text:
Under The Radar: "Real Baseball" Returns
By Nico Mar 6, 2021, 9:52am PST
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"Slappy McSlapslapslaperson!"
Rick Scuteri-USA TODAY Sports
This offseason, the A's traded Khris Davis's majestic long fly balls to right field for Elvis Andrus' ball slapped through the right side hole. Was there ever a better time to make this swap?
Don't get me wrong — the home run, and slugging, aren't going anywhere, but more of those fly balls may be going only as far as the warning track. MLB gets few things right (but enough about blackouts, extra innings and doubleheaders), yet even a broken clock is right twice a day and MLB has hit a rare bullseye in reintroducing a deadened, instead of more tightly wound, baseball.
"Chicks dig the long ball" is a misleading meme. Whether you are a chick or a dude, Homerun Derby is not the most exciting brand of baseball. Less reliance on slugging, and more reliance on contact skills, simply makes baseball a far more exciting game to watch.
In a "dead ball era," you see elements of the game that were shelved for the better part of 30 years: The stolen base, the hit and run, the suicide squeeze, the "two strike approach". In other words, nuanced and creative baseball, not just "grip it and rip it in any count".
That's not Khris Davis' game, but it is Elvis Andrus', and while the A's will still slug perhaps this season we will see more emphasis on cutting the corner of the second base bag going from 1st to 3rd then the tedious recitations of launch angle and exit velocity.
"The Book" reminds us that your #2 hitter should be your best all around hitter but in the "old school" days, which include dead ball eras, the #2 spot often featured a slappy, high contact hitter whose jobs included taking pitches for a base stealer, "hitting behind the runner" to find the right side hole, and making contact in hit-and-run counts.
This describes Andrus, Tony Kemp, and Vimael Machin (who my voice recognition software wants to call "gmail machine"), players whose value may have been enhanced when they loosened the seams on this year's baseball.
And don't worry: Matt Olson could hit a wet sponge 450 feet. The A's will still hit HRs, but how refreshing to think that small ball, and a two strike approach, might be returning to the game. You cannot tell me that a triple followed by a suicide squeeze is not more exciting than yet another solo HR. Or that you don't want to torment an innocent puppy when a player swings from his ass on a two-strike pitch with a runner at third and one out.
And let's face it: As the game evolves, so do the relative values of different skill-sets. I am happy to see qualities such as contact skills, all fields hitting, situational approach, and versatility rewarded.
Welcome back, real baseball. We have truly missed you.


text:
Strategic plan and financial objectives
Ingenico Group 2021: strategic plan & financial objectives
Ingenico Group (Euronext: FR0000125346 - ING), the global leader in seamless payment, is presenting its 2021 objectives during a Capital Market Day held in Paris.
Our ambition: becoming the most proactive and trusted payment partner
Accelerate Retail profitable growth and restore B&A competitive edge
Focus on client centricity to capture value along the entire payment chain
Execute a global transformation through the implementation of the Fit for Growth plan
Simplify our organization to gain agility and efficiency
Improve Ingenico growth and margin profile creating value for all stakeholders
Organic CAGR 2018 to 2021 above 6%
EBITDA* of c. €700 million in 2021
€100 million of EBITDA impact in 2021 derived from Fit for Growth plan execution
45-50% of FCF/EBITDA conversion*
Above 35% pay-out ratio
Nicolas Huss, Chief Executive Officer of Ingenico Group, commented:
I am very excited today to present Ingenico's new strategy and financial ambition for 2021. Over the past decade, through several transformational acquisitions, we have repositioned Ingenico Group across the entire payment value chain, from a pure payment terminal leader to a full payment services leading provider. Our goal now is to fully leverage and optimize Ingenico's asset portfolio through the execution of our Fit for Growth global transformation plan bringing the Group to the next level. We are embarking on this journey with a new leadership team focused on making Ingenico the most proactive and trusted partner of the payment ecosystem. The expansion of the Group offering along with a more agile and efficient organization will enable Retail to accelerate its profitable growth and B&A to restore its competitive edge. Ingenico aims at reaching an average organic growth rate above 6% over the period 2018 to 2021 and an EBITDA of c. €700 million in 2021 with a 45% to 50% free cash flow conversion. We are fully in motion to deliver Ingenico new strategy creating value for all stakeholders."
The New Ingenico: bringing the Group to the next level by 2021
The payment industry has been booming over the past decades, from the first electronic cards and POS equipment, to the multiplication of payment means. While the migration from cash to electronic transactions remains a driver, specific vertical dynamics and merchant needs are new catalysts, quite as much as the technology changes themselves. Those drivers have widened the competitive landscape, attracting new players but opening new opportunities for Ingenico Group.
Led by a new leadership team, the Group aims at accelerating its growth profile while improving its profitability. By 2021, this transformation will bring Ingenico Group to the next level, generating 2/3 of its revenue and more than 50% of its EBITDA in payment services.
With a full end to end offer approach, Ingenico focuses on client centricity, selling directly to merchants and indirectly through partners. Its dedicated technology strategy, coupled with a clear focus on selected merchant and customer verticals, will bring to the market differentiated solutions.
The Group: restore flexibility and agility through the Fit for Growth plan
The Group's transformation goes hand-in-hand with a streamlining program in order to bring more flexibility and agility to Ingenico. The Fit for Growth is a holistic transformation plan encompassing 33 work streams in 6 programs: (i) Operating model, (ii) Retail acceleration, (iii) B&A Revival, (iv) Technology transformation, (v) G&A streamlining, and, (vi) Procurement optimization. Therefore, the Fit for Growth plan is expected to generate €100 million of EBITDA impact in 2021, with €40 million in Retail and €60 million in B&A As part of the operating model program, the Group will reorganize its legal structure, ERP landscape and analytical structure to create by the end of 2019 two sub-groups, one for B&A and one for Retail. This new organization will enable each Business Unit to gain transparency, accountability in performance monitoring as well as increase its own business agility.
B&A: be the trusted technology partner in the new world of payment acceptance
As the POS market is transforming, through rapid technological evolution, B&A is adapting his offering to this new ecosystem. From the Android POS to its global positioning and local know-how, B&A already has all the relevant assets to seize new business opportunities. In the coming three years, the business unit will concentrate its efforts at leveraging its leadership on Tetra, accelerating the worldwide deployment of Android devices and bringing effectiveness into its organization. Therefore, B&A is expected to grow between 0% to 2% over the next three years and to reach c. €300 million of EBITDA in 2021, including €60 million of savings derived from the Fit for Growth plan.
Retail: be the most proactive partner in the new world of commerce
Retail is evolving in a rapidly changing environment. Over the past few years, Retail has transformed itself in one of the key payment players providing solutions directly to merchants or through partners. Thanks to strategic acquisitions, organic investments and a complete reorganization, revenues and profitability have significantly improved over the past 3 years. The business unit is now accelerating its growth profile, through 10 Fit for Growth initiatives focused at deploying the SMB repeatable operating model, strengthening Global Online vertical go to market, expanding Enterprise offering, materializing Payone synergies and proposing a unique customer experience through technology orchestration. Therefore, Retail is expected to reach 11% to 12% organic growth in 2021 and to reach an EBITDA of c. €400 million at this time, including €40 million of savings derived from the Fit for Growth plan.
Ingenico Group 2021 plan
Ingenico Group has set itself the following 2021 financial objectives (after IFRS 16 application):
Revenue: The group expects to achieve an organic CAGR 2018-2021 above 6%.
EBITDA: The group targets an EBITDA of c. €700 million in 2021, including €100 million of savings derived from the Fit for Growth plan.
Free cash-flow: The group has the ambition to reach a free cash-flow conversion rate of 45-50%.
Pay-out ratio: above 35%
(*) After IFRS 16 application. The Group estimates the IFRS 16 impact on 2019 EBITDA at +c.€30m with no impact on free cash flow
Laurent Marie
(T): +33 1 58 01 83 24
Email: laurent.marie@ingenico.com
Access to all our

redpajama_set_name: RedPajamaCommonCrawl


Join us as we celebrate the resurrection of Jesus! We have a great day planned that everyone will enjoy. All kids will have an opportunity to participate in incredible children's environments and will receive a free gift. Invite everyone you know to celebrate with us, at one of our three experiences. See you there!


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Troma Entertainment, the longest running truly independent film company in American history, is proud to announce that KitSplit, the high quality film equipment rental service, will be presenting the World Premiere of Troma's first VR Experience, Heart of Fartness: Toxie's Toxic Twin Trauma at the IFP Media Center in Brooklyn, NY, June 29th, 7pm, it was announced today by Lloyd Kaufman, President of Troma Entertainment and creator of The Toxic Avenger.
Toxie has a major midlife crisis and must travel to a mythical land called the "Heart of Fartness", deep in the Panamanian jungle, in order to regain his place as the first Super-Human-Hero from New Jersey!
Inspired by Francis Ford Coppola's classic documentary, "Apocalypse Now" and Joseph Conrad's "Heart of Darkness," Troma Entertainment's first VR experience, "Heart of Fartness: Toxie's Toxic Twin Trauma," is a visionary 15 minute VR movie. Shot on location in Panama, New York, New Jersey, and the San Blas Islands.
"Have you ever seen a Troma film? If 'yes' then you know that Troma is synonymous with truly gonzo and, some might say, inspiring, head crushing, blood gushing, boob popping, mash-up's of horror, sci-fi and schlock comedy. If you've never seen a Troma film you've for sure seen some of Troma's influences, like Troma protégée James Gunn's Guardians of the Galaxy, Trey Parker and Matt Stone's South Park, or Quinton Tarantino's Grindhouse. Either way, you're in for a treat on June 29th, when we premiere Troma's first virtual reality film experience." stated Lisbeth Kaufman, co-founder of KitSplit.
Included in this 15 minute Tromasterpiece of Virtual Reality is music from Nigerian artist BJ Sam. Sam's song, "Mon Amour" was personally selected by Lloyd Kaufman and can be heard here:
Today we present new music from African artist BJ Sam. BJ Sam is a Writer...
BJ Sam gets the global radio love with his hit record "Mon Amour" – Millions of fans send the love !!!Africa's BJ Sam Premieres New Music With Visual For Single "Hear The Angels Sing"


text:
import pygame
from pygame.locals import *

from Colors import *

class Ball:
	def __init__(self, surface, color, position):
		self.layer = surface
		self.color = color
		self.init_X = position[0]
		self.init_Y = position[1]
		self.var_X = self.init_X
		self.var_Y = self.init_Y
		self.radius = position[2]
		self.width = position[3]
		self.change_X = 5
		self.change_Y = 5

	''' CREATING BALL '''
	def create_Ball(self):
		self.center = [self.var_X, self.var_Y]
		pygame.draw.circle(self.layer,self.color,self.center,self.radius,self.width)
	''' BALL MOVEMENT '''
	def play_ball(self,direction=1):
		self.var_X += self.change_X
		self.var_Y += self.change_Y
	def bounce_backX(self):
		self.change_X *= -1
	def bounce_backY(self):
		self.change_Y *= -1
	def score(self):
		self.var_X = self.init_X
		self.var_Y = self.init_Y
	''' BALL POSITION (CENTER) '''
	def get_Pos(self):
		return {"x" : self.var_X, "y" : self.var_Y}
	''' MANUAL CONTROL FUNCTIONS (DEBUGGING) '''
	def moveUp(self):
		self.var_Y -= self.change_Y
		if self.var_Y <= 16:
			self.var_Y += self.change_Y
	def moveDown(self):
		self.var_Y += self.change_Y
		if (self.var_Y+self.radius) >= 486:
			self.var_Y -= self.change_Y
	def moveLeft(self):
		self.var_X -= self.change_X
		if self.var_X <= 16:
			self.var_X += self.change_X
	def moveRight(self):
		self.var_X += self.change_X
		if (self.var_X+self.radius) >= 566:
			self.var_X -= self.change_X

redpajama_set_name: RedPajamaGithub


text:
/**
 * Setting Model Class, this is an example of a model class
 * @class This is the setting Model class, inherits from Model.
 * @param {TiMVC} app TiMVC class object
 */
var Setting = function(app){
	/**
	 * @type TiMVC
	 */
	this.App = app;
	/**
	 * @type string
	 */
	this.dbTableName = 'setting';
	/**
	 * @type Array
	 */
	this.attributeNames = ['key','value'];
	/**
	 * @String
	 */
	this.primaryKey = 'key';
	/**
	 * @type Pointer
	 */
	var self = this;

	/**
	 * did you know? this class inherits from /mvc/components/model.js
	 */

	/**
	 * get value from setting table by key
	 * @param {String} key
	 * @returns value from setting table or null if not found
	 */
	this.getSetting = function(key){
		var r = self.findByPk(key);
		var value =  r.rowCount>0 ? r.fieldByName('value') : null;
		r.close();
		return value;
	}

	/**
	 * set value from setting table by key
	 * @param {String} key
	 * @param {String} value
	 */
	this.setSetting = function(key,value){
		if(self.getSetting(key)==null){//insert as new setting
			var sql = "insert into " + self.dbTableName + " (key,value) values (?,?)";
			self.Db.conn.execute(sql,key,value);
			return;
		}
		var sql = "update " + self.dbTableName + " set value = ? where key = ?";
		self.Db.conn.execute(sql,value,key);
	}

	/**
	 * Deletes value from setting table by key
	 * @param {String} key
	 */
	this.delSetting = function(key){
		self.delByPk(key);
	}
}


text:
Crans-Montana: preparations for the European and World Cup races are on schedule
Preparations for the two European Cup events (19/20 February) and the three World Cup races (24-26 February) are continuing at full speed. Marius Robyr, President of the Organising Committee, is satisfied with the work that has been carried out by the different teams. From Wednesday onwards, they'll have the support of 140 soldiers from the 20/1 Mountain Infantry Company, under the command of First Lieutenant Caspar Zimmermann. Piste Manager Patrice Morisod has arrived from St. Moritz to lend his assistance to Race Director Markus Murmann, with the aim of providing the athletes with a skilfully and competently prepared piste. A pleasant meeting on the Mont Lachaux piste: Swiss-Ski transferred some of its speed racing athletes by helicopter from St. Moritz to Crans-Montana, where they trained yesterday and continue today on the Mont Lachaux piste, which will host them next week for the Audi FIS World Cup events (from left to right :Priska Nufer, Tina Weirather, joana Hählen and Corinne Suter)). On behalf of the Organising Committee and piste teams, Ewald Steiner presented a lovely bouquet of flowers to Michelle Gisin, Alpine Combined World Champion, and Otto Jaggi congratulated Tina Weirather, World Super-G Silver medallist. Marius Robyr was delighted by this important visit. The presence of these newly crowned World Champions and some other medals-holders promises wonderful and passionate races to come, and Crans-Montana is already looking forward to it.
Michelle et Tina


Because the rights afforded by copyright law are exclusive to the copyright owner(s), you will infringe copyright if you make use of the copyrighted work without the permission of the copyright owner(s) - for example, if you copy or adapt a copyright work, or make it available on the internet.
The best way to avoid copyright infringement is to ensure that you don't use anything created by someone else. Simple as that.
If you do use someone else's work, make sure you have the necessary permissions – this will usually take the form of a license from the copyright owner(s), which you may have to pay for. There are certain instances where you may be able to use excerpts of copyrighted material without a license – for example, if you use a small part of someone else's work for the purposes of criticism or review, or if your use constitutes "fair use" under applicable law (particularly U.S. law) – however, discussion of these exceptions is beyond the scope of this guidance. If you intend to use any part of a copyright work in reliance on any of the statutory exceptions, you should seek legal advice first.
Did you record and produce the track yourself or do you have permission from the producer or record label that made the sound recording?
What if I uploaded the track as private, isn't that okay?
Even if it is for your own personal use, you won't be allowed to upload a copyrighted track to your SoundCloud profile as a private track, as it is still possible to share private tracks to other listeners.


text:
Hayne is irreplaceable: Hopoate
Mon 2 Mar 2015, 02:11 PM
Of all the reasons to watch yet another chapter in the famous Parramatta-Manly rivalry kick the footy season off for 2015, the former Mormon missionary will make for compelling viewing.
Has he played for the other team before? Check. Is he playing in a new position? Check. And does he hate the Sea Eagles? Well, the son of the infamous John Hopoate isn't so much a hater as he is a lover.
After all, Will Hopoate did get hitched last weekend.
"I'm no romantic person," he interjected on Monday. "But it was a memorable day for the both of us and I'm sure something we'll always remember."
Not least because he and his new wife postponed the honeymoon to ensure he lines up in the famed No.1 jumper this Friday night against his old club.
While much of the build-up has centred around Anthony Watmough's dramatic defection from the northern beaches to Sydney's west – Kieran Foran's rumoured move there and Manly's supposed intention to steal Brad Arthur back also got some headlines too – many eyes will also be fixated on the first bloke to step into Jarryd Hayne's boots in almost a decade.
The fact that Arthur will name Hopoate on the same day his predecessor apparently announces which NFL team he'll play for is typical rugby league theatre.
Yet the 22-year-old insists there's no pressure that comes with taking Hayne's spot in the limelight.
"Not so much. I think Jarryd's irreplaceable," he said.
"There's things he can do that I certainly can't. He's a freak of a player. I'm not going to try and fill Jarryd's shoes, I'll just hopefully play the best footy I can. And if it benefits the team, that's a bonus."
For that to happen, he says, opening his mouth is going to be a part of it.
After entering the League as an introverted 18-year-old rookie on Manly's flank back in 2011, Hopoate intends on extracting all the skills he learnt from his two-year sabbatical as a Mormon missionary to ensure Eels fans aren't asking where the Hayne plane is on Friday night.
"Talking is something I really want to improve on. I feel I slowly am. So I'll be guiding the boys around a bit more in defence I hope it can be beneficial to my team," he said.
Asked whether his activities with the Mormon mission helped him do that, he replied: "I believe so. For the two years that's what we did pretty much every day, just talking and talking. So that skill has definitely rolled off into my playing now, especially for that of a fullback."
The other element crucial in shifting Hopoate will be his fitness.
Having just come to grips with the speed of a faster competition upon his return last season, the NSW representative says it's entirely plausible that he'd have to call on the services of wingman Reece Robinson during the match.
"Probably if I get tired. Reecey, he's great for our team. He can play wing and fullback, which is a benefit for us. I think if the lungs aren't going too well, then I'm sure I might call Reecey to help me out," he said.
"It's obviously been a challenge. There's more running, more lateral movement in the fullback position. I played there most of my juniors pretty much, so it's not something completely new – just reminding me of the things I was doing before and extra tips from Brad and the staff."
Speaking of tips, Hopoate isn't shy about mentioning a bloke who taught him a thing or two about playing custodian, either. A bloke he'll be matching up against this weekend in Brett Stewart.
"'Snake' was a great impact on me at Manly as a kid. There's things that he taught me that I valued and still remember. I'm grateful for those little lessons," he said.
And he might have to call upon every single one of them in a blockbuster season-opener that'll be compelling viewing with a packed Pirtek Stadium already close to selling out.
"There's always that great spark, Parramatta-Manly, Round 1, Friday night. It's a great event and I'm sure us and them are excited and ready to go for the fans," he said.
Eels halfback Chris Sandow participated in some light running drills on Monday morning and is expected to be named in Arthur's side on Tuesday, while veteran Beau Champion is also believed to get first crack at partnering Ryan Morgan in the centres.


The chief of army in Algeria has a chance of becoming the hero of the century. Will he take this opportunity?
Algerians reject their newly appointed Interim President Abdelkader Bensalah. This caretaker leader was approved this week by the parliament. He is expected to restore stability after President Abdelaziz Bouteflika resigned in early April. Within mere 90 days Algeria is supposed to elect a new president.
However, the regime has not tuned into the message of the suffering people. The message from the street is, "Leave, all of you!" For a good reason, the protestors do not trust Bensalah to lead the transition; he is a close associate of the former president. Think of what happened a few years ago in Yemen when the vice president replaced the president in response to the uprising.
The problem is wider than Bensalah. Last month Bouteflika installed one of his cronies, Noureddine Bedoui, as prime minister. He shuffled the cabinet without bringing in reformers. His third regressive move was to appoint traditionalist Tayeb Belaiz as Chief of the Constitutional Council. In short, a reactionary cabinet, working with a feeble interim president and a weak constitutional chief, as a team, do not raise expectations for serious reform in Algeria.
The trouble with veterans of war is ego. The struggle to achieve independence from France was heroic. All Algerians ought to be proud. But the leaders of the 1950s liberation have not lived up to the ideals of freedom and justice after their independence was achieved. Regretfully, yesterday's change agents are today's oppressors. Algeria's current political system evokes ideas from the narrative of Frants Fanon's The Wretched of The Earth. Fanon, an Algerian psychiatrist and a popular writer, was active in the struggle for independence. He warned freedom fighters not to copy colonialists when they reach power. Fanon coined the term "neocolonialist" to explain how "third world" leaders mimic manipulative foreign powers in oppressing their own people with old colonial tactics. Take a look at the modern history of the Arab world and you will appreciate Fanon's foresight.
The uprising intends to continue staging rallies of discontent until the hierarchy of the regime steps down. Whether Algeria's civic resistance will succeed or not, depends on how flexible the military establishment will be; and how united, resilient and peaceful the demonstrators will be over the next few weeks.
Media pundits wonder. Algeria defies prediction and things are changing fast. Experts offer more questions than answers. Marina Ottoway, a Middle East fellow at the Wilson Center, was a panelist in "Algeria's Protests and the Prospects for Change"- an event which took on April 4th at the Arab Center Washington DC. Ottoway highlighted the need for protestors to "organize groups to become a political a force." This will take ample time, she added. The rebels must "avoid provocation of the army" and maximize "participation of all" pressure groups. In this panel, Hugh Porter, of Tufts University, offered an "analytical tool" to examine Algeria's track toward democracy. Porter challenged young reformers to shape the future; the older generation seems to be fixated on the "past." He wondered whether society will grant the "Hirak"( Arabic for social movement) the legitimacy it needs to plan for radical reform. He was not sure if the army would shift its role from being an "actor" to being an enabler. Porter's final analytical variable was about leadership and consensus. He asserted that "consensus is in the DNA of the Algerian culture."A revolution which seeks to please all parties will shoot itself in the foot, Porter implied. Is this another way of saying that the revolution must generate inspiring leadership?
Algerians are right to demand that their military establishment must return to the barracks and end its adventures in politics and business. The problem of the military doing business is region-wide. The armies of the Arab world care more about defending rulers than protecting their people.
General Ahmed Gaid Salah is the most important man in Algeria today. As the chief of Algerian armed forces, Salah could chose to support a regime that has expired in legitimacy, or he could decide to support an uprising which is searching for democracy.
Salah could become the bridge between the protestors and the regime. Salah has already expressed in public his loyalty to the demonstrators. He was the first to give the necessary nod for Bouteflika to resign. He has shown in other ways that he is open to some reform. But the General's mixed political record, his patriarchal mindset, his fear of his comrades, his level of trust of the young and revolutionaries, all such factors, make this writer wonder if Salah is clear- eyed enough to read history correctly.
The challenge for the uprising's leaders will be to stay on board with the army working jointly on a set of principles and to plan for an open political transition. The military and the protestors must find their own way to change Algeria. The Tunisia model may offer some lessons, but Algeria must discover its Algerian model of state building. The Egyptian model illustrates what not to do.
The difficulty to predict the future of the uprising lies in the fact that there is no exact science of state craft; building democracy is an art, and each state is unique in its circumstances.
Unless the military changes its focus from power to service the Arab Spring will be stuck in the mud for decades. When the military starts listening to the street we will start celebrating the Arab Spring.
Salah, your people wish to work with you.


text:
\section{Introduction}
The Jarzynski equality~\cite{Jarzynski97a,Jarzynski97b} is one of the few exact
results in the context of out-of-equilibrium statistical physics. This simple and
elegant relation applies to systems initially prepared at thermal equilibrium and
then driven out-of-equilibrium by varying a control parameter $h$ from say $h_1$
to $h_2$. The probability distribution of the work $W$ extracted during the
experiment is related to the free-energy difference $\Delta F=F(h_2)-F(h_1)$
between the two equilibrium states at values $h_1$ and $h_2$ of the control
parameter by:
	\begin{equation}
	e^{-\beta\Delta F}=\langle e^{-\beta W}\rangle.
	\label{eq1}
	\end{equation}
Remarkably, this relation gives some information about the
equilibrium state at the value $h_2$ of the control parameter even though this
state has never been reached by the system. For a cyclic transformation, one recovers
the Bochkov-Kuzovlev relation $\langle e^{-\beta W}\rangle_{\rm Cycl.}=1$~\cite{Bochkov81}.
As recognized by Crooks, the Jarzynski equality can be derived from a more general
fluctuation theorem~\cite{Crooks99}. It  has passed experimental, see for
instance~\cite{Liphardt02,Ritort03,Douarche05} as well as numerical~\cite{Lua05} tests.
In both cases, the importance of a sufficiently accurate sampling of the tail
of the probability distribution $\wp(W)$ has been emphasized. Since the pioneering
experiment on DNA by Liphardt {\sl et al.}~\cite{Liphardt02}, the Jarzynski
relation is now widely used in chemistry and biophysics to estimate equilibrium
free energy differences based on experiments or short-time out-of-equilibrium
numerical calculations. However, the way the interaction with the thermal
bath is taken into account in the original Jarzynski's demonstration has been
criticized~\cite{Cohen04}: the interaction is assumed to be weak enough
to be neglected. It means that the system cannot exchange heat with the
bath. Equation (\ref{eq1}) was thus claimed to fail since one expects that the
system tends to relax to an equilibrium state by exchanging heat with the bath.
For Jarzynski's response, see~\cite{Jarzynski04}. As far as
we know, no experiment has provided any evidence of this failure yet. In this paper,
we present a Monte Carlo study of the 2D Ising model with a Glauber dynamics.
For such Markovian dynamics, the interaction with the bath is properly taken
into account by the transition rates. The criticisms do not apply to this case
and the demonstration given by Jarzynski in appendix of
reference~\cite{Jarzynski97b} is exact.
\\

In the context of spin models, up to now few studies have taken advantage of
the Jarzynski equality to calculate the free energy. Results have recently been
obtained for a single Ising spin~\cite{Marathe05} and in the mean-field
approximation~\cite{Imparato05}. We present a Monte Carlo investigation of the
two-dimensional Ising model. Numerical details of the calculation are
presented in the first section. The three next sections correspond to calculations
with an initial equilibrium state at different temperatures:
in the paramagnetic phase ($\beta=0.2$), the ferromagnetic phase ($\beta=0.7$)
and at the critical point ($\beta\simeq 0.4407$).

\section{Numerical procedure}
We study the two-dimensional Ising model defined by the usual Hamiltonian
	\begin{equation}
	{\cal H}(\{\sigma\})=-J\sum_{(i,j)} \sigma_i\sigma_j-h\sum_i \sigma_i,
	\quad\sigma_i=\pm 1
	\end{equation}
where the sum extends over nearest-neighbors on a square lattice. In the following,
the exchange coupling is fixed to $J=1$. Lattices with sizes from $32\times 32$ to
$128\times 128$ and periodic boundary conditions have been considered. The
system is first prepared in an equilibrium state without magnetic field using
the Swendsen-Wang cluster-algorithm~\cite{SwendsenWang87}. In the paramagnetic
and ferromagnetic phases, the system was first equilibrated using 200 Monte
Carlo Steps (MCS). At the critical point, we used 1000 MCS to circumvent the
critical slowing-down. This last value is a safe bet since it is more than two
orders of magnitude larger than the autocorrelation time $\tau_E\simeq 5.87(1)$
at $T_c$ and for $L=128$~\cite{Salas96}. We then let the system evolve
according to a local dynamics, i.e. using the Metropolis
algorithm~\cite{Metropolis53}, during $n_{\rm iter.}$ Monte Carlo iterations
while the magnetic field $h$ is linearly increased. In the following, $h$
denotes the final magnetic field reached after $n_{\rm iter.}$ iterations.
The work is calculated as
	\begin{equation}
	W=-\int_0^h Mdh=-\int_0^{t_f} M(t)\dot h dt
	\simeq -{h\over n_{\rm iter.}}\sum_{i=0}^{n_{\rm iter.}-1} M_i
	\end{equation}
i.e. as the average magnetization during these $n_{\rm iter.}$ iterations times
the magnetic field $h$. Note that $W$ is the mechanical work and not the work as
usually defined in thermodynamics~\cite{Narayan03}. Let us emphasize that the
demonstration of (\ref{eq1}) given by Jarzynski at the end of his second paper on
the subject~\cite{Jarzynski97b} requires a well-defined protocol: first a sudden
change $\Delta h$ of the magnetic field is performed leading to a work $-\Delta
hM_i$ where $M_i$ is the magnetization and second a Monte Carlo iteration is
made which allows the system to relax and exchange heat $Q=\Delta E=E_{i+1}-E_i$
with the bath. Note that when $n_{\rm iter.}=1$, the Jarzynski relation is
equivalent to the thermodynamic perturbation. The experiment is repeated $n_{\rm
exp.}=100,000$ times. Instead of restarting the whole simulation, we used the
last spin configuration obtained without magnetic field and did 10 further
Swendsen-Wang MCS at $T\ne T_c$ and 50 at $T_c$. This last value is almost ten
times larger than the autocorrelation time. Autocorrelations between two
successive experiments are thus smaller than ${\rm exp}(-50/5.9)\simeq
2.10^{-4}$ and will be neglected in the following. Averages are computed as
	\begin{equation}
	\langle f(W)\rangle=\int f(W)\wp(W)dW
	={1\over n_{\rm exp.}}\sum_{\alpha=1}^{n_{\rm exp.}} f(W_\alpha)
	\end{equation}
where $\{W_\alpha\}_\alpha$ is the set of values obtained when repeating $n_{\rm
exp.}$ times the numerical experiment. Errors are estimated as
$\sqrt{[\langle f^2\rangle-\langle f\rangle^2]/n_{\rm exp.}}$ as expected from
the central limit theorem for uncorrelated random variables.

\subsection{Paramagnetic phase}
As the temperature is increased in the paramagnetic phase, the correlation
length becomes smaller and eventually gets smaller than the lattice spacing. One
can thus consider the system as a set of free spins. The dynamical evolution of
the probability distribution of each of them is governed by the Glauber master
equation~\cite{Glauber63}. Since individual spins relax very rapidly to
equilibrium, the probability distribution of the work $\wp(W)$ is expected to
be Gaussian~\cite{Marathe05}. It is indeed what is observed numerically for
$\beta=0.2$, as can be seen in Figure~\ref{fig1}. We have checked that there is
no observable deviation from a Gaussian law in the tails. Calculation of the coefficient
of excess $\gamma=\langle (W-\langle W\rangle)^4\rangle/\langle (W-\langle
W\rangle)^2\rangle^2-3$ gives small values between $3.10^{-3}$ and $10^{-2}$ for
the different simulations performed.
\\

\begin{center}
\begin{figure}[!ht]
        \centerline{\psfig{figure=Gaussiennes-J=0.2-h=0.02.eps,height=7cm}}
        \caption{Probability distribution of the work in the paramagnetic phase
	($\beta=0.2$) when applying linearly a magnetic field $h=0.1$ at different
	rates: $n_{\rm iter.}=2,5,10$ and $20$ (from right to left). The monotonous
	curves correspond to Gaussian fits.}
\label{fig1}
\end{figure}
\end{center}

\begin{table}[!ht]
\begin{center}
\begin{tabular}{@{}*{6}{l}}
$h$ & $n_{\rm iter.}$ & $\langle W\rangle$ & $\Delta F$ (Jarzynski) &
$W_{\rm diss.}=\langle W\rangle-\Delta F$ & $\Delta F$ (Gaussian approx.) \\
\hline
0.1 & 2 &
$-8.83(6)$ &
$-4.5(1).10^{1}$ &
$3.6(1).10^{1}$ &
$-4.69(3).10^{1}$
\\
0.1 & 5 &
$-2.155(5).10^{1}$ &
$-4.70(10).10^{1}$ &
$2.5(1).10^{1}$ &
$-4.70(3).10^{1}$
\\
0.1 & 10 &
$-3.068(4).10^{1}$ &
$-4.8(1).10^{1}$ &
$1.7(1).10^{1}$ &
$-4.67(3).10^{1}$
\\
0.1 & 15 &
$-3.523(3).10^{1}$ &
$-4.68(1).10^{1}$ &
$1.16(2).10^{1}$ &
$-4.68(3).10^{1}$
\\
0.1 & 20 &
$-3.777(3).10^{1}$ &
$-4.678(9).10^{1}$ &
$9.0(1)$ &
$-4.68(3).10^{1}$
\\
0.1 & 30 &
$-4.059(3).10^{1}$ &
$-4.683(5).10^{1}$ &
$6.23(8)$ &
$-4.69(2).10^{1}$
\\
\hline
1.0 & 2 &
$-8.578(6).10^{2}$ &
$-1.667(5).10^{3}$ &
$3.7(1).10^3\ \dagger$ &
$-4.6(1).10^{3}$
\\
1.0 & 5 &
$-2.0500(5).10^{3}$ &
$-2.616(2).10^{3}$ &
$2.4(2).10^{3}\ \dagger$ &
$-4.5(2).10^{3}$
\\
1.0 & 10 &
$-2.9068(4).10^{3}$ &
$-3.523(5).10^{3}$ &
$1.5(2).10^{3}\ \dagger$ &
$-4.4(2).10^{3}$
\\
1.0 & 15 &
$-3.3037(3).10^{3}$ &
$-3.711(5).10^{3}$ &
$1.0(2).10^{3}\ \dagger$ &
$-4.3(2).10^{3}$
\\
1.0 & 20 &
$-3.5270(3).10^{3}$ &
$-3.864(4).10^{3}$ &
$0.8(2).10^{3}\ \dagger$ &
$-4.3(2).10^{3}$
\\
1.0 & 30 &
$-3.7663(2).10^{3}$ &
$-4.019(3).10^{3}$ &
$0.5(2).10^{3}\ \dagger$ &
$-4.3(2).10^{3}$
\\
\hline
10. & 2 &
$-4.5445(5).10^{4}$ &
$-5.2532(5).10^{4}$ &
- &
$-3.0(5).10^{5}$
\\
10. & 5 &
$-9.1721(3).10^{4}$ &
$-9.5794(5).10^{4}$ &
- &
$-1.9(6).10^{5}$
\\
10. & 10 &
$-1.12169(2).10^{5}$ &
$-1.14980(5).10^{5}$ &
- &
$-1.5(5).10^{5}$
\\
10. & 15 &
$-1.19695(2).10^{5}$ &
$-1.21706(4).10^{5}$ &
- &
$-1.5(4).10^{5}$
\\
10. & 20 &
$-1.23634(1).10^{5}$ &
$-1.25357(5).10^{5}$ &
- &
$-1.4(3).10^{5}$
\\
10. & 30 &
$-1.27737(1).10^{5}$ &
$-1.29189(5).10^{5}$ &
- &
$-1.4(3).10^{5}$
\\
\hline
\end{tabular}
\end{center}
\caption{Estimates of the average work $\langle W\rangle$, the free energy
difference $\Delta F$, the dissipated work $\langle W\rangle-\Delta F$
and the free energy difference using the Gaussian approximation in the
paramagnetic phase ($\beta=0.2$) for different magnetic fields $h$ and
transformation rates. The estimates of the dissipated work $W_{\rm diss.}$
marked with $\dagger$ have been computed using $\Delta F$ as given by the Gaussian
approximation because the Jarzynski equality fails in this case to give
stable values. In the case $h=10$, we do not even give any estimate
since the Gaussian approximation leads to errors bars larger than the estimate
of $W_{\rm diss.}$.}
\label{Table1}
\end{table}

The free-energy $\Delta F$ can be measured using the Jarzynski equality
(\ref{eq1}), either directly or by using the assumption that the work $W$ is
Gaussian distributed:
	\begin{equation}
	\langle e^{-\beta W}\rangle={1\over\sqrt{2\pi\sigma_W^2}}
	\int e^{-\beta W-(W-\langle W\rangle)^2/2\sigma_W^2}dW
	\Leftrightarrow\ \Delta F=\langle W\rangle-{\sigma_W^2\over 2k_BT}.
	\label{eq2}
	\end{equation}
This last relation was first obtained by Hermans~\cite{Hermans91}. In both
methods, the free energy difference should not depend on the experimental
protocol, in our case the rate at which the magnetic field is grown.
Our numerical results are summarized in Table~\ref{Table1}. For a small magnetic
field $h=0.1$ (to be compared with $J=1$), the two methods give, as expected,
estimates of $\Delta F$ in agreement independently of $n_{\rm iter.}$, i.e. of
the rate at which the transformation is performed. Using the Jarzynski relation
(\ref{eq1}), the slower the transformation, i.e. the more reversible, and the
more accurate the estimates are. Due to the amplification with the factor
${\rm exp}(-\beta W)$, the relevant information is in the negative tail of the
distribution. Insufficient sampling of this tail may lead to deviations of the
estimate of $\Delta F$. However, these deviations remain relatively small in our
system, as can be seen in Table~\ref{Table2}. The worst case is $\Delta
F=-40(2)$ obtained for $n_{\rm iter.}=2$ and $n_{\rm exp.}=1562$ while
$\Delta F\simeq -46.8$ for a larger statistics. The Gaussian assumption
(\ref{eq2}) turns out to lead to estimates of $\Delta F$ less noisy than
equation (\ref{eq1}) and that do not seem to depend on $n_{\rm iter.}$ (see
Table~\ref{Table1}). The relevant information comes in this case from the more
probable part of the distribution. However, as can be seen in
Table~\ref{Table2}, the estimate gets noisier faster for low statistics than
using the Jarzynski relation (\ref{eq1}). We also checked that the free energy
differences are extensive (Table~\ref{Table3}). When intermediate magnetic fields
$h=J$ are applied, the Jarzynski equality fails to give estimates of $\Delta F$
independent of the transformation rate while it is still the case for the
Gaussian approximation. When larger magnetic fields are applied, the two methods
fail to give estimates of $\Delta F$ for large transformation rates, i.e.
$n_{\rm iter.}$ small. A much larger statistics would be then required. As
well-known in the context of thermodynamic perturbation, one can circumvent
the problem by dividing the interval $[0;h]$ in smaller pieces and resorting to
several simulations to estimate $\Delta F$ in each of them.
\\

\begin{table}[!ht]
\begin{center}
\begin{tabular}{@{}*{6}{l}}
$n_{\rm exp.}$ & $\langle W\rangle$ & $\Delta F$ (Jarzynski) &
$W_{\rm diss.}=\langle W\rangle-\Delta F$ & $\Delta F$ (Gaussian approx.) \\
\hline
1562 &
$-3.80(2).10^{1}$ &
$-4.67(5).10^{1}$ &
$8.8(7)$ &
$-4.7(2).10^{1}$
\\
3125 &
$-3.76(2).10^{1}$ &
$-4.63(3).10^{1}$ &
$8.7(5)$ &
$-4.6(1).10^{1}$
\\
6250 &
$-3.78(1).10^{1}$ &
$-4.62(2).10^{1}$ &
$8.4(3)$ &
$-4.6(1).10^{1}$
\\
12,500 &
$-3.765(8).10^{1}$ &
$-4.63(2).10^{1}$ &
$8.7(3)$ &
$-4.65(7).10^{1}$
\\
25,000 &
$-3.773(6).10^{1}$ &
$-4.67(2).10^{1}$ &
$9.0(2)$ &
$-4.67(5).10^{1}$
\\
50,000 &
$-3.777(4).10^{1}$ &
$-4.68(1).10^{1}$ &
$9.0(2)$ &
$-4.68(4).10^{1}$
\\
100,000 &
$-3.777(3).10^{1}$ &
$-4.678(9).10^{1}$ &
$9.0(1)$ &
$-4.68(3).10^{1}$
\\
\hline
\end{tabular}
\end{center}
\caption{Estimates of the average work $\langle W\rangle$, the free energy
difference $\Delta F$, the dissipated work $\langle W\rangle-\Delta F$
and the free energy difference using the Gaussian approximation in the
paramagnetic phase $\beta=0.2$ with $h=0.1$ and $n_{\rm iter.}=20$
versus the number of experiments $n_{\rm exp.}$ used for the calculation of
the averages.}
\label{Table2}
\end{table}

\begin{table}[!ht]
\begin{center}
\begin{tabular}{@{}*{6}{l}}
$L$ & $n_{\rm iter.}$ & $\Delta F/L^2$ (Jarzynski) & $\Delta F/L^2$ (Gaussian approx.) \\
\hline
32 & 2 &
$-2.86(2).10^{-3}$ &
$-2.87(3).10^{-3}$ \\
64 & 2 &
$-2.87(4).10^{-3}$ &
$-2.86(2).10^{-3}$ \\
128 & 2 &
$-2.73(6).10^{-3}$ &
$-2.86(2).10^{-3}$ \\
\hline
32 & 5 &
$-2.85(1).10^{-3}$ &
$-2.84(2).10^{-3}$ \\
64 & 5 &
$-2.85(1).10^{-3}$ &
$-2.84(2).10^{-3}$ \\
128 & 5 &
$-2.87(6).10^{-3}$ &
$-2.87(2).10^{-3}$ \\
\hline
32 & 10 &
$-2.85(1).10^{-3}$ &
$-2.86(2).10^{-3}$ \\
64 & 10 &
$-2.849(7).10^{-3}$ &
$-2.85(1).10^{-3}$ \\
128 & 10 &
$-2.94(7).10^{-3}$ &
$-2.85(2).10^{-3}$ \\
\hline
32 & 20 &
$-2.865(8).10^{-3}$ &
$-2.87(1).10^{-3}$ \\
64 & 20 &
$-2.850(5).10^{-3}$ &
$-2.85(1).10^{-3}$ \\
128 & 20 &
$-2.855(5).10^{-3}$ &
$-2.85(2).10^{-3}$ \\
\hline
\end{tabular}
\end{center}
\caption{Estimates of the free energy difference $\Delta F$ in the
paramagnetic phase ($\beta=0.2$ and $h=0.1$) for different lattice sizes $L$
and transformation rates $h/n_{\rm iter.}$.}
\label{Table3}
\end{table}

\begin{center}
\begin{figure}[!ht]
        \centerline{\psfig{figure=dF-Para.eps,height=7cm}\quad\quad
	\psfig{figure=Wdiss-Para.eps,height=7cm}}
        \caption{On the left, free energy density $\Delta F/L^2$ versus the final
	applied	magnetic field $h$ in the paramagnetic phase ($\beta=0.2$) for
	the slowest transformation rate considered ($n_{\rm iter.}=30$). The
	curve corresponds to a non-linear fit with the expression (\ref{ExprdF}).
	On the right, dissipated work $W_{\rm diss.}$ with respect to the number of
	Monte Carlo iterations $n_{\rm iter.}$ for $h=0.1$. The curve is a
	two-parameter non-linear fit with the expression (\ref{ExprWdiss}).}
\label{fig2}
\end{figure}
\end{center}

The results presented above can be understood by assuming that the system
behaves as $N$ independent Ising domains with an average magnetic moment $m$.
The free energy difference between the equilibrium states with and without
magnetic field $h$ reads
	\begin{equation}
	\Delta F=F(h)-F(0)=-Nk_BT\ln\cosh{mh\over k_BT}
	\label{ExprdF}
	\end{equation}
The numerical data are in very good agreement with this law as can be seen in
Figure~\ref{fig2}. The best fit is obtained for the parameters $N\simeq 0.13L^2$
and $m\simeq 4.62$ which means that the characteristic size of the domains is
of the order of $\xi\sim\sqrt{L^2/N}\simeq 2.8$ and that the domains are not
at saturation, $Nm/L^2\simeq 0.6$. At equilibrium, the magnetization is
expected to be
	\begin{equation}
	M_{\rm eq.}(h)=-{\partial F\over\partial h}=Nm\tanh{mh\over k_BT}
	\simeq N{m^2h\over k_BT}
	\label{MChpMoyen}
	\end{equation}
Let us assume the phenomenological evolution equation
	\begin{equation}
	{\partial M\over\partial t}=-{M(t)-M_{\rm eq.}(h)\over\tau}
	\ \Leftrightarrow\ M(t)=M(0)e^{-t/\tau}
	+{1\over\tau}\int_0^t M_{\rm eq.}(h(t'))e^{-(t-t')/\tau}dt'
	\label{EqMvtPara}
	\end{equation}
where $\tau$ is the relaxation time. The work extracted from the system
when the magnetic field is increased linearly, i.e. $h(t)=\dot ht$, reads
	\begin{eqnarray}
	W=-\dot h\int M(t')dt'
	&=&-\dot hM(0)\big(1- e^{-t/\tau}\big)-{\dot h\over\tau}
	\int_0^t\int_0^{t'}M_{\rm eq.}(h(t''))e^{-(t'-t'')/\tau}dt'dt''
	\nonumber \\
	&\simeq &-\dot hM(0)\big(1- e^{-t/\tau}\big)-{\dot h^2Nm^2\over\tau k_BT}
	\int_0^t\int_0^{t'} t''e^{-(t'-t'')/\tau}dt'dt''		\\
	&=&-\dot hM(0)\big(1- e^{-t/\tau}\big)-{\dot h^2Nm^2\over k_BT}
	\left[{1\over 2}t^2-\tau t+\tau^2\left(1-e^{-t/\tau}\right)\right]
	\nonumber
	\end{eqnarray}
where $M_{\rm eq.}$ has been replaced by its weak-field expansion
(\ref{MChpMoyen}). Starting the experiment from the paramagnetic phase, i.e.
$M(0)=0$, and subtracting the reversible work
	\begin{equation}
	W_{\rm rev.}=-\dot h\int M_{\rm eq.}(t')dt'
	\simeq -{\dot h^2Nm^2\over 2k_BT}t^2
	\end{equation}
one gets finally
	\begin{equation}
	W_{\rm diss.}\simeq {\dot h^2Nm^2\over k_BT}
	\left[\tau t-\tau^2\left(1-e^{-t/\tau}\right)\right]
	=\dot hM_{\rm eq.}(h)\tau\left[1-{\tau\over t}\left(1-e^{-t/\tau}
	\right)\right]
	\label{ExprWdiss}
	\end{equation}
As can be seen in Figure \ref{fig2}, the expression fits well the numerical
data for $h=0.1$. The non-linear fit gives $\tau\simeq 2.23$ for the relaxation
time and $m\simeq 4.72 $ assuming $N=0.13L^2$. Note that the estimate
$m$ is compatible with the one calculated from $\Delta F$ ($m\simeq 4.62$).
The estimate of the relaxation time $\tau$ is small as expected for
such a high temperature. For larger magnetic fields, the dissipated work is
still nicely fitted by the expression (\ref{ExprWdiss}) but the fit gives
too small average moments $m$. This is due to the fact that the expression
(\ref{ExprWdiss}) was derived in the weak magnetic field limit.

\subsection{Ferromagnetic phase}
In the ferromagnetic phase $\beta=0.7$, the probability distributions $\wp(W)$
display two well-separated peaks corresponding to the work performed by systems
in each one of the two initial ferromagnetic ground states. The average $\langle
e^{-\beta W}\rangle$ is dominated by the peak at more negative values of the
work. As a consequence, the Gaussian approximation applied only to this peak
leads to estimates of $\Delta F$ in very good agreement with those obtained
with the Jarzynski equality (Table~\ref{Table4}). Since the two peaks are not
centered around zero, averages over the most negative peak were computed in
practise by selecting configurations for which the work $W$ is smaller than the
average of the smallest and largest works. A large gap separating the two peaks,
the average work would have given the same results. As can be seen in
Table~\ref{Table4}, the estimates of $\Delta F$ do not show any dependence on
the transformation rate and give compatible values using the Jarzynski equation
(\ref{eq1}) and the Gaussian approximation (\ref{eq2}).
\\

\begin{table}[!ht]
\begin{center}
\begin{tabular}{@{}*{6}{l}}
$h$ & $n_{\rm iter.}$ & $\langle W\rangle$ & $\Delta F$ (Jarzynski) &
$W_{\rm diss.}=\langle W\rangle-\Delta F$ & $\Delta F$ (Gaussian approx.) \\
\hline
0.1 & 10 &
$1.0(5).10^{1}$ &
$-1.622740(7).10^{3}$ &
$1.633(5).10^{3}$ &
$-1.624(5).10^{3}$
\\
0.1 & 50 &
$7(5)$ &
$-1.622732(5).10^{3}$ &
$1.629(5).10^{3}$ &
$-1.624(2).10^{3}$
\\
0.1 & 250 &
$4(5)$ &
$-1.622735(5).10^{3}$ &
$1.627(5).10^{3}$ &
$-1.624(1).10^{3}$
\\
\hline
1.0 & 10 &
$-2.4(5).10^{2}$ &
$-1.63057(3).10^{4}$ &
$1.607(5).10^{4}$ &
$-1.63(4).10^{4}$
\\
1.0 & 50 &
$-1.40(5).10^{3}$ &
$-1.630612(4).10^{4}$ &
$1.490(5).10^{4}$ &
$-1.63(2).10^{4}$
\\
1.0 & 250 &
$-6.22(3).10^{3}$ &
$-1.6306156(9).10^{4}$ &
$1.009(3).10^{4}$ &
$-1.631(7).10^{4}$
\\
\hline
10. & 10 &
$-1.076(2).10^{5}$ &
$-1.63676(1).10^{5}$ &
$5.61(2).10^{4}$ &
$-1.6(2).10^{5}$
\\
10. & 50 &
$-1.3313(10).10^{5}$ &
$-1.637355(8).10^{5}$ &
$3.061(10).10^{4}$ &
$-1.64(7).10^{5}$
\\
10. & 250 &
$-1.4475(6).10^{5}$ &
$-1.637402(2).10^{5}$ &
$1.899(6).10^{4}$ &
$-1.64(3).10^{5}$
\\
\hline
\end{tabular}
\end{center}
\caption{Estimates of the average work $\langle W\rangle$, the free energy
difference $\Delta F$, the dissipated work $\langle W\rangle-\Delta F$
and the free energy difference using the Gaussian approximation with the most
negative peak in the ferromagnetic phase ($\beta=0.7$) for different magnetic
fields $h$ and transformation rates $h/n_{\rm iter.}$.}
\label{Table4}
\end{table}

In a sense, the physics is simpler than in the paramagnetic phase. Before
applying the magnetic field, the initial magnetization is either $+M_0$ or
$-M_0$ with small fluctuations around these two values. When applying a small
magnetic field, i.e. $h=0.1$ in our case, the magnetization does not change
much so that the work is either $-M_0h$ or $+M_0h$. According to Jarzynski
equation (\ref{eq1}), the free energy reads
	\begin{equation}
	\Delta F=-k_BT\ln\langle e^{-\beta W}\rangle
	=-k_BT\ln\left[{1\over 2}e^{-\beta M_0h}+{1\over 2}e^{\beta M_0h}\right]
	\simeq -M_0h+k_BT\ln 2
	\end{equation}
Using the saturation magnetization $M_{\rm sat}=L^2=16384$, one obtains indeed
a good estimate of $\Delta F$. The average work is small $\langle
W\rangle=(-M_0h+M_0h)/2=0$ so that the dissipated work is $W_{\rm
diss.}=\langle W\rangle-\Delta F\simeq -\Delta F$. For larger magnetic fields,
$h=1$ and $h=10$, this approximation is not valid anymore: the magnetization
tends to reverse itself if it was initially in the opposite direction of the
field. However, since the Jarzynski equality (\ref{eq1}) is dominated by the
systems for which the magnetization was initially in the same direction than the
field, one still expects that $\Delta F\simeq -M_{\rm sat}h$. But the average
magnetization now moves towards $-M_{\rm sat}$ so $W_{\rm diss.}>0$. Obviously
dissipation is thus mainly due to the systems for which the initial magnetization
was in the ``wrong'' direction.

\subsection{Critical point}
We now present results at the critical point $\beta_c={1\over 2}\ln\left(1+
\sqrt 2\right)\simeq 0.440687$. Like in the ferromagnetic phase, the probability
distributions $\wp(W)$ display two well-separated peaks. Due to finite-size
effects, the initial state has indeed a non-vanishing magnetization of sign
either positive or negative due to the $Z_2$ symmetry ($\sigma_i\rightarrow
-\sigma_i$) of the Ising model. In contradistinction to the ferromagnetic case,
the two peaks do not have a Gaussian shape. The free energy differences
$\Delta F$ calculated from the Jarzynski equation (\ref{eq1}) are presented for
two different magnetic fields in Table~\ref{Table5}. For the smallest magnetic
field $h\simeq 0.023$, the free-energy turns out to be independent of the
transformation rate $h/n_{\rm iter.}$: the maximum deviation from the average
is of the order of one standard deviation. For the largest magnetic field
$h\simeq 0.23$, a systematic deviation is observed.

\begin{table}[!ht]
\begin{center}
\begin{tabular}{@{}*{6}{l}}
$h$ & $n_{\rm iter.}$ & $\langle W\rangle$ & $\Delta F$ (Jarzynski) &
$W_{\rm diss.}=\langle W\rangle-\Delta F$ \\
\hline
0.022692 & 2 &
$-1.6(7)$ &
$-2.690(7).10^{2}$ &
$2.67(1).10^{2}$
\\
0.022692 & 10 &
$-1.1(7)$ &
$-2.697(4).10^{2}$ &
$2.69(1).10^{2}$
\\
0.022692 & 50 &
$-7.5(7)$ &
$-2.704(5).10^{2}$ &
$2.63(1).10^{2}$
\\
0.022692 & 100 &
$-1.39(7).10^{1}$ &
$-2.701(4).10^{2}$ &
$2.56(1).10^{2}$
\\
0.022692 & 150 &
$-1.85(7).10^{1}$ &
$-2.698(2).10^{2}$ &
$2.513(8).10^{2}$
\\
0.022692 & 250 &
$-2.87(7).10^{1}$ &
$-2.699(1).10^{2}$ &
$2.411(8).10^{2}$
\\
\hline
0.226918 & 2 &
$-2.4(7).10^{1}$ &
$-2.897(2).10^{3}$ &
$2.873(9).10^{3}$
\\
0.226918 & 10 &
$-1.87(7).10^{2}$ &
$-3.009(2).10^{3}$ &
$2.822(9).10^{3}$
\\
0.226918 & 50 &
$-7.93(6).10^{2}$ &
$-3.103(1).10^{3}$ &
$2.310(7).10^{3}$
\\
0.226918 & 100 &
$-1.362(5).10^{3}$ &
$-3.133(2).10^{3}$ &
$1.771(6).10^{3}$
\\
0.226918 & 150 &
$-1.680(4).10^{3}$ &
$-3.136(2).10^{3}$ &
$1.456(6).10^{3}$
\\
0.226918 & 250 &
$-2.017(3).10^{3}$ &
$-3.143(1).10^{3}$ &
$1.126(4).10^{3}$
\\
\hline
\end{tabular}
\end{center}
\caption{Estimates of the average work $\langle W\rangle$, the free energy
difference $\Delta F$, the dissipated work $\langle W\rangle-\Delta F$
at the critical point for two different transformation rates
$h/n_{\rm iter.}$ and two magnetic fields $h$.}
\label{Table5}
\end{table}

We made simulations for ten values of the final magnetic field in the range
$h\in[0.023;0.23]$. The singular part of the free-energy is expected to scale at
the critical point as
	\begin{equation}
	F_{\rm sing.}(h)\build\sim_{T\rightarrow T_c,h\ll 1}^{} h^{1+1/\delta}
	\label{Scaling}
	\end{equation}
Neglecting the contribution of the regular part, we fitted $\Delta F$ as given
by the Jarzynski equality with the scaling form (\ref{Scaling}). The data display
a nice power-law behavior but fluctuations are observed for fast transformations
($n_{\rm iter.}\le 10$) at large magnetic fields. The estimates of $1+1/\delta$
and $\delta$ are collected in Table~\ref{Table6}. As the transformation
gets slower, and thus $n_{\rm iter.}$ larger, the numerical estimate gets
closer to the exact result $\delta=15$. For the fastest transformation
$n_{\rm iter.}=2$, the relative deviation of the numerical estimate from the
exact result is of order of 100\%! Note however that much better estimates are
obtained when restricting the fit to the smallest values of the magnetic field:
$\delta=19.9(7)$ for $h\le 0.018$ and $\delta=14.1(6)$ for $h\le 0.013$
when $n_{\rm iter.}=2$. Since error bars take into account all sources of
statistical fluctuations, the deviation may be explained as a systematic bias
due to a too small number of experiments for the calculation of the average.
As can be seen in Table~\ref{Table7}, when $n_{\rm exp.}$ is made smaller
the estimate of $\delta$ indeed increases. The effect is dramatic for fast
transformations: a relatively good estimate of $\delta$ is already obtained for
$n_{\rm iter.}=250$ when averaging over only $n_{\rm exp.}=1000$ experiments
but the same deviation from the exact result $\delta=15$ is not even
obtained with $n_{\rm exp.}=100,000$ experiments for $n_{\rm iter.}=50$.
More stable estimates of $\delta$ are obtained for a smaller system, $L=64$, for
which $\delta$ does not display a systematic deviation but fluctuates between $14.0(1)$
($n_{iter}=2$) and $14.1(2)$ ($n_{iter}=150$) and remains below the exact value
because of finite-size effects.

\begin{table}[!ht]
\begin{center}
\begin{tabular}{@{}*{6}{l}}
$n_{\rm iter.}$ & $1+1/\delta$ & $\delta$ \\
\hline
$2$ & $1.024(7)$ & $42(1)$ \\
$10$ & $1.045(6)$ & $22.2(3)$ \\
$50$ & $1.059(5)$ & $17.0(1)$ \\
$100$ & $1.064(4)$ & $15.7(1)$ \\
$150$ & $1.065(3)$ & $15.36(7)$ \\
$250$ & $1.066(2)$ & $15.13(5)$ \\
\hline
\end{tabular}
\end{center}
\caption{Critical exponents $1+1/\delta$ and $\delta$ obtained by power-law interpolation
of the free energy $\Delta F=F(h)-F(0)\sim h^{1+1/\delta}$ with ten magnetic fields
in the range $[0.023;0.23]$ at the critical point for different transformation rates
$h/n_{\rm iter.}$.}
\label{Table6}
\end{table}

\begin{table}[!ht]
\begin{center}
\begin{tabular}{@{}*{6}{l}}
$n_{\rm exp.}$ & $1+1/\delta$ & $\delta$ \\
\hline
$10^2$ & $1.060(10)$ & $16.6(3)$ \\
$10^3$ & $1.066(7)$ & $15.1(2)$ \\
$10^4$ & $1.065(3)$ & $15.44(8)$ \\
$10^5$ & $1.066(2)$ & $15.13(5)$ \\
\hline
\end{tabular}
\end{center}
\caption{Critical exponents $1+1/\delta$ and $\delta$ obtained by power-law interpolation
of the free energy $\Delta F=F(h)-F(0)\sim h^{1+1/\delta}$ with ten magnetic fields
in the range $[0.023;0.23]$ at the critical point for different number of experiments
$n_{\rm exp.}$ in the slowest case $n_{\rm iter.}=250$.}
\label{Table7}
\end{table}

As already mentioned, the two-peak structure of the probability distribution of the
work $\wp(W)$ differs from the ferromagnetic case. As can be seen in Figure~\ref{fig3},
the left peak, which dominates the average in the Jarzynski equality (\ref{eq1}) and
thus the free energy difference $\Delta F$, moves monotonously to the left as the
magnetic field is increased. The right peak moves first to the right, up to a certain
magnetic field before pursing to the left. This behavior can be understood by assuming
that the dynamics of the magnetization is governed by the Langevin equation
	\begin{equation}
	{\partial M\over\partial t}=-{\delta{\cal F}\over\delta M}\simeq \kappa h(t)
	\ \Leftrightarrow\ M(t)\simeq M(0)+\kappa\int_0^t h(t')dt'
	\label{eqLangevin}
	\end{equation}
where the link with equation (\ref{EqMvtPara}) is made by considering $\kappa$ as a
magnetic susceptibility divided by the relaxation time $\tau$. It is sufficient for
the discussion to consider $\kappa$ as constant. For a single realization, the initial
magnetization $M(0)$ is non-zero due to finite-size effects. When the field is increased
linearly, i.e. $h(t)=\dot ht$, the work extracted from the system up to time $t$ is
	\begin{equation}
	W=-\int_0^t M(t)\dot hdt=-M(0)\dot ht-{\kappa\over 6}\dot h^2t^3
	=-M(0)h-{\kappa\over 6}h^2t
	\label{WorkTc}
	\end{equation}
When $M(0)<0$, the work initially increases and eventually at $h_t=3|M(0)|/\kappa t$ starts
to decrease as can be observed in Figures~\ref{fig3} and~\ref{fig4}. In our case, no turning
point is observed for $n_{\rm iter.}=10$ because the magnetic fields remain too small. The data
presented in the inset of figure~\ref{fig4} reproduce the linear behavior of $\big(W/h-W_0)/n_{\rm iter.}$
versus $h$ predicted by equation (\ref{WorkTc}). Higher order terms are observed only for
the slowest transformations. When the initial magnetization is initially in the same direction
as the magnetic field, i.e. $M(0)>0$, the work is always negative. For very slow transformation
rate, the magnetization is expected to follow the magnetic field, i.e. to behave as the
equilibrium magnetization $M_{\rm eq.}\sim h^{1/\delta}$. Taking into account the magnetic
field dependence of the $\kappa$, one should expect in this case the solution of the Langevin
equation (\ref{eqLangevin}) to scale as
	\begin{equation}
	W_{\rm rev.}\sim -\int_0^h {h'}^{1/\delta}dh'\sim -h^{1+{1\over\delta}}
	 \end{equation}
This behavior is indeed observed: a power-law interpolation of the position of the left
peak versus the magnetic field leads to exponents $\delta=14(1)$ for $n_{\rm iter}=150$
and $250$ compatible with the exact result $\delta=15$.

\begin{center}
\begin{figure}[!ht]
        \centerline{\psfig{figure=Proba-Tc-Niter=10.eps,height=7cm}\quad\quad
	\psfig{figure=Proba-Tc-Niter=100.eps,height=7cm}}
        \caption{On the left, probability distributions $\wp(W)$ versus the work $W$
	for a fast transformation $n_{\rm iter.}=10$ for four different final magnetic
	fields $h=0.004, 0.017, 0.031$ and $0.044$ (from bottom to top).
	On the right, probability distribution $\wp(W)$ versus $W$ for an intermediate
	transformation $n_{\rm iter.}=100$ for the same values of the magnetic field
	(from bottom to top).}
\label{fig3}
\end{figure}
\end{center}

\begin{center}
\begin{figure}[!ht]
        \centerline{\psfig{figure=Travail-Tc-PicPos.eps,height=8cm}}
        \caption{Average work $\langle W\rangle$ of the right peak of the probability
	distribution at the critical point versus the final magnetic field $h$
	for different transformation rates, i.e. $n_{\rm iter.}$ from 2 to 250.
	In the inset, $\big(\langle W\rangle/h-M_0\big)/n_{iter.}$ where $M_0$ has been
	adjusted to the value $M_0=9016$ is plotted versus $h$ to check the linear
	behavior predicted by (\ref{WorkTc}).}
\label{fig4}
\end{figure}
\end{center}

\section{Conclusions}
The Jarzynski equality offers the possibility to estimate free energy differences
in a very simple manner in Monte Carlo simulations. Despite the fact that this
relation is exact in the case of a Markovian dynamics, it has to be used carefully.
As already shown by several authors, we observed systematic deviations for strongly
irreversible transformations due to an insufficient sampling. These systematic deviations
are caused by the fact that the average $\langle e^{-\beta W}\rangle$ is dominated by
very rare events $-W\gg 1$ that may require a large number of simulations to be
properly sampled. This limitation of the Jarzynski equality is a strong one:
the error cannot be estimated simply. When the distribution of the work is Gaussian,
it has been shown that the number of experiments has to be grown exponentially with the
dissipated work $W_{\rm diss.}$~\cite{Ritort02}. We have observed that the Gaussian
approximation (\ref{eq2}) may still give reliable estimates of the free energy difference
$\Delta F$ when the Jarzynski equality fails as for example in the case of intermediate
magnetic fields applied on a paramagnet. Unfortunately, the Gaussian approximation is valid
only for one-particle systems~\cite{Mazonka99,Speck04} or systems with short-range
correlations like paramagnets but not at the critical point. However, the Jarzynski equality
turned out to be useful at small magnetic field. It was reliable enough for instance to
estimate the critical exponent $\delta$. For this purpose, the Jarzynski equality may be
useful since a single Monte Carlo simulation is required if the work is measured at
different times.

\section*{Acknowledgements}
The laboratoire de Physique des Mat\'eriaux is Unit\'e Mixte de Recherche
CNRS number 7556. The authors would like to thank the Statistical
Physics group and especially Olivier Collet for stimulating and illuminating
discussions and Bertrand Berche for critical reading of the paper.

redpajama_set_name: RedPajamaArXiv


Normally this card is a guy with three wands, looking out to sea, waiting for his ships to come in, making it a card of expectation. The figure has invested his passion, and there's the hint that dreams come true.
Clearly Becky needed to be at her computer, the way we saw her for the first time, writing her fan fiction. (That's actually a screen-shot of her computer screen inside the laptop… I like the little details.) I figure this moment takes place after she's met Chuck and learned that it's all real– her dreams have begun to come true.
The hardest part was figuring out how to get any guns, let alone three, into a picture with Becky, who we've never seen hunt with one. It took me *forever*. But I eventually decided that as a fan-girl, she'd have Winchester rifle posters on her wall, and a replica of the Colt on her desk. Problem solved!


text:
Empowerment Workshop
Returning to My Mother's House
Rhythm of Compassion
Professional Empowerment
Empowerment Life Coach
Empowerment Workshop Trainer
Empowerment Design and Facilitation
Practice of Empowerment in Organizations
Practice of Empowerment in Communities
Practice of Empowerment and Climate Change
Practice of Empowerment
Changing the Game
Organizational Empowerment
Low Carbon Diet
Cool Community Campaign
Cool Corporate Citizen
Cool Community Corps
Low Carbon Diet Coaching Program
Household CO2 Calculator
Sustainable Lifestyle Campaign
Sustainable Lifestyle FAQs
Citizen Sustainability Assessment
Resilient Community
Livable Neighborhood
Children's Sustainable Lifestyle Program
Behavior Change Research
Societal Empowerment
Transformative Social Change
The Cool Block
IMAGINE Program
Reinventing the Planet
Audio Programs The Way of the Spritual Warrior
About Empowerment Institute
About David Gershon
About Gail Straub
A Brief History of Empowerment Institute
In 1981 David Gershon and Gail Straub founded Empowerment Institute to explore the question: how do you empower people to grow and realize their full potential? They wanted to shift from focusing on fixing problems and healing the past, to focusing on what we want for our lives, our organizations, our communities, and our world—and how to achieve it. Enabling people to envision and realize their dreams was the approach they called "empowerment." The term "empowerment" was new in the vernacular of transformation, as was their approach. This transformative social innovation soon began attracting attention.
People came to learn about empowerment for themselves, their organizations, their communities, and their causes. They came from all over North America, Europe and Latin America, but also from Afghanistan, Darfur, Rwanda, South Africa, China, Russia, and India.
They included social entrepreneurs, community organizers and environmentalists; Fortune 500 corporate leaders, organizational change consultants and business school professors; life coaches, health-care professionals, therapists, educators, and personal development trainers; nonprofit managers, government executives and politicians; young and old, male and female, and embodying every race and ethnicity.
Over the years what evolved was an extraordinary learning community—a global empowerment laboratory to help refine their methodology and explore its breadth of application in society. David and Gail wrote their best-selling book, Empowerment: The Art of Creating Your Life As You Want It to help popularize their research. The writing process brought further refinement to their model and the book's success attracted yet more people to their trainings. Along the way, Gail and David became master practitioners of empowerment.
David and Gail continued to evolve their empowerment work by adapting the model and methodology to other initiatives. Included among these was a global transformative event created at the height of the Cold War, the First Earth Run. In partnership with the United Nation's Children's Fund (UNICEF) and ABC Television, they organized the historic passing of a torch of peace around the world. This simple and profound act of global unity offered at a moment of great fear in our world was able to engage the participation of twenty-five million people in sixty-two countries, the world's political leadership and, through the media, an estimated 20 percent of the population on the planet. It was an extraordinary confirmation of the efficacy of the empowerment methodology.
Building on this growing body of knowledge and experience, David began applying his empowerment expertise to large organizations and cities. The versatility of the empowerment methodology enabled it to achieve behavior change, talent development and cultural transformation in organizations and sustainable lifestyles, livable neighborhoods and disaster-resilient communities in cities. Based on this behavior change research, David has written eleven books including his award-winning Social Change 2.0: A Blueprint for Reinventing Our World, and best-selling Low Carbon Diet: A 30 Day Program to Lose 5,000 Pounds.
Gail applied her behavior change acumen to issues of women's empowerment through a global initiative for the empowerment of women called IMAGINE. This initiative trains empowerment facilitators to deliver the Empowerment Workshop to disenfranchised women in developing world countries. IMAGINE is being implemented in Afghanistan, Brazil, India, Jordan, Kenya, Nigeria South Africa, and Sudan. Another of Gail's contributions to women's empowerment is her award-winning memoir, Returning to My Mother's House: Taking Back the Wisdom of the Feminine. She has also written the critically acclaimed The Rhythm of Compassion: Caring for Self, Connecting with Society.
And the results from this research and application … a robust and rigorously tested transformational model that has stood the test of time. If you choose to participate in one of Empowerment Institute's training programs know that you are also participating in a global empowerment movement—a movement that aspires to nothing less than changing the world … one person and one dream at a time.
Empowerment Institute is the world's preeminent consulting and training organization specializing in the practice of empowerment. Its empowerment methodology has been applied over the past three decades to achieve measurable and sustainable behavior change at the individual, organizational and community level. A major academic research study described this methodology as "unsurpassed in changing behavior."
Empowerment Certification
Empowerment Institute is a three-part professional training leading to certification. It is based on David Gershon and Gail Straub's world-renowned work on empowerment and their mastery of personal growth facilitation developed over the past thirty years.
Next training program is in Amman, Jordan, and begins January 11–15, 2017.
A framework and methodology
for changing behavior, developing talent
and transforming a culture.
To learn more click here
A framework, methodology and tools
for changing behavior, community engagement
and large system transformation.
A comprehensive blueprint for designing
transformative social innovations
and large-scale societal change.
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text:
You are currently on this page - School Lunch Program
School Lunch/Breakfast Program
Free school lunch/breakfast now available for ALL school district students!
The U.S. Department of Agriculture (USDA) and the Food and Nutrition Service (FNS) unexpectedly announced nationwide waivers to allow the continuation of FREE meals to all students through the National School Lunch Program from now through the end of the school year.
Through this program, breakfast and lunch will be served at no charge to all students. The USDA and FNS reserve the right to withdraw any or all of the nationwide waivers subject to the availability of funding.
All River Falls School District students will be able to take advantage of this new benefit, including elementary students, hybrid students, distance learning, and virtual/e-school students.
FACE-TO-FACE LEARNERS
Elementary School Students:
Elementary students wanting breakfast/lunch will need to tell their classroom teachers their breakfast/lunch choice the day before they plan to have a meal.
Hybrid In-School Students:
Students will go through the breakfast/lunch lines for the days they attend school in person.
AT HOME LEARNERS (Take Home Meals)
Hybrid At-Home Students:
Students will need to order meals through our on-line process for the days they are at home. Please see the ordering information below.
Virtual/E-School/Distance-Learning Students:
Virtual/e-school/Distance-Learning students will need to order meals through our on-line process. Please see the ordering information below.
HOW DO I ORDER TAKE HOME MEALS?
Meals for hybrid at-home students, virtual/e-school, and Distance-Learning students will be available through the end of the school year at no charge.
You will need to order meals each week through a google form to receive take-home meals. Please see links and the meal ordering calendar below.
Orders must be submitted by 12 noon on Thursday for the following week.
Please order meals through your respective Google form link:
HYBRID EARLY
HYBRID LATE
VIRTUAL/E-SCHOOL, & STUDENTS IN DISTANCE-LEARNING DUE TO CLOSURES
HYBRID RENAISSANCE
Do I need to fill out a form for each of my students individually?
Yes, please fill out a separate google form for each student needing meals.
What is the deadline for ordering meals?
How do I pay for meals?
All meals will be free of charge through the end of the school year.
Where/when can take home meals be picked up?
Hybrid student meals: Students will pick up meals as they leave school for the week. Hybrid Early students will pick up after school on Tuesday; Hybrid Late students will pick up after school on Friday. Pickup will be available from 2:45-3:15 pm in the cafeteria of your student's school (REN, MMS, and RFHS.)
Virtual/E-school/Distance-Learning student meals can be picked up at Meyer Middle School on Tuesdays and Fridays from 2:45 pm to 3:15 pm. Parents can pick up meals at door #211. Please enter through the south parking lot. Pick-up will be easily accessible to ensure safety and minimize contact.
What if my student doesn't pick up a meal that was ordered?
Please make every effort to pick up a meal that was ordered to reduce waste and staff time spent in preparation.
Contact Food Service Director, Bob Miles: bob.miles@rfsd.k12.wi.us
USDA Nondiscrimination Statement Update In accordance with Federal civil rights law and U.S. Department of Agriculture (USDA) civil rights regulations and policies, the USDA, its Agencies, offices, and employees, and institutions participating in or administering USDA programs are prohibited from discriminating based on race, color, national origin, sex, disability, age, or reprisal or retaliation for prior civil rights activity in any program or activity conducted or funded by USDA. Persons with disabilities who require alternative means of communication for program information (e.g. Braille, large print, audiotape, American Sign Language, etc.), should contact the Agency (State or local) where they applied for benefits. Individuals who are deaf, hard of hearing, or have speech disabilities may contact USDA through the Federal Relay Service at (800) 877-8339. Additionally, program information may be made available in languages other than English. To file a program complaint of discrimination, complete the USDA Program Discrimination Complaint Form, (AD-3027) found online at http://www.ascr.usda.gov/complaint_filing_cust.html,and at any USDA office, or write a letter addressed to USDA and provide in the letter all of the information requested in the form. To request a copy of the complaint form, call (866) 632-9992. Submit your completed form or letter to USDA by: (1) mail: U.S. Department of Agriculture, Office of the Assistant Secretary for Civil Rights, 1400 Independence Avenue, SW, Washington, D.C. 20250-9410; (2) fax: (202) 690-7442; or (3) email: program.intake@usda.gov.
Food Service Office
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The River Falls School District participates in the National School Lunch/Breakfast Program and we are committed to serving nutritious, high quality and affordable meals that appeal to children and teenagers. Our meals, provided through Chartwells School Dining Service, are planned and prepared to meet the Dietary Guidelines for Americans emphasizing less fat, saturated fat, sodium and sugar.
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text:
extern const int vendors[];
libusb_device_handle*  findAndInitAccessory(
		libusb_context* ctx,
		const char* manufacturer,
		const char* modelName,
		const char* description,
		const char* version,
		const char* uri,
		const char* serialNumber);
libusb_device_handle* setupAccessory(
		const char* MANUFACTURER,
		const char* MODELNAME,
		const char* DESCRIPTION,
		const char* VERSION,
		const char* URI,
		const char* SERIALNUMBER,
		libusb_device_handle* handle);
int checkAndroid(libusb_device_handle*);
void determineEndpoints(libusb_device*);
void deInitAccessory();
#endif // INITIALIZE_H


The U.S. trade deficit shrunk to $57.6 billion in August, as rising exports offset higher costs for imported oil, the Commerce Department reported on Oct. 11 The lion's share of the deficit came from oil imports and from China, but excluding those factors, the trade balance showed improvement.
Adjusted for inflation, it was the lowest level since February 2004, and in absolute terms the lowest since January, Commerce Department figures showed.
The trade gap was also better than the average analyst expectation of a deficit of $59.5 billion, and marked a 2.4% drop from July's revised figure of $59 billion. Exports rose 0.4% in August to a record $138.3 billion, helped by the weak dollar. Imports meanwhile fell 0.4% to $195.9 billion.
Oil prices remained a big factor in the deficit, accounting for $24.3 billion of the deficit, with the average price of an imported barrel hitting a record $69.09.
The other big factor in the deficit was China, which accounted for $22.5 billion of the deficit even though the figure was down 5.4% for the month.
The improvement in the trade deficit is generally positive for the economy since it means more economic output is coming from domestic sources. It also eases pressure on the dollar by reducing outflows of the U.S. currency.


Head to Publix and pick up a nice deal on your favorite Applegate Products and get the makings of a cheap breakfast. After coupon and sale, you can grab sausage for as little as $2.16 or bacon for just $2.99 per pack.
We believe taste starts on the farm with the way animals are raised. All Natural. No Antibiotics. Worry Free Meat. Humanely Raised.


text:
package org.tud.inf.st.pccs.provider;

import java.util.Collection;
import java.util.List;

import org.eclipse.emf.common.notify.AdapterFactory;
import org.eclipse.emf.common.notify.Notification;

import org.eclipse.emf.common.util.ResourceLocator;

import org.eclipse.emf.ecore.EStructuralFeature;

import org.eclipse.emf.edit.provider.ComposeableAdapterFactory;
import org.eclipse.emf.edit.provider.IEditingDomainItemProvider;
import org.eclipse.emf.edit.provider.IItemLabelProvider;
import org.eclipse.emf.edit.provider.IItemPropertySource;
import org.eclipse.emf.edit.provider.IStructuredItemContentProvider;
import org.eclipse.emf.edit.provider.ITreeItemContentProvider;
import org.eclipse.emf.edit.provider.ItemPropertyDescriptor;
import org.eclipse.emf.edit.provider.ItemProviderAdapter;
import org.eclipse.emf.edit.provider.ViewerNotification;

import org.tud.inf.st.pccs.ConcreteSyntax;
import org.tud.inf.st.pccs.PccsFactory;
import org.tud.inf.st.pccs.PccsPackage;

/**
 * This is the item provider adapter for a {@link org.tud.inf.st.pccs.ConcreteSyntax} object.
 * <!-- begin-user-doc -->
 * <!-- end-user-doc -->
 * @generated
 */
public class ConcreteSyntaxItemProvider
	extends ItemProviderAdapter
	implements
		IEditingDomainItemProvider,
		IStructuredItemContentProvider,
		ITreeItemContentProvider,
		IItemLabelProvider,
		IItemPropertySource {
	/**
	 * This constructs an instance from a factory and a notifier.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public ConcreteSyntaxItemProvider(AdapterFactory adapterFactory) {
		super(adapterFactory);
	}

	/**
	 * This returns the property descriptors for the adapted class.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public List getPropertyDescriptors(Object object) {
		if (itemPropertyDescriptors == null) {
			super.getPropertyDescriptors(object);

			addStartwithPropertyDescriptor(object);
			addMultiLineCommentIndicationStartPropertyDescriptor(object);
			addMultiLineCommentIndicationEndPropertyDescriptor(object);
			addSingleLineCommentIndicationStartPropertyDescriptor(object);
			addIdPropertyDescriptor(object);
		}
		return itemPropertyDescriptors;
	}

	/**
	 * This adds a property descriptor for the Startwith feature.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	protected void addStartwithPropertyDescriptor(Object object) {
		itemPropertyDescriptors.add
			(createItemPropertyDescriptor
				(((ComposeableAdapterFactory)adapterFactory).getRootAdapterFactory(),
				 getResourceLocator(),
				 getString("_UI_ConcreteSyntax_startwith_feature"),
				 getString("_UI_PropertyDescriptor_description", "_UI_ConcreteSyntax_startwith_feature", "_UI_ConcreteSyntax_type"),
				 PccsPackage.Literals.CONCRETE_SYNTAX__STARTWITH,
				 true,
				 false,
				 true,
				 null,
				 null,
				 null));
	}

	/**
	 * This adds a property descriptor for the Multi Line Comment Indication Start feature.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	protected void addMultiLineCommentIndicationStartPropertyDescriptor(Object object) {
		itemPropertyDescriptors.add
			(createItemPropertyDescriptor
				(((ComposeableAdapterFactory)adapterFactory).getRootAdapterFactory(),
				 getResourceLocator(),
				 getString("_UI_ConcreteSyntax_multiLineCommentIndicationStart_feature"),
				 getString("_UI_PropertyDescriptor_description", "_UI_ConcreteSyntax_multiLineCommentIndicationStart_feature", "_UI_ConcreteSyntax_type"),
				 PccsPackage.Literals.CONCRETE_SYNTAX__MULTI_LINE_COMMENT_INDICATION_START,
				 true,
				 false,
				 false,
				 ItemPropertyDescriptor.GENERIC_VALUE_IMAGE,
				 null,
				 null));
	}

	/**
	 * This adds a property descriptor for the Multi Line Comment Indication End feature.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	protected void addMultiLineCommentIndicationEndPropertyDescriptor(Object object) {
		itemPropertyDescriptors.add
			(createItemPropertyDescriptor
				(((ComposeableAdapterFactory)adapterFactory).getRootAdapterFactory(),
				 getResourceLocator(),
				 getString("_UI_ConcreteSyntax_multiLineCommentIndicationEnd_feature"),
				 getString("_UI_PropertyDescriptor_description", "_UI_ConcreteSyntax_multiLineCommentIndicationEnd_feature", "_UI_ConcreteSyntax_type"),
				 PccsPackage.Literals.CONCRETE_SYNTAX__MULTI_LINE_COMMENT_INDICATION_END,
				 true,
				 false,
				 false,
				 ItemPropertyDescriptor.GENERIC_VALUE_IMAGE,
				 null,
				 null));
	}

	/**
	 * This adds a property descriptor for the Single Line Comment Indication Start feature.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	protected void addSingleLineCommentIndicationStartPropertyDescriptor(Object object) {
		itemPropertyDescriptors.add
			(createItemPropertyDescriptor
				(((ComposeableAdapterFactory)adapterFactory).getRootAdapterFactory(),
				 getResourceLocator(),
				 getString("_UI_ConcreteSyntax_singleLineCommentIndicationStart_feature"),
				 getString("_UI_PropertyDescriptor_description", "_UI_ConcreteSyntax_singleLineCommentIndicationStart_feature", "_UI_ConcreteSyntax_type"),
				 PccsPackage.Literals.CONCRETE_SYNTAX__SINGLE_LINE_COMMENT_INDICATION_START,
				 true,
				 false,
				 false,
				 ItemPropertyDescriptor.GENERIC_VALUE_IMAGE,
				 null,
				 null));
	}

	/**
	 * This adds a property descriptor for the Id feature.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	protected void addIdPropertyDescriptor(Object object) {
		itemPropertyDescriptors.add
			(createItemPropertyDescriptor
				(((ComposeableAdapterFactory)adapterFactory).getRootAdapterFactory(),
				 getResourceLocator(),
				 getString("_UI_ConcreteSyntax_id_feature"),
				 getString("_UI_PropertyDescriptor_description", "_UI_ConcreteSyntax_id_feature", "_UI_ConcreteSyntax_type"),
				 PccsPackage.Literals.CONCRETE_SYNTAX__ID,
				 true,
				 false,
				 false,
				 ItemPropertyDescriptor.GENERIC_VALUE_IMAGE,
				 null,
				 null));
	}

	/**
	 * This specifies how to implement {@link #getChildren} and is used to deduce an appropriate feature for an
	 * {@link org.eclipse.emf.edit.command.AddCommand}, {@link org.eclipse.emf.edit.command.RemoveCommand} or
	 * {@link org.eclipse.emf.edit.command.MoveCommand} in {@link #createCommand}.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public Collection getChildrenFeatures(Object object) {
		if (childrenFeatures == null) {
			super.getChildrenFeatures(object);
			childrenFeatures.add(PccsPackage.Literals.CONCRETE_SYNTAX__OPERATORS);
			childrenFeatures.add(PccsPackage.Literals.CONCRETE_SYNTAX__KEYWORDS);
			childrenFeatures.add(PccsPackage.Literals.CONCRETE_SYNTAX__PARSERS);
			childrenFeatures.add(PccsPackage.Literals.CONCRETE_SYNTAX__METAMODELS);
			childrenFeatures.add(PccsPackage.Literals.CONCRETE_SYNTAX__REGEX);
		}
		return childrenFeatures;
	}

	/**
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	protected EStructuralFeature getChildFeature(Object object, Object child) {
		// Check the type of the specified child object and return the proper feature to use for
		// adding (see {@link AddCommand}) it as a child.

		return super.getChildFeature(object, child);
	}

	/**
	 * This returns ConcreteSyntax.gif.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public Object getImage(Object object) {
		return overlayImage(object, getResourceLocator().getImage("full/obj16/ConcreteSyntax"));
	}

	/**
	 * This returns the label text for the adapted class.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public String getText(Object object) {
		String label = ((ConcreteSyntax)object).getId();
		return label == null || label.length() == 0 ?
			getString("_UI_ConcreteSyntax_type") :
			getString("_UI_ConcreteSyntax_type") + " " + label;
	}

	/**
	 * This handles model notifications by calling {@link #updateChildren} to update any cached
	 * children and by creating a viewer notification, which it passes to {@link #fireNotifyChanged}.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public void notifyChanged(Notification notification) {
		updateChildren(notification);

		switch (notification.getFeatureID(ConcreteSyntax.class)) {
			case PccsPackage.CONCRETE_SYNTAX__MULTI_LINE_COMMENT_INDICATION_START:
			case PccsPackage.CONCRETE_SYNTAX__MULTI_LINE_COMMENT_INDICATION_END:
			case PccsPackage.CONCRETE_SYNTAX__SINGLE_LINE_COMMENT_INDICATION_START:
			case PccsPackage.CONCRETE_SYNTAX__ID:
				fireNotifyChanged(new ViewerNotification(notification, notification.getNotifier(), false, true));
				return;
			case PccsPackage.CONCRETE_SYNTAX__OPERATORS:
			case PccsPackage.CONCRETE_SYNTAX__KEYWORDS:
			case PccsPackage.CONCRETE_SYNTAX__PARSERS:
			case PccsPackage.CONCRETE_SYNTAX__METAMODELS:
			case PccsPackage.CONCRETE_SYNTAX__REGEX:
				fireNotifyChanged(new ViewerNotification(notification, notification.getNotifier(), true, false));
				return;
		}
		super.notifyChanged(notification);
	}

	/**
	 * This adds {@link org.eclipse.emf.edit.command.CommandParameter}s describing the children
	 * that can be created under this object.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	protected void collectNewChildDescriptors(Collection newChildDescriptors, Object object) {
		super.collectNewChildDescriptors(newChildDescriptors, object);

		newChildDescriptors.add
			(createChildParameter
				(PccsPackage.Literals.CONCRETE_SYNTAX__OPERATORS,
				 PccsFactory.eINSTANCE.createTerminal()));

		newChildDescriptors.add
			(createChildParameter
				(PccsPackage.Literals.CONCRETE_SYNTAX__KEYWORDS,
				 PccsFactory.eINSTANCE.createTerminal()));

		newChildDescriptors.add
			(createChildParameter
				(PccsPackage.Literals.CONCRETE_SYNTAX__PARSERS,
				 PccsFactory.eINSTANCE.createParserDefinition()));

		newChildDescriptors.add
			(createChildParameter
				(PccsPackage.Literals.CONCRETE_SYNTAX__METAMODELS,
				 PccsFactory.eINSTANCE.createMetaModel()));

		newChildDescriptors.add
			(createChildParameter
				(PccsPackage.Literals.CONCRETE_SYNTAX__REGEX,
				 PccsFactory.eINSTANCE.createRegularExpression()));
	}

	/**
	 * This returns the label text for {@link org.eclipse.emf.edit.command.CreateChildCommand}.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public String getCreateChildText(Object owner, Object feature, Object child, Collection selection) {
		Object childFeature = feature;
		Object childObject = child;

		boolean qualify =
			childFeature == PccsPackage.Literals.CONCRETE_SYNTAX__OPERATORS ||
			childFeature == PccsPackage.Literals.CONCRETE_SYNTAX__KEYWORDS;

		if (qualify) {
			return getString
				("_UI_CreateChild_text2",
				 new Object[] { getTypeText(childObject), getFeatureText(childFeature), getTypeText(owner) });
		}
		return super.getCreateChildText(owner, feature, child, selection);
	}

	/**
	 * Return the resource locator for this item provider's resources.
	 * <!-- begin-user-doc -->
	 * <!-- end-user-doc -->
	 * @generated
	 */
	public ResourceLocator getResourceLocator() {
		return PccsEditPlugin.INSTANCE;
	}

}


Does your project call for stainless U-Bolts? 304 Stainless Steel ? 316 Stainless Steel?
No matter the type or size of u-bolts that your project calls for, Lightning Bolt & Supply has 100,000sq ft of fasteners and u-bolts ready to ship. Sizing ubolts often time make people nervous for the fact that nothing measures 2 inches on a 2″ u-bolt. Once you understand that u-bolts are sized by the "PIPE" size they hold, things start to make a lot more sense. In addition, the diameter of the stock size is also important. Lastly, longer u-bolts (i.e. long-tangent u-bolts) can be a great fit for items that require extra threads.
U-bolts are a type of industrial fastener most commonly known for securing piping in which liquids and gases flow. Their main function is to provide a clamping force to hold together two components. The U-Bolt, by no surprise, is shaped in the letter "U" and is threaded on both ends. The unique shape of the U-bolt helps provide an added amount of stability when securing piping or other material.
Initially U-bolts were measured based on the size of the pipe that they were supporting – ex: a 2" U-bolt would support a 2" pipe. This is still a common way of identifying U-bolts, although a more precise measurement can be made by measuring the thread size, thread length, inside diameter, and inside height.
Although commonly thought of for securing pipes, the U-Bolt has proven to be very adaptable, and has various applications across a wide range of industries, including the automotive, construction and architectural industries. For example, they can be used as anchors for roofs and foundations, and support for frames, cables, and conduits. In the automotive industry, U-bolts are used for engine shaft component support. U-bolts have been proven to be a versatile industrial fastener. U-bolt plates, which are also kept in stock, are commonly used with U-bolts for further support.
Here at Lightning Bolt and Supply, we stock a large selection of U-Bolts in a wide variety of materials and finishes. Among these are: Low grade carbon plated zinc, 304 stainless steel, 316 stainless steel, neopreme coated, and Hot-Dipped Galvanized U-bolts. Fig. 137 type U-bolts are a very popular item that we have IN STOCK.
Why Lightning Bolt for 304 stainless u-bolts and 316 stainless u-bolts?