ and using (\[oo\])–(\[mixed brackets\]).
Mimicking the proof of theorem \[thb\] and using (\[dera\]), it is easy to prove that theorem \[blabla\] implies the identity $$\llbracket \Gamma ,\langle X\rangle \rrbracket =\langle \llbracket S,X\rrbracket \rangle -\frac{1}{2}\langle \llbracket S,S\rrbracket X\rangle
_{\Gamma }, \label{bb2}$$ for every ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$-independent local functional $X$. Thus we have the following property.
The identity $$\frac{\partial \Gamma }{\partial \xi }-\llbracket \Gamma ,\langle X\rangle \rrbracket =\left\langle \frac{\partial S}{\partial \xi }-\llbracket S,X\rrbracket \right\rangle +\frac{1}{2}\langle \llbracket S,S\rrbracket X\rangle _{\Gamma } \label{proveg}$$ holds for every action $S$ such that $\delta _{l}S/\delta {\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }_{\alpha }$ is $\Phi $ independent, for every ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$-independent local functional $X$ and for every parameter $\xi $. \[cora\]
If the action $S$ has the form (\[assu\]) and $X$ is also ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$ independent, applying (\[backghost\]) to (\[bb2\]) we obtain $$\llbracket \hat{\Gamma},\langle X\rangle \rrbracket =\langle \llbracket \hat{S},X\rrbracket \rangle -\frac{1}{2}\langle \llbracket \hat{S},\hat{S}\rrbracket X\rangle _{\Gamma },\qquad \llbracket \bar{S},\langle X\rangle \rrbracket =\langle \llbracket \bar{S},X\rrbracket \rangle -\langle \llbracket \bar{S},\hat{S}\rrbracket X\rangle _{\Gamma },\qquad \langle \llbracket \bar{S},\bar{S}\rrbracket X\rangle _{\Gamma }=0,
\label{blablaback}$$ which imply the following statement.
If $S$ satisfies the assumptions of (\[assu\]), $\llbracket \bar{S},X\rrbracket =0$ and $\llbracket \bar{S},\hat{S}\rrbracket =0$, where $X$ is a ${\mkern2mu\underline{\mkern-2mu\smash{C}\mkern-2mu}\mkern2mu }$- and ${\mkern2mu\underline{\mkern-2mu\smash{K}\mkern-2mu}\mkern2mu }$-independent local functional, then $\llbracket \bar{S},\langle X\rangle \rrbracket =0$. \[corolla\]
Finally, we recall a result derived in ref. [@removal].
If $\Phi ,K\rightarrow \Phi ^{\prime },K^{\prime }$ is a canonical transformation generated by $F(\Phi ,K^{\prime })$, and $\chi (\Phi ,K)$ is a functional behaving as a scalar (that is to say $\chi ^{\prime }(\Phi ^{\prime
},K^{\prime })=\chi (\Phi ,K)$), then $$\frac{\partial \chi ^{\prime }}{\partial \varsigma }=\frac{\partial \chi }{\partial \varsigma }-(\chi ,\tilde{F}_{\varsigma }) \label{thesis}$$ for every parameter $\varsigma $, where $\tilde{F}_{\varsigma }(\Phi
,K)\equiv F_{\varsigma }(\Phi ,K^{\prime }(\Phi ,K))$ and $F_{\varsigma
}(\Phi ,K^{\prime })=\partial F/\partial \varsigma $. \[theorem5\]
*Proof*. When we do not specify the variables that are kept constant in partial derivatives, it is understood that they are the natural variables. Thus $F$, $\Phi ^{\prime }$ and $K$ are functions of $\Phi
,K^{\prime }$, while $\chi $ and $\tilde{F}_{\varsigma }$ are functions of $\Phi ,K$ and $\chi ^{\prime }$ is a function of $\Phi ^{\prime },K^{\prime }$. It is useful to write down the differentials of $\Phi ^{\prime }$ and $K$, which are [@vanproeyen] $$\begin{aligned}
\mathrm{d}\Phi ^{\prime \hspace{0.01in}\alpha } &=&\int \frac{\delta
_{l}\delta F}{\delta K_{\alpha }^{\prime }\delta \Phi ^{\beta }}\mathrm{d}\Phi ^{\beta }+\int \frac{\delta _{l}\delta F}{\delta K_{\alpha }^{\prime
}\delta K_{\beta }^{\prime }}\mathrm{d}K_{\beta }^{\prime }+\frac{\partial
\Phi ^{\prime \hspace{0.01in}\alpha }}{\partial \varsigma }\mathrm{d}\varsigma , \nonumber \\
\mathrm{d}K_{\alpha } &=&\int \mathrm{d}\Phi ^{\beta }\frac{\delta
_{l}\delta F}{\delta \Phi ^{\beta }\delta \Phi ^{\alpha }}+\int \mathrm{d}K_{\beta }^{\prime }\frac{\delta _{l}\delta F}{\delta K_{\beta }^{\prime
}\delta \Phi ^{\alpha }}+\frac{\partial K_{\alpha }}{\partial \varsigma }\mathrm{d}\varsigma . \label{differentials}\end{aligned}$$
Differentiating $\chi ^{\prime }(\Phi ^{\prime },K^{\prime })=\chi (\Phi ,K)$ with respect to $\varsigma $ at constant $\Phi ^{\prime }$ and $K^{\prime }$, we get $$\frac{\partial \chi ^{\prime }}{\partial \varsigma }=\frac{\partial \chi }{\partial \varsigma }+\int \frac{\delta _{r}\chi }{\delta \Phi ^{\alpha }}\left. \frac{\partial \Phi ^{\alpha }}{\partial \varsigma }\right| _{\Phi
^{\prime },K^{\prime }}+\int \frac{\delta _{r}\chi }{\delta K_{\alpha }}\left. \frac{\partial K_{\alpha }}{\partial \varsigma }\right| _{\Phi
^{\prime },K^{\prime }}. \label{sigmaprimosue2}$$ Formulas (\[differentials\]) allow us to write $$\frac{\partial \Phi ^{\prime \hspace{0.01in}\alpha }}{\partial \varsigma }=-\int \frac{\delta _{l}\delta F}{\delta K_{\alpha }^{\prime }\delta \Phi
^{\beta }}\left. \frac{\partial \Phi ^{\beta }}{\partial \varsigma }\right|
_{\Phi ^{\prime },K^{\prime }},\qquad \frac{\delta _{l}\delta F}{\delta
K_{\alpha }^{\prime }\delta \Phi ^{\beta }}=\left. \frac{\delta _{l}K_{\beta
}}{\delta K_{\alpha }^{\prime }}\right| _{\Phi ,\varsigma },$$ and therefore we have $$\frac{\delta \tilde{F}_{\varsigma }}{\delta K_{\alpha }}=\int \left. \frac{\delta _{l}K_{\beta }^{\prime }}{\delta K_{\alpha }}\right| _{\Phi
,\varsigma }\frac{\partial \Phi ^{\prime \hspace{0.01in}\beta }}{\partial
\varsigma }=-\int \left. \frac{\delta _{l}K_{\beta }^{\prime }}{\delta
K_{\alpha }}\right| _{\Phi ,\varsigma }\left. \frac{\delta _{l}K_{\gamma }}{\delta K_{\beta }^{\prime }}\right| _{\Phi ,\varsigma }\left. \frac{\partial
\Phi ^{\gamma }}{\partial \varsigma }\right| _{\Phi ^{\prime },K^{\prime
}}=-\left. \frac{\partial \Phi ^{\alpha }}{\partial \varsigma }\right|
_{\Phi ^{\prime },K^{\prime }}. \label{div1}$$ Following analogous steps, we also find $$\frac{\delta \tilde{F}_{\varsigma }}{\delta \Phi ^{\alpha }}=\frac{\partial
K_{\alpha }}{\partial \varsigma }+\int \left. \frac{\delta _{l}K_{\beta
}^{\prime }}{\delta \Phi ^{\alpha }}\right| _{K,\varsigma }\frac{\partial
\Phi ^{\prime \hspace{0.01in}\beta }}{\partial \varsigma },\qquad \frac{\partial K_{\alpha }}{\partial \varsigma }=\left. \frac{\partial K_{\alpha }}{\partial \varsigma }\right| _{\Phi ^{\prime },K^{\prime }}-\int \frac{\delta _{l}\delta F}{\delta \Phi ^{\alpha }\delta \Phi ^{\beta }}\left.
\frac{\partial \Phi ^{\beta }}{\partial \varsigma }\right| _{\Phi ^{\prime
},K^{\prime }},$$ whence $$\left. \frac{\partial K_{\alpha }}{\partial \varsigma }\right| _{\Phi
^{\prime },K^{\prime }}=\frac{\delta \tilde{F}_{\varsigma }}{\delta \Phi
^{\alpha }}+\int \left( \frac{\delta _{l}K_{\gamma }}{\delta \Phi ^{\alpha }}+\left. \frac{\delta _{l}K_{\beta }^{\prime }}{\delta \Phi ^{\alpha }}\right| _{K,\varsigma }\frac{\delta _{l}K_{\gamma }}{\delta K_{\beta
}^{\prime }}\right) \left. \frac{\partial \Phi ^{\gamma }}{\partial
\varsigma }\right| _{\Phi ^{\prime },K^{\prime }}=\frac{\delta \tilde{F}_{\varsigma }}{\delta \Phi ^{\alpha }}. \label{div2}$$ This formula, together with (\[div1\]), allows us to rewrite (\[sigmaprimosue2\]) in the form (\[thesis\]).
[99]{} B.S. De Witt, Quantum theory of gravity. II. The manifestly covariant theory, Phys. Rev. 162 (1967) 1195.
L.F. Abbott, The background field method beyond one loop, Nucl. Phys. B 185 (1981) 189.
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see also S. Weinberg, *The quantum theory of fields*, vol. II, Cambridge University Press, Cambridge 1995.
D. Anselmi, Renormalization of gauge theories without cohomology, Eur. Phys. J. C73 (2013) 2508, [13A1 Renormalization.com](http://renormalization.com/13a1/), arXiv:1301.7577 \[hep-th\].
G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. I. General theorems, Commun. Math. Phys. 174 (1995) 57 and arXiv:hep-th/9405109;
G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. II. Application to Yang-Mills theory, Commun. Math. Phys. 174 (1995) 116 and arXiv:hep-th/9405194;
G. Barnich, F. Brandt, M. Henneaux, General solution of the Wess-Zumino consistency condition for Einstein gravity, Phys. Rev. D 51 (1995) R1435 and arXiv:hep-th/9409104;
S.D. Joglekar and B.W. Lee, General theory of renormalization of gauge invariant operators, Ann. Phys. (NY) 97 (1976) 160.
D. Anselmi and M. Halat, Renormalization of Lorentz violating theories, Phys. Rev. D 76 (2007) 125011 and arXiv:0707.2480 \[hep-th\];
D. Anselmi, Weighted power counting and Lorentz violating gauge theories. I. General properties, Ann. Phys. 324 (2009) 874, [08A2 Renormalization.com](http://renormalization.com/08a2/) and arXiv:0808.3470 \[hep-th\];
D. Anselmi, Weighted power counting and Lorentz violating gauge theories. II. Classification, Ann. Phys. 324 (2009) 1058, [08A3 Renormalization.com](http://renormalization.com/08a3/) and arXiv:0808.3474 \[hep-th\].
S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in *An Einstein centenary survey*, Edited by S. Hawking and W. Israel, Cambridge University Press, Cambridge 1979.
K.S. Stelle, Renormalization of higher-derivative quantum gravity, Phys. Rev. D 16 (1977) 953.
E.T. Tomboulis, Superrenormalizable gauge and gravitational theories, arXiv:hep-th/9702146;
L. Modesto, Super-renormalizable quantum gravity, Phys.Rev. D86 (2012) 044005 and arXiv:1107.2403 \[hep-th\];
T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys.Rev.Lett. 108 (2012) 031101 and arXiv:1110.5249 \[gr-qc\];
L. Modesto, Finite quantum gravity, arXiv:1305.6741 \[hep-th\].
H. Kluberg-Stern and J.B. Zuber, Renormalization of nonabelian gauge theories in a background field gauge. 1. Green functions, Phys. Rev. D12 (1975) 482;
H. Kluberg-Stern and J.B. Zuber, Renormalization of nonabelian gauge theories in a background field gauge. 2. Gauge invariant operators, Phys. Rev. D 12 (1975) 3159.
D. Colladay and V.A. Kostelecký, Lorentz-violating extension of the Standard Model, Phys. Rev. D58 (1998) 116002 and arXiv:hep-ph/9809521;
D. Anselmi, Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model, Phys. Rev. D79 (2009) 025017, [08A4 Renormalization.com](http://renormalization.com/08a4/) and arXiv:0808.3475 \[hep-ph\];
D. Anselmi, Standard Model without elementary scalars and high energy Lorentz violation, Eur. Phys. J. C65 (2010) 523, [09A1 Renormalization.com](http://renormalization.com/09a1/), and arXiv:0904.1849 \[hep-ph\].
S.L. Adler and W.A. Bardeen, Absence of higher-order corrections in the anomalous axial vector divergence, Phys. Rev. 182 (1969) 1517.
D. Binosi and A. Quadri, Slavnov-Taylor constraints for nontrivial backgrounds, Phys. Rev. D84 (2011) 065017 and arXiv:1106.3240 \[hep-th\];
D. Binosi and A. Quadri, Canonical transformations and renormalization group invariance in the presence of nontrivial backgrounds, Phys. Rev. D85 (2012) 085020 and arXiv:1201.1807 \[hep-th\];
D. Binosi and A. Quadri, The background field method as a canonical transformation, Phys.Rev. D85 (2012) 121702 and arXiv:1203.6637 \[hep-th\].
D. Anselmi, A general field covariant formulation of quantum field theory, Eur. Phys. J. C73 (2013) 2338, [12A1 Renormalization.com](http://renormalization.com/12a1/) and arXiv:1205.3279 \[hep-th\].
D. Anselmi, A master functional for quantum field theory, Eur. Phys. J. C73 (2013) 2385, [12A2 Renormalization.com](http://renormalization.com/12a2/) and arXiv:1205.3584 \[hep-th\].
D. Anselmi, Master functional and proper formalism for quantum gauge field theory, Eur. Phys. J. C73 (2013) 2363, [12A3 Renormalization.com](http://renormalization.com/12a3/) and arXiv:1205.3862 \[hep-th\].
B.L. Voronov, P.M. Lavrov and I.V. Tyutin, Canonical transformations and the gauge dependence in general gauge theories, Sov. J. Nucl. Phys. 36 (1982) 292 and Yad. Fiz. 36 (1982) 498.
P. van Nieuwenhuizen, *Supergravity*, Phys. Rept. 68 (1981) 189.
S.J. Gates, M.T. Grisaru, M. Rocek and W. Siegel, [*Superspace or one thousand and one lessons in supersymmetry*]{}, Front.Phys. 58 (1983) 1-548, arXiv:hep-th/0108200.
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Q:
How to put debug point
I've a php file calling another php file which sometimes calls another php file to execute some actions (all through ajax).
What I use to do was to echo at different points to know upto where the codes are executing properly. But with this approach, I can keep echo-ing.
So how do I know upto where my code is executing?? Is there a tool for Google Chrome browser to detect it??
A:
In your web browser, click the wrench icon, then "Tools", then "Developer tools". You can debug and step through JavaScript, you can see a timeline of requests with the request and response headers and bodies fully inspectable, etc. You should be able to debug all your AJAX request without any additional software/plugins.
|
Despite his recent legal troubles, rapper DMX received some good news yesterday (May 16), when a Maryland judge overturned a $1.5 million defamation judgment against him.
The judgment, which was handed down in January, came as a result of a defamation of character lawsuit brought against DMX by Monique Wayne.
The suit stemmed from allegations the rapper (born Earl Simmons) made during a 2006 interview with Sister 2 Sister magazine.
In the story, Simmons claimed he was raped by Wayne while staying at a hotel in Baltimore in 2003.
Simmons comments triggered a $6 million lawsuit that was filed by Wayne in Prince George’s County Circuit Court in Upper Marlboro, Md., in October 2006.
The rapper was later ordered to pay Wayne $518,400 in compensation and $1 million in punitive penalties after missing a scheduled court hearing for the case in January.
Soon after, Simmons hired The Murphy Firm, a Baltimore-based law firm, to dispute the ruling.
According to reports, the New York native was unaware that a hearing was scheduled to take place.
Despite the initial outcome, Hassan Murphy, a managing partner of The Murphy Firm, was happy to see his client vindicated by the new ruling, which was handed down by Judge Thomas P. Smith.
“Today a very large judgment was vacated by Judge Smith,” Murphy told AllHipHop.com in a statement. “The judge clearly agreed with us that Mr. Simmons was never properly notified and therefore he threw out the judgment.”
Although the overturned judgment ended Simmons’ week on a good note, the rapper is still mired in legal drama.
Earlier this month, the rapper was arrested on numerous motor vehicle charges stemming from a January incident that involved him driving 114 mph on a local highway with a suspended license.
On Thursday (May 15), Simmons pleaded not guilty to various felony drug charges and animal cruelty charges, after arriving an hour late to a court appearance in front of Maricopa County Superior Court Commissioner Lisa VandenBerg.
The court appearance followed a May 9 raid of the rappers Cave Creek, Arizona home that came after a seven month investigation into animal cruelty charges. |
Q:
Find matching strings in table column Oracle 10g
I am trying to search a varchar2 column in a table for matching strings using the value in another column. The column being searched allows free form text and allows words and numbers of different lengths. I want to find a string that is not part of a larger string of text and numbers.
Example: 1234a should match "Invoice #1234a" but not "Invoice #1234a567"
Steps Taken:
I have tried Regexp_Like(table2.Searched_Field,table1.Invoice) but get many false hits when the invoice number has a number sequence that can be found in other invoice numbers.
A:
Suggestions:
Match only at end:
REGEXP_LIKE(table2.Searched_Field, table1.Invoice || '$')
Match exactly:
table2.Searched_Field = 'Invoice #' || table1.Invoice
Match only at end with LIKE:
table2.Searched_Field LIKE '%' || table1.Invoice
|
Creative Worx
I am an artist whose main focus is on abstract pieces. I love to draw and doodle a design and I love to paint. I love the expression and individualism that art has given me. Art makes me happy and I truly enjoy doing it. I hope you enjoy my work! :) |
WoW Tailoring Guide 1-600
This WoW Tailoring Guide details the most efficient method of leveling Tailoring from levels 1 to 600 in the World of Warcraft. Tailoring is a primary profession (of which you can only choose two at any point in the game) and allows your character to create a variety of items such as armor, bags and clothing. Tailoring probably complements the Enchanting profession better than any other, as the items that are crafted with Tailoring can be disenchanted to provide materials for Enchanting.
Updated for WoW patch 5.2
This guide focuses on making the training path easier by using patterns that can be learned from Tailoring trainers and patterns with the most easily obtained materials.
It also looks to make the items that are Green or better quality, as these can then be disenchanted. Unless stated otherwise, all the patterns used in this guide can be purchased for a Tailoring Trainer of appropriate level.
If you’re having trouble collecting the cloth required for tailoring patterns, then take a look at the Cloth Gathering Guide for locations (with maps) of the best mobs to farm.
1Alliance players purchase from: Neii in the Traders’ Tier, The Exodar1Horde players purchase from: Deynna in The Bazaar, Silvermoon1There is also a neutral vendor to purchase from: Eiin in the Lower City, Shattrath
2This pattern grants 3 levels at a time3This pattern grants 4 levels at a time4These patterns are available to purchase for 1 x Spirit of Harmony each from vendors in the Vale of Eternal Blossoms. Vale of Eternal Blossoms is accesible after completing the quest A Celestial Experience (requires level 87)
Alliance Vendor is Raishen the Needle in the Shrine of Seven Stars
Horde Vendor is Esha the Loommaiden in the Shrine of Two Moons
Specializations
As of WoW patch 4.0.1 the tailoring specializations of Mooncloth, Shadoweave and Spellfire have been removed from the game.
I hoped you found this WoW Tailoring Leveling Guide useful and that it has helped you on your way to level 600. Please leave a comment to let me know what you think. |
--- record.c.orig 2001-08-14 20:10:46.000000000 +0800
+++ record.c 2011-09-05 15:09:11.000000000 +0800
@@ -31,14 +31,18 @@
** May 25, 2000 Ver 1.0
*/
-#include<stdio.h>
-#include<fcntl.h>
-#include<sys/types.h>
-#include<pwd.h>
-#include<ctype.h>
-#include<errno.h>
+#include <sys/types.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <unistd.h>
+#include <sys/stat.h>
+#include <fcntl.h>
+#include <pwd.h>
+#include <ctype.h>
+#include <errno.h>
-#include"record.h"
+#include "record.h"
+#include "xjump.h"
#define FS '\t' /* field separator */
|
Q:
Append to closest div class (multiple divs with same class on page)
I'm trying to append content into the closest div class with name ".infoCatcher", but as of now it is appending to all divs with that class on the page.
How do I append this to the closest div?
I have this:
$(document).on('click', '.btnMoreInfo', function () {
$('.item').closest('div').find('.infoCatcher').append('<div class="moreInfo info">' + '</div>');
});
And HTML:
<ul>
<li>
<button class='btnMoreInfo'>More</button>
<div class='infoCatcher'></div>
</li>
<li>
<button class='btnMoreInfo'>More</button>
<div class='infoCatcher'></div>
</li>
<li>
<button class='btnMoreInfo'>More</button>
<div class='infoCatcher'></div>
</li>
<li>
<button class='btnMoreInfo'>More</button>
<div class='infoCatcher'></div>
</li>
<li>
<button class='btnMoreInfo'>More</button>
<div class='infoCatcher'></div>
</li>
</ul>
Thankful for help!
A:
Try .siblings. Converted your code to fiddle. Working version is here
$(document).ready(function(){
$(document).on('click', '.btnMoreInfo', function (e) {
alert('Yes');
$(e.target).siblings(".infoCatcher").append('<div class="moreInfo info">More Content..' + '</div>');
});
});
|
Scars of Love
Scars of Love is a 1918 Australian silent film. It is a lost film about which little is known except it is a melodrama featuring a Red Cross nurse and an Anzac soldier which climaxes in the European battlefields of World War I in which both leads die. It deals with the sins of the father visiting the children.
Production
The film was most likely made by wealthy amateur enthusiasts. It was shot in Melbourne.
It was re-released in 1919 as Should Children Suffer.
References
External links
Scars of Love at National Film and Sound Archive
Category:Australian films
Category:1918 films
Category:Australian drama films
Category:Australian black-and-white films
Category:Australian silent feature films
Category:Lost Australian films
Category:1910s drama films |
1. Field of the Invention
The present invention relates to a health check system, a health check apparatus and a method thereof for providing information on a user's health using a sensor.
2. Description of the Related Art
For example, Shuichi Kurabayashi, Naoki Ishibashi, Yasuo Kiyoki: “Scheme for Realizing Active Type Multidatabase System in Mobile Computing Environment,” Proceedings of Information Processing Society of Japan, 2000-DBS-122, 2000, 463-470 and Shuichi Kurabayashi, Naoki Ishibashi, Yasushi Kiyoki: A Multidatabase System Architecture for Integrating Heterogeneous Databases with Meta-Level Active Rule Primitives. In Proceedings of the 20th TASTED International Conference on Applied Informatics, 2002, 378-387, disclose an active meta-level system that dynamically interconnects devices of databases or the like.
However, these documents neither disclose nor even suggest any health check system, health check apparatus or method thereof for providing information on a user's health by adaptively using sensors. |
Project Summary - Ventricular arrhythmias remain the single most important cause of sudden cardiac death (SCO) among adults living in industrialized nations. Great progress has been made in identifying genes underlying various Mendelian disorders associated with inherited arrhythmia susceptibility as models for understanding more common causes of SCO. The best studied familial arrhythmia syndrome is the congenital long QT syndrome (LQTS). The observation that not all mutation carriers have equal risk for experiencing the clinical manifestations of LQTS (i.e., syncope, sudden death) has motivated the hypothesis that genetic factors other than the primary disease-associated mutation can modify the risk for disease- related morbidity and mortality. This proposal is the first competing renewal of R01-HL68880 which has funded a multi-national translational research collaboration to identify and characterize clinical predictors and candidate genetic modifiers in a large, unique LQTS founder population in South Africa (SA-LQTS). We have hypothesized the existence of two types of modifier genes: genes which affect myocardial repolarization and produce an arrhythmia-prone substrate, and genes which affect the propensity for triggering events acting through the autonomic nervous system. Specific Aim 1 describes our ongoing efforts to collect detailed information regarding the phenotype of the SA-LQTS population. We plan to continue our current focus on major clinical outcomes but will also explore more deeply for intermediate phenotypes related to abnormal myocardial repolarization and autonomic tone. For independent testing of candidate modifier gene hypotheses, we will also use a second large LQTS founder population ascertained in Finland (Fin-LQTS; 80 families, > 600 mutation carriers) that is associated with a different KCNQ1 mutation. The addition of this second LQTS founder population coupled with an important new collaboration with genetic epidemiologists at Columbia University will ensure that our observations are valid and have broad implications. In Specific Aim 2, we will examine the molecular mechanisms responsible for genetic and autonomic influences on the major repolarizing myocardial ionic currents. Finally, in Specific Aim 3 we will study genetic and epigenetic mechanisms to explain variation in the transcription of KCNQ1 and other genes that may act to modify the clinical expression of LQTS. The goals of this study are consistent with the mission of NHLBI. Relevance to Public Health - Identification of long QT syndrome (LQTS) modifiers will enhance our understanding of the pathophysiology of an inherited cause of sudden cardiac death (SCO), provide valuable new information to promote more accurate risk counseling for LQTS families, and will contribute to our understanding of more common arrhythmia syndromes associated with highly prevalent cardiac diseases (e.g. ischemic heart disease and congestive heart failure) that are burdened by a high incidence of SCO. [unreadable] [unreadable] [unreadable] |
Penicillium atrovenetum
Penicillium atrovenetum is a fungus species of the genus of Penicillium.
Further reading
H. Raistrick, A. Stössl: Studies in the biochemistry of micro-organisms. 104. Metabolites of Penicillium atrovenetum G. Smith: β-nitropropionic acid, a major metabolite*
See also
List of Penicillium species
References
atrovenetum
Category:Fungi described in 1956 |
Non-alcoholic fatty liver disease, Metabolic syndrome, Obesity, Insulin resistance, Liver fibrosis, NAFLD treatment Sažetak: Nonalcoholic fatty liver disease (NAFLD) has, although it is a very common disorder, only relatively recently gained broader interest among physicians and scientists. Fatty liver has been documented in up to 10 to 15 percent of normal individuals and 70 to 80 percent of obese individuals. Although the pathophysiology of NAFLD is still subject to intensive research, several players and mechanisms have been suggested based on the substantial evidence. Excessive hepatocyte triglyceride accumulation resulting from insulin resistance is the first step in the proposed 'two hit' model of the pathogenesis of NAFLD. Oxidative stress resulting from mitochondrial fatty acids oxidation, NF-kappaB-dependent inflammatory cytokine expression and adipocytokines are all considered to be the potential factors causing second hits which lead to hepatocyte injury, inflammation and fibrosis. Although it was initially believed that NAFLD is a completely benign disorder, histologic follow-up studies have showed that fibrosis progression occurs in about a third of patients. A small number of patients with NAFLD eventually ends up with end-stage liver disease and even hepatocellular carcinoma. Although liver biopsy is currently the only way to confirm the NAFLD diagnosis and distinguish between fatty liver alone and NASH, no guidelines or firm recommendations can still be made as for when and in whom it is necessary. Increased physical activity, gradual weight reduction and in selected cases bariatric surgery remain the mainstay of NAFLD therapy. Studies with pharmacologic agents are showing promising results, but available data are still insufficient to make specific recommendations ; their use therefore remains highly individual. |
Artificial intelligence
Devices, machines and vehicles that are fully autonomous will become a reality during the next 20 years. The Global Digital Foundation will explore the social, legal and economic implications of this development. |
Q:
HttpClient java.net.UnknownHostException exception when the CURL command passes
I am trying to use httpclient to make make a call to Jenkins to get a list of jobs.
When I run my code, I get an UnknownHostException.
I tried to make the same request using curl and I was able to get the result. I am not sure how to interpret this.
void nwe() throws ClientProtocolException, IOException {
HttpHost target = new HttpHost("https://<JENKINS_URL>/api");
CredentialsProvider credsProvider = new BasicCredentialsProvider();
credsProvider.setCredentials(
new AuthScope(target.getHostName(), target.getPort()),
new UsernamePasswordCredentials("username", "password"));
CloseableHttpClient httpclient = HttpClients.custom().setDefaultCredentialsProvider(credsProvider).build();
HttpGet httpGet = new HttpGet("/json");
httpGet.setHeader("Content-type", "application/json");
BasicScheme basicAuth = new BasicScheme();
HttpClientContext localContext = HttpClientContext.create();
CloseableHttpResponse response1 = httpclient.execute(target, httpGet, localContext);
System.out.println(response1.getStatusLine());
}
The CURL command on the same URL gives me the expected output
Thanks,
Amar
A:
Read the JavaDoc for HttpHost:
Parameters: hostname - the hostname (IP or DNS name)
So you should use just (omit the protocol and context):
HttpHost target = new HttpHost( "<JENKINS_URL>" );
and then HttpGet the /api/json part.
Cheers,
|