Right from everybody. So I'm originally I was supposed to talk about LibreOffice Asia But since we have a separate session around 6 o'clock, so I'll be Talk about more about the LibreOffice in Sri Lanka. So the way we Started and how the things going on. So I'm Danish Kanawin from Sri Lanka and so I Actually, I started my localization when I was at the Red Hat Localization team with these guys. So So after some time I quit and then I was keep contributed. So so So we started with the real open open obis then we moved to LibreOffice 3.2 localization and actually at that time ICTA agency helped me a lot because actually Since they had to introduce more Terms to LibreOffice or actually what they did they said they can get the help from someone who Into translation. I mean a problem just book translation So actually they print all the PO files and ask that guy to review all the things because that person is not into IT So for him, it's not convenient to use their Translation tool like localize or PO Poed it so So it went somehow Whatever. Yeah, he gave us a feedback after correcting everything. So I had to fix everything again and push it to the upstream and 2011 during a force for cow conference in Sri Lanka. We launched LibreOffice Singhala and We did the QA workshop to cover all the lead test so with the help of 15 guys So we divided them into six teams to cover each and All the products of LibreOffice actually at that time it was open office and So each team has to test it on the given Application it's a Writer so each team has to test it on both Windows and Linux to find if there is any issues other than typos. So So whatever typos we found we fix on the during the event itself and the we found few bugs so we File the bugs at the same time. So nothing remain for the next day. So This was the so these are few images from the event and This was the launch event LibreOffice 3.2 and In 2011 When we were launching LibreOffice 3.2 the help was not Translated at all. So it was really huge. So the approach was get community to translate it because the Previous translation was just myself and some of my friends helped me time to time but It wasn't not that easy to complete Help translation. So we ran so on 27th April so In 2011 so we conducted 27 hours translation marathon. So we got More than 70 contributors so most of people they have never translated but they would They were interested in contributing to a community project and So one of the ideas to let everyone to contribute and also Make a noise about the product. So some of them actually they heard about The product on the first that was their first time they heard about the product. So So this is one of the This is from University of Kalanin students or 35 students from this university. So they joined from their own lab. So Few of us were Helping them because we didn't had a style guide or nothing. So only the government closer. That was not enough to run this event but We were using IRC to help all the people and some of them were actually They were using some offline tools like localize and they uploaded later But we we did one thing actually we asked for the university students Actually, we asked them to use a particular component. Otherwise, it's really hard to find Who did what but to be honest, there was a problem with the end result because Yeah, they they did translate we could finish 47 or 47,000 words within 27 hours, but the thing is quality of the translation is not that good So some of them translated even the HTML syntax because they don't Most of them they don't know about translation. So so in that case, actually, it's our problem So we should have give them a proper guide. So So I hope in future, I mean as a LibreOffice community, so we can Run, I mean this kind of event. I mean that globally. So it's not just Completing some work, but again, we can make some noise. It's a community awareness Yeah, and later Earlier actually the Microsoft Office was clearly mentioned in textbooks in school textbooks. So with the help of Various people, it's not a one-man show, but we could be able to This is the current textbook in Singular textbook published by Mr. Feducation with the help of National Institute of education. So you can see as you can see so both Microsoft and LibreOffice Writer it's mentioned here. So Even here you can see each step mentioned in both Both the Microsoft Office and LibreOffice and we we did a Workshop to jealous in order to Make an awareness about open source because they don't whenever we run an event. They don't know about open source or Because we should educate them then they know about open source The ICT agency help us to conduct this event and to 25 journalists were Participated and some of them wrote at least one article after this Yeah, so In So in 2011 we did a awareness campaign in local government authorities in the one of the Provinces Sri Lanka. So this idea was to introduce open source tools like LibreOffice and Firefox and right now, actually we were not pushing them to Install I mean we were just introducing but there was no such a migration at all but somehow Late recently the actually today they update me. So they have started the E local government project So this project project is ongoing now. They have deployed Actually that they have already Windows machines with the Microsoft Office obviously But they so they have deployed 10 machines to each organizations so with GNU Linux or this in this machine store. Obviously they use LibreOffice and I started our project called Hantala Linux is a Fedora remix. So it was deployed in nine national schools in Sri Lanka. So this was just Deployed in around 2011. So in In these these schools, so we shipped not just a LibreOffice, but also we Push ship the LibreOffice documentation. So complete documentation who so So whenever you Create an account. So you will definitely get the Copy of the LibreOffice documentation in the home directory. So it's kind of like make Because most of some of the schools, they don't have internet in that case You have easy access to the LibreOffice documentation So since we didn't had any budget to print the manual. So this is what we did And Yeah, sorry So actually this was a downloaded More than 40,000 copies. So according to the source forge Yeah, there is an ongoing project From minister of education. So it's about a deploy in 1000 school labs So which is consistent. Okay, some of the schools getting 20 Systems per lab. It's our 40 systems. It's based on the number of students in the school. So Unfortunately at the last moment Microsoft were able to jump into this project. Now this project was supposed to be here Fully open source project But now it's they managed to get the Microsoft Windows and now it's going like a dual boot So we can't guarantee that teachers using Only LibreOffice or only Linux And yeah, so the whatever I have mentioned so far it's a Actually effort from the all the people ICT agency minister of education national institute of education And the ongoing project for the local government is from minister of local government and provincial councils And even in many universities and uh Linux user group in Sri Lanka. So, um, That's it about our Sri Lanka The things happening in Sri Lanka and I will have a few suggestions for Asia. So actually If you compare with LibreOffice project with other Open source projects like Fedora or Noam or KD whatever. So The contribution from Asia is really less. I mean, there are a few Yeah, for even for the localization, there are I mean, I think all the English languages supporting, but there are some I think it's still we need Contribution from other countries, but even localization is not the only way someone can contribute especially I think really few contributors to the development and I think even italo mentioned that he needed support for the marketing stuff. So I think even the next thing is Yeah, so we have um, I mean So even for us, we have like a common issues and common culture and so actually sometimes most of time So the issues So for me, I can get a solution from some other country. So idea is actually my plan was to have a discussion among the Communities in the Asia. So and even in future So I hope if it's really good if we can host a LibreOffice Asia Meet up or conference to get more people and and and because there are even here There are only few people attending this event. So it's really good if more people can interact with the Even LibreOffice developers or whoever that the other people like the people in the mental level Yeah, we have already discussed this with italo and sofi and so we ask them to you know Connect this kind of Conference or event, you know in asia. Yeah, or you know some middle place in asia typically india or something or wherever it is possibly so And by the way, the we have created a mailing list for those who interested so we can use this mailing list to Keep update with the ongoing upcoming events and even to share the Successful stories or even if you have a issue if you have an issue so we can share with other people So, yeah, this idea of LibreAsia conference because we can have hackathons even Talks translation screens Even for fedora actually are so actually I'm a part of fedora. So fedora we have a um Fudcon in apax or and even we do a yearly plan for the upcoming events and we do even planning for the swags everything so we We have we get all the list of events to be conducting the next year So then we plan the swags accordingly because we don't Uh produce swags in each and every country for example dvds So we produce there for example last time We got the dvds from India so then we distribute uh within the other countries We are still some my heart Libre office stickers over there. Yeah You were taken. Yes. Yeah Yeah Yeah, thank you. Uh, so, uh, I don't know if we have enough time but uh, so anyway If you have any questions regarding the my previous Slidesit for the regarding Sri Lanka. So Just It's amazing. Uh, what you all organize I'm really feeling jealous seeing you having a meeting with Seven people or whatever stuff Um, where do you find all the time? Do you have time in your job or just personal question or at that time? All in the evening No, I I was not working at that time. Yeah, so, uh, so I could I had enough time So, uh, so actually I I finished one of my Project with the ICT agency and I was waiting for a proper job So at and I was going around the country for the running for events So, uh, I met various people including the government officers or this for this event actually It was not just a youth that even like, uh, uh, all those people So even they joined someone from the, uh, direct One person joined he was a director of government re-injuring. So So there was no such an age level. So me Yeah Oh, yeah, uh, to be honest, I don't know the exact situation, uh, but it's dependent on the, um teachers because, uh, as he mentioned in What is that, uh, Microsoft challenge or something right in Vietnam? So actually it's happening in Sri Lanka also. So when they use the word challenge, so actually if I'm not wrong It's about making presentations using, uh, Microsoft, uh, in prayer, uh, sorry, uh, power point Sorry Yeah, uh, so, uh So that if I'm not wrong, that's the, uh, uh, they are marketing like you can do some visual basic or whatever the language is But actually, uh, what's the reality is they make presentations and they select, uh, regional wise and they have a global, uh, Something yeah, so that's the reality. So then, uh, teachers they They like Because yeah, we are humans, right? Anyone like to go to a foreign country and get a scholarship. So so it's they So they are trying to, uh, uh Get the attraction and, uh So, uh, in Sri Lanka and there is another thing, uh, um, intellectual property law is Actually, it's there and uh, some a few years ago. Actually, there were some incidents like, uh, um, they're actually the Well, I think department of law is actually they, uh, they This is one of the company those who they were using a prior date a copy and copies of windows and it was a One incident that because actually they find, uh, I don't I can't remember the amount So most of banks they already moved to, uh, at the time it was open surface office So they have moved from microsoft office to open office So I don't know how numbers, uh, in the uh, public but some of them already migrated But it wasn't done by ourselves. I mean if they, uh, they knew, okay, this this is a good product for them. So, uh, there was no such a, um, big, uh Community involvement like in, uh, in Italy. So these are like a small stuff. Yeah Because gaming so you have to leave this Yeah stage. Okay. Thank you


Hi, this is Dr. Don. I had a question about how to add a cumulative frequency curve to a histogram if you don't have the data analysis tool pack. All you need is your basic histogram. Here we've got it set up. We're going to add a column for our cumulative frequencies and all we need to do is just to go equal, get our first cell, and then the second cell is equal to of course the cumulative which is the sum of the first cell and the second cell. Now I can just copy that down to get my values for my cumulative frequency. Now to add it to the existing chart we just click inside the chart area to make sure you've got the chart selected and then right click select data and when it opens up it'll show you the data series that you already have over here highlighted in the marching ants and if you wanted to edit it you could just click on edit but right now I'm just going to add so I'm going to click add and it wants in the first cell the series name make sure you've got a title that you want in a cell and I want to click that although I think you can actually type in a label there a text value if you want but I'm going to do it this way so I could go back and modify that in the future if I need my series values make sure you delete the stuff that's already in there if you leave any of that in there it won't work so delete it make sure it's clean and then select your values and then click okay and okay and you can see it offers up not quite what we want we've got two histograms or two bar charts actually because we haven't cleaned that one up yet all we need to do is to click on one of the orange bars which is our cumulative and then we're going to change series chart type and we've got some options up here you can hover over those there's the custom which is what we have now and we could have the stacked area which is not what we want we've got a clustered column with the line on a secondary axis which is what we want I think and we've got just the custom column with a line which would be on the primary axis let's select the one with the line on the secondary axis that looks good so I'm going to click okay so there I've got my histogram with the cumulative frequency line added and of course you would probably want to go over here and add a legend and then add your titles as appropriate to your axes and to the chart but that's the basics of adding a secondary data set hope this helps


China says debris from its out-of-control Long March 5B rocket landed in the Indian Ocean and most of it burned up in Earth's atmosphere. Wait till you hear this. Remnants of China's largest rocket launched last month plunged back through the atmosphere on Sunday morning. It landed west of the Maldives in the Indian Ocean and ended days of speculation over where the debris would hit. After monitoring and analysing at 224 AM GMT on May 9, 2021, the last-stage wreckage of the Long March 5B Yaotou launch vehicle has re-entered the atmosphere, the China-Manned Engineering Office said in a statement and added that most of the components burned up in the re-entry. The US Space Command confirmed the re-entry of the rocket over the Arabian Peninsula but said it was unknown if the debris impacted land or water. The exact location of the impact and the span of debris, both of which are currently unknown at this time, the monitoring services space track which uses US military data confirmed the re-entry. And it tweeted that, everyone else following the Long March 5B re-entry can relax, the rocket is down. We believe the rocket went down over the Indian Ocean but we are waiting on official data from the US Space Force. US and European authorities had been monitoring the rocket, which was travelling at a speed of 4.8 miles per second. A difference of just one minute of time and re-entry translates to hundreds of miles of difference on the ground and earlier predictions had the rocket landing in several possible locations from the Mediterranean Sea to the Pacific Ocean. According to the experts, with most of the Earth's surface covered by water, the chances that it would hit land in a populated area were extremely low and the likelihood of injuries were even lower. But uncertainty over the rocket's orbital decay and China's failure to issue stronger reassurances in the run-up to the re-entry fuelled anxiety over its descent. China's foreign ministry said on Friday that the re-entry was highly unlikely to cause any harm. The Long March 5B rocket comprising one core stage and four boosters lifted off on April 29th and contains what will become living quarters on a permanent Chinese space station. And this rocket is set to be followed by 10 more missions to complete the space station. In May 2020, pieces from the first Long March 5B fell over the Ivory Coast, damaging several buildings but no injuries were reported. And debris from Chinese rocket launches is not uncommon in China and in late April, authorities in the city of Xi'an issued a notice to its people to prepare for evacuation as parts of the rocket were set to land in the whole area. The latest remnants of the Long March 5B rocket make up one of the largest pieces of space debris to ever have returned back to the Earth. But what do you guys think about this one anyway? Comments below and as always, thank you for watching.


Hey friends welcome again to another session on factorization of algebraic expressions and in the series We are solving a lot of questions so that you become comfortable with problem solving Comfortable with factorization of algebraic expressions So again, we have been given this expression where it is x cube plus 3x square plus 3x minus 7 and We have to you know factorize it right now Have we learned anything where you know or for that matter if you have to approach this What all do we know? We know splitting the middle term. We know how to take commons. We know how to use algebraic identities So can something be used here now if you notice there are two threes here this three and this three and there's a cube term Now if you recall our a plus b whole cube identity was what? Guys a cube plus 3 a square b plus 3 a b square plus B cube is it it now the same thing if it is you know a plus one instead of now B as you know if I keep B as one so what do you get you get a cube plus 3 a square Plus 3 a plus one now. This is where I wanted to draw your attention Right, so a plus one cube is this and now see this is something familiar Isn't it so if I just add one to it it becomes a cube and once it becomes a cube Then difference of cube we have learned so and how to factorize difference of cubes So that's what we are going to take the approach like okay, so x cube plus 3x square Plus 3x and then I simply add one to it right to complete the cube now You'll say if I add one you are changing the expression. Yes, correct We are changing the expression. So hence to compensate. What do I need to do subtract that one from it? Right, so I basically added one and subtracted one so that it becomes same correct and this was minus seven anyways now Advantages that you see this is this becomes x plus one whole cube. How using this this Identity and this one this whole this whole thing becomes x plus one whole cube and this this is minus 8 Now could you sense something? Yes, so this is x plus one whole cube Minus two whole cube two cube now We have already learned how to factorize difference of two cubes, which is nothing, but you take x plus one Minus two then within other brackets x plus one whole squared Minus or other plus x plus one times two plus two squared Is it which which formula folks for a cube minus b cube? My identity is a minus b a square plus a b plus b square isn't it so we use the same thing and Then this is going to help us in factorization So hence x plus one minus two is simply x minus one and here What is it open up the bracket so x square plus 2x plus one x plus one whole square will be written like that This will become 2x plus 2 when you open this bracket up you will get these two terms and then plus 4 Isn't it and it's a matter of surf simplification so x minus one and Square term is only one and 2x plus 2x becomes 4x and My dear friend 1 plus 2 plus 4 is 7 so This is how the factorization would look like Okay, so Mmm Yep, so x minus one x square plus 4x plus 7 so I checked it also. It's absolutely correct Okay, so what did we learn learning is it might not be resembling our standard formats, but you have to be Observant and you can see that You can you bring it to some kind of known format? So what did we do here? We just brought it to the Cube format and difference of cube format and difference of cube. We know how to factorize


You have to roll with like, he was saying, he's like, MP. He's like, okay, but it's like anything.  You dump it in, try to get it all the way around. Get it around in this ring, and then get it around all the way. You dump your JP8. You'll set this to high. You'll light on.


This is a brand new, brilliant show that has never been seen before, never been done before. We are taking people on a roller coaster ride, a body transformation, but it ends up so much more than that. It's about getting these people to know more about health, fitness, body confidence, their image, everything. We just want to help people. We aren't happy the way they look physically or mentally. This show is all about reaching your full potential, realising what you can become. It's all about following the journey. People discovered that they can move their body and they didn't realise before because they were really super lazy. Regular people working really hard experiencing the ups and downs of trying to reach their fitness goal. We're going to be getting people putting a good fitness into them and transforming their bodies. Changing people's lives. Not just how you look but how you feel as well. I describe the show with three words as inspirational, emotional and unique. There's no show out there that's like it. Badass, strong bodies. Fun, fit, friendly. Sweaty, sweaty and tears. Transformative, inspiring, entertaining. It's f***ing brilliant. Is that three? What is the most shocking moment? Someone really seems to be making headway. They are smashing it. The weight is dropping off, the confidence is flying. What does she do? She goes near your cupcake. For me the most shocking moment of the show was when my client decided to let me down.  Seeing people almost throw up. Pretty shocking. The funniest moment is when one of my guys nearly passes out in his first workout. When my client attempted to do a high jump, let's just say he screwed it up.  It got sweaty and hilarious. There is so much scope for people to hurt themselves in my show and although I know everyone's sitting at home thinking, you're a terrible person, we all laugh when someone hurts themselves. We just do. The most emotional moment of the show is definitely the reveal at the end.  Seeing them have an internal transformation and find their power. It's so emotional when you see the people transform and they've oozing with confidence. Changing their bodies. Getting stronger, faster, fitter. Completely different people and it brings a tear to my eye. Start to finish. Candy floss vibes. Care Bears would be very proud. One thing that I learnt is that people want shortcuts. People always want the easy route and I'm sorry but it just ain't that easy. You have to have patience with people and respect that everyone is different. Everybody has their challenges and their struggles on their journey. I've been blown away by just how strong people are. One thing I learnt whilst filming was that not everyone knows what a burpee is. After this you will.  People should watch this show because it's something different where we try and do something good for people. You're going to get to see and follow people's journeys, see what people can become. It will inspire you most definitely. It's relatable. Who hasn't gained a bit of weight? If you want to learn about fitness and how you can transform your body you definitely need to watch our show.  It is everything about body confidence. It's everything you need. Inspirational, energetic and emotional you have to watch. And there's some profit lads in it.


And still talking about insecurity until Lia Sharibu is freed from the captivity of terrorists, the call for a release will be heightened. These were words at the launch of a book in her honour as a heroine of the Christian faith put together by cleric Pastor Afiu Kuteyi, the report. Arriving for the event, though a cherry one, but the cracks here is very unpalatable. It is a book launch in honour of 19-year-old Lia Sharibu, who has been in Boko Haram's captivity since she was 15. Four years on, the narration hasn't changed. Very little has been said about her since she's been in captivity. There have been rumours, something said, but do we know it is true? We can just say that there are rumours even up to now. So there's no verified information on her welfare and well-being of what exactly is happening to her until date. The 218-page book with seven chapters emphasises Lia's resoluteness in the face of captivity, a move celebrated more in the Christian Dome. Despite the pace of remaining in captivity, Lia still trusts God. Like many of us, the author observed that this young girl would not consider her life more important than her faith. She treasured her faith more than her own life and brought to bear the famous Queen Esther quote of, if I perish, the Nigerian government while counting on the support of other non-state actors need to intensify its efforts to secure the release of Lia and in good time too. The author asserts that although the flight of Lia remains the primary focus of this book, the heart of the author and I think and I'm sure the heart of everybody in his world also go out to every other victim of the heinous crime of kidnapping and terrorism across Nigeria and the world at large. February 19, 2018 in Dapche, Yobes state, a dark night where daredevils kidnapped 110 secondary school girls including Lia from their hostel. Other girls have long been released but one. There is a date for all those who are misleading our youth and who are politicizing issues of religion, issues of ethnicity and you know what have you and using these to divide us as a nation.  As a matter of fact, the way forwarder in the book, maybe you need to read the book for governments to pay more attention to the security officers, their welfare, remuneration, equip them better than they are now. Then as a matter of fact, social welfare for the people because the way it is now in the country you discover that most of our youths, able-bodied, they hide and so it becomes very easier for them, for the terrorist group to engage them and to employ them. In captivity, she becomes the heroine of faith as all eyes are on the government of Muhammad-U-Buhari to fulfill its promises of freeing Lia Sherubu. Loretta Chiyogo, Plus TV News. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Symposium on Applied Deep Learning in Bioinformatics, August 11, 2023. In an earlier video, I told you that we are organising a summer school on applied deep learning in Denmark. This was so popular that we unfortunately had to decline most applicants. However, we are organising a symposium too. So if you're interested in hearing about cutting-edge research from the Bertus Anders Delgado, Arne Elafson, Henrik Nielsen, Sampo Pysalo, Simon Rasmussen, Ole Winter, Jan Gorotkin and you sincerely sign up before the registration deadline on August 4th. There's no registration fee, the link is in the description and I hope to see you in Copenhagen.


Sure, one second. So welcome, everybody. We start today with our fourth lecture. Before starting, is there any question for the previous lecture or any doubt? OK. So not a doubt, but a clarification. So the entropy definition, which based on trajectory, clearly is not a state-dependent variable. But in thermodynamics, entropy is like a state-dependent variable. Why do you say it's not state-dependent variable? In a sense, it depends only on the state-dependent means initial and final state rate. Here, it depends on the whole trajectory, if you look at it. Yeah, yeah, but be careful. One thing is the total entropy production, which depends on the whole trajectory. And the other thing is the system entropy. System entropy is what its state function in a microscopic thermodynamics, classical thermodynamics. And here, in a way, it depends only on the initial and the final state, but it is through p. So it's p of x0 and p of xt at the final time. So you could say, OK, it doesn't depend. It depends only on the initial and the final. But it depends on the p. And the p depends on the whole trajectory. So in reality, it's not the case, OK? So it is different, essentially. So you have p of x0 and p of xt and logarithms. This is what is entering the equation. So it's not exactly the same thing as in classical thermodynamics, OK? OK. But be careful when you identify what is a state function and what is not. And be careful in confusing system entropy with entropy production. Entropy production is related to the probability for the entire trajectory. And system entropy is related to the probability at the initial time and to the probability of the final value of the trajectory at the final time. OK, it depends. So the system entropy depends on the solution of the focal plank or of the master equation at time 0 and at time t. Whereas the entropy production on the solution at all intermediate times, all right? OK, yes, yes. OK, I can go later in the whiteboard and we discuss this if you want, OK? OK, OK, sir. OK, any other question? Right, so then I'll go ahead. Today, yesterday we were a bit slower than expected. So I broke the lecture of baptism relations in two parts. So today in the second part, it will be much more relaxed. I still had that question about last time you mentioned in the reverse trajectory, we start with the x t, which is at equilibrium. But one thing is not clear to me in experiment. You measure. So you start with x 0, let's say, and go to x t. And at x t, you're going to measure the work till x t only, right? OK, OK. I have the answer for this in the next slide, OK? Be patient, OK? So this is a recap from what I explained yesterday, Krux and Jarsinski. And this is the setup. The setup is the following. You have a forward process. The forward process starts in an equilibrium state with control parameter lambda 0. This is what you see in the blue curve below. So we need an equilibrium time. And we start with a Hamiltonian with a control parameter lambda 0. And then we start driving lambda with a protocol lambda t for a finite time tau. This is what this blue line going up means, right? So we are driving the system. And at some point, we stop changing the control parameter and we freeze the dynamics with this value, which should be lambda tau, OK? So the main point that you have to realize is that in this process, there is only work done on the system in the ramp. In the beginning, in the equilibrium, there is no work done on the system because the Hamiltonian is not changing. So keep this in mind, OK?  The only work that you care is what happens in the middle, which is starting from equilibrium and ending in non-equilibrium, very important, generally in non-equilibrium. Unless the process is very slow, then you will end in equilibrium, right? This is the forward process. The backward process is as follows. You start with the Hamiltonian in equilibrium, but with a different control parameter with lambda tau. And you drive it backwards in time. Well, I mean, time goes always forward, but what you're doing is the time-reversed protocol. So instead of going from lambda 0 to lambda tau, you do from lambda tau to lambda 0, as I show here in this red curve on the right, OK? Again, we start in equilibrium, we drive backwards, and we reach a non-equilibrium state, but then we let the system relax to equilibrium. Very important, the only place where you do work is in the ramp, right? You don't need, in the backward process, to start in the same x that you ended in the forward process. Very important, OK? I hope this qualifies your question. I hope. Yes, sir. All right, all right. Then what you need to do is you measure the work in the ramp in the forward process. This is what I showed in the first formula, partial H with respect to lambda d lambda. So you just measured the working for a single trajectory. And you collect histogram of many realizations of the same process, OK? You measure in each of these trajectories, you measure the work from time 0 to time tau. And you obtain a histogram or a distribution. And then you do the same in the backward process. So you have a different initial state from a different equilibrium state. You drive it with this protocol, and then you collect the work from time 0 to time tau. This is what I show in the formula in the second formula. OK, just to realize that x dagger is the trajectory that you're obtaining in this backward experiment. Lambda dagger is the driving in the backward experiment and so on. Very simple. It's much more simple than what you were thinking about. OK, this is the setup. And the result is the following. This is what I showed yesterday. The distribution of the work in the forward process. So the probability to get a work for value w is related to the probability in the reverse process to get a work of value minus w. So when you plot the histograms, you see that they cut in the free energy change. This is a good prediction for all these type of models like Landjeven or master equations, right? OK, this is the setup for Krux. For Jarsinski, very important. OK, give me a second. Just be aware of something. In Krux, there is two physical process, forward and backwards. Two protocols. In Jarsinski, there's only the forward protocol. Only one protocol. And what we showed, and you can see it very nicely, I proved this from this so-called mother fluctuation theorem, but you can also prove Jarsinski from Krux. So you want to know the average of e to the minus beta work minus free energy. You average with the forward distribution. And then you use in the second line, I'm using Krux theorem. So I change e to the minus beta dissipation times pfw by p reverse minus w. So what you get is an integral over all work values of the distribution in the backward. And that's one, because it's a normalized distribution. So e to the minus beta w minus delta f on average is one. And as I said, I start and finish in equilibrium. Free energy is not stochastic here. So I can take out from the average delta f, and I get that the average of the exponential of the non-equilibrium work equals e to the minus beta the equilibrium free energy change between the initial equilibrium. And the final equilibrium, which is not the end of the protocol, is after relaxation, OK? I hope now it's more clear. But it is very important that you realize that all these theorems or relations have assumptions. And the assumptions you have to go through, read the paper carefully, and understand, OK? In this field, it's more important that you understand things that you are a mathematician, OK? This is concepts and physical research, physics, OK? All right, so now I will, for completeness, I will discuss experiments that people have done to test these results. So the first experiment, it was really a breakthrough. It was published in Science, which is one of the most important journals in science, in all fields of science, not only physics. In this paper, they did the following experiments. You have on the left a particle in an optical trap, a second particle connected to a pipet, and what they do is they link DNA between these particles and they pull the DNA, much like if you take a rope and you pull the rope, OK? But this rope is very small, so it's affected by fluctuations strongly. So if you pull like this, you won't get the same rope in each of the pulling, but it will be different because of the fluctuations. This is what you see in panel B on the top. You see that at some fast pulling speeds, for example in the green curves, the trajectories that follow the force, so here they can measure the force done in the colloid because the optical trap can be used to sense the force. The force is different in each realization of the same process. So this is a manifestation of fluctuations. And you can use these trajectories to measure the work done in each of the trajectories. And what they get is what you see in the panel D on the right, these are distributions of work or of the dissipation for different pulling speeds. And now you can use the formula that they show in the middle, which is just Yersinski's quality solving for delta F. And you just do e to the minus beta w. You collect values of w and you do the average not of w, but of e to the minus beta w. You do the average of that quantity, you take the log, you multiply by KBT, and you get the free energy. This is what is shown in the last figure. It's not OK. Back then, experiments were not as precise as now. So there is an error bar of 0.5 KBT, which they can argue. And they see that the difference between the theoretical value of the free energy and what you get from molecular dynamics and what you do from non-equilibrium pulling, it's very small. So the theorem was tested with great accuracy in this science paper. OK, this is for Yersinski's quality. And Yerski's quality has an issue, which is it is dominated by, so this average of exponential is dominated by very negative values of the work. So you need to find very rare events in order to have a precise measurement of the work. So this is, let's say, a negative, or not negative, but it's a shortcoming of this equality, that you really need to find rare events in order to have a very precise measurement of free energy. All right, that's for Yersinski. And for Krug's theorem, there was a very analogous experiment published in Nature, so also a very big journal here in which what they did was a very similar experiment, but with an RNA, well, I put here DNA. I think they did with DNA and with RNA, hair pins in which, OK, you can see top left figure. This is the hairpin. So it's like a rope, which is making like a loop. And they pull from the two streams, and they open it and close it. So you can see curves of opening and closing this hairpin in different colors. So you see the orange going up and the blue going down. So what you see, and it's very important, is that there is a hysteresis curve. So it's not the same when you do like this, but when you go back. And this is a signature of non-equilibrium in a way. So what you can do with this data is measure the work in unfolding and the work in refolding. And these are like they obey the assumptions of Krug's theorem. And you can collect the work in unfolding and refolding and plot the histograms. So what you see on the right, you can, for example, look at the red histograms. You see, first of all, the data is not perfect Gaussian distributions because it is very difficult to collect this data. So maybe they have 20 runs or 50 runs.  It is not a simulation. This is not an equation in the blackboard. This is very difficult to get. Maybe it takes years to make this experiment. And what you see is there is a red histogram on the right. This is the distribution of the work in unfolding. And a red histogram on the left with dash lines, which is the histogram, Krug's theorem is probability for minus the work in the reverse process. And you see they cut more or less in 110 kbts. Then this is done at a given speed. You see, or a given pulling speed, which is 20 piconewton-second. You can do this slower. And this is what is shown in the green curve. When you do it slower, the histograms change because you're dissipating less. So the average work is getting closer to the free energy. But still they cut in the same place, the histograms. They cut in 110 kbts. And when you do it even slower, the histograms get narrower, but they also cut in 110 kbts. So this is a manifestation of Krug's theorem in a way. They are cutting same system, but at different pulling speeds. The histograms of the work cut in the same place, which is the free energy change. And moreover, they can compare this cutting point. Well, they put it here in kilocalories small. You can convert kbts to kilocalories small very easily. And they can compare with what you get with molecular dynamics. Molecular dynamics is you do the simulation with all the atoms and molecules of the herping. So it's something very, very expensive and precise. And they see that the free energy that you get from Krug's theorem is within experimental errors the same as what you get with molecular dynamics. So it's really, really good, this theorem. It's good because you don't need to pull infinitely slowly. You can do this quite fast. It is very practical. And finally, on the bottom right, what you get is the logarithm of the ratio between the histogram forward and the histogram in the backward. And they are linear with W, as I showed you yesterday in the theory. So this is what you, something you predict in the theory and something you can see very clear in a very complex experiment because this is not just a Langevin equation. It's something much more complicated. It's a biopolymer in water with exclude volume effects, et cetera. So it's something really nice. That's why this paper was in nature, actually. All right, so there were more recent tests. Yesterday I was talking to you about a recent experiment, well, not so recent, but we did something like this with optical tweezers. It is not such a, now many labs are doing these experiments. So what we do is we have a colloid in a trap and then we move it, we move the center of the trap to the right, measure the work, let it relax, move it to the left, measure the work, let it relax and so on like this, okay? You can do this at different temperatures and collect the, he's going to have the work. This is what you see bottom right. He's going to have the work change when you do the process of different speeds or at different temperatures. And on the left, I showed the ratio between the symmetry function. So the ratio between this log of PFW divided by P reverse minus W. And you'll see the slope is changing because we could do the experiment at different temperatures. So the temperature has an effect on changing the, you see the slope of this curve, right? So with this, I finish from here and I'll now share my whiteboard to continue a little bit with the theory. So do you see my whiteboard now? Yes, yes, yes. Okay, thank you, thank you. Okay, so the first thing I'll do and it's something really nice, it's to explore the consequences of Yershinsky quality. So yesterday, I explained that Yershinsky quality says the following, W equals E to the minus beta Delta F. Okay, in other words, you can also, okay, me a second because this is not working very well. You can also say that exponential of minus beta W minus Delta F equals to one, right? Very nice. And now the first consequence that comes out and it's very simple and it's the second log and you can see it from the following. So first of all, let me discuss that this is a recap of mathematics, which is Jensen's inequality, which is the following. So if you have a convex function, as for example, the exponential function, there's a convex function like this, let me call it fc of x and this is x. It is very easy to show that the value, these are two points and you take the average of these two points, which is here. The value of the convex function at the average, which is something like this, is smaller or equal than the average of the, between this point and this point, which is the average of fc evaluated at x, okay? This is Jensen's inequality. So this is true for any convex function and in particular, we can take here e to the x is smaller or equal than average of e to the x, okay? Very simple, all right? So now we can apply this inequality to Jensen's inequality. So what we say is that e to the x will be e to the minus beta, w minus delta f will be one, okay? This is e to the minus beta, w minus delta f, right? And this is greater or equal than e to the minus beta, w minus delta f. So the average dissipation comes out here, right? So from this, well, you say e to the minus beta, this is greater, smaller or equal than one. So we are just saying, okay, this is the function e to the minus x, okay? This is the function e to the minus x versus x. So this, okay, to be greater or equal than one, this is one, this must be negative. Therefore, all the elements must be negative. So in the end, we get that w minus delta f must be always greater or equal than zero. So applying Jensen's inequality to this Jensen's case relation, we get the work minus the free energy is greater or equal than zero, which is nothing but the second law. So we get the second law out of this. W greater or equal than delta f, okay? So Jensen's equality and Krug's theorem are in a way a generalization of the second law because they provide more information than the second law and they give the second law as a corollary. So it's just convexity applied to this equality imply the second law, which I discussed before in my lectures, okay? Just simple math from here gives you the second law. All right, so now I'll introduce something which I believe is more exciting, which is the extent of second law violations. So this you can find in some papers by Krzysztof Czenski, which he called second law violations with quotation marks, okay? Okay, so let's recap a little bit and discuss the fact that the distribution of the work when you do a process infinitely slowly as this type of shape. So when the process is done very slowly, it goes on distribution, picked, highly picked at the free energy. However, when you do a process faster, you are out of equilibrium, you have here delta F and typically you will have distribution that will be like this, okay? This will be W and then we'll have, this will be B of W. Okay, sometimes I was putting PFW, but now there is no reverse process. I will just discuss one process. This will be the average work which will be, so the second law means that the average of this distribution is greater than the free energy change. That's the statement of the second law. And now what is very important is that this region that I put, okay, this region here, it's what it's often called this second law violation, see quotation marks. So these are events in which the work done on the system is below the free energy change in all these states, okay? And this can happen, you can do an experiment and find this. So the question that, okay, so first of all, let me just formalize this close, this is close to equilibrium, P, sorry, I don't need here at the F, P of W close to equilibrium. Get close to delta W and delta F. This is close to equilibrium, equilibrium. And here we will have non-equilibrium. Here the super sum won't be exactly delta W minus delta F. What we get in non-equilibrium is that the average is greater or equal than delta F, okay? And now I will ask the question, which is the following. What is the probability of the left negative tail? So how likely is that we are, for instance, getting values of the work here in this tail? I will call this distance xi, okay? And xi will be greater or equal than zero. So I would like to know what is the probability? It's the probability that the work, I can call it this PR, it's not the probability density, but it's the probability that the work minus delta F is smaller or equal than minus xi. Sorry, I did a mess here. So I have to take this out, exactly this, okay? What is the probability that work minus free energy change is smaller or equal than xi? What is the value of this probability? And this is what is called the extent of the second law of violations in some of the works by Kerstiarsinski, right? So I'll try to give an answer to this, and there is an elegant way to give at least a bound to this quantity. And the elegant way is just using Kerstiarski equality. So we will do as follows. So I would like to know what is the probability that the work minus the free energy change is smaller or equal than minus xi, okay? What is this? This is just the area under the distribution from minus infinity to this value. Just integral minus infinity to delta F minus xi of dw p of w, okay? This is the definition of what is the probability that the work is below the free energy by a quantity xi, right? So having said this, this is an equality, it's clear. And we can show because in this area, here, w minus delta F minus xi is negative here, okay? So work minus free energy is smaller. It's smaller than xi, w minus delta F minus xi is negative. So this means that in this area, let me do here a star. In this region, so w minus delta F minus xi or plus xi actually, sorry, plus xi. This is negative, which implies that e to the minus beta, w minus delta F minus xi is negative. Greater equal than one. You have this inequality in all this region. So this implies that we can do this here, integral from minus infinity to delta F minus xi of dw e to the minus beta w minus delta F minus xi, okay? W minus delta F minus xi, okay? Because this is greater than one, so then we can do this inequality and then keep p of w here, okay? So up to here we have a lower bound and now something we can do is delta F is a number, xi is a number, the integral is over dw. So all the w's stay in, all the things that are not with w, they go out of the integral. So we can say that this is equal to e of beta, delta F minus xi and then integral minus infinity to delta F minus xi dw e minus beta w p of w, okay? So let me just do this a bit better, sorry. Excuse me, yes? What was the definition of xi? Because I was supposed that it is the w minus delta F. No, so xi, xi is a number, it is equal to delta F minus delta F minus delta F. No, so xi, xi is a distance. So we are looking at, so this point here is w minus delta F minus xi, okay? Ah, I see, okay. Okay, so it's just a distance away from delta F, okay? Okay, thanks. Okay, so just parameter. All right, so we're now in this part, which is the integral of minus infinity to delta F minus xi of this. And now we recognize that this is a positive number. This is always greater than zero. And we can then say that all this integral can be bounded by beta delta F minus xi is smaller or equal than making the integral for minus infinity to plus infinity of d w e minus beta w p of w, okay? Because this is a distribution, this is always positive. This is always positive. So this integral is larger than this integral. I'm just doing an inequality between this integral and this integral, okay? So now we are here. What is this? This is e to the minus beta w p w and we can apply Krug's theorem. I didn't call this, okay, I can call this pf. The beginning I didn't put it, but this is, let me call it forward process. So this one is nothing but equal to e beta delta F minus xi and then integral, well, actually, I don't need to write it like this. So it's very simple to show that this last thing that I obtained is e to the minus beta w in the forward process, okay? I don't even need to do, sorry, I was a bit exaggerated with the notation. I don't need this, okay? This is just e to the minus beta w and e to the minus beta w, following Jarsinski's equality, is e to the beta minus beta delta F. So e beta delta F minus xi e minus beta delta F. This is Jarsinski's equality. So this goes with this, and we get e minus beta xi. And this is a very nice result. You can see, because we are saying the probability of second law violations, probability to get the work minus theorem to be low, a given amount is, you see, smaller or equal, smaller or equal, than e to the minus beta xi, okay? So in other words, let me just to capitulate probability that work minus the free energy is smaller or equal than minus xi is smaller or equal than e minus beta xi. So this means, well, this means, basically that the left tail of the distribution of work is more than exponentially suppressed in the thermodynamically forbidden region, okay? So values of work that are forbidden classically are very unlikely and are forbidden and suppressed more than exponentially. This is what this result means. So I recapitulate. This is the average. This is the free energy. So the probability to be below all this area and this distance is xi is a smaller or equal than e minus beta xi, right? I hope this is more or less clear. Okay, if not, please ask me any question. And this is one of the key consequences of the theorem. And now the rest of the lecture, I will try to generalize a bit what I explained by discussing what is called detailed and integral fluctuation relations for entry products. So the results I just showed can be also generalized slightly to entry production, which is stopped. So as you see in isothermal systems the entry production is work minus free energy. So if I get a theorem for the entry production and I take the particular case of an isothermal system, I will get a practicing theorem for the work and the free energy. Detailed and integral fluctuation relations for entry production. Okay, so again this is explained very well in the paper of Udo Seifert. The same I discussed the other day. It's BRL 2005. 2005. Okay, and the setup is what I also explained in my second lecture. The setup is a non-equilibrium driven Markovian process in which there are the obtained trajectories, which for example is X, X0. Sorry, I think you left your microphone on Macha Molybden. So there's some noise happening there. XT and the time reversal trajectory will be X plus 0 to X plus T, which is XT to X0 is the time reversal. And we consider a non-equilibrium driven Markovian process. All right. So again, non-equilibrium driven Markovian process, which includes those that are described by Fokker Planck equations or those described by master equations. Okay, this is a broad class of systems. So what can we get here is that if we consider a specific choice of initial and final states, we can use again the so-called model, like this one theorem, this one, and show that instead of putting now the dissipation, we can put the entry production. This is more general than what I showed before in my lecture. In my lecture, my previous lecture from yesterday, I put here the dissipation, but I proved everything with path probabilities. So it is much easier and much more natural to consider the entry production, which, remember, is nothing but entry production up to time T or associated to a trajectory till the X bar is KB logarithm of the probability for the trajectory divided by the probability in the time reversal process to see the corresponding time reversal trajectory. If you put this here, you can easily, very, very easily prove this theorem for functionals that are even on the time reversal. Okay, same thing as I explained yesterday. And now if you take, instead of omega, yesterday I took as omega, one of the cases was a delta of W function equal to the W, so the delta that the work equals to small w. Now you can take something similar but use omega to be, for example, the delta of the total entry production associated to a trajectory to be equal to S and delta plus the analogous as I explained yesterday. If you plug in this here, what you get is a very similar theorem as yesterday, but like this probability in the forward process that the entry production up to time T equals to S times E to the minus S and KB, be careful. Now S is a value, it's a number. Here is a function of a trajectory. Here is a number. A dummy variable, you could say, is equal to the probability in the reverse for the entry production to be equal to minus S. So same steps as yesterday. This gives the so-called detailed practice on theorem for entry production, probability in the forward process is dot T equals to S divided by the density in the backward for entry production to be equal to minus S equals E S divided by KB. This is the so-called detailed practice on theorem. This is very, very exciting. Sorry for this. This is the detailed practice on theorem for entry production. Of course, you can consider process with driving like the ones I was introducing yesterday and today in which you have something like this in the forward and something like this in the backward. This will be driving, but you can also have processes that are out of equilibrium in which the driving is constant. So for example, you can have something like this. This is the forward and this is the backward. So forward and backward are the same process. One example is, for instance, if you think about a ring, you have a particle in a ring and there is an homogeneous field, velocity field pushing in this direction. Here, there is no driving. The Hamiltonian is changing in time. It is a fixed condition of non-equilibrium and the single particle has more tendency to move to the right than to the left. Sometimes it will jump backwards, but it will do like this and backwards and this and backwards and backwards and this. It will move more clockwise than counterclockwise. This is called non-equilibrium steady state, which often people write it also like this, non-equilibrium steady state. In this case, the forward and the backward process are the same. So you say lambda plus t equal lambda t and this is for general driven. And here I will do for non-equilibrium steady states. The reverse process is equal to the forward process and equal to lambda. So it doesn't change in time, but you are out of equilibrium. In this case, forward and reverse are the same process and we write it just like this. We write it as t equals to s divided by p equals to t equals to minus s equals, there's the same p here. Very important. Same process. It's a question in the chat. Yes, please. Would you read it? I can read it to you. Would you please explain again how can we determine that the backward trajectory is exactly the forward process happening in reverse? Consider the fact that the process is happening in non-equilibrium state. Yes, okay, be careful because in this question you are mixing two things, trajectory and process. But okay, let me try to explain this maybe with an example, which I'm trying to find in my slides. One second. I think in these slides I don't have it, but I think a good picture, one second. Okay, I'm trying to find a presentation where I have a good illustration. So a good image is better than 1,000 words. This is what you say in Spanish. Okay, so let me stop sharing and I will share something else and share screen. This one. Okay, so for instance, if you have, sorry, this is something else. Don't be scared about the formulas and things. If you see this figure, this is like a roller coaster potential, no? So if you could put a particle there and let it relax to the minimum and flag to it there. But you can also put a torque around this ring. We don't see the picture. Sorry? We don't see the picture. Oh, sorry. All right, all right. You see it now? No, we see numerical tests, language and dynamics, and then it's all blank. There's no picture. There's no picture. Maybe if you don't, if you just show the... Okay, I'll try to... If you just show the problem without the full screen, I think it's okay. Okay, okay, okay. Okay, you see it now, no? Yes. Okay, so this is a particle in a ring and if on top of having the ring, one has a torque. So if the particle is here, it's feeling a potential but also a torque. And this torque doesn't change in time. This creates a non-equilibrium steady state because the torque is pushing the particle moving clockwise all the time. Or you can also think about this particle in a ring. There is a torque all the time pushing the particle. So there is someone pushing the particle with a net velocity. And this is a non-equilibrium steady state because there is a current. You could have this process without the torque and that would be an equilibrium motion, okay? No current. Particle will move the same to the right and to the left. But if I have a torque, I have a current and this is a non-equilibrium steady state. And here there is no time-dependent change of a potential. It is fixed. There's a non-equilibrium condition and it's fixed. That's why the forward process and the backward process are the same because it is not changing in time. Okay, I have another something else I could show you. Okay, I think I had an illustration in another talk. Okay, I think I can also discuss this in my whiteboard. So in other words, when you have a protocol, okay, sorry, it's not very nice but okay, this will be lambda of t. So you could have different options. So one option is lambda t equal to zero. And the other option is lambda t in here. This is I'm doing nothing. This means equilibrium. Okay, here this would be zero. Another option is lambda t changes in time following a protocol. Could be for example something like this. This is a general non-equilibrium process. Okay, this is a driven process. I'm changing the Hamiltonian. I have a parameter in the Hamiltonian that is changing in time. And this will be, I'm not in equilibrium. And I'm fixing the parameter at a value of this non-equilibrium. This is the non-equilibrium steady state. And you see, if I reverse this blue line, I get the same thing. So it's the same process forward and backwards. However, if I reverse the red line on the top, this is different forward and the reverse. That's why we use pf and pr. So I'm going to just make a reply your question. I cannot see the chat. So we hope. Thanks. Okay. Great. I'm trying my best to explain this. Okay. So, so far, I proved a little practice on theorem, which for non-equilibrium state states, which is simpler than general driven. It means the following for non-equilibrium state states. The second law tells you that if you do this non-equilibrium state state many times, you have trajectories of entropy production. It's a function of t of time. And you will have trajectory like this. The second law tells you there is a positive drift. And the probability of this event. To be at time t in value s is much, much higher than the probability of, for example, reaching minus s. This is much less likely. Okay. So you will see a lot of trajectories going up. You will see another one coming here. And another one here. So you will see exponentially more trajectories here with respect to here. And this will depend on which level you look at. So this is what the theorem is saying. p s dot equal to s divided by p s dot equal to minus s, is e to the s divided by kb. Okay. So the farther I put these barriers, the more different they will be. Okay. And be careful on this is not the first part. It's time. It's something else.  Very important. For crossing barriers and first passage, I can, I will explain in my last lecture, which is part of my recent theory. Okay. This is, you can cross what it means is you are here at time t, and you are here at time. All right. Very good. So now this was the detail for this on theorem. The integral for this on theorem is just the following e minus s dot. Okay. Okay. This you can anticipate is equal to one. No, this is the same as e to the mind. The same thing. We will have this s dot minus infinity to plus infinity, E minus s dot. So now the variable random variable is a stop, and then be of a stop. Now I use this. So PS e to the minus s is PS equal to minus s. So this would be the s dot. Sorry, not like this. P. So this is very simple. P of s dot minus stop. Okay. And this goes from minus infinity to plus infinity. So this is the same as the, as saying the integral of the s dot. The s dot for minus infinity to plus infinity, which is one. So this is the version is normalized. This is one. Therefore, we have this. This is true for non agreeable state states and for general Markov process driven process for this type with time dependent driving and for this type. Okay. Equal to one. This is called the integral fluctuation relation for entry price. Integral. Why integral because it's obtained from the detail by integrating. Just like the integral fluctuation relation for the replies. Of course, I repeat the same thing with Jensen inequality. So Jensen inequality implies this imply that. That's the second law is totally. Is greater or equal to zero. Okay. Good. So, so far, I think I've gone through almost everything I wanted. And just to let you know that as thought has a positive slope. So this is growing. This is what this means in reality. This is growing in time on average. This is the average of many. You will do like this. So it's a process that grows. And you should be a bit amazed by this because my did you have a process that grows in time. You have a stop. This was tea. And this is the process that it has the reasons but it has a tendency to grow. Okay. So when you have something that grows with time. You take a negative exponential. It to the minus a start. Okay. So it grows. It's growing. So it to the minus S. I would expect this to. To go down. No. With something like this. So remember a start at zero. Equals to zero. So this means that it to the minus a start at zero equals to one. So we start. So this one starts from one. But it on average. This one grows like this. This is the average of many trajectories of interaction. But here, this process is very special. The. The one that generates E minus a stop that is a stop interaction grows, but is negative exponential. Is totally flat. It's not changing in time. So it is equal to one. That's a, you should be a bit surprised and you should realize that. There is something special in this process. In entry production. Typically. When you have stochastic process that grows. Typically it's negative exponential decreases. Typically, but not in this case. And this is something very, very deep in reality. And it has something, some connections. This is because you will see in my last lecture. And this is related to something that is called Martin's. So we'll show that. And this is my recent theory with my collaborators that this process is very, very special. And it is a martingale process in non equilibrium statistic. Okay. However, okay, this will be the, in the last two, this will be a very technical lecture at the end, which I will show you very, very recent results and experiments as well. But please, and keep in mind that this is true. Also for driven processes, not only for. The states, but also for the process, as it is. So, more or less, this is it. I wanted just to explore and consequences of these theorems. And. So I leave the floor for questions, if there is any. And a lot of questions. Sir, can you explain why in the beginning for the experimental proof of the Jarzynski relation, you said the rare, like the rare fluctuations are important. I didn't get that part. Well, because you need to do this. Okay. So you need to calculate something like this. Okay. So this is the integral. T w. E minus beta. P f. Okay. So somehow you see this as an integral, but in reality, you have to see that you can do this from histograms. For example, and we'll have a sum of what is the probability to get the work of w w i. You're doing a beating and e to the minus beta w i. So there, there is a following that when you make this sum, which values of the work will be dominant. It's also ready to do some auto classification. So when that is very negative, this exponential will be very, very large. You see. So therefore, the negative values of work will be dominant in this, in this habit. But so probability distribution, it could be that itself could be exponentially decaying, right? I mean, could be, it depends on the case. It depends on the physical process. Yeah, depends. There are many examples. I can send you a reference if you want where this type of average, if you do it very nicely, just with regular beams. This can, can be this average is highly biased as well. So even though, even if you'd have infinite samples, there will be a statistical bias in this, in this average. So just to be very careful on how you, how you estimate this. Okay. And there has been a lot of research on estimating and using proper, with proper estimator of the probability distribution. So I can send you some papers. It is not an open area of debate right now, but 10 years ago, there was a lot of people working on this. So you have to be very careful. Also, on the following idea, I told you that, okay, you have crux relation. So you have forward. Yeah. And then the reverse and I was saying, okay, very nice. So reverse is cutting here. Great. But just realize something that when you do this type of experiments, you are saying that, okay, here is W. And here is Delta. Okay. So this will work. As long as these two are close enough. If you do the process infinitely fast. Well, you will have one histogram here. One histogram here. This will be the average of work. And here will be the type. So what do you do here? Imagine you do an experiment and you have histograms. This. So this is a big problem. So this means that these theorems are useful, but they have a limitation. And W is, if this is for example, a 100 KVTs. And I suffered this problem myself in my research in many times. This is 10 KVTs. You have a problem you will never see in a short experiment, you will never see this. So you have to use some techniques to extrapolate these histograms and see where did we cut.  You have to take into account these are universal relations, but they have a limitation for applications. And the limitation is that we can use this if we do the process infinitely fast. This doesn't work. Plus, okay. You can create turbulence, the fluid, et cetera. So it's not so easy. Okay. So close to equilibrium. This is easy to see. It's not out of equilibrium, but not so far. Okay. Okay. Just one last question is related to this. So. Negative entropy parts. I mean, trajectories are very rare. Right. So is it okay to say that. It depends on the system. Depends on the system because. Okay. Total entropy negative is rare. Okay. You're saying it still depends on. It's rare. But imagine I give you a model that is. I don't know. Two. And I tell you the rates are as follows. This rate is two seconds minus one. And this is 1.5 seconds. Okay. This is also two. This is two. And these are 1.5 1.5. Okay. What is a trajectory of negative entropy? So a trajectory of positive entropy will be. Going with the flow. So for example, going for one to two. And this is a cycle. And this is an entropy. It's taught in the cycle, which is okay. You have done a cycle. You return to one. So the system entropy is zero here. So the, sorry, the only. Contribution. Sorry. The only contribution that you have is three times the heat. So it will be three times logarithm. Of a forward rate divided by grade two divided by 1.5. Okay. And this is positive. Right. But now you can have a backward jump about what cycle, because there, this is two. And this is a 1.5. They're very close to each other. So you can have a trajectory going like this. Right. So it's not that rare. So you have the lives on the rates strongly. If you are close to equilibrium, you have much more likelihood to see negative entropy events, which will be a cycle against the flow and in that case, you will have a stock. Will be a minus three. to divide by 1.5 in this cycle okay and the probability of this and this one is very easy to calculate it's just you know it's a monk of change so it's the product of the position rates all right so it's not that difficult what counts is how asymmetric are the rates how different are the rates in one direction and in the other yeah yeah I understand actually the my question how I mean somehow these trajectories are related to works which are really rare in the sense when you calculate work from the same trajectory and entropy from that same trajectory rare entropy trajectories have somehow related to rare work I mean trajectories is well you don't need to think so much so so think about this this example so negative entropy is trajectories that aren't common and positive entropy status that are common so when you see a trajectory actually this is given in in the formula so the formula says the reproduction of a trajectory is kb the logarithm for the probability of the trajectory divided by the probability of the time reversal so if you see a typical trajectory this will be positive because the it's it's a probability of the atypical is smaller than of the typical but if you see an atypical atypical trajectory the atypical this one will be smaller than one so it will be negative okay because its time reversal will be more likely so it's it's all about how typical trajectory with respect to its its time error okay right then of course we we relate then this to to physics because every jump here we relate it to heat because we say kij divided by kji is related to heat e minus beta q i to j so this is the way we we connect to physics you know yeah so we can connect it to entropy I I get that but we like it's not like it's not a logical statement to say that high work trajectories will also be I mean they will be rare but not because of this reason no no they will be also from this reason also as well because with the work what I show you the other day is that the work for a trajectory minus the free energy change is divided by the temperature is the same as a stop okay in an isothermal system this is equal to this so there is a relation between work and irreversibility direct so there is as well so in a sense these two I mean trajectories for rare trajectories work and the entropy are like rare events right in the sense if the yeah okay but but but a rare event in the dynamics it's also a rare event in the work okay so if it's rare in in in the probability it implies that the you get a rare event in the work which is negative work so so if a trajectory is very rare this is very negative and the work is very negative very much very small with respect to to the depth that's the point yeah you can work with simple examples for example the other day I was talking with about the optical tweezers that you drag at fixed velocity you work you you you write the equation for the work and you will see rare rare events are this one the particle it's advancing so instead of lagging behind when the particle is here are rare events and these are events where the work is negative we're extracting work so you can really see the best way you see is with examples the best yeah right try to work this example and you will see okay so any other question so if not then we thank Edgar again for his lectures and we meet next week have a nice weekend have a nice weekend and see you on Monday I will discuss engines on Monday so let's stop here


Hey everyone, it's Hari Swaminathan from optiontiger.com. I wanted to announce the regularization of this earnings reports trades which just started this past quarter for the third quarter in October and November. But now I'm going to regularize this and it's going to run four times a year. So as you know there are four earnings reports every year and they come out starting in January, April, July and October. And in each of these you can expect to get about 12 to 15 strategic trade opportunities. Just in the one that happened so far, we took about 15 trades and I think three were losers. One was a break-even but net on an average of a 10 contract position I think we ended up with a positive $8000. But let's jump into the details of this service and I can explain it better. As we know earnings reports happens four times a year after every quarter. So the earnings season starts in January and goes into February and then it starts again in April, goes into May and it starts in July and goes into August and finally it starts in October and goes into November. Using options earnings can provide some very explosive opportunities. Now by definition earnings events are a speculative event and so sometimes you can have big hits and sometimes you can have big misses. But if you apply a consistent methodology using the volatility expansion and the volatility crush after the event you can construct some very good trades. And of course if trades don't go your way then you have to get into the standard trade management risk management practices and these are also covered in this service. So on each earnings report service you can expect about 12 to 15 trades on major stocks depending on what the outlook is and the analyst reports are. I am talking about the big liquidity stocks like Google, Apple, Amazon and many others then these are the stocks that we will be taking the trades on. The earnings course will run both on Udemy as well as my website www.optiontiger.com but there is an advantage or rather there is a disadvantage on Udemy where I can only send four emails a month. So I recommend you sign up on the website. The course will be $195 both on Udemy and the website and students will get the earnings max product for free and this is a $197 value right there and you are better off getting this product before the earnings trade starts and so this freebie earnings max will only be available on optiontiger.com. So if you sign up on optiontiger.com you will get the earnings max product for free. It is a $197 value and if you already have it then you can choose another max product as well. We also have an annual service here so if you buy all four quarters you can get it for a discount at $647 and there is a PayPal link right here that you can use to subscribe otherwise if you just want to go in for one service at a time it will be $195 and you can see it on this webpage and please also watch the next video which gives you an overview of the earnings max product itself. If you have any further questions please email us at info at optiontiger.com. Thank you.


Hi, I'm Matthew Coast, head dating coach and founder at CommitmentConnection.com and in today's video, we're going to talk about why men pull away after intimacy. And if this is your first time to our channel, make sure that you go and hit the subscribe button so that you can get more videos on how to have the relationship that you've always wanted. So let's get started. So why do men pull away after intimacy?  And it's usually after either some type of sexual experience that they had together, or it's because of some kind of emotional intimacy that they had together. And so I'm going to talk about both of them. We're going to talk about the sexual experience first, and then we're going to move on to the emotional experience. And I'm going to tell you a little bit about how to get over this hump, how to make sure that he continues to want to pursue you even if you guys have that emotional intimacy together. So first is sex, right? So when we can talk about this from a biological standpoint, when a guy, when a woman, when two people have sex together, there's this hormone that's released. It's called oxytocin, right? It's this bonding hormone. And for a woman, the more oxytocin that is released into her body, so the stronger the sexual experience that she had with a man, the more and deeper of an emotional connection she feels with the guy. So for a guy, it's a completely different experience, different biological experience that he has is because when oxytocin is released into a man's body, what ends up happening is his testosterone actually drops when oxytocin is released. And so testosterone is what makes a man kind of feel that drive, right? That drive to go after a woman, to court her, to be romantic with her, to do all those things with her. And so if his testosterone drops, there's a good chance that he's going to kind of pull back and pull away. And so the second thing that you want to think about is that there's a power dynamic that happens in every situation. So women before sex have a lot of power, right? So men are the ones that come and pursue, chase, approach. They're putting in all the effort. They're putting in all the work. They're doing everything before sex, right? And they're doing it to get this woman.  And it can even out, depending on how the guy feels about himself, about how the woman feels about herself, about how valuable each of these people are, the power dynamic can shift after sex. And so if there's not a deep emotional investment that a guy has in a woman before the sexual interaction, there's a very high chance that he's going to have kind of this sobering moment where he's like, whoa, you know, like, what am I doing here? Is this something that I want to continue to pursue?  And if he doesn't feel invested, if he doesn't feel like you're this amazing, valuable, awesome woman that he met, right, which can happen if you didn't connect with him in the right way, then there's a good chance that he'll end up pulling away from you, or completely ignoring you or disappearing on you, ghosting on you, that kind of stuff happens all the time. So let's talk about emotional intimacy for a second. So if a guy connects with you in a deep emotional way, why do men pull away after that happens?  And that's not really true usually. That's usually not true. What's usually the case is that a guy is afraid of getting into a relationship with the wrong woman. So guys from what I've experienced being both a men's dating coach and a women's dating coach is that guys take relationships and being committed very, very seriously, right? So a lot of times women come to me and they're like, oh, I slept with this guy and now I want him to commit. And I'm like, is this guy even a really good guy for you? And usually they don't even know. Guys tend to be a lot more logical about this, right? So they look at this and they're like, am I, you know, there's a lot of things that a guy needs. If he's going to get into a relationship, if he's going to continue to get closer to a woman, if he's going to look at a woman and want to get married to her, there's a lot of things that he needs to experience. He needs to make sure that she's the right woman. So there's this thing, right? So men need to make sure that one that they're in a good position, right? From a standpoint of like financial position, from a bunch of different, the biggest one I ever see is financial, right? So a lot of times women are like, they connect with a guy and the guy's not ready or whatever. And it's because he's not financially ready. And she's like, well, what is any of that matter, right? It's love. That's what's important. Well, to guys, it's not just love. Love isn't the only thing that's important here. There's also, you know, as a man, we're expected to be the providers. And even if we aren't expected to be that from a biological standpoint, we don't feel like men if we can't kind of take care of and be providers for women. And while that for a woman is like, well, you should get rid of that or whatever. And I hear women say that all the time. It's like, you know, should you get rid of feeling like a woman?  But a lot of guys, it's a real issue for them. And you have to consider that beforehand. And so the other thing that you have to consider beforehand is how does he feel about you as a woman, right? Are you the type of woman that he wants to get into a commitment with, right? Or some type of relationship or, you know, some type of marriage with, right?  And it's so much fun and all these things. But I can't find a woman that I really want to be in a relationship with, right? And there's a lot of different things that make a guy feel like he wants to be in a relationship with a woman. One is the, is he in love, right? That can be a big factor. But love isn't the only thing. It's by far not the only thing. I actually, I'm going to be doing a video here soon on what makes a man feel like your relationship material, but there's other things, right? Like alignment, right? Does he feel like you're the type of woman that he can grow with? Another one is, you know, his emotional experience that he has when he's around you. Are you guys fighting all the time?  Do you guys share similar values? Do you feel, does he feel like you're somebody that he can hang out with and be with and, and is a good friend to him? You know, those are all big things that a man can consider. And if he ends up getting emotionally intimate with you and he doesn't feel like some of these things are in check or right with you, there's a great chance that he'll pull away. It's not fair, but that's what ends up happening. What a man really wants is a woman that he feels is high value, right?  He will continue to chase you. He will continue to pursue you. He will commit to you. He'll want to get married to you.  Thanks for watching this video. If you're ready to know exactly what to say and do to attract the man and the relationship you've always wanted, click on the button on the right hand side of this video and go to our website.


Well, I have feelings about that, obviously a great start there and you finished the game well as well. Did you feel like you created enough chances in between the start and the opening and the end of the game, the last 15 minutes? Yeah, it was a funny game. I'm disappointed, you know, off the wall scrappy in the first half, you know, we weren't keeping the ball, we weren't clean with our passes, we weren't moving the ball quickly, we had a clear plan, particularly building up against them with a back five, we weren't doing that, it took us a long time to do that, it was, you know, a direct pass in behind, we know that we can get them in that way as well and that was good, but prior to that, you know, we were split open and they had a one-on-one with the keeper. That's just not us. So the discipline wasn't there, you know, we didn't play to the game plan, although we were one near luck, you know, there was a lot of work to do, I wasn't happy at all and I expressed that to them. Look, we had more of the ball than them, we had more shots on target than them, you know, all that sort of stuff. So if you want to look at the stats, but yeah, at home, it wasn't good enough and it's not going to be good enough if we're going to continue to be the team that we want to be. It was a kind of three and a half minute delay for that BAR over the offside, was it? Is it just taking too long to do it? Were you happy with the call in the end? Of course I'm going to be happy with the call, but it does take a long time. Yeah, a very long time. You know, a colleague spoke about the stoppages last week, Carl, Carl Vitt, and we trained to play a quick game. That's what we do. We want to play quick free kicks, quick throw-ins. Our whole playing style is based around that, but it is what it is. Obviously there was more to it they saw in there, but what can I say, you know, it's a process, we're quite used to it now. What do you do? You just got to get on and make sure that everyone's mentally switched on, you know, after breaks like that to get going again. But the other dissonant goal, were you aware of this new rule that the... Yes, yes, you are. So you immediately happened you were... Yeah, play on. Yeah, I was waiting for the ball to be taken by one of my players and quick play a quick free kick because they had a lot of bodies around the ball and we wanted to play quickly and I thought that was a great opportunity to play on the counter there. I just want to give someone else a chance. Michael, just what do you feel you need to work on most? And obviously your defence has been pretty tiny, one goal... With the ball, yeah, yeah, with the ball, yeah, yeah. We need to be cleaner, you know. There were patterns there that we worked on that were great and we broke through them, we just have to be better, you know, cleaner, more aggressive with our passing and just move the ball quicker, you know, and be cleaner with our first touch. Our positioning is good. The timing of the positionings and the runs and things like that, they're there but we're just not the first touch or receiving it with the right side of the forward or, you know, moving the ball a bit quicker and just getting it because we broke through them every single time when we worked on the things we worked on. We wanted to drag their wingbacks into our fullbacks and then create combinations around the side and every time we did that, we got through them and it was very, very good. But there's always a lot to work on. It's still very old in the season. It's a brand new team, a lot of players, but that's the main thing, you know, with the ball. That'd be a key focus for us this week. Excuse me, I don't do the AI on a day-to-day basis. What's the situation with the Byzantinian squad this year? Yeah, he's injured at the moment. Yeah. Any ideas when he's lying to you about that? Oh, you know, he's training, he's working hard. We're hoping in the next two to three weeks. Yeah. And everybody put up OK from today? I think so. I hope so. I was, you know, I lifted the tone of my voice a little bit at halftime, so, yeah, it's important that we get a reaction this week. We need to freshen them up. We didn't look sharp today as well, you know, as a coaching staff, and we all need to get together and review, you know, why that was the case today. It was a humid day, I'll get that. Probably the most humid that we've either trained or played in, you know, but that's no excuse. You know, we train them a certain way and condition them to be acclimatised for this kind of weather. And I told them, get used to it. In the wild west, it's going to get warmer and even more humid. So, you know, but we didn't lose, you know, but I do feel like it was two points dropped for us. I really do. Why have you seen from Brandon Borrello in his first three games with the CFC's ability to beat guys one-on-one has become really important and helps you guys kind of create some chances on that right-hand side? You just answered it for me. Thank you. That's what he does. He's a great character in the plays.  He gives us a lot of energy when you're taking third as well. He works hard off the ball too. Fantastic character. Really good, you know, he's... He's really developed his game in Germany. And that's what he does, you know, and he doesn't... He's not one of those guys that went over there for one year and came back straight away, you know, who stayed there for a number of years. And he's got that German mentality about him, you know. But he's a great kid and the intention is for us to provide the service for him to get back into the soccer ruse and back overseas where he belongs. But we need to refine a few things as well in him. You know, he's had a bit of a few little niggly injuries here and there while he was overseas the last couple of years, but we work hard on all our plays to get their bodies right, like Kallim, Yangi, there's a lot of these guys who haven't had a lot of football in the last couple of years that we've worked really hard to get them back in the park and doing what they do best. Thank you. Thank you very much.