Hello and welcome back to the craft box. My name is Brenton today We're on episode 29 of the privateer walkthrough last time if you haven't checked it out already. We Made our way over into Port Regal. We met Capbeard We did things and stuff and at the end I had to defeat 10 mollybone ships and that took forever But we've done that now off-camera. So yeah, that's basically what we've been up to and Essentially, I had a mark here the whole time. Good job. Essentially, we need to talk to Capbeard again Let us go and do that then So yeah, we we're kind of getting into like the main part of Port Regal now we Hopefully we should be doing a lot of things today. Hopefully. I really hate how we can only go three-speed in here It's really annoying Yeah, so anyway, that that will be cool once that's good I don't actually know what we have to do left I know we have to do what we're doing now and then we have to eventually go into Fort Elena, but I don't actually know I Don't actually know when that is Because that could be a while away or it could be like in just a bit So I don't know if we're gonna be doing that today or not. Who knows to be honest. I don't With cat like thread. Oh, I think I remember this one the name just rings a bell of struggle like I Really, I often remember like the quest names if they're like a struggle like If they're a struggle, I'll like remember them mostly Yeah, I Don't think I like let's Let's find out. Let's go and talk to Gilbert though bum bum We also got a new ship last episode, I believe so yeah, that's that's cool. It's lit It's actually really good. So it made defeating and collecting or defeating 10 ships so much easier because you have to do that again and again and again and Port Regal like it's just a common theme and Yeah, I would highly suggest getting a ship a new ship before Port Regal or when you're in Port Regal Just because it's a great idea Yeah, pretty much Bum-bum-bum-bum Okay, and secret entrance I know exactly what we're doing This has a lot of defeat them defeat them things so we'll probably skip a whole lot because I want to get a lot done today Yeah, I'm trying to get like all but Fort Elena basically up to Fort Elena done today I think will be a good idea. I don't know how How long that is or how like Like how much that's gonna take But like I just think that's a good idea. Do we have any companion training points? That is a great question. I Did press you right? Yes, maybe I don't know who knows We have zero that's a shame isn't it? Yeah, so this is a really cool. We little back entrance very bumpy apparently But it leads up to another secret entrance which happens to be Sewers Wow, what a surprise Wow, okay, so basically I mean I'm gonna go all out and we're gonna We're gonna finish all of Port Regal today just because we can And that gets it out of the way I think I think that's what we'll do and then episode 30 will be back and I'm cool ranch I think that's what I'm gonna do. So I will skip a lot of battles But yeah, we'll do this one first because first battle why not be mish he Job with the pelican remember yeah, we've already met him. He's not good yet still So yeah, he was the one who we met who's still Norville the pelican We probably don't know that well, we probably you probably don't remember because like We didn't actually listen to the dialogue, but who is that guy? And if you listen to the dialogue, he basically says that there as well So yeah, that was fun First strike nice. So last time we also got Yago who is fantastic Best private air companion In my opinion that I've seen so he just looks so cool. He's like so different To everything well, he was until we got contested, but that's not until like Ages away. So, you know, you know, he's just so different, you know, just different and I love a bit of different It's and diversity Let's do that we will do We'll do that we'll do that and We'll do first strike Don't want to hit the guy with first strike because it's probably not a good idea I don't want to take unnecessary damage. It's not good Okay, you're a half-file fantastic double tap onto him. That's good Okay, best flyer nice. We will also get double tap, which is good Fantastic look at that. I'm impressed. I'm happy one down Yago does so much. It's fantastic. They like the same. It's really funny Okay Okay, and what are you doing? No, please they don't know it to me We are going to hit him then if he's gonna hit me I will hit him. I mean Actually, probably dodges probably good. I'll just probably a good one to have we'll do that We'll do that and you can do that Fantastic Dodge is really good because hopefully Iago can get some repost. I think he has repost. I'd hope so But yeah, that would be good Fantastic both of them are half-health now, which is great Epic nice. We're just cutting like crazy. Fantastic burst fire. Fantastic. Look at that. He's nearly dead. Oh the dodge cheeky Wouldn't expect that one I've watched bye Bye You I'm One thing that I'm really upset about this uses this uses the models of all of the Presidio companions except Momo and I personally love Momo. He is like Great Momo is fantastic. Like his model is just Like we say it a lot and like when we in the Skull Island facing like the mortals, but like it's just so nice Like I just enjoy it a lot So yeah, that's just how I feel about Momo and it's kind of sad that we don't actually See him and with these guys Yeah, yeah Go that that that done, okay Cool, fantastic. Can you kill? Yes? Fantastic double tap, which is a bit weird, but that's fine Why are you dodging so much? What is your problem? Why do you have no accuracy? Do I need to accuracy you up? He's literally got No, we're gonna do that. Hopefully it's a bit more. That would be nice. That would be ideal We'll see if that works Okay, up and super hit nice Yay, he doesn't have bladestorm or anything, but like yay We can basically kill now. I will probably heal And so, yeah Get a bit of health back because half is great Especially since it's probably another fight. I think Okay, get some of these chests And we will continue on ones and to the governor's mansion But but but but but uh Millie. Hello. Let's um collect you Cuz Millie is great. Usually I do that at the start of the episode, but I forgot Millie I'm so bad We will Train for cool ranch. Can we do now? No, we can't I would like don't have enough. Um, I don't have enough Pet equipment things so Yeah, it's kind of bad Okay, we don't need to listen to you. We have good reasons. Let's get it done But captain remember this if any harm comes to that girl, you'll answer me for it Scond with Mabel that sounds really bad, but I don't know she know what a scond means. It just sounds bad Who knows? Um, I really like making your companions fall down. It's quite funny. Uh Uh Just just you know, I just like it Mabel. Hello. Bye.  Okay, I will skip this battle Just because I would face red coats multiple times before surely So yeah, I'll be back in just a bit. Okay. I am back We're out now. You had to defeat two red coats I thought, you know, we've we've done that so many times. I just skip it all because I mean we're skipping dialogue anyway So there's no point cutting in between But yeah, we go back to cat beard and we get new Okay, so I'm gonna defeat a billion armada ships and I'll be back in just a bit What's the side quest captain every okay then? But yeah, I'll be back in just a bit once I've defeated ten armada ships in the Port Regal Skyway. Yay lucky me I'm so happy. I am a back We just finished off defeating a whole bunch of those ships took absolutely ages But we are back did that and now we need to go and complete sabotage Okay, I think that is on the dreadnought so it's we way way So I'll be back in just a bit once I'm there Okay, I am back. We're at the dreadnought now. It's a sigil. It's it's not hard to miss. It's behind Port Regal, you know, just as yeah, if you're you must be blind if you can't see it but we're here and We are defeating these guys. I'll do one bit along camera. And if we need to do more I will do it off camera just because We're going quick. We go and quick. We're speeding through this area. I am sick of Port Regal I don't like it So we're going quick Got a speed sometimes So yeah, let us get some accuracy and dodge Always a good thing to have They're going to move up a bit these guys are probably gonna hit, you know, the other one might who will have a yugo. No, okay Maybe maybe still No, oh, yes, okay, that's cool attack blot repost nice thing Tastic So yeah, these guys aren't too hard. They have their level 25. So Nothing too difficult Which is good. Um, we're gonna do that. We're gonna do That that that What did I do oh Yeah, that's right. We're doing that. Okay. Good job Brent. Good job for getting what you're doing. Good job. Good job Okay, I felt fantastic Okay, you kill no, you can't unfortunate If we crit though, that would have been good. Oh the dodge on pointer. Yes Thank you overwatch First fire Okay Nice fantastic Look at that. I feel like the game sounds like really low And I don't actually know why so we're gonna bump them up a tad Just because we can doesn't make much of a difference, but maybe make my Things down who knows we'll just do this epic I'm putting a lot more now, which is Kind of well, it's not kind of good. It's good. I just don't know how like out of where I'm putting like what Wait, okay. Well, that's two of them down, which is good to lift just the Musketeers musketeers are always like some of the hardest things because Especially if you're going if you're like melee you they're quite hard to do sometimes they can't be Just gonna reduce their dodge because we don't want them dodging anything because that would be bad We can't have that one. Hopefully we crit a lot more Not that it makes too much of a difference, but like if we create that would be great Okay Don't actually expect Bonnie and to crit much because she doesn't have much agility And it's probably not enough to do the musketeers, but Yago the dodge on a Yago is so flippin good like yes, please Yes, please Fantastic and one left that was not too bad Okay, there we go done fantastic.  That's that done Let us collect the chests quickly roll there. Hello Let's go up here. Where are we going going up? Oh, we've got to go down. That's right I think there's a little battle down here, but I don't know. Yeah, there is I don't like this. Oh, I just want to go Oh There's another like three battles. Um So essentially Where are we even going? Oh, I miss the stairs. Good job. I was not paying attention and miss the stairs That is always what happens to me Um Okay, I'll be back once I've defeated these guys. Okay. I am back I'm don't know if we finished but um that goal was to destroy the powder kegs. Okay. We did fantastic So basically there's four powder kegs two in the back Around here and then there's like two on the sides and it's like really easy just super easy I didn't realize that's what that was so sorry about that one Then we do this one Fantastic and defeat more Basically what we do now is we defeat a whole bunch more and then we just set the whole place a light So I'm gonna skip all that because we've basically just done that now Um, and I'll be back when I'm at cat bed or whoever we need to talk to next Okay, we are back at cat bed finish that Yay level up fantastic Um, so yeah, this is essentially fort alana. I'll be skipping a lot of it just because it is super long Um, so I'll tell you more when I'm at fort alana. Okay, as I said, I am now back. Um We're at fort alana Beast of a place this is a dungeon and it takes quite a while So I will definitely be skipping a lot of what happens in here If you want to see the whole dungeon get all of the dialogue and see basically me play through all of the dungeon Go and check out the musketeer walkthrough Um It'll be probably titled fort alana because it was probably its own episode Um, so yeah to start off. We need to defeat recodes.  Who is this? Um, and essentially you just walk down here And you do things and stuff.  Dick said he's down the stairs. So yeah, essentially. We're basically freeing napoleaguan Worm your way down here. Um, so yeah, we'll do this battle on camera just because we will do some stuff Um We will do Sure, we'll do that we will You can stay where you are. You can move up. You can move up even more done. Fantastic. Okay Uh, so yeah, the red coats aren't hard. They're essentially just what you've been facing for like forever And they're in this battle as well, obviously so nothing too frightening So don't be afraid of that one They're just going in the fire. It's fantastic. Honestly. I'm impressed obviously English is not my strong point apparently Um, uh, we don't have another one that's unfortunate. We'll do accuracy. We can't hit with you. You useless person We can hit all of them and reduce their dodge, which is always good and we will go for corporal leg with iago Okay Um, fantastic So yeah, the red coats don't actually have that much health, which is fantastic I have a feeling that this guy kind of cheats, but I don't know Oh, if that was a block there that would have been good. Oh well Like I just have a feeling that he cheats. No, he doesn't maybe not. No, he doesn't. Okay Sometimes you just don't know Because I mean bosses aren't really documented Well in the wiki in my opinion I find it hard to like understand whereas like the wizard 101 it's like easy because like it's all loud and like Different color and it's all set out well, but like the pirate 101 wiki isn't as good Which is a shame, but I mean it's not that hard And I mean most of the bosses that cheat are like quite well known anyway, so Yeah, um, we will do That we will do that we will do that done. Fantastic. Okay Okay Double tap fantastic And burst fire nice, okay First strike fantastic dodge. Here we go. He's gone. Yay We defeated Clegg. That was easy. Yago is honestly really good at this level like So good Nice Um, millie. Hello. Nice to join. Nice of you to join us Uh, we will do this we will do that that and that done Fantastic. Okay Okay, and double tap into a super fantastic Oh, hello two down one to go Just as well we went for him Yago does so much damage honestly I'm impressed. I am impressed. Can we kill with millie? No, not quite. He had a bit more health than I Thought oh well. Um Okay, there we go. He's so gone. Bye. Yay. Amazing Uh And we will probably have to fight someone else not that wouldn't be a surprise Um Here's mustang sally though. So that's nice. Um Yeah, you do Okay, I'll be back once I've defeated these armada officers and troopers and marksmen and all that sort of stuff. Okay I'm back. We just finished off that battle and napoléguin Oh, hello. Don't really care about you. We will see you later. Um There's napoléguin fantastic being I love napoléguin honestly.  He basically says oh, we might see it later And we end up seeing him later Um, somehow he ended up trapped down there. Don't know how I don't really care Let's get him his hat. Um So that is a Yeah Yeah, so yeah, yeah, that's some fun So there's a companion training term there just so you know, I'm not like the best I don't know exactly where they all are, but like I know there's one there just because it's obvious But I'm not the best. So I'll be back once I've defeated these rig coats Okay, just finished off that battle easy peasy. Um Um, yeah, we we're not gonna think about that one He's getting worse.  That's fun. Um, okay And Essentially, I think we just have to leave at this point. Am I correct about that one? Let us find out now about that one And see if I can find it.  So I'll be back once I am finished and probably at cat bed again I'm assuming. Yeah, once I'm at cat bed, I'll be back. Okay. I am back. So You just have to defeat a whole bunch of enemies to get out, but we're back at cat bed. Um, and we're now level 32 Which is fantastic Um, and then there's a whole bunch dial Oh And then we are going over to Governor Stanley and port regal. So I'll be back when I'm there Okay, I am back Here we go with governor stanley. Hello. Bye. Bye One final matter captain and fear of the brass monkey has escaped from fort alena. We'll be careful Oh the brass monkey has escaped. Um, okay, I'll be back when I'm at gortez Okay, I am back gortez is all right here And that is where we're going to end off this episode. Um, thank you for watching. We got So much accomplished today Um, I'm really impressed at how much we did Uh, I mean it took me forever to record this video. So I I hope you enjoyed the kind of like short kind of snippets of what happened. Um If you enjoy that like comment, so I know that's what you want more of I don't know. Did you enjoy it? Who knows? Um comment if you liked it. Who knows? But thank you for watching me to leave a like and subscribe And if you've already subscribed press the little bell So you know exactly when I post another video and remember craft outside the box


When the narcissist forces you to have a child When they force you to have a child against your will Against your freedom of choice They will persuade you to have a child with them By using force or threats or they will emotionally manipulate you They will refuse to use birth control Or they will lie and say that they are using birth control Or they will say that they are infertile They will say that they are not able to get pregnant Because they don't care about how it will affect your life Or the child's life They don't even care about how it will affect their own lives They will emotionally manipulate you And then they will sexually abuse you They may even threaten and intimidate you This has happened to a lot of people Who have been victims of narcissistic abuse They have gotten pregnant against their will Or the narcissist has taken their control over whether or not they choose to have a child By refusing to use birth control Lying about using birth control Or saying that they are infertile Which then resulted in them having a child with someone Who they did not want to have a child with Which may not mean that they don't love or care for the child But what it does mean is that they have been trapped in a situation Where they've had a child with someone They didn't choose to have a child with Against their will And against their freedom of choice Narcissists are abusive They are possessive and controlling They will force you to have a child with them So that they can have power over you They can influence your behaviour And direct the course of events They want to keep you under their control They want to dominate you When the narcissist forces you to have a child with them It can make your life very difficult Because they will hold you financially responsible for the child And raising a child takes up a lot of time Which can then affect your work It could cause you to lose your job Which could affect your performance at income But the narcissist doesn't care They're not concerned with how their behaviour will affect you They will lie about taking birth control Or they will poke holes in the condom They will take away your choice to decide whether or not you want to have a child Because they want to maintain power over you They want to control the relationship They want to make it difficult for you to leave them So that they can secure you as their source of supply So that you always have to deal with them So that you can't get away from them so easily When the narcissist forces you to have a child with them They will abuse you financially They will steal money from you They will say that they need money for the child But then they will spend it on themselves You might have made it clear to the narcissist That you do not want to have a child with them But they will lie about taking birth control Or they will poke holes in the condom They will say that they are infertile To cause you to have a child against your will Against your freedom of choice There is nothing wrong with having a child It is a beautiful thing But there is something very wrong with forcing someone to have a child It destroys the experience And some people do not want to have a child Which is their right You should not force someone into parenting a child Because by doing that You would be taking away their free will You would be taking away their right To decide whether or not they want to have a child Which can be a very traumatic experience for them It is abuse And abuse is wrong Thank you for watching I hope this video resonated with you Please like, comment, share and subscribe If you would like to donate My PayPal link is in the video description Coaching inquiries You can email me at coaching.narsafiver.uk Thank you for watching and I'll talk to you soon


Turbulent Mixing and Beyond 6 International Conference 10th University Program. The program was supported by the US National Science Foundation, the US Department of Energy, the Abdul Salam International Center for Thoretical Physics, the New York University as well as the University of Western Australia. Financial support was provided. So Turbulent Mixing and Beyond Program is a scientific program that has been organized with a certain goals in mind. And the goal that we had in mind when we were organizing it 10 years ago was to expose the generic problem of non-equilibrium. Those days we were saying Turbulent, these days we're just saying non-equilibrium and Turbulent processes to a broad scientific community, to promote the development of new ideas and tackle the fundamental aspects of this problem, to assist in applications of novel approaches in a broad range of phenomena where these processes occur and to have a potential impact on technology. From the very beginning, the TMB program or Turbulent Mixing and Beyond program was a program that was established for scientists and by scientists that was established as a solely merit-based program and that is shaped by requirements of academic credentials, novelty and information quality. In fact, actually we do know that we study very complex processes and we would like to set certain standards of quality and quality criteria. TMB program was founded back in 2017 years ago with the support of international scientific community as well as national and international funding agencies and institutions. Today our community unites thousands of researchers from academia, national laboratories, corporations, industry at both early and advanced stages of their careers. If I would like to give some numbers actually for the TMB program, since 2007, as I mentioned, there was a substantial support from the direct sponsorship of the TMB program from funding agencies such as the National Science Foundation, Air Force, Office of Naval Research Department of Energy as well as institutions including the University of Chicago, NYU, Carnegie Mellon University, International Center for theoretical physics is our basic primary sponsors, CEA in France, UWA, ILE, Russian Academy of Sciences as well as there is an estimate for the participant contributions because usually the funding that is being provided by sponsors we apply for publications and for support of those who cannot support their travel to the conference where there is a significant part of people who are coming just with support of their own institutions. TMB conferences were organized in 2007, 9, 11, 13 and 14. They were organized as ACTP regular and hostage activities and as well as it was once organized as a school back in 2009. It also was once invited mini-conference of the American Physical Society meeting in the plasma physics division in 2013 and it also invited as a symposium on interfaces and mixes by the US National Academy of Sciences which will be held in November 2017. Since in these 10 years we published essentially 16 books and the 16th book that we have with us is this book and I kindly point your attention that even though it looks like very innocent it's actually the regular publication because it has an ISBN number and we placed this ISBN number very purposefully on this book because quite often the information, especially high quality information that is presented at the conference is sensitive. However, as long as we have an ISBN number this information is a formal citation record and as well as the record. In addition to these publications, of course, which have been published by the ACTP, we also published a number of topical issues, focus issues, invited issues in physical script, we published with the philosophical transactions of Royal Society and Royal Society Publisher which included theme issues and edited research books as well as we are preparing now the special feature issue in the precedence of the National Academy of Sciences in the US. So, if we will Google, even though it's not kind of really strict criteria but it's still a number, if we will Google today that for Turbulent Mix and MV-On we will find approximately 1,500,000 results or so. I believe that this number will be dropping out sometime in the fall but still it's a good estimate. So, TMB program, TMB conference, essentially they designed to build the bridges because the conference itself provides the opportunity to bring together scientists from many different areas including high energy density physics, plasmas, fluid dynamics, Turbulent, geophysics, astrophysics, optics and telecommunications and we did have these presentations at some earlier stages. Mathematics, applied mathematics, probability statistics, data processing and computations focus their attention on the long-standing scientific problem and as well as on the connection to reality and why we are talking about connection to reality because in fact we do tackle fundamental problems which play important role in a broad range of phenomena and for which actually there are no well-designed methods so we do need to understand how to formulate the standards of quality. The TMB community members, they are leading experts and researchers at advanced and early stages of their careers. There are also graduate students from developed and developing countries and this mixture of senior people and younger people is quite important for the success of the program. What is important for the program is that it's based, it's actually a science-based program. In this conference we found that in our communications that TMB related problems haven't come as a set of outstanding research issues. The solution can significantly advance a variety of disciplines in science, technology and mathematics and that our community itself involves participants who conduct highly innovative research and their interactions strengthen the community more. Non-equilibrium processes, these are processes that play a broad, a key role in a broad range of phenomena from astrophysical to atomic scales with conditions of high and low energy density including inertial confinement, fusion, magnetic fusion, light-material interaction, non-equilibrium heat transport, material transformation under impact, shocks, explosions, blast waves, supernova, accretion disks, early universe formation, stellar, planetary and non-business convection, planetary interior, mountain leader spirtectonics, premixed combustion, oceanography, atmospheric flows, non-canonical, well-bounded flows of supersonics and supersonics, as well as in many processes in cutting-edge technologies such as laser micromachining, nanoelectronics, free space, telecommunications, applications in aeronautics and aerodynamics, as well as in oil and gas, gas and oil production industry. So, in fact, a reliable quantification of these non-equilibrium and turbulent processes is a highly formidable task because the theoretical description is one of the most challenging problems in theoretical physics and the addressing complexity of this problem may expand the horizon of modern theory of partial differential equation, may encourage the development of novel perturbative integral and stochastic approaches, is actually calling for connections, for new connections to establish between kinetic processes at microscopic scales and processes at continuous scales. It also suggests and actually encourages the development of new methods for predictive numerical modeling for the error-estimated uncertainty quantifications. If you will be discussing non-equilibrium processes on the experimental side, these are very challenging problems because they are hard to systematically study, implement, and control in a well-controlled laboratory environment due to the high sensitivity and transient character of the dynamics and this sensitivity and transient character of the dynamics impose higher than usual requirements on the accuracy and special temporal resolution of the measurements as well as on the data acquisition rate. And in fact, we are now returning back probably in terms of the science development to the questions that have been asked by scientists maybe a few hundred years ago. How can we ensure that essentially we are getting the opinion-independent result? How can we ensure which is the scientific result is supposed to be? How can we assure that we might eliminate the influence of an observer on the observation results as well as on the data interpretation? So, from this perspective, non-equilibrium processes is an intellectually leech and highly fascinating problem. Its exploration may have a transformative effect on our understanding of a broad variety of physical phenomena on fundamental principles of mathematical modeling as well as on the technology development. And with this idea in mind, we have been working pretty hard. I hope we have been productive, efficient, I believe, in our studies on non-equilibrium dynamics. We have obtained and reported solid and fundamental results and have made and reported discoveries. And about this, we will be discussing actually during the conference sessions as well as during the roundtable discussions and, you know, the public lectures, et cetera. So, we have organized now the six International Conference Tense University Program. We have certain objectives in mind which are listed here. It's actually, and they are tightly connected to the goals of the problem. Our TMB conference actually consists of invited lectures that are usually, you know, 30 to 35 minutes long. Contributed talks that are from 25 to 30 minutes long. From posters, there will be one roundtable session on Thursday as well as open discussion. What the roundtable is, it's an informal discussion under which, at the end of which we are going to elaborate a set of action items to proceed further. And in addition to the roundtable posters, we will have also the two competitions, which are the competitions for the young poster, for the young scientist award, which is here, as well as the competition for the best poster. So, as I mentioned, you know, as a community, we are a part of a TMB community that unites currently about 2,000 researchers. Our mailing list contains over 5,000 emailed addresses and our community is growing while it still actually remains pretty, I would say condensed because its natural bounds are set by the requirements of academic credentials and quality of research. Now, at TMB 2017, we have about 150 people. We will have 195 contributions of 375 others, and it includes about 50 to 60 invited lecturers. So, all our participants include students and young researchers, and 30 of them will be competing with the oral presentations and 30 of the poster presentations for the best poster and actually TMB for your award. We have seasoned scientists, members of the leading scientific institutions, as well as the National Academy of Sciences, industry and high tech, as well as worldwide. And then we have such a broad international community, one of the important words that actually drives the behavior within this community is a key word for us, is essential respect, because, you know, we studied challenging problems and we would like to be respectful to our problems, to our results, to our work, and to one another. Here's a list of the organizers of the TMB program, which includes members of the Organizing Committee, Young Scientist Award, Best Poster Award, as well as Financial Support Committee. There is a member of the Local Organizing Committee, Ken, which is Marcelle. You have... Yes, I'm nervous so much, but actually, my point was that if you have any questions, then follow the members of the scientific advisory committee because of course we keep everyone who has been ever involved in this. And I can't ask you to applaud him, because here, while, you know, he formally will not be associated with the team. Okay, thank you so much. And also, we break the logistic systems from the ACTP because this is a really unique place worldwide and it's essentially always was and probably will be the point of East-West communication, especially these days, because the, you know, overall political situation becomes more complex, but ACTP in this situation remains the place where people really focus on scientific development, regardless the country of origin, gender, age, you know, and other sense. And we would like to express our gratitude to the Conference Support Office and Ms. Federica Del Conte, who did enormous really work because organizing, you know, 150 people, it's a huge work, usually standard ACTP activities are smaller in size, it's probably one of the biggest. To financial office, who usually very accurately handles all the finance that is provided by the sponsors as well as the ACTP. The Visa Office and Mr. Adriano Maggi, who helped many of you to get the visa on time. Housing Office and Ms. Titzana Batazian, Ms. Elizabeta Capella, as well as Publishing Office and Ms. Sabrina Wiesentyn and Ada Arden Ateli, Computer Office and Johannes Grasbenberg, who works at the ACTP for a very, very long time and, you know, many of you might just, you know, have an internet access to his help, as well as to the Science Dissemination Unit and Dr. Enrique Canezza, Carla Fonda and Marca Zanara. And I kindly point your attention that all the ACTP, all the presentations that will be handled here as well as in the earlier lecture hall, they are video recorded and they will be available online essentially one hour after the presentation. So we essentially have a live broadcast. We also gratefully acknowledge the support of the National Science Foundation, Department of Energy in the US, the International Center for theoretical Physics in Italy, the New York University and the University of Western Australia. So, TMB 2017 is organized to advance the state of the art in our understanding of fundamental physical properties of non-equilibrium processes, to have a conspicuous, positive impact on their predictive modeling capability and physical descriptions, and overall to have a better control and understanding of these complex processes. As usually, the success of the TMB program, because it's a program organized by scientists, for scientists and by scientists, consists just from the successful work of all of us. And I strongly encourage, and you are strongly encouraged by the organizing committee to highlight the strongest parts of your work when you are giving your presentations and when you are discussing your work with your colleagues as well as the students. So, welcome to the TMB 2017. I would like to actually also return maybe to remind one of the first letters which has been sent to me back in 2007 by Eugenie Meshkov. Yes, and I'm very glad that now in 2017 this will be the first time when he attends this conference. So, yes. Regarding the formal structure, I kindly ask you to open now the program and to proceed with me such that I could explain which is which, where and how. I do not have questions anymore. The program, this is the booklet. The program usually lists only the title of the talk and the name of the presenter. The booklet, there is a complete list of the contributors as well as the institutions. The booklet, there is a list of authors which you can find in appropriate presentations. The presentations here are scheduled as separated by the TMB scenes. They go by the last name of the structure before our standard routine. Actually, we have our sessions running from 9 to 10. 10 to 10, 30, there is a coffee break. And from 10 to 12, 30, there is a two-hour session. Then there is one hour and a half for lunch. From 2 to 4, 30, there is a coffee break. And then there is an afternoon session from 4.30 to 6. There are actually a few exceptions because while we try to keep the term of time of the coffee breaks and time of the lunch, the more or less set, they are not set in stone. In fact, we do prefer for people to spend time of the coffee break maybe as short as 15 minutes. If the coffee is available, it will go to the left-hand side to the first floor, there is a bar and also over there, there is a coffee machine. Now, we will have a parallel session. We will have parallel sessions, unfortunately, even though we will try our best not to have them. Yes, I will do it. Thank you so much. We will have parallel sessions. The parallel sessions will not be run, so there will be the sessions that don't have parallel sessions like this session, and there will be the sessions that will have a parallel session. So the parallel sessions, they will be scheduled, they are scheduled in earlier lecture halls. So in order to go there, we just need to go from there, from this hole to turn the right and follow the signs. It's a smaller lecture hall, however, and the presentations that are scheduled there, as a rule, there are several sessions which are dedicated to the TMB for use award, as well as there are other sessions where people present longer 25-minute talks as regular contributions. I strongly ask you, especially our invited lecturer, strongly encourage you to attend the TMB for you sessions. They are marked separately in this program, and please let us know your opinion about the works because the students and young researchers, they take the TMB for you competition very seriously. There will be the poster session, which will be in the poster hall around the main lecture hall on Tuesday at 5.30. There will be one public lecture, which will be given by Dr. Srinivasan, and it will be not only for us, but also ICTP-Wide, which is scheduled on Wednesday from 2.00 to 3.00. And there will be also the roundtable discussions, which will be from 5.30 until 7.00 p.m. in the Oppenheimer room. It's those who have attended the TMB conference in the past. You know what it is. It's actually the room that has a real roundtable. So we will be sitting around this roundtable. And we will have a banquet from 7.00 to 9.00 on Wednesday. And we will also have a reception, farewell reception on Friday from 7.00 to 9.00. So I think we are ready to start. And I would like, as a continuity of the session, to invite Professor David Campbell to start his talk. And I kindly point your attention that Professor David Campbell was one of the at our 2007 conference. Better movements. You're reading my title? Yes. I'm reading your title. Because these days he will be discussed, Professor Campbell from Boston University will be discussing intermittent mind-body dynamics at equilibrium. Thank you, Susnana. Thank you for all here. So good morning. Good morning. Good morning. Et cetera, et cetera. It's a real pleasure to be here, to give a talk at this turbulent mixing and beyond. As Susnana said, I gave a talk at the very first conference. And I actually talked on the same subject, the Fermi-Postulon problem. Although it's not apparent from the title. What that indicates is not that I'm stuck in one area, rather that that problem is so important and has been so influential that it's influenced the study of nonlinear dynamics and non-equilibrium phenomena since it first started. So let me first mention that this work was done in collaboration with Carlo Daniele and Sergio Sege Flach, and has already been published in Fisbeve. And at the end of the talk, there'll be a short quiz and you're supposed to tell me what those two fingers mean. So I want to talk about the context, because the equipartition and the thermalization in many body systems, and it was focused, I want to focus on the first study that really showed that this might not be a trivial problem, the pioneering work of Fermi-Postulon and the failure to observe equipartition. From those original simulations, there are four questions that arise immediately. I will have only time to focus on only one today, and this is what are the origin of these Fermi-Postulon recurrences, which I will tell you about. What happens if you crank up the energy density, that is the energy in the lattice per particle? Will the original data go to equilibrium? And finally, and this is a subject which is relevant to our non-equilibrium dynamics, how do you find equilibrium and what are the dynamics or what is the dynamics at equilibrium? Since I want to make sure I get to the results, independent of time constraints, what we find is that even in equilibrium, the FPU dynamics exhibit very large fluctuations, you can call it intermittent dynamics, which are driven by some sort of stickiness due to coherent structures that exist in normal mode space, so-called cube breathers, which I will explain briefly. And these cube breathers also explain the recurrences. If the coherent is not trivial, it's quite complicated. Thanks to a referee who challenged whether our results were general, we're able to show that in the Klein-Gordon system, which has a different form of non-linearity, again, these coherent structures cause sticky dynamics and these are intrinsic localized modes, so this is what I hope to cover in the next 35 minutes. So here are the three gentlemen, Fermi, Pasta, and Ulam. In 53, working at Los Alamos with a machine called the Maniac for mathematical analyzer, numerical integrator, and computer, they tried to study the question of how equal partition and thermalization occur in a very simple classical non-linear dynamical systems. Now, for those of you who have seen the movie Hidden Figures, or know the book Hidden Figures, this is the hidden figure in the FPU problem, Mary Singleton, she was Mary Singleton, she actually wrote the code that they ran, and there's a great article by Thélie Dachois in Physics Today describing her role. The Hidden Figures, of course, were the computers, the African American women who worked in the space program, but she was a hidden figure in the FPU problem. So this is a picture of the original L.A. U.R. preprint, the last from Los Alamos National Laboratory. I actually had the last paper copy that they distributed. Fortunately, I made copies of it before somebody took it. So here's the original preprint. Studies of non-linear problems won, you'll notice that. Here are the authors, and you'll notice that there are Fermi, Pasta, and Ulam, and there is Mary Singleton. She did the work, but she didn't write the report out, so it's the FPU problem. This is the abstract from that paper, and the important thing here is to notice that the key conclusion is the results show very little, if any, tendency toward equal partition of energy and freedom. This system did not go to thermal equilibrium, did not go to equal partition, and the question was why? And of course, the fact there were no further studies is sadly led to the fact that Fermi died in 54, and therefore the work was not continued. I won't go through the whole preprint, but I want to call out a couple of things. Here, notice the aim of establishing experimentally the rate of approach to equal partition of energy among the various degrees of freedom. This is experimental mathematics. This is the first time, really, that a computer was used to study an analytic problem that was untouchable, sorry, a problem that was untouchable analytically, and let me read you, if I can hear, what von Neumann said. Our present analytic methods seem unsuitable for the solution of important problems arising in connection with nonlinear partial differential equations, and in fact, with virtually all problems in pure mathematics. Really efficient high-speed computing devices may, in the field of nonlinear partial differential equations, as well as many other fields which we now are difficult or entirely denied of access, provide us with those heuristic hints which are needed in all parts of mathematics for genuine progress. So von Neumann wrote that in 1947, he knew the purpose of computing was not numbers, but insight. And one final point here, notice that at least Mary Tzingo got an acknowledgement for the work she did in coding the problem. Okay, so how many people actually know in detail what the FPU problem was? Wow, two hands. Okay, I'm glad I have, I am very glad I put in this introduction. So this is the FPU problem. It's a nonlinear chain, so I should say sorry, it's a chain of masses coupled by nonlinear springs. So this is a, so we have 1, 10 fixed walls and they studied n equals 32 and 64, mass m coupled by potential v, and of course v, the simple term here is Hooke's law, linear restoring force, but these cubic and quartic terms are nonlinear terms. Now FPU knew, it's easy to prove, that if you have only the linear term, the system could never go to equilibrium, you know that, you analyze, Fourier analyze the initial state, the Fourier coefficients stay the same, they just rotate with phases, so you'll never go to equilibrium. They knew that, but they thought that adding this nonlinearity would lead to immediate, almost immediate, equilibration. And this is a quote that Ulam wrote in Fermi's selected works. I'll take you, you can read it yourself, but the point is, what they found was a very surprising result to Fermi and he called it a little discovery in providing limitations in the belief that any kind of mixing and thermalization would happen as soon as you put in nonlinearity and this did not happen. So what actually did happen, how we study it? Well typically, we would study a system starting from its linear limit, so the two coefficients from the cubic and quartic terms are said to be equal to zero. We then get a simple equation of motion, which we all record linear, this is the linear phonon dispersion relation from solid state physics and if we look at assuming that yn has this form, we put a lot of spacing for convenience, then provided that we have this dispersion relation relating omega, the frequencies, to k, the normal modes or momentum, if we have this dispersion relation this problem can be solved. So now, if we have a weak nonlinearity, alpha, let's look at only alpha, beta is zero, and we expand in terms of normal modes, then this separates the problem into weakly coupled harmonic oscillators. Here are the harmonic oscillators, omega k has that sine dependence, so these are uncoupled, and here's alpha and there's a coupling coefficients which can be calculated, but coupled with normal modes. So for stronger nonlinearity, FPU expected that whatever the initial conditions, the normal modes would share the energy equally over time. And so the question is, what actually happened? So for n equals 32, I'm going to show you some results of the so-called alpha model excited in the lowest normal mode. Only the few lowest modes were excited. In fact, in the FPU problem, only modes one to five were excited. The original study, hand plotted, reprinted in Fermi's collected works, and it's a little hard to see, especially from the back, so let me walk you through it. This is the initial state all the energy is in the lowest mode, the simple sine mode that goes to zero at both ends. It starts there, precipitously this falls down, mode two starts up, mode three, mode five, looks like mode four comes biggest here, then mode three, then mode two, and then mode three, mode four, and then we come back to where mode one comes almost back to its initial state. This is in a very short period of time, you can't read this, but this has n equals 32 parameters, alpha is a quarter, and the delta t squared for the numerics was one-eighth. So you see what we have are recurrences in the FPU problem. This is the same problem, so it's a stronger non-linearity, you would expect this therefore would go more quickly to equal partition equilibrium. In fact, the repeat cycle, the referendum on recurrence is much closer in time, it comes sooner. These recurrences are to 97% the initial energy is back in the initial state. Now, in case anybody is wondering whether this is a Poincare recurrence in a non-linear dynamical system, Poincare recurrence is somewhere over in Slovenia. So this is a very, very surprising result, a shocking result. It really is if if you show the movie of a glass of water having been poured out, reassembling in the glass, going back to the initial state. Now maybe they didn't run it long enough. So in fact, later, and now Mary Menzel, Mary and single Menzel published the result themselves, they ran the FPU Alpha problem much longer and what they found was not an approach to equilibrium, but a super recurrence. So instead of having 97% of the energy back in the initial state in a finite time, much shorter than the Poincare recurrence time, they went to almost 99%. So these FPU recurrences were a huge surprise. They actually led to the whole development of nuclear science, to the development of the concept of solitons and Hamiltonian chaos from this. I don't have time to go into that in detail, but I will say that the FPU dynamics were well. So the point is they didn't absorb your partition, the energy stays localized. These unfortunately, thanks to Bill Gates, my simulations here are not active in the actual PowerPoint presentation. So what I'll do if I have time later on is show you some actual time evolutions of the motion in normal mode space and the motion in real space and you'll see that these things stay localized in normal mode space. So here are the three questions, or three of the four that I mentioned before. What is the origin of the FPU recurrences? Most people are familiar with the ideas of Zabowski and Kruskal, who in 1965, actually developing the word soliton, showed that the FPU problem was closely related, if you took a continuum limit, to the Kordaveg-DeVries equation, which is completely integrable. So in that sense, the Fermi-Postulon problem was in some sense for low energies close to an integrable system, and that's why it didn't go to equilibrium. Actually, a more precise explanation, due to Flock and his collaborators in 2005, called cube breathers, these are linearly stable, coherent structures in the FPU system in momentum space, in normal mode space. So periodic motions in normal mode space that are linearly stable, and they actually explain the recurrences quantitatively in terms of times, when they occur. A good question is, what happens as you increase energy? It turns out that's well studied. This was the original work by Izraelov and Chirikov in 65, which led to using the Chirikov overlap criterion led to the understanding of when you should have stochasticity and approach to equal equal partition in FPU. And then there have been many, many studies taking the original FPU data, not increasing the energy. Original FPU data will the Fermi-Postulon problem reach equilibrium. And there are a huge number of studies. The answer seems to be yes, but on an exceptionally long time scale. So now let me give you the warning because it's easy to confuse. These so-called cube breathers have nothing to do with quantum mechanics. They are coherent structures that are localized, typically exponentially, in normal mode space around some particular normal mode. So there are exact solutions, periodic solutions linearly stable around that involve some modes around the normal mode but are exponentially localized around that mode. Okay. So now let's do some serious work trying to see how we define equilibrium in the FPU problem and how we would approach it. Well equal partition means that all the modes must have the same energy on the time average, obviously not instantaneously, but over time the average would be the same. So here is the energy in a normal mode its momentum and its frequency times its location our frequencies have the same the same structure as before. This is the energy of an individual mode compared to the total nu k. So we will track two variables the participation ratio which just is the inverse of the sum of these squares. This tells you how the energy is divided up among the different modes if they're all equal and the participation ratio takes a simple sign simple structure. And then a logarithmic like quantity sorry an entropy like quantity which is defined by s of t which is nu log nu and we'll look at the normalized version of that which is s of t minus s max divided by that, eta is limited between 0 and 1 by its definition. So these two things are going to be our measure of whether we're at equilibrium. Now what do we mean by equilibrium? What we mean is that the averages exist, this is our definition of it you can argue about this, but this is a standard definition, that the averages exist and that they can be computed from the Gibbs distribution. So I won't go through the details, I have it on slides if people want to see the gruesome details, but if you calculate these quantities p and eta for Gibbs distribution then you find that eta is 1 minus the Euler constant over the log of the number of particles in the system minus s0 and the inverse participation ratio is 2 over n, where n is the number of particles in the system. Question of course, sorry I couldn't hear yes whereas what? The temperature? So this is a confusion this beta is 1 over kT, the other beta it doesn't have to appear it doesn't have to appear you have to do the calculation I can show you the calculation but you know the fact that a system can go to equilibrium at any temperature at any temperature you can define equilibrium and if you define equilibrium in terms of the values of these two variables in a Gibbs ensemble you get those results beta is 0, that's infinite temperature infinite temperature may be an exception, but I show you the calculation, it's surprising but if you think about it at any temperature a system can go to equilibrium that's the point and this is the result for the FPU problem independent of temperature sorry? for the selected? I mean you can define the same thing for 5 fourth, the point is if you define these quantities this is a participation ratio of the individual energies relative to the total and this is an entropy which was first used in the 90s by Cassetti and Poinot and the Italian groups you will find just by straightforward calculation that those are the values I admit it's surprising but if you think about the fact you know a system can go to equilibrium at any temperature then it's not so surprising I'll show you the gory details in private if it were so assuming that's true let's consider the manifolds on which eta and p, the averages over time achieve their equilibrium values which we'll call fn f of eta and f of p now these manifolds co-dimension 1 manifolds so they're generalized ergodic Poincare sections and what happens as a given dynamical trajectory moves through this very high dimensional phase space and equals 32 64 dimensional phase space it will pierce these manifolds an infinite number of times as the trajectory goes to infinity the time intervals between the piercings will contain information on whether and when the dynamics visits a sticky region of phase space if you have a very long time integral interval between two passages you know you've gotten stuck somewhere away from equilibrium there's something sticky out there in the original fpu problem n equals 32 eta should have this value 0.1218 and 1 over p is n over 2 so it's 16 so these are the values that we should see if we run an fpu simulation to equilibrium if it had equilibrium right? everybody clear on this? because otherwise I've lost you right? okay oh yes the next slide takes a long time to come up because the it's printed in details so these are actual from our runs of the values of eta instantaneously and p instantaneous values are shown in black which is why that slide took so long to come up because it's a bitmap the average values over a time window are shown in red and you see the eta you can show it starts at 1 and p starts at 1 comes down over time and the average eventually goes to this value which is in fact this dotted line is 0.12 0.1218 value okay p goes up to 16 you can see that the different colors are for different values of epsilon remember epsilon is the energy density the energy you put in the total system divided by the number of particles and fpu energy is was very small for larger epsilon you put more energy in the system it goes faster and faster to the equilibrium value right? that's the blue curve the red curve and the green curve you see small fluctuations around equilibrium and the magenta curve this is log 10 in time scale so this is 10 to the 10th units and the fpu epsilon is 4 times smaller than this epsilon here in magenta so it's way out here when it will finally approach equilibrium here's actually a calculation of the time to the equal partition using the t eta this is the eta variable going to its equilibrium value versus epsilon so here's epsilon in log of epsilon the open circles are data from paper of casetti at all I'll show you the reference in a minute they sort of predicted that fpu would be 10 to the 11th if you extrapolate this curve you get 10 to the 11th the black field data black field circles are our data again we find our guess is that tfpu is 10 to the 15th which actually would be actually to get to that value would require depending on how you do it between 14 and 80 years on our cpu or 3 months to a year on a gpu cluster these are very very very long time scales and that's of course assuming that there isn't another see this is the vertical this is the value of the fpu value of epsilon what they actually study is out here and you see it's going to be at least 10 to the 14th and notice that there is a kink in the slope that casetti at all did not see right here at about point 0.01 which makes our data go at a rise faster and we can't say for sure that there isn't another kink there so the ecopartition time is well beyond the scope of current calculations to make the value that fpu used now of course going back to this picture it'll come back yeah I'll come on back well I'll ask you to remember the picture where we saw that as you increased epsilon you went faster equilibrium this is the casetti at all reference it's a central reference in this field anybody wants to copy it down I'll leave it up for a couple more seconds so the message is you could tend to equilibrium but one of the initial important calculations grossly underestimated the equilibrium time and it looks like it's a lot longer so this is probably one of the two most important slides in my talk for the new results what we see here are the time intervals these are the time intervals between subsequent piercings of the manifold remember I said you have this manifold around and it pierces it these are the time intervals this is the interval number so t1, t2, t3, t4 and you can see that there are long excursions in phase space so here's an interval this is in time, this is the value of eta and you see that here's the equilibrium value for this whole long time period which is of order 10 to the 6th 10 to the 5th the system is out of equilibrium question? okay so if you plot the distribution functions for the return times of eta as a function of r of t you find that you find a power law tail for this distribution this is a fit of the power law which depends on epsilon for large values of epsilon it falls off rather rapidly so you don't go away from equilibrium very long and the first moment is finite but the second moment diverges if gamma is too small this is also true in the correlation functions now the difference between the red curve which is where you have eta above equilibrium value and the blue curve where eta is below its equilibrium value is pretty obvious physically namely it's much more likely the system will be away from equilibrium than more equilibrated this is more equilibrated than the value of eta you expect naive the thing that Kazeti did they assumed eta equals 0 was what they were looking for and that's not correct it's the 0.1 to 1a value so what is the origin of this stickiness? here's an example of the in normal mode space so there are 32 normal modes 1 to 32 here's the time and here's what you see excited you see strong localization in normal mode space around a high value of k this is for epsilon fairly reasonable and there's a definite localization in normal mode space the scale is such that the light colors are way up here at the top indicating that the energy is highly localized in one of these cube readers there are similar results for 5 fourth classical 5 fourth field theory on a lattice obeys this equation notice that the non-linearity here is what we call on-site it doesn't depend on the difference between two sites but it's on-site so it's a different kind of non-linearity so it's a different system in this system this supports so-called generalized modes or discrete readers here's a picture from an article that Sergei Flaouf, Yuri Kipscher and I wrote for physics today and I'll go through it in some detail what you see here is the 5 fourth equation for a certain value of delta x I think it's actually delta x equals 10 so it's a very large value I should say obviously as delta x goes to 0 this becomes a continuum equation this is just the discrete version of the second derivative so it's a partial differential equation but for large delta x this is a couple lattice problem like the FPU problem and here is the region as n goes to infinity this region becomes dense with the phonon spectrum and this is a phonon spectrum it has a finite mass gap from about the square root of 2 to the square root of 2 plus 1 over 10 squared square root so there's a finite region in which the phonons can exist is everybody happy with that? these are delocalized linear excitations and these arrows here are what's called omega breather these are the breather frequencies and what you see here are two kinds of breathers stare at these for a minute and tell me what you think the characteristic of this breather is and the characteristic of that breather so in this one what do I mean by that? this is the amplitude of the solution at this n equals 0 here is the next neighbor and then 0 beyond that here's another one amplitude of two sides what you see here is an optical like alternating discrete breather which has a frequency above the continuum here and an acoustic breather which has a frequency below the continuum these are discrete systems they are localized exponentially localized on the lattice now notice that if this frequency which is about 1.3 is below the continuum and all harmonics of it are above the continuum there's no way it can couple and it can't decay there's no localized mode in 5 fourth similarly this state is already above the continuum so all its harmonics are above it so it can't decay so these are stable modes and exist actually in any spatial dimension if we actually do the same simulations like as in the FPU case for the 5 fourth case we see the strong organization now in real space so this is now lattice sites 1 to 32 and we see that in this case at about n equals 22 it has most of the energy and it exists there for quite a long time and again the pdf of the distribution is power law this time as epsilon increases it gets smaller but the result is the same in terms of localization that there are these localized excitations either in normal mode space the cube breathers they continue the 5 fourth breathers which account for the stickiness and the deviation from simple dynamics at equilibrium so let me summarize I'm going to finish on time maybe a little ahead I introduced the idea maybe a little too fast of the famous Fermi-Pasta-Ulam recurrences and the FPU paradox namely that the system did not go to equilibrium we gave a natural definition of equilibrium in terms of the observables and whose behavior can be followed in time both eta and p we can calculate them at any time on any trajectory so we know their values and we found that they go to an equilibrium value but when they go to that equilibrium value there are non-trivial intermediate dynamics where the system deviates goes off equilibrium in a matter of time and that's due to stickiness of orbits that are related to locally stable coherent structures in both the Fermi-Pasta-Ulam case and 5 fourth we've actually tested this method with other observables and can be extended to other models and so what we have actually is a new quantitative way to probe out of equilibrium dynamics and the relaxation to equilibrium in high dimensional systems here again is the reference and with that I'll thank you and thank my collaborators Carlo and Sergio, Sergei thank you


topic I'd like to discuss with you how to use a scientific method or process to create knowledge and at the same time to use this process to solve problems. Nowadays understanding and competency on the scientific process and how to use it is now an imperative to function meaningfully in an increasingly science-driven society. Scientific knowledge is characterized by certain elements. Objectivity that means one has to be unbiased if you are to practice science and the products of science must be an objective or unbiased knowledge system. It must also be credible as well as reliable. These are important in the creation of the scientific knowledge so that the result will provide you a logical and reasonable explanation of what you can observe as well as provide a probable predictions of events using the knowledge system. Talking about scientific objectivity and reliability and credibility, this equates to the value of advocacy, critical thinking, faithfulness to the facts that you are using and the absence of personal bias. All this must be now inputted in the different steps in the scientific process mainly and most importantly is in the problem identification and formulation. I believe that research must be problem-driven. Secondly, in the hypothesis generation as well, in the hypothesis testing as well and more importantly also in how you interpret the results of your experimental or scientific activity. Carl Popper is a prominent science philosopher of our generation and he says that scientific objectivity is freedom and responsibility of the researcher to pose refutable hypotheses meaning that the element of falsifiability is always in the content and consciousness of the researcher. This means that any knowledge system must be in the form that it is falsifiable or it can be proven false rather than proven true. He also says that to test this hypothesis without relevant evidence and to state the results in an ambiguous fashion accessible to any interested person for them to evaluate for themselves. Thomas Kuhn who is also one of our science philosophers observed however that it is very difficult to be objective. It is always in nature that we look at things within our own perspective and therefore it is theory-laden. It is almost impossible to make observation without being influenced by one's belief or theory or mindset or paradigm. As you see here science requires you to be objective yet it is acknowledged that we have difficulty being objective because we are by nature biased in how we look at things. Walter who is a one of the professors at the University of Queensland says that all scientists are directive to gather observations from the perspective of a particular theoretical framework. In other words we see things from our own bias eyelets. We see what we want to see. We believe in what we want to believe in and we practice this every day without being aware that we are citing Albert Georgie who is a noble awarding physiology and medicine says that to see what everyone has to have seen to think no one has thought about is the way to go and practice good science. Thomas Kuhn relates this to what he calls revolutionary science and he suggests the need to question current thinking by proposing alternative thinking and this must be something that is consciously done by anybody practicing science to always offer an alternative to what we have concluded and this lecture is about the very critical role of always having alternative paradigms in how we practice science. Critical for one to be scientifically objective to my mind in the practice of science is equipping one with a mindset that is less blind. Being able to formulate scientifically revolutionary questions that shall lead us to formulate global scientific models with more powerful explanatory and predictive values. The aim of this lecture is to provide some ways and insights in how one can be objective in the practice of science. It is not the intention of this lecture to dwell on the philosophical aspect of scientific objective. The central thesis of this lecture is that scientific objectivity in the conduct of the scientific method must consistently consider and weigh the merits of alternative theories in the formulation of the scientific question, the hypothesis, and the testing of hypotheses as well and more importantly in the interpretation of the results. This is to avoid being dogmatically influenced by what Kuhn referred to as the pitfalls of the theory-led observations. The nature of science is that the most common misunderstanding about science is that scientists seek and find truth. They don't, they make and test models. Making sense of anything means making models that can predict outcomes and accommodate observation. Truth is simply a model and this is from Neil Chug Senfield who is an American physicist. So in other words, science is about developing models. It's about developing and knowledge systems as how we interpret what we observe. It is not truth. It is simply a model. Now if we look at the scientific process, the most common scientific process now is the hypothetical deductive approach and it must be in the context of this thinking of falsificationism. The alternative of course is the inductive approach but there are problems when we are to use the inductive approach and Hemtel in 1965 referred to the problems of the inductive approach as the latent polyphoenix. The most accepted now is the hypothetical deductive approach and following this process there are some steps one has to follow. First and foremost the problem in question identification and formulation, hypothesis generation and formulation, hypothesis evaluation and testing through experimentation and interpretation of the results. This is now what is most accepted protocol in the scientific process. Moving into the problem identification and formulation, the requirement is that it must be tested. What does it mean? It means it must be subject to experimentation and the indicators and the results are detectable, measurable, differentiating and discriminating. Another good example is the question is the water hot or cold. Is this a scientific question? Can it be it can be privately answered by different people and therefore not a scientific question? It is also not possible to design an experiment to answer the question how to differentiate hot from cold, how to measure hot and cold, how to detect hot and cold. Moving now as I said earlier that alternative paradigms are very critical. The ecological question why is there an increase in the abundance of an organism over time in a defined area and let us now analyze this in the context of alternative paradigms. We can look at ecology from different levels of integration or organization. One can look at it from the organismic point of view. We can look at it as well from the population point of view, a community point of view as well as an ecosystem level point of view and each level has different fundamental assumptions. So if we are to ask the question why is there an increase in abundance of an organism over time in a defined area and if we are to look at this from the point of view of organismic framework or context the question has to be looked at from the point of view of the physiological, behavioral, genetic and morphological evolutionary adaptations of the organism. And if we are to compare this with the framework of population context the question has to be looked at from the point of view of what is the intrinsic rate of increase in population regulatory mechanisms involved in the population meaning why is the population increasing and what are the mechanisms behind the increase. As you will see the organismic is more looking at the behavioral, the physiological and the evolutionary adaptations while the population context is more on looking at the system at the population level rather than organismic. Moving forward if you are to now to look at it from the community context the issue or the question of why population increase can be looked at it from the point of view of species richness in the community why there are many species there and how it relates to population increase it can be in the context of food work architecture what is the complexity of the food work and how you relate this to the population increase. At the higher level of organization one can look at it from the point of view ecosystem and now you answer this question from the perspective of what is happening to the energy level or flow in the system and the nutrient cycling and availability that allows the population increase. So this is what I meant by looking at alternative paradigms when we now look at a question in the conduct of our scientific research. Having said that the question why is there an increase in abundance of an organism over time you need to find a link can also be looked at it from another framework we can look at it as well from the evolutionary context at the moment there are two schools of thought of how evolutionary and adaptation evolve first school says that organisms are subject to evolutionary forces that will optimize their fitness in their environment meaning individuals and the population continuously evolve new properties that allow them to survive in an environment the alternative however is organisms are subject to evolutionary forces but the idea of optimization of fitness does not occur so if you are now to interpret that question the assumptions in the first school of thought is very much different from the assumptions that you are making when you are to adapt the second school of thought. Proceeding the merits of alternative context of frameworks and paradigms in the identification and formulating questions into scientifically testable form should lead one to be a critical analysis of the fundamental assumptions of one's worldview and often revolutionary science is attained when one goes to look at the basic and fundamental assumptions and this is drawn when we ask questions and bring out alternative way of looking at things in other words having done something one has to be cautiously always looking for alternative explanations and this is what drives scientific process productive by this process objectivity is promoted and eventually if observed in the conduct of the scientific process shall result to a kind of scientific model that is revolutionary with stronger exploratory and predictive properties moving now on to the second step of the scientific process having discussed earlier the importance of alternative paradigms in the formulation of questions let's now see how this can be important in hypothesis generation and formulation a hypothesis is a possible answer to the question or a solution to the problem reductively generated meaning using existing acceptable theories to explain or to provide answers to the problem or question and these are from fundamental assumptions that have undergone rigorous scientific testing and prevailing accepted knowledge systems there are certain characteristics of hypothesis first and foremost it must be testable meaning it is supposed to be falsified a common problem in the practice of science is that we formulate hypothesis in such a way that it cannot be falsified and the only way the only reason therefore would be that it is accepted now that is somehow for ourselves we have to formulate hypothesis in a way that it can be rejected conditions are well defined when to reject hypothesis experimental design must be in a way that it can reject rather than accept hypothesis the word concepts that you are using must be well defined measurable discriminating and differentiating let us take an example in the case of species identification taxonomies by experience we have some idea which is actually hypothesis of the identity of an organism whether it is where what family genius it belongs or even the species being an expert in a group of organisms after having done that the taxonomies will be out using a what we call a taxonomic key which is actually a knowledge system developed by scientists themselves in the group of organism that you are interested hypothesis is accepted when the organism fits the taxonomic key in the description of the different organisms hypothesis on the other hand is rejected when the organism fits the taxonomic key description of another species when the organism does not fit unknown or undescribed species to science as a resulting conclusion a series you will see parameters are well defined it is detectable measurable differentiating and discriminating what are the fundamental assumptions of the species concept model in taxonomy right first species are evolving or constantly subject to change in morphology physiology behavior and genetics as they adapt to their environment there are morphological differences between species and these are evolutionary stable and consistently observable in all individuals of the species this morphological differences or what we call key species characters are reliable indicators of the presence of a reproductive gap between species and the reproductive gap is the ultimate determinant of species at least for animals have we said that taxonomic species as it is defined and operationalized it's not inclusive meaning cryptic species cannot be detected by this instrument what are cryptic species these are more morphologically scenic species but are not interrelated and therefore they are they belong to different species the species concept as used by taxonomies may not be functional when we are to talk about microorganisms and to a large extent when we use it for plants the point here is that the fundamental paradigm of a species used by taxonomies is not exclusive and does not apply to all if you are to search the literature there are 126 models of what a species is there is what we call morphological species concept and this is based on the morphological similarities and ignores other differences such as DNA or inability to reproduce between individuals there is also what we call the morphological species concept any group of organisms organisms that currently or potentially are produced with each other there is also ecological species concept defines a species as a group of interrelated organisms that occupy or adopt to a single niche there is also what we call the recognition species concept a set of organisms that can recognize each other as potential mates there is also what we call affinity species concept a set of organisms that are phenotypically similar and that look different from other sets of organisms another one is phylogenetic species concept now hypothesis generation and formulation must also bring to the open the relevant alternative paradigms that generated the hypothesis and are contextualized from the paradigm or framework that one is using and I'm referring here in this example the species concept that you are using now what species concept to use one requires you to examine the more deeper fundamental assumptions of your frame such as your concept of evolution adaptation speciation and how you interpret natural selection a very important mechanism in evolution alternative context of paradigms must be considered to maintain objectivity and credible scientific knowledge in terms of the explanatory and predictive value of the resulting scientific model and knowledge the value of being mindful of the alternative paradigms from where the question problem and hypothesis are contextualized is a leading one to examine the most fundamental assumptions and understanding the working paradigm from where the question and hypothesis are based on and how this is differentiated from alternative paradigms being aware of alternative paradigm should lead one to identify and use measurable parameters that are discriminating and differentiating between accepting and rejecting hypothesis the alternative paradigms should lead us to formulate hypothesis in a form that is falsifiable as well as design experimental tests of hypothesis that clearly defines the scenario when to reject each hypothesis both in the case of mutually acceptable and not mutually acceptable hypothesis in closing your assumptions are your windows on the world scrub them off every once in a while and the light won't come in and this is according to Isaac Asimov and to Bernard Baruch millions of the apple fall however it was only Newton to ask the question of why and why probably what led Newton to ask the question is something that is quite inspiring in other words asking the question of why the apple fall when there are millions having seen the apple fall probably at the time Newton has a question his framework of looking at his role was quite different from the millions also the apple fall as well and this is the kind of science that we need in school we are taught to see things by teaching us the prevailing theories and laws of our scientific discipline it is our hope that students after understanding these theories and laws will be critical enough and creative to provide their own original framework of how to see things how they how to see the world and offer alternatives this is to my mind how major discovery in science is made


So we've seen quite a number of blocks initially and this time around I'm going to talk about the blocks that are located in the widgets section. Now these are blocks that we've been used to seeing on the front end of the WordPress like for example latest comments, latest posts, latest calendar, archives, RSS feeds, tag clouds and we usually find these under appearance and then we go to widgets and that's how we usually find them. But since our WordPress is going for front end editing or making sure that you can have any content that you want in any page of your website that you do have, these have been turned into blocks and any other widgets that are still remaining are also being converted into widget blocks. So for example if I wanted to find out the latest posts I can just hit that block and you'll see that we have the Hello World article showing up in our latest posts block right here. Now we're able to throw this and make it full width if we need to we can change this and make it into a grid view. For example if it had an image we can add all that content and see it here or we can just leave it under list view. Now of course when we click it's linkable to the new page that we do have here but I just want to see the other options that we do have. So for example we can choose to show the post date of that particular post. We can choose to show also the content and we know Lorem Sam is good and that's the content and we can even choose to say maybe we want to show 100 words of this particular post and maybe if the excerpt was a lot longer than this we could be able to determine how many characters we want to show. We could show the full post for example now we're showing the full post but we'll go for the excerpt and just leave it as so. We can sort from the oldest to the newest right now we have only one article there we can choose to say we only want that content that is in a particular category and we can choose and say maybe we want let's say five items of our latest posts. So these are the options that are available for us and we can add also the CSS class. So what I'm going to do is I'm going to update this, go to our posts and add just a new dummy post here. So we're going to call this a dummy post for widgets block. So we're going to add another Lorem Sam piece here and just make this have let's say two blocks of paragraphs in there and what I'm going to do is I'm going to publish and push it available and then I'll just add to this block itself I'm going to add a new category to this post I'm going to add a new category the category that I'll call widgets so that we can see some differences. I'll hit enter and on hitting enter update. So when we come back to our post here where we added the latest posts block you're going to see that this block actually needs to update itself. So right now we're showing this we want to see five items if I save this you'll see that because I chose demo content as the category we only have one item here but if I choose to say let's bring all the categories you'll see both articles showing up we can show from the newest to the oldest so it automatically sorts itself we can toggle on and off the dates when these were written we can choose to say we don't want the post content so we just have the title and the date and then we can save this. So all widget areas in our WordPress will now have the ability of having these widget blocks showing up in those areas. So if I reload our page here you'll actually see that all our posts are coming up and they're being shown. So this is something that you could use in your articles just to showcase and allow your users to follow up on any other content that you've made but probably wasn't available or you want them to switch from one category to another. The other block that I would like us to look at is actually in the widgets section is the categories block. So equally this works like the posts block, the latest post block except that this one just shows only the categories that we do have. So we can choose to show them as drop downs, we can show hierarchy, we can show the post counts that are available in them. So if we save this and then go back and reload our page you'll see that we have a drop down here and if we choose and say we want the demo content when we click on it you'll see it's going to bring in a URL, it's taking us to the category of demo content and that's how it simply works. So depending on what you want to use here it allows us to express and show our content on the front end in different ways so if I reload how this looks like you'll see that we have our categories and it's showing the number of posts that are available in each of those categories. So we'll take away the hierarchy and if we take away the post count then it looks as it should be. So we can show the latest comments, we can show our calendar, we can add a search bar, for example we can add a search bar in there, we can also add an archives category so this is showing the December categories that we've created and we can also show tag clouds and the calendar itself. So we're able to add this and we will see that on this different dates of course we had different posts. So that's how the whole widget section, what used to be widgets is being turned into blocks so we are able to apply a number of settings to this but most of them you realize it's only adding CSS changing whether they will be full width, left aligned, center aligned and that is what's available so try it and see what it does for you in your blog so you can see how you handle your content and express it on your front end. So one of the blocks that has really been stable throughout this whole process is what we call the short code widget. Now with the short code usually there are plugins that are developed to do particular things and once we run the short code it's able to do calculations and give us on the front end what we are looking for. Others are just contact forms, for example if you use contact form 7 you will see that you're able to put your short code here and it will be, you'll get a form on the front end that is sending back information. So currently I'm using Wukamas and Wukamas has a number of short codes it uses for example the Wukamas checkout short code and this allows for Wukamas to checkout on this particular page that you do have here. So I'm going to use the Wukamas underscore card short code here that will allow Wukamas exhibit my card on this particular page so if I update this and then come and reload this page you'll actually see that it's saying my card is empty so I have to go back to the shop and now that I don't have any products it makes it funny but ideally I would shop and then I would be able to see the information on my page so that's how the short code widget works so it doesn't have any extra settings you just place in your short code and it will run your short code functions and calculations or whatever it is you just place them on your front end and that's how the short code widget works


Hi and welcome to the session. Today we will learn about properties of addition and subtraction of integers. First of all, let us see closure under addition. This states that integers are closed under addition. In general, for any two integers a and b, a plus b is an integer. Let us take one example for this. Suppose we are given two integers minus 9 and 15, then minus 9 plus 15 is equal to 6, which is an integer. So, we can say that integers are closed under addition. Now, next property is closure under subtraction. This states that integers are closed under subtraction. In general, if a and b are two integers, then a minus b is also an integer. Let us take an example. Here we are given two integers 15 and minus 9. So, 15 minus minus 9 is equal to 24, which is an integer. Thus, integers are closed under subtraction. Now, let us learn about commutative property. This property states that addition is commutative for integers. In general, for any two integers a and b, a plus b is equal to b plus a. For example, let us take two integers minus 3 and 11. So, we have minus 3 plus 11 is equal to 11 plus minus 3, which is equal to subtraction is not commutative for integers. Next is associative property. This states that addition is associative for integers. In general, for integers a, b and c, a plus b plus c the whole is equal to a plus b the whole plus c. For example, suppose we are given three integers minus 5, 3 and minus 2, then minus 5 plus minus 2 the whole is equal to minus 5 plus 3 the whole plus which is equal to minus. Lastly, we have additive identity. So, let us see what is the additive identity for integers. Here, 0 is an additive identity for integers. That is, for any integer a, a plus 0 is equal to 0 plus a is equal to a itself. For example, for the integer minus 9 minus 9 plus 0 is equal to 0 plus minus 9 which is equal to minus 9 itself. Thus, we have that 0 is the additive identity for integers. Thus, in this session, we have learnt the properties of addition and subtraction of integers. And with this, we finish this session. Hope you must have understood all the properties. Goodbye, take care and have a nice day.