Hello everyone, I am Mrs. Meenakshi Shrigandi from Walton Institute of Technology, Shalapur. Welcome to the video lecture on Dynamic Implementation of Singularly Link List. Learning outcome, at the end of this session, students will be able to explain the dynamic implementation of Singularly Link List using C programming. Definition of Link List A link list is a linear data structure in which the elements are not stored at contiguous memory locations. It is a data structure consisting of a collection of nodes which together represents a sequence and are linked using pointers. In this example, it shows a link list. These elements are nothing but the nodes and each node is having a different location which are linked by using pointers. Definition of node in a link list A node is an element in a link list. It consists of two parts that is a data part which contains the information and the address part which is nothing but a pointer to the next node and hence also known as the next part. This is the node representation which consists of two parts that is the data part and the address part. The data part holds the information whereas the address part holds the address of the next node. Types of link list There are three types of link list that is a Singularly Link List which contains a single link to the next node. A circular link list Here in this, the last node is not terminated by annul. Instead, a link is taken from this and it is pointed to the first node. Singularly Link List In this, it consists of two links that is one link is going to the next node and the other node is going to the previous node. Let us see the dynamic implementation of Singularly Link List. For that, we need the structure declaration. Here we use a structure to declare a node and a node contains two parts that is a data which contains the information and the next part which holds the pointer to hold the address of the next node. So your structure is declared that is a struct node in this data and the next part are declared. Let us see the operations on the link list. Here we are going to discuss some modules. Those are InsetNodeModule which is used for insertion of an element in the list. DeleteNodeModule which is used for deletion of an element from the list. SearchNodeModule which is used for search for a particular element in the list. DisplayModule which is used to display the elements in the list. Let us see the first operation that is inserting a new node. There are three ways for insertion of a node in a link list. Those are at the front of the link list after a given node at the end of the link list. Recall and answer what is the algorithm for insertion of a node in a single link list. Pause the video for some time and note down the answer in your book. This is the algorithm for insertion of a node in a single link list. This algorithm is in detail explained in my previous videos. For more details you can refer my previous videos on insertion of a node in a single link list. Here we are going to discuss the InsetNodeModule. For that we are going to declare two pointers that is new and current and a variable integer x. After that we are taking the element from the user and that is stored in x. This is the value of the new node. After this we are allocating the memory to the new node by using the malloc function. So here we are creating a new node which consists of two parts. In the first part we are storing x and in the next part of the new node we are storing null temporarily. First we are checking if the list is empty. If the list is empty then the new node becomes the first node. So for that list is assigned to new. Else indicates that the list is not empty then we check for the proper place for insertion. For that first we are initializing the pointer current which is pointing to the head node that is list. Here we are checking if the value of the new node is less than the first node then new node becomes the first node. That is the case that the new of next is now assigned to list and list is assigned to new. Else we need to traverse the linked list to find the proper place for insertion. We need to traverse till current is not equal to null and x is greater than current of next of data. If this condition becomes true then every time we need to move the current to the next node. After that is done when we reach the proper place for insertion then new of next is now assigned to current of next and current of next is now assigned to new. Let's see the deletion of node from the linked list. There are two ways for deletion of a node from the linked list. First node of the linked list or from anywhere in the linked list. Try to recall and answer what is the algorithm for deletion of a node from a single linked list. Pause the video for some time and note down the answer in your book. This is the algorithm for deletion of a node from a single linked list. This algorithm is already explained in detail in my previous video. For more details you can refer my previous video on deletion of node from single linked list. Here we are going to discuss about delete node module. For that again we are going to declare two pointers that is trail and current and a variable x. First we are collecting the value of x from the user that is representing the value of the node to be deleted. First we are checking if the list is equal to null. If the linked list is empty then no node to delete. In that case we are only printing a message that no node to delete. Else indicates that the linked list is not empty for that we need to traverse the linked list. First we are initializing the pointer. Trail is assigned to null initially and current is pointing to the head node that is the list. And we need to traverse the linked list till we get the node to be deleted. That is still this condition somewhere that is current is not equal to null and current of data is not equal to x. If this condition becomes true every time we need to move trail to the current place and current is moved to the next node. After traversing if current is not equal to null this indicates that the node to be deleted is present in the list. Trail is equal to null. This condition indicates that the node to be deleted is the first node. If that is the case then only we need to make list equal to list of next. Else indicates that the node to be deleted is in between two nodes. For that only we need to make trail of next equal to current of next. Else indicates that current is equal to null after traversing the linked list. This indicates that the node to be deleted is not present in the linked list. Try to think and answer what is the algorithm for searching a particular node from a single linked list. Pause the video for some time and note down the answer in your book. For searching a particular element in a single linked list. Initialize x with value of the node to be searched. Initialize the current pointer to the head of the list. Travels the list till we reach the node to be searched or till we reach the end of the list. If current is equal to null then print node to be searched doesn't exist. Else print node is found. Here we are going to discuss the search node module. Again here we are going to declare a dummy pointer called as current and a variable x. First we are checking if the list is equal to null which indicates that the list is empty. If the list is empty then no node to search. Then print that no node to search and return back. Else indicates that the list is not empty. If the list is not empty then we need to traverse the linked list to search the required node. For that we are initializing the pointer current to list and we are taking the value from the user in x that is the node to be searched. And we are traversing the linked list till current is not equal to null and current of data is not equal to x. That is we need to traverse the linked list till the node to be searched is found or current is not equal to null. If this condition becomes true every time current is moved to the next node. If current is equal to null this indicates that after traversing if current is null the node to be searched is not found. Then in that case only print the message that node is not found. Else indicates that after traversing if current is not null the node to be searched is found. Then here we are displaying the message as node has found. Then the last module is the display module. In this we are again declaring our temporary pointer called as current. And first we are checking if the list is empty. If list is empty then no node to display. Here we are only displaying the message as list is empty and written back. Else indicates that the list is not empty and we need to traverse the list to display the nodes. Here we are initializing the pointer current to the list and we are traversing the linked list till current is not equal to null. Traverse the list and display the data pointed by current. Repeat this till current is not equal to null. So if this condition current is not equal to null this condition if it becomes true then every time we need to print the data which is pointed to by the current and after that is done current is moved to the next node. This process is repeated till current is not equal to null. Here it complete all the modules for the dynamic implementation of singly linked list. These are my references. Thank you.


It's YouTube. So we have to do an update video. This is like a monthly thing now here. I didn't want to be that guy, but judging from the comments and what I've seen on the analytics, people actually like when I talk about what's going on in my personal life, along with things coming up to the channel. It's honestly kind of mind-blowing because I'm pretty boring.  I truly mean that. So I left you hanging last time when I talked about the issues at home with my wife, Lindsay. Quick recap. Super quick. She has Crohn's. She's been on Crohn's medication, Humera for five years. It either A stopped working or B is causing side effects or C is working fine and there's something else at play. We actually still don't know. Six months later, she was taken off Humera. She doesn't really have much of a flare-up going on in her stomach, which means the Humera maybe was still working. That's great. Can't go back on Humera because of medication like that once you're off it. I don't know. I'm not a doctor, but apparently you can't go back on right away or at all. It's above my pay grade to understand the logistics of it. All I do know is out of all the doctors we've seen, no one seems to know Dick.  The problem she's having and has been having for six months is with her feet slash calves.  It looks like she stepped in an anthill and every ant on the block and their cousin came over and bit her up, but they're not bites. We don't know what they are, but they don't go away. They're incredibly painful and every seven or so days she just can't walk on them.   We are on a decent path though. They did keep her for three nights at a hospital at the, what is this place called, Mayo, I think? No, Mayo won't see us. Mayo Clinic, one of the greatest clinics and hospitals in America. Housed out of my hometown, Minnesota, rejected our plea. After several doctors stated the case, Mayo decided a month later after looking it over, we're kind of at capacity. We're not going to take any hillbillies from South Carolina, which is where we now reside. Perfect timing. So we're kind of up a creek without a paddle. That's an expression people said in the 60s. I still say it now. There actually is another Mayo, which is in Jacksonville, Florida. It's about, it's about four hours from where I'm at right now. So we thought, you know what, we're going to force their hand. We'll just drive up to the Jackson, Florida and make them see us. I guess it's drive down. We did. Left the kids home. They're old enough now to fend for themselves. And if worst case scenario, we have to stay overnight there. Actually, that would have been best case scenario, because then they would have looked at her with a team of people, then the neighbors would take over, watch the kids. Didn't come to that. We drove all the way down there. She was admitted to the ER. They see that she's down to 98 pounds, which is incredibly thin for my wife. Not that she's big, but that's just an unhealthy weight for anyone. And yeah, they just kind of sent us home. They're like, sorry, nothing we can do. Nothing we can do. So after a lot of shenanigans and hospitalizations, we finally have her on prednisone, which she wasn't able to keep in her system before. It's working now. It's not a cure. All it does is keep her feet from swelling to the point of, you know, discomfort and what's the opposite of mobility? Unmobility? I don't know. I'm not a doctor or a literate person. She is fine. She's getting better, but this is not a cure. Her feet are not cleared up. She still has Crohn's. She always will. And her new medication hasn't arrived yet. So in the meantime, I've just been kind of doing a lot of stuff around the house, the cooking, the cleaning, blah, blah, blah, blah. Why do you care? Why do you care? Well, because the channel suffers when I'm not on my schedule. Remember, I'm a pretty boring dude, but I'm juggling a lot all the time juggling. So between my real full-time job, where I design and develop websites, I also have this hobby on YouTube. It's like, it's like, makes an embarrassing amount on YouTube, but thanks to Patreon support, it kind of offsets the miserable ad sense. We're going to get to the Patreon stuff in a sec though. Okay, that's the update on Lindsey. She's actually doing better. She's doing quite a bit better thanks to the prednisone, but that cannot stay in her system forever. It's a steroid. Not good to be on those too long. So they still have to figure out what's happening. Oh yeah, they also found polyps in her lungs. We believe it's not cancer. I think they ruled out all the bad stuff, but they are going to do a biopsy. I believe this fry. I don't know anymore. I don't know. It's up in the air when they can see her. That's another fun thing. Everything's always scheduled like three weeks out, sometimes a couple months, because there's just a shortage all over the place. Again, great timing. Great timing to move. Okay, family drama out of the way. Appreciate everybody that has reached out and given advice, given support, talked about different diets. She's on a diet already. She doesn't have dairy.  Listen, she's got Crohn's. A carnivore diet is not going to fix that, regardless of whatever some yahoo tells you. Different diets will work for different people. That's not going to solve her problem, but she's been on diets for a very long time. She juices celery every morning. Apparently, that does something. It helps her. Whether it's a placebo effect or otherwise, as long as it's helping her, I'll drop the $35 a week on celery. Now to the channel stuff. Like I said, YouTube payout is embarrassingly bad. It's been bad for years. It used to be pretty good. Used to make, for how it works, if you don't know by now, is for every 1000 views a video gets within 24 hours, that can range anywhere from $3 to $8. So if I post a video day one, it gets like 1500 views, 2000 views. I'm looking at maybe $7.50. Day one is the most important time for your video, for 99% of people's videos on YouTube. Because that's when your subscribers are going to watch. That's when you jump in. After that, lately it seems like the video's dead. I don't know what happened. Any of my videos that are older than a few months are just completely irrelevant. YouTube doesn't push them. People don't search for it because everything is very much yesterday's, yesterday's news. I want tomorrow's news now. People are always ahead of things now. So anything that's older is just not, is not relevant. It's challenging because I used to have movie feuds that brought in a lot of money. It got a lot of new subscribers generated a lot of interest.  It's done. You're done with that. And so it was a waste of my time to do because it took a lot of time. And the subscribers didn't seem to be jumping on it like they were or they weren't getting notified, which was a problem for many years. There's a lot of issues. Some of it my fault. Some of it YouTube, some of it just the nature of things changing over the course of a decade. And that's all fair. The Patreon stuff that I offer definitely helps. You can also do it on YouTube via the YouTube Join membership. And one of the perks I've offered now is a Mithril membership. There's also an Unobtainium one. That one is purposely named Unobtainium because it's $100 a month. Obviously you can cancel it anytime. But the perk there is you can keep getting a new movie request every single month and you can do one show request. So if you want a new episode of Movie Feuds, I have to do it. I've changed how Mithril works. It used to be every single month you got a movie request. That became a problem for me to keep up with because it's a good problem to have. It means people were actually on board like 30 bucks a month. He reviews a movie. That's a sweet deal. It's too sweet of a deal. Now some people will be like 30 bucks a Kimmy or even 30 bucks to review a movie. Okay, here's the thing. I worked for ScreenRant for a full year last year. I was there. I was making my own show over there. It was called Real Rivalries. It was awesome. It got canceled. Like all the ScreenRant stuff got canceled because that channel is garbage now. I was doing the editing. I was doing the writing. I was doing the on-camera acting. So I did the whole thing from beginning to end and I was getting 350 a video. That's how ScreenRant pays out. Each person gets 100 and some bucks. So if you're an editor, 100 some bucks. If you're a writer, 100 some bucks. So it all totals out to 350. If you're doing all three, you get the whole honeypot. Now 350 a week to do the one video. That was sweet side money. It's not amazing, but it's a fair price for the work I'm putting in. So 30 bucks for essentially a similar video. Obviously I'm not doing as much extravagant stuff. There's no green screen. I'm knocking out. There isn't video clips constantly. I'm not writing them out as much, but I still take notes to these videos. I still have to watch these movies.  I don't even know how to illegally stream it. It's just, it's wild. So here is what I had to do and this rubbed some people the wrong way. I understand, but again, I wasn't expecting people to turn out for this. I'm so happy they did. Instead of raising the price, I just said, okay, if you stay with me on Mithril, you get a new movie request every three months. So that's more like $90, which still I think is a steal. And the whole point isn't necessarily so that you keep getting movie requests. That wasn't my intention. I thought it was to support me first and foremost, and then the perk that you get is the movie review. Regardless, it was just too much to handle. So I moved into every three months. Down the road, it might even change again. I just don't know, but that seemed based on the trajectory of things that I could keep up with that. Now here's my plea. Here's my request to people that are on Mithril. Thank you. I love you. You're the greatest.  Please. I beg of you.  I won't point out any movie requests from the past or the future. I'm just asking if you could maybe think about just how it would really help the channel and be fun. So when I came up with the Mithril membership, I thought, okay, people are going to let me have it. It's going to be fun. They're going to make me watch like 50 shades of gray or twilight or, you know, baby's day out or something funny that a lot of people remember because it's either nostalgic or trashy or it was in the, you know, it was in the zen geist of history. But instead I'm getting things that maybe, you know, went to select theaters in 1994 or were straight to DVD or it was some, you know, just like underground film that they saw in graduate school and it's just not interesting for a whole lot of people that subscribe to my channel. And worse, it actually hurts me in the algorithm. So how YouTube runs, and I understand this is a very long ranty video, but I'm laying out some knowledge here and you can take it and put in the bank, save it for later if you want, how YouTube currently operates is engagement. So if I put out a video like it's Ant-Man 3, MCU still does very well. If I was smart, I would just do MCU videos, but I'm not. Ant-Man 3 gets a few thousand views. Great. Avatar 2 gets eight to 10,000 views. Fantastic.  Watch time dwindled. Likes dwindled. Comments dwindled. YouTube sees that and they go, oh, okay, maybe this channel's not that hot. People don't seem to be interested consistently in this channel. I see he did okay for a couple, but now the next two didn't even hit a thousand views combined. Not a good look, sir. Not a good look. So then I stopped getting recommended in the algorithm. So while, yes, the support on Patreon's fantastic, and I did make this promise to watch and review whatever you choose, please don't. Please don't make it so obscure. Think about how it can be fun and helpful for everyone involved. That's my plea. I'll still review whatever you want if it's a movie, but I will be a little bit upset about it. Okay, that's it. Mithril is on YouTube and on Patreon. So those memberships are available in both places. What else do we have to talk about? Well, I have a second channel, Adam After Dark. It launched miserably because I got busy with a bunch of other stuff. That's non-movie related things. If you remember from back in the day, I used to do a show called Adam Rantz Issues, and it was just like the dumbest stuff you could possibly imagine. Buffalo Wild Wings, not releasing the wing count, which I noticed has come up again recently in the news. Taco Bell for getting to give me a straw.  Just random non-consequential things. I don't know if non-consequential is a word. Inconsequential is toilet paper not being the right direction, observational humor in a ranty, upset fashion that makes it sound like it's the worst thing in the world. I love doing that show. It's a lot of fun. There's a lot of videos that are completely locked behind the paywall. At $1 on Patreon and YouTube, $1 you get access to 300 videos. Adam Rantz, it's got movie feud stuff. It's got The Cringe, which is another show I'm bringing back to TikTok as a series, but that's way down the road. I'll talk about it when I actually get it done. But for right now, check out Adam After Dark, trying to get to that first 1,000 subscribers on YouTube. I'm going to be putting out at least one video a week there. That's the goal. This is still very much the focus. That was a lot to cover. I was shot out of the cannon, but I just want to end with things are okay at home. Lindsay's doing all right. Still don't have answers. Mithril's awesome. It's been a great boon to this economy, to my mental state. We just got to get it in a right place for everyone. We just got to make those videos a little bit more exciting and engaging for more people to watch so we can pull them into the channel, so we can lock them in. And one day, I can say, you know what? This YouTube thing, it was worth all the trouble. It was worth the hustle. We made it. And that Mithril membership actually will help me get there is the goal. Okay, anyway, that's it. That's everything I believe. And yeah, thank you guys once again for all the support. Please like, please sub, notification bell. I forget to mention that. The notification bell has not been rung. Only 10% of my subscribers have rung that bell, so that's another thing I have to point out. And hopefully I see you next time. Take care.


talk about diffusion from convection. So first of all, I would really like to thank the organizers for the invitation and also for the ingenuity in organizing this conference, and I'll discuss basically how diffusion can emerge from convective or ballistically propagating modes, which is the work ID together with Iacopo and Takato. So okay, the motivation behind doing this study is basically centuries old, so trying to understand microscopic origins of transport coefficients of our normal transport, ideal transport arises and what are really the kind of the physical properties of the system that influence it. And the thing that we wanted to do is basically tell something about these quantities without referencing or without dwelling into the intricate integrability structures such as form factor expansion. So and the reason for trying to do that is that possibly we might hope that applicability of the method that we developed goes beyond integrable systems, maybe also beyond single dimension, but also to reflect somehow from more physical perspective about some results that were previously derived in integrable systems. So at this point, I would also like to mention the work from Ben, where he puts some of the ideas I'll present in a more formal and more rigorous framework. So let me start by first discussing a couple of basic ingredients which basically underlie our approach without going into too many technical details. So the basic idea, as was the case in many preceding talks, is to somehow take a hydrodynamical limit. So and the way we do it is basically take, let's say an infinite system divided into small but still large cells and then look at what's happening to local operators that extend throughout these so-called fluid or hydrodynamical cells. So basically these are the operators that are just sums of some local or quasi local densities over these hydrodynamical cells. And an assumption that is usually used, that was also used on Monday at many instances is so-called assumption of local equilibration, where one assumes that locally the system, after long enough time, is described by some generalized Gibbs ensemble, where the description should be correct if one includes all of the quasi local conserved quantities. So one of the main properties, so GGE is actually a plastering property, which basically tells us that if you're considering some local properties which are encoded in local observables, basically you don't need to care what the value of chemical potentials is far away from your hydrodynamical cell. But this intuition expands from just local expectation values also to local connected correlation functions. And one can actually prove if one considers endpoint connected correlation function, that basically we can forget about all of the connected correlation functions that do not include quantities that are all localized at a single hydrodynamical cell. There are of course corrections due to the boundaries. So of course at boundaries there will be one over L corrections if L is the size of your hydrodynamical cell. So the second notion that is very important and was well, was basically already introduced on Monday by Takata is a notion of normal modes. So normal modes are just some excitations on top of a homogeneous background. So it would just say thermal state. Then you excite some local excitation and then you look what's happening. As Takata nicely explained what starts happening is that you see many peaks propagating throughout your system and basically how you can identify normal modes. You just look at the packets that are traveling with the different velocities and usually they are also spreading in some way, either diffusively or super diffusively. And how one can obtain these normal modes is just by diagonalizing the Drude matrix which is the time average current-current auto correlation function. Also the eigenvalues of these Drude matrix not only gives us the combinations of conservations corresponding to the normal modes, but also the velocities with which they are propagating through our system. So the second important quantity which will be at the center of my discussion is the Onsager matrix which carries more information than just the Drude weight. It tells us how these peaks that are propagating through our system are spreading in time. So basically it tells us what the width of this spread is. And in particular if this quantity is finite, I should also mention that the Onsager matrix is connected to diffusion matrix through the Einstein relation. So just by susceptibility of charges. So and if diffusion matrix and Onsager matrix are finite, of course transport is well okay the spreading is diffusive. But these two quantities are also directly related to what I motivated my talk with. So the transport coefficients namely Drude weight tell us about ideal conductivity while Onsager matrix tell us about normal conductivity in our system. So the primary idea behind obtaining the results which I'll show to you is something that we call hydrodynamic expansion. And the idea is to try to identify the modes or the operators, in some sense the operators of the level of correlation function, but this is already technical. So let's say just identify some operators which survive the hydrodynamic limit. So where we send the size of our hydrodynamic cells to infinity. And of course the operators that survive such a limit are quasi-local conserved quantities because they are actually conserved in the system. So if you increase it, there where we will not decrease. So what we did is we basically take a current in source as a current operator. We say okay we will look at what this current operator does to some density matrix. And basically what we do is is just expand the current operator in this equilibrium state in terms of this quasi-local densities, which also depends on the position of our hydrodynamic cell. In particular what turns out to be important is the first order in this expansion and the second order in this expansion, at least for what we want to do. There are also higher order terms, but one can show that they will not be important. And there is only a remainder and I will kind of, for most of the talk, I'll forget about this remainder. I'll only comment about it in the conclusion. So one can look at this hydrodynamic expansion also as expanding the density matrix around some homogeneous stationary density matrix in terms of local or quasi-local densities of charges. So after one done this expansion, one can simply take the expression for say through the weight matrix and insert the expansion into the definition. And what we actually can see is that the only contribution that is non-zero is the first order in this expansion when we are considering through the weights. And we were actually able to reproduce a well-known result which is obtained from hydrodynamic projection or Mazur bound, which basically tells us, so you can see here, it tells us that through the matrix is equivalent to the products of overlaps of charges and currents and then there should be a new source of sensitivity matrix. But one can of course always choose a nicer basis and in particular probably the nicest basis is normal mode basis which has a diagonal and normalized susceptibility matrix. So in the normal mode basis, through the weight is simply equivalent to the projection of current J, so Jk here and here, onto the conservation law Nk. Okay, here there should be some other. So this k is not the same as this k, sorry for this. And yeah, we should also project the second current to normal modes and this gives us the through the weight. So what's important here is basically that we have obtained some information about the dynamics in our system from considering purely statical quantity such as susceptibility or overlaps of the currents with our normal modes. But we can play a similar game by considering Onsager matrix. So asking ourselves, okay, how will these peaks that are propagating through our system spread with time? And it proves to be useful to redefine a bit our current basically taking away the ballistic contribution of our current. And if we do this, the Onsager matrix makes relatively simple. So we can play a similar game once again and obtain a result which is a bit more complicated. But in some sense, what's important is that actually from this result one can see the relation to the theory of non-linear fluctuating hydrodynamics, which on which I'll comment more later on. But once again, if we go to this nice normal mode basis, the Onsager matrix is simply equivalent to the projection of the current onto the products of conservation laws divided by the difference of their velocities. Okay, here I should comment that we're not claiming that this is a full Onsager matrix in general because we only took into account the part of our hydrodynamic expansion coming from the expansion of the density matrix or the current operator, which will expect the densities of local conservation laws. In principle, what could come into play is less local conservation laws. But for now, we don't care about it. So let's see how far actually this result took us. Well, I should also mention that this result is quite nice as well because basically we get the information, some part of the information in general, about how this normal mode spread simply by diagonalizing the Drude weight matrix, which tells us just about the velocities and the structure of these normal modes. So we see that we can learn some finer detail about the dynamics already just from Drude weights. Okay, so let me now clarify how our result manifests itself in different setups. Namely, there were quite a few results that preceded our study. So the first bound on diffusion constant, as far as I know, was one by Tomasz in 2014 where he lower bounds the diffusion constant, in particular the spin diffusion constant by quadratically extensive conserved quantities. And indeed, one can make a natural connection with our study because as I showed you before, what we have here is basically the products of conservation which is a quadratically extensive quantity. So because n is quasi local, the product that took quasi local is actually quite extensive. But one can even make a quantitative connection with this result. And then there was also a result which connected diffusion constant or lower bound with the diffusion constant by the curvature of the Drude weight. And once again, in special cases, one can immediately see this result from our study. So the systems that are under the most scrutiny in this conference are integrable systems and in integrable systems, the exact expression for the diffusion constant or Onsager matrix has been obtained using the thermodynamic form factor expansion and also via kinetic approach. And what we can show is that actually the expression that we obtained saturates the Onsager matrix, which was exactly computed in integrable systems, which means that the only contribution to diffusion constant or Onsager matrix actually comes from the fluctuations of local conservation laws. So the second order expansion of our current or of our density matrix in terms of densities of conservation laws. Okay, there is a further insight that we got from this result, which is understanding a peculiar relation between diffusion constant, which we observed year and a half ago, between diffusion constant and Drude self-weight. So the diffusion constant was shown to be, for some cases, connected to the curvature of the Drude self-weight. And indeed, if one analyzes our result in a bit more detail, one sees that this will happen whenever one of the normal modes, so whenever, so when the requirements for this overlap between the current and the products of two normal modes for it to be non-zero is some, let's say, symmetry restriction, which fixes one of the velocities to zero. So if this is the case, then what we claim is that the diffusion constant is equivalent to the Drude self-weight, which is a particular quantity similar to Drude weight, where instead of taking integral time average of current-current-alto-correlation function, one just looks at the current-current-alto-correlation function locally. So finally, there is also a relation to the non-linear fluctuating hydrodynamics, which has actually been an inspiration for doing this study, and in particular, performing the expansion of the current. But before I tell you a couple of words about non-linear fluctuating hydrodynamics, let me just mention KPC equation, which was already presented for integrable and non-integrable models on Monday by Vira Nyakopo. And what's important, the important point, one of the important points about this equation is that it actually corresponds to the universality class, which is not diffusing. So it's super diffusive, which means that the spreading of your normal modes is faster than in the diffusive case. And what has been observed historically is that actually anomalous behavior emerges in numerous classical one-dimensional systems, in particular unharmonic oscillators and so on. And this has been explained by Herbert with non-linear fluctuating hydrodynamics, so which, well, one of the statements probably the simplest one one can make is if there are no symmetry restrictions, if we are away from any special point, and if we have a conservation law, one-dimensional systems will exceed its super diffusive behavior. And the way one obtains this is in the spirit very similar to what we have done. So it's basically expanding the expectation value of the current in terms of conservation laws in stationary states up to the second border, and then adding some phenomenological noise and diffusion, which was already discussed by Acopo last week. And one can see that basically what we get if this G, which is just the second order expansion of the current with respect to the conservation laws is non-zero is something that's essentially K-PZ equation. So if this is the case, non-linear fluctuating hydrodynamics predicts the divergence of the diffusion constants, but even more it gives us the dynamical exponent. But also if we look at our result, we can see that whenever we have, so let me go back to our equation, so whenever we have two normal modes, let's say, which have a non-zero overlap with the current, and they have provided that they have the same velocity, we see that this expression will actually be divergence. So everything works out consistently. And so let me stress again, and this result is not specialized to just integrable systems. It holds also for non-integrrable systems. Okay, so let me now go back to our expansion and basically make an overlook of what I hope can be done in this direction. So the first question that was kind of put under the rug is what are the other contributions to diffusion constant? And it's clear that there should be other contributions to diffusion constant. In particular, if we consider models with zero due to weight, then the convective contribution to the diffusion constant, so the expression, the main expression that I was showing you is zero. But we know that in general, when we have non-integrrable models, at least we should expect diffusive behavior. So there should also be other mechanisms giving rise to diffusion with non-integrrable models at least. So one option is that there are some dramatically extensive conserved quantities which are not somehow simply related to local conservation laws.  So there might exist some quadratic extensive quantities which are not simply given by the products of two local conservation laws, which might give rise to diffusion in non-integrrable systems or even noisy systems. Another question which is I guess more straightforward is to address the question of higher cumulants of the current. So we're able to obtain, through the weight, obtain some contribution to the diffusion constant, are there contributions to higher cumulants of the current. And finally, it would be very nice to go beyond one dimension, in particular at least to the flat length, to the two-dimensional one. Because we know that there are, first of all, a couple of very interesting results coming from ADS-CFT, some universal bounds on diffusion. And secondly, transporting two-dimensional systems is also related to one of the greatest questions in condensed matter physics, which is high temperature supercomputing. Okay, so with this I would like to finish and thank you for your attention. Thank you. Are there any questions we have? Yeah, let's say three minutes for questions. Just unmute yourself and ask. So can I ask? Yeah, I'm Lorenzo here. Yeah, so very naively, is there maybe any way where you can use this expansion of the reduced density matrix in terms of quasi-local conservation laws to compute one-point functions in given an equilibrium steady state, say? In equilibrium? Well, I mean, so any, say, Heisenberg chain you want to compute local one-point functions, say, sigma xj, sigma xj plus one. Well, in principle, you would have to, I mean, what I was assuming here is that you can anyway compute the overlaps of currents with charges. And in particular, that would mean if you wanted to calculate expectation values that you have to calculate also the overlaps, which is even harder.  So maybe your method allows us to give some idea. I mean, I don't think it makes calculating the expectation values. You mean not the dynamics, it's just the expectation value, either thermal states or GGE states? No, it doesn't simplify it.  So I think, I mean, I don't think you can profit anything from this analysis. Thanks. Other questions? Hi, Marco, could I ask you a question? Yeah, of course. So the divergence of the diffusion constant you mentioned, is that cutoff dependent in any simple sense or sorry or not? The divergence of the diffusion constant that you described went with the copropagating mode. Yeah. Is there any simple sense in which that cutoff dependent or cutoff? You mean by in the number of conservation laws? For example, for like the like the spin diffusion constant. Okay. Yeah, so now we haven't dealt with the divergence and emergence of KPC using this in integrable spin chains. So what I was discussing in the scope of non-linear hydrodynamics is the case when you have just a couple of conservation laws in that. And if you have some diagonal contribution, the diffusion constant will diverge. So I think, I mean, as you know, I mean, this business with KPC and spin chains is quite technically involved and yeah, one should in principle introduce some cutoffs. Yeah, can I just add, so when you have these divergence, at least in the with fine number of conservation laws, you can actually work out a little bit more and bound the super diffusion exponent instead of trying to bound the diffusion constant, which you find something divergent, you can find the super diffusion exponent, but you have to use some kind of Hilbert space construction with that. I don't know how to do this in the in the form that Marco was explaining here. Yeah, so there is that that's explained in the paper that by Ben, which I showed in the show. Other question.


Hey guys, what is up? Welcome to my channel. For today's review, I am going to be testing out the Natasha Denona Glam palette for you. So if you want to hear my thoughts, see how I did this look. I also talk about a little bit of a comparison between the Sultry palette and just keep watching. This is my first time filming in 10 days. It feels so good to be back in my element and what way to bring filming back than to bring in the newest Natasha Denona palette. At this point, I really kind of feel like a veteran when it comes to reviewing Natasha Denona palettes. If you're new to my channel, I actually basically have reviewed every single palette that Natasha Denona has come out with up to this point. So I do think I have pretty good experience with Natasha's formula at this point. So it's pretty easy for me to judge upon first impressions. So like I said, this is a first impression, but I do have a lot of background knowledge. So this guy, of course, the Natasha Denona Glam eyeshadow palette, it is $65. I love that basically every palette she's come out with is now the smaller size. She also has the Love palette and I believe it's called the Sunrise palette in this packaging. And I just love that it has holes in the back and you can put a needle through and you will be able to pop the individual shades out if you would like to do that or rearrange the shades. This is my favorite packaging probably because it's the most sturdy and I like getting a large number of colors for a smaller price. Because beforehand she was doing palettes that basically were like twice the price with bigger pans and I like smaller pans. I have a big eyeshadow collection. This is available on the Natasha Denona website Sephora and it should be coming to Beautylish very soon if it's not already up right now. It's only available online, but it will be available September 14th in stores if you want to go check that out. It does not say it's limited edition. I think honestly this isn't going to end up being limited edition because it's kind of a staple that her collection needs. So you have very nice light gray silver packaging. When you open it up, you have a nice big mirror and then you have your 15 shades. Online this is described as an everyday palette that creates super dramatic smoky eyes as well as a variety of natural and extreme glam looks. And I have to 100% agree with that description wholeheartedly. This is a glam palette. When this palette came out so many of you guys were tagging me and you were like I know you're going to love this. A cool tone palette. If you don't follow me, I have been asking Natasha to come out with a cool toned palette. She needed it. I was tired of all her worms. I don't typically gravitate towards warm tone palettes. Of course, I wear any eyeshadow color. I don't mind. I don't mind a warm look, but I love cool toned palettes. I really have a deep appreciation when brands come out with them because there's just not so many on the market. Like if I were to come out with a makeup rayon, my first palette would be a cool tone palette because I think there really is a lack of cool tones in the makeup industry right now. A lot of people are scared of them. They might think it washes them out. Cool tone doesn't always mean like gray and silver. I know I'm wearing that right now, but I like more neutral cool tones. So maybe not necessarily a super gray. I did play with that today. But I think my everyday preference is probably more neutral cool tones. But that's beside the point. I really feel like she heard me. She listens to me. I said, you need a cool tone palette and she did it. So I'm personally very happy about this now. I know it's a particular taste for cool tone palettes. So some people or I would say a lot of people maybe weren't pleased with this color story, which I can understand, but people need to give cool tones a chance. Like they're just not trendy, but they're so nice to guys. Some information that she gave out in her Instagram stories, all of these are brand new shades. It's in her typical matrix kind of layout, meaning you can create a look going this way, this way, or in a square, which you can kind of see that developed. I mean, I don't know if every which way is going to create an amazing look. I do think with this overall tone though, all of these colors are going to match each other. So that's very awesome. Like you can kind of pair any shadow in here and it's going to look good in a look. Also something interesting about this palette is she didn't give them like a themed name, the individual shades like she normally does, which I'm totally okay with. She named them like center eyelid, outer eyelid, inner corner, basically the parts of the eyes that she would recommend placing them. So if you're a beginner, that may be very helpful for you. But of course, it's just a recommendation. You don't have to. But even when I was applying them, I found I was applying them where she would apply them. So that could be helpful and I don't know. I don't really care for shades to have a name, if I'm being honest. So I don't mind this, but it does take away from the story. And I feel like she always does have stories as far as her shade names go, but it's a new approach and I don't mind it. So there are five true mattes in here and then five shimmers. Now, I think there's a little bit of differentiation within the shimmer finishes.  Some I think bridge more towards foiled. And then there's a couple that have kind of her crystal powder that she puts into her formulas. Like these two right here have that little bit of an extra glimmer crystal glowiness to them. Overall, based on my swatches, this seems to be a very consistent palette. A lot of times, I would say 99% of the time with Natasha's palette, there's always one that even by swatching, I can tell it's not going to be good. She's playing around with formulas when she shouldn't have. In here, every single formula is consistent and creamy and packed with pigment. I have swatched this multiple times, felt every single shade. We're good guys. A consistent palette. I love Natasha so much and it's a little bit disappointing to me whenever there's a dud in her palette. There's not a dud in here, I promise. The color story of this guy, very, very cool toned and I love that. You do have some more, not warm, but brown based neutrals, those are kind of my cup of tea. And then you also, especially like down in this area, they're more gray based cool tones. So I want a little bit more gray with my look today, but on an everyday basis, I do prefer the more neutral, cooler, brown tones. But I like that you have two different options and I think having the brown based cool tones and the gray based cool tones really make this a very complete cool toned palette. And not a lot of brands do this. A lot of times with cool tone palettes, they really only do grays. And as I've been saying throughout this video, I like cool tones, but I don't want like gray and silver all the time. I don't think brands capitalize enough on the neutral, brown cool tones. And I'm so happy that this palette has it. Critiques that I saw was that you can't get that many looks with these colors. I will say taking a look like, yeah, they're kind of in a similar tone. And I don't think maybe that this is the most versatile palette as far as the types of looks that you can get. But that's not really the point. This is a cool tone palette. You're gonna get cool tone looks out of this. And I'm happy she didn't put pops of color like navy or purple or something like that. This is a true wearable and glam smoky palette. And she really stuck with her guns and I really appreciate that. I do. The one critique that I do have is that I wish there were some deeper transition shades in here. I feel like the Mads, like she does have a black and a bit of a more chocolatey brown. She has good basic transition colors. I feel like there's a lot of like these light shimmery shades that we have. They would use maybe as like an inner corner color. She could have taken out one or two of those to add in a little bit more variety in the transition shades. But that's my only critique really. Before I get into the tutorial, I just want you to know quality across the board on this guy. Really fantastic. Super buttery matte. Super creamy metallic foiled shimmers. Very easy to apply. Everything blended out great. So I'm gonna take you to the tutorial so you can see how I got this look. I'm using my Mac paint pot all over as my base and this is an Esum W25 brush. With the Wayne Goss number three brush, we're gonna use the shade right here. It is labeled as transition and I definitely wanted to try it out. So it's a very light shade. If you all have, I would say even like a light medium skin tone in up. This can look potentially a little bit ashy. I'll let you take a look on me. So this is just barely crossing the line as a transition shade. I think it's a great versatile shade. It's a great all over lid color no matter your skin tone. But labeling it as a transition shade might be a little bit of risky territory. But it worked out for me in this case. Wayne Goss number four, we're gonna start slowly building the crease. You guys know I'm all about starting light, slowly adding in the deep shade. And I am doing a slight halo technique. Not like a crazy halo eye by any means, but just building some definition both in the inner and outer corner. As you can see, these are blending quite seamlessly. Now we're taking the shade right here. It's called smoke and it's a nice neutral cooler toned brown. This type of shade is just one of my most used shades in the world. You use them for so many different looks and it adds depth without being quite as dramatic as a black. And as you can see, I'm focusing that on the inner and outer corner. I'm using a refer number one brush. Then we're going to go in with the original brush that we used and blend that out. Unfortunately, I'm not using a ton of shades in today's look. This is just a first impressions, but you guys know, I'm quite familiar with the Natasha formula. We're going to take this shade right here. It's labeled as an outer eyelid color. This particular shade almost has that like crystal, extra shiny formula where you can see little tiny reflex. It does a lot with the formulas. I know my nails are really long and gross. I just ripped off all of the gel polish that I had on, which is so bad for your nails, but whatever. And so I placed down the inner and outer part of my eyelid with my Wayne Goss number seven. We're going in this shade right here. So this is just a light to mid tone silver shade and it's labeled as a center eyelid shade. So that's what I'm using it for. Of course, for this look, you can definitely bring more light to the eye by using one of the even lighter shades that she has. But I want to keep this one pretty silvery smoky like and I'm going to take my big fluffy brush, blend that all out. So I basically have an all metallic silver eye and then those matte shades are working as that underlying definition. I most definitely had to mess around with the black shade, which is right in the center. It's called lash line. I'm just patting or rolling in my Wayne Goss number five brush. It's just a pointy brush.  A way you can get such a soft wing is not using a super defined brush. So using just like a simple pointy brush like this just to build kind of an aura of the shape and then I'm blending whatever's left along the lash line. So just like that subtle definition. One of my favorite smoky eye tricks. Just take a black. It might seem scary. I promise you it's not on a pencil brush. Just work it out along the lower lash line. Like I said, it seems very harsh not having anything underneath but I find it to look really nice when you take an eyeliner. I'm using the Wayne Goss eye coal in obsidian. Make sure you tight line all the way around grabbing my BK two of seven. We're going to use this shade right here, which is the lightest silver that's called inner corner. And I'm going to do just that put in my inner corner. You can also put it right in the center of the eyelid to really add some extra light. But I think I'm just going to leave it like this. So creamy and pigmented. It's a bit much. I'm not always super in love with completely gray silver toned looks. Like even though I love a cool tone sometimes gray is still a little bit too much for me but when you're going for it really got to go for it. So line your lashes and I'll show you the final look. And with the lashes I use these base blue cosmetics lashes in flying lashes. Treat me. They are so pretty but lashes this complete a look. Love this. So I did get some questions as to how this compared to the ABH sultry palette. So I did some side by side swatch comparisons with you. Overall, they are very similar. I would say, you know, if you're tight for money and you have the sultry, I don't think that you would need the glam palette, especially because ABH does have a really fantastic formula also. But the cool tone lover in me just feels like the market really lacks cool tones. So I'm really excited that this one is on the market. So I'm going to show you the comparisons now. If you were to ask me how close the sultry is to the glam palette, I have every single color from the glam palette swatched on top and then all of the similar colors from the sultry on the bottom. Now the sultry definitely has a few shades that were not even close to the glam. So I just didn't even put down something close. The ratio of colors is very different. I think that the glam palette has more like inner corner highlighty center of the lid kind of shades, whereas the sultry is actually a bit deeper. The sultry I think overall has a little bit more warmth and a lot of that is pulled into by the red shade that they have in there. But the colors also just look a little bit deeper to me, whereas overall this palette is a little bit more gray and a little bit more light. That being said, kind of across the board, I would say if you have the sultry palette and you're content with that number of cool tones, you don't grab for it a lot. I would say you don't need the glam palette, but if you're like me and you just love cool tones and there's just not enough cool tone palette out right now, the glam is definitely a great grab for palette, but you do get some more depth out of the sultry. Anyways, yeah, they're pretty close. There's a lot of close matches. All right, you guys. So that is all I have for today's review. If you couldn't tell, I really love this palette. I don't think it's everybody's cup of tea, but if this is your color story, just like it's mine, just know that the quality you're getting in here is really fantastic. You're not going to get a dud in here. You guys know I love sharing my love for cool tones and I want to push them on to you guys, but if it's not your color story, it's not your color story, but give it a go. Seriously, this is a perfect palette. I'm so happy that she brought this out. This is one of my new favorites in her life. I really need to do a re-ranking video because she's added a lot of palettes and as of now, this one is my current favorite just because I'm so excited about it. So that's all I have for today's video. I hope you guys found it helpful. If you aren't subscribed to my channel already, I would absolutely love it if you would consider taking the time to do so and I'll see you guys in the next one. Bye.


Thanks for that report. Glenn, moving on, roadworks in the Rodney Bay area enter a heightened phase as the road improvement project being undertaken by the Ministry of Infrastructure progresses. More from Herma de Mac. The Rodney Bay area is one of the busiest in the country and the road improvement project aims to alleviate their traffic rules experienced by daily commuters. The project is currently in the first of two phases. Phase one encompasses the widening of the road for folly and capabilities, drainage and slabbing works, pedestrian sidewalks and the placement of roundabouts. The second phase includes the building of walkovers, placement of median barriers and road lighting. Communications officer in the Ministry of Infrastructure, Ports Energy and Labor Shannon LeBorn says this project will vastly improve the user experience and safety of pedestrians and drivers. We'd appreciate historically the main Rodney Bay junction has been identified as a point of and a cause of traffic congestion. We have people leaving Rodney Bay wanting to turn right onto the highway to the castries and people heading southbound. So a bit of a conflict there. So this project will address the situation, improve the flow of traffic, improve safety for both motorists and pedestrians, pedestrian sidewalks. You have two lanes heading north, two lanes heading southbound. So it's going to be a four-lane stretch of road once successfully completed and you also have overhead walk pass for pedestrians as well, adding to the safety elements of this undertaking. The project manager in the Ministry of Infrastructure, Tai Beaches, Robert says deliberate efforts ensure that current roadworks do not affect daily commute of road users. The number one thing we took into consideration was the traffic and the bulk of our work has been done at night time purposely for that reason. We try our utmost best not to affect the traffic. We've had discussions with the Royal Central Police Force traffic department and we come at night, we do our bulk of work with detour traffic as we work in conjunction with the police department and during the day we allow the traffic to flow comfortably and any of our guys you see here in the day is basically doing some preparation in the drains which will not affect the traffic in any way. After stakeholder consultations the Ministry is considering the relocation of bus stops. The Rodney Bay Road Improvement Project is a design construct finance agreement with fresh start construction and management systems by the Ministry of Infrastructure. The first phase of the project is expected to be complete in four weeks. From the Government Information Service, Hermione Mock reporting.


Greetings ladingtons! Today I thought to elaborate a bit upon the mig tau question. Now I will make a separate mig tau video later on. This is just a response to some comments I saw on the female hypergamy video and I've seen this before too and it states that it's good that certain guys do not reproduce because that will have an eugenic effect. So it's good that these mig tau are going their own way because if they're not strong enough to attract a female it's good that they are not spreading on their genes. Now this is a view I would like to contest. I would strongly like to counter signal this view because attracting a female in the modern world does not equal having strong genetics and I will explain this with an example. So imagine if you have a genius, a guy who is completely committed to his research in biology. That is what he does. Every single day he wants to get into the grind, advance humanity's understanding of biology. So he goes into this lab every single day. That is what he does. That is his passion. Now obviously he perhaps haven't met so many girls in his life. Perhaps he isn't the most chad, perhaps he isn't the most confident, but he's a decent guy at least and then we can look how big are his chances if he is a bit nerdy, if he is a bit shy, if he is a bit socially incompetent. Now obviously he will have a terribly hard time attracting a fair maiden. Is it a good thing or a bad thing that his unique high intelligence genetics aren't being passed on to the next generation? Yeah it is obviously a tragedy. Those sort of people are to a large part responsible for the greatness of European civilization. That we have had these people who have been able to commence a certain endeavor. All our scientists for example they have been able to do so because they've had a society backing them up and they have been able to spread their genes because society has provided a wife for them. Today it's a completely different thing and that is in my view at least. I don't view it as a title of oh you have strong good genetics because you can find a mate. Sure a lot of guys who are really solid they have found a mate and I'm extremely happy for them, but it doesn't really work the same today as it did 500 years ago or 300 years ago. The people who couldn't spread their genetics back in the day 300 years ago that was something absolutely wrong with them. Society said you know we must kill you off because you're not good for society. Today it can be the case that certain guys simply do not have access to any females because there aren't any females physically speaking in their vicinity. We know in the west that the more people who are moving into the cities it's usually women so therefore these women end up some of them becoming bitter cat ladies and then you have guys out in the countryside without a fair maiden. Now obviously yes a lot of guys who can't attract a female perhaps there's something wrong with them but there's also a very large group of guys who have good genetics but they can't spread them because they can't attract a female because of various reasons. So yet again to take the example of the genius in biology. He will probably in the modern age he will not spread his top tier intelligence genetics on because he can't he can't afford to spend the time and energy on how to learn to attract women. So he's in a bit of a bad situation there whereas a few centuries ago he would have a stable wife at his side from an early age wife who can greatly help him in his endeavors. That's something we need to be clear about as well that genius he can be a genius because he have people backing him up. So if we look upon a lot of inventors and philosophers in western civilization yeah a lot of them have had beautiful wife by their side. Now imagine if they had not had that imagine if they had not had access to a society that provided them with certain things such as a woman. Yeah they would probably be in a much worse situation. So anyway my criticism of this statement that it's good that certain guys do not reproduce. No in the modern world good genetics strong genetics isn't necessarily the same as being able to attract females. Certain females they're attracted to absolutely horrendous guys who have low intelligence etc. That is regrettable and certain guys and I'm especially talking about a bit more nerdy technique oriented science oriented guys who they go to high school among other men because usually science is dominated by men then they go into university with other men then they go into a profession which is then perhaps researching certain things in whatever scientific field they spend their time with other men. They don't have access to that many encounters with females and they can't compete with Chad who is out getting all the women and that in my view is not good at all. So we see have my criticism of Migitao I'm not a Migitao myself I do think all good laddingtons all good legionaries strive to get a fair maiden strive to get a good fair maiden that you can have children and a stable family with but if you are in a position where you can't get a female for whatever reason it might be your fault because something is wrong with you but it also might be the fault of the modern world and I'm not saying that it's the women's fault it's the fault of how our society is looking today so as I said before 300 years ago society would have taken care of these sort of things today these guys they're being left without and that is regrettable. So that's my thoughts. Next XO boom