Cyber crime is a very important topic in today's date and time. The news reported that in Pakistan alone in the last three years, the number of cybercrimes have increased by 83%. Now with the advent of internet and internet becoming ubiquitous and becoming an essential part of the lives of almost each one of us, it is only understandable that that also led to an increase in cybercrimes. Now we want to look at in this lesson that what cybercrime is and you know what are its categories, what are its types and then what are some safety tips through which we can remain safe from the cybercrime. The main objectives of this lesson include an exploration of cybercrime, creating a basic awareness about cybercrime, gaining more knowledge about cybercrime and understanding the risks of harmful online behavior. Now let's, before we you know look at the downsides of cybercrime and how we can protect ourselves from cybercrime, let's first see that what exactly is cybercrime. Now as in regular societies and regular day-to-day lives, we have you know we were subjected to crime, we have robbery, we have theft. Similarly when the birth of internet gave birth to a cyber society which is the virtual variant of an actual society, naturally that cyber society is marked by cybercrime. Cybercrime can also be referred to as a computer crime and it is a crime which essentially involves a computer, a mobile and a network. The computer may be used as a weapon for crime or the poor computer may itself be a target.  Now who are, who is committing this cybercrime? The ones who are committing cybercrime are called cybercriminals. Now they are, they are those individuals who are doing crimes by using computer as a target or as an object. Again let's look into a bit more detail what exactly is cybercrime. Now for instance when you purchase a home it comes with a door and a lock. You always ensure that the door and the lock exist and are working properly. You may even purchase security systems. Likewise your computer system is almost like your house and security tools are needed just like how in an actual home you need a door and you need a secure lock. Similarly your computer which is synonymous with your home in order to protect it you require security tools as well and if someone breaches into your computer system you know and excesses all your personal accounts tempers your data it is the criminal who is committing that particular crime. Let's look at some of the categories of cybercrime but before doing so you know I want to share with you that the cybercrime first originated in the US in the 1960s. Types of cybercrime or let's say more specifically examples of cybercrime included that you know somebody broke into the system of Brooklyn College New York and tempered with the academic transcripts of students. Then moving on in year 1978 Pacific National Bank security database because it was hacked that led to a loss of millions and millions of dollars. So you know these are just some examples of cybercrime which started in 1960s. So technically cybercrime is not a new concept but its frequency with you know passing time has become much higher. So now let's look at the categories of cybercrime. Cybercrime can be against an individual which means that the type of crime is in the form of hacking, identity theft, bullying against a certain individual. Similarly cybercrime can be against property also which means that just like how in a real life you know a criminal can rob a bank can steal somebody of their money. Similarly in in the cyber world they can steal a person's bank detail and misuse the credit card details or you know to to take money out of someone's account. They can access someone's password and again you know use those passwords in order to let's say steal or rob money from them. Then moving on cybercrime can be against the government also. Now although this one is not as common as the first two where the cybercrime is committed against an individual or is committed against property however nevertheless it does exist. In this category the criminals they hack government websites, military websites or this circulate a certain propaganda. A cybercrime against the government is also referred to as cyber terrorism. After looking at the categories of cybercrime let's look at the types of cybercrime. Cybercrime can be in the form of hacking. Hacking you may have all heard this term is in simple terms illegal access into a computer system without the permission of the computer owner. Then the second type can be software piracy. This crime occurs when a person violates copyrights and unauthorized and you know and does an unauthorized use of software or someone's intellectual property. The third type could be cyber stalking. This is a crime in which the attacker harasses or threatens a victim using electronic communication such as email, instant messaging or messages posted to a website or a social networking site. Stocking, cyber stalking essentially means that you know somebody is following your activity or the internet or in the physical world and actually using that to blackmail you or harass you or misuse and abuse you. Moving on to other types of cybercrime that can include the use of a malicious software. Now malicious softwares are internet based softwares of programs that are used to disrupt a network. The software is used to gain access to a system to steal sensitive information or data or cause damage to software and hardware. You know malicious softwares could include you know sending in viruses, sending worms, sending Trojan horses, email bombings, sending you with a lot of spam emails, email and let's say you know finishing up the storage of your email. These are all forms of cybercrime as well. The fourth form can be an identity theft where a criminal assesses data about a person's bank account, about a person's credit card, debit card or his or her passport or other ID information and then uses that to you know to either to further commit a crime or you know uses that to steal money or valuable possessions from an individual. Another type of cybercrime can be cyberbullying. Cyberbullying is when the internet and related technologies are used to bully other people. What is bullying? It is a deliberate repeated and hostile manner in which you know a intimidation or fear is inculcated into a person. Cyberbullying can be done where text messages, images, personal remarks posted online as well as through hate speech. Moving on and looking into other types of cybercrime and other one includes denial of service attack. Now what is a denial of service attack? It involves flooding a computer resource with more requests than it can handle. This causes the resource example for instance a web server to crash thereby denying authorized users the service offered by the resource. This as especially the females may be aware that during sales seasons you know you have the website of certain big brands where certain individual mafias let's say or certain individuals send in so many requests or make so many attempts that to genuine buyers it when they try to access that website they're not able to and that is and then that prevents them from actually buying that thing firsthand and are then forced to buy that as in the black market. So that is just one example of a denial of service attack. Moving on and looking into other examples of cybercrime it includes email spamming and spoofing. You all may have experienced that sometimes there are emails random emails which are sent out to thousands of people. So you know those are the kinds of email that one can receive then it is so that you know that you receive an email that appears to have originated from one source whereas actually it was sent from another source. You may have you know seen those examples where you see that you know somebody from your friend's account on a social network site is asking you for money that too is let's say an example of a certain cybercrime. Another type of cybercrime is computer vandalism. Computer vandalism is that you're damaging or destroying data rather than stealing or misusing it. When you're damaging and destroying somebody's data this is called computer vandalism. Moving on well I could give you you know and more examples of cybercrime and list down various other cybercrimes but you know while crime exists it is important to look at some of the safety measures or precautions which individuals or individuals around them can take in order to prevent themselves from these attacks of cybercrime. For instance firstly on your computer systems use antivirus software. You know this is the basic fundamental step which actually prevents your computer system from a lot of attacks from viruses, trojan horses, worms then secondly insert firewalls. Thirdly uninstall any unnecessary softwares available. Fourthly always maintain backups especially of important crucial data especially of data which you had to which you had to create with a lot of effort. Further never send your credit card number or your passwords to any site which is not secure. Moving on avoid sending you know your photographs or videographs or videos especially those of a personal nature to to strangers. Lastly do not open emails from strangers or you know emails which from this subject or from the title seem to be suspicious. This especially prevents your system from unwanted attacks. Moving on don't respond to harassing or negative messages in comments. You know responding to harassing messages or you know cyberbullying does not solve the problem so do not do that it just makes you part of a certain vicious cycle. Further like anything educate yourself learn about safe use of internet, learn about internet privacy and try to implement it. Keep your operating system up to date. If you have any updates please do include them. Change your passwords frequently and use hard to guess passwords. Further don't share access to your computer with strangers and even with acquaintances. Sometimes you know we are often subject to cybercrime because those people who are not whom we do not get fully trust but their acquaintances and not realizing the threat of cybercrime we end up sharing our computer systems or passwords with them. So definitely do not share your computer systems and your passwords and your details with strangers but also be very careful and mindful when you are doing it with the acquaintances. If you have a Wi-Fi network please protect it using a password and disconnect from internet when it is not in use. So when we looked at this lecture or let's say this lesson which was an introduction to cybercrime we were able to realize that just how a regular society is subjected to crime a cyber society which is a virtual variant of a regular society is subjected to cybercrime. There are various types various kinds of cybercrime however in order to remain safe in order to protect yourself in order to protect your loved ones please make use of antivirus softwares firewalls security patches be careful with the you with with sharing your credit card details with opening suspicious emails with you know with the use of your passwords because it's always best to practice these safety measures then become a victim of a certain cybercrime.


Hello, hello, yes. OK, so welcome to this afternoon session. It's a pleasure to introduce José Antonio Carrillo, Imperial College London. And he will give how many tugs are you giving? Two tugs. So a short course on the degenerate Keller-Siegel model, fair competition and diffusion dominated regimes. OK, thank you very much. Thank you to the organizers for the kind invitation here. And so today I want to report about some recent works in the direction of the Keller-Siegel models with degenerate diffusion, mainly about stationary states for these kind of problems. And I will basically concentrate on two particular regimes that I call fair competition and diffusion dominated. You will understand in a few slides what they refer to. OK, so what's the outline of the two tugs? So first, I would like to explain you the motivation for this, from where I came with these kind of questions and why I'm interested in answering some of those precise questions. And then I will concentrate first on telling you the different regimes and explaining you from where it comes. Then I will discuss on the fair competition case that, as the name says, it means that it's a kind of competition between two different mechanisms that is somehow fair. And then I will concentrate on the diffusion dominated case. OK, so I will do a kind of mixture between blackboard and slides. So I will prove some things on the board and remind you some computations on the board. OK, so the first part about the motivation. So what I want to do is to minimize interaction energies. We will see why I want to do that and why this is connected to those problems I mentioned. So let's start by just fixing a bit of basic ideas. So let's assume that we have m particles which are interacting by an interaction potential that I'm going to call u. And an interaction potential for me is going to be just a symmetric potential, which is c1, except maybe at the origin. OK, so there could be a singularity at the origin. Anyhow, we'll assume that there is some value for the interaction potential at 0. I will give the value 0, even if there is a singularity. And when I talk about the interaction of m particles, I mean this kind of interaction. You can think about it as coming from Newton's law. So I have m particles which are interacting through Newton's law, where you have the second derivative equals to the mass time acceleration equals to the sum of forces. And you can think this as the term that is coming from the sum of forces. So say the presence of a particle at position xj is producing a force onto the particle at position xi, which is in the direction of the vector xi minus xj, and with certain strength that is given by the potential u. So that's why you have gradient u xi minus xj. Then the mj's are just weights for the effect of each particle. Assume that they are equal, it will be 1 over n. The viewer will assume that each particle produces an effect of 1 over n onto the other. And then you are adding all the forces. So this is like the sum of the forces. But what do you have here, the first derivative? Because I assume that somehow the inertia term is negligible. And I assume also that there is a kind of dissipative term. So there is a kind of damping term in the equation. So as you write m x dot dot plus k x prime equals sum of the forces, then you are just neglecting the inertia and bringing then first order differential equation instead of a second order differential equation. So somehow you are assuming that the particles, quickly without inertia, they adjust their velocities to the sum of the forces. So it's the simplest interaction between n particles. Good. If you want to write now, instead of a particle system, you want to write a continuum model, then you want to pass to an equation for the mass density of particles or the probability density of particles. So I'm going to call rho tx the density of particles at time t, meaning by that this gives me the probability of finding particles at location x or then the local mass at location x. It depends if I want to normalize or not the total mass of one or not. OK. So if I want to write something continuous, I can just follow what I did here for the particles in a continuous way. So in fact, probably I should explain a bit more this relation. I don't know if somebody has talked about mean field limits before or not, but probably not. So what you can do is, given this n particle system, you can associate to the ODEs the following measure that I'm going to call it the empirical measure. I'm going to call it mu n, which is the sum from 1 to n of the weights mi and adidac at location xi of t. xi of t is the solution of the ODEs. So this, obviously, is a measure that depends on t. And it gives you exactly the value corresponding if it's a deterministic measure. If you want, in the sense it tells you precisely the locations of the particles because you have this combination of adidac deltas, OK? So you define this. This is usually called the empirical measure. And now if you look at the right-hand side of this, you can think about that, the sum mi gradient u xi minus xj, j different from i. Somehow you can think about this as the gradient of u combined with the mu n. Of course, it would be the case if the potential is smooth. And since it's a metric, the gradient of u at 0 is 0. So this is exact. And then the fact that I'm taking j different from i doesn't make a difference. So now you see more or less the idea. You see that if you think about this as the empirical measure, what you are expecting is that when you get more and more particles to approximate the continuum density row, then somehow this probably you could expect that this converges in some sense as measures to some limit. And if you are able to identify the limit, let me call it row t, maybe you can even say you can give the evolution for that row of t. So answering this question, answering if there is a limit and there is a law for what is the evolution of row t is what is called the mean field limit, OK? And there are plenty of works both for these kind of equations and for kinetic equations trying to derive rigorously macroscopic equations out of the dynamical systems. In this case, under certain assumptions on the potential u, you can do that. And in fact, now you see what you expect is that somehow when you take more and more particles, this will be approximating this gradient u comb of mu n. Hopefully, it will be approximating when n goes to infinity by gradient u comb of the density row of t. And then what you expect is to have a velocity field given by this formula, where you have the sum of the forces again. Every infinitesimal part of the mass of row is producing a force at location x given by gradient u x minus y. You integrate your sum, you get the total force. And then the velocity field is going to be minus that quantity, OK? So the minus is just by convention for the potentials how I'm using it. So in other words, you expect to have at the continuous level of velocity field, which is given by that convolution with the gradient of row with the gradient of u. And then another question is, what is the law for the evolution of row? And what one can expect is that the evolution of row is given by a continuity equation. And this is a kind of exercise for the students present in the audience. You can check that, at least if you use a smooth, let's say C2, we bound the second derivatives just in case. You can check that mu n of t is a distributional solution of this equation that they have there. So of d rho dt plus divergence of rho u equals 0. And u given by minus the gradient, sorry, b, I call it. And b given by minus gradient of u, combined with the density. With initial data, which is just the sum of the deducts of the initial locations, that's pretty easy to see. And that's a good exercise to understand what is happening. So it's not a surprise that you expect this equation at the limit because somehow already at the discrete level, they are solutions. So this can be rigorously proved also in the case in which u is not as smooth as what I was saying here, but this requires other techniques that I'm not going to discuss today. And anyhow, I want to concentrate on this kind of model for a while. OK, so the next thing I want to say is about the potential u. So typically, in many of the applications that you would like to use this, let's assume for simplifying our life that u is radial. So u of x is a function of modulus of x. Let's say k of modulus of x, OK? Typically, this k is a function of r of modulus of x. You're going to expect to be decreasing and then increasing. And what it means is decreasing means that the potential is repulsive at short distances with the signs that I chose here. While, so up to here, say, in the other particles, I'm located at position x. The other particle is at position y. The force that I feel is repulsive if I am at a distance less than this. Let me call it l, the minimum. While if I am at a larger distance, I will feel an attractive force. And typically, the potentials that are interested in many of the applications are repulsive attractive potentials. So the next thing I want to comment is about the repulsive part of the potential. Well, I really don't care right now. I could go to plus infinity or to a constant and have some saturation. These are, I will treat different cases. Both are interesting, yes, for different reasons. But today, mostly in my talk today, there are going to be potentials that are going to decay to zero, in fact. Yeah, well, but both are interesting, a priori. Then the next thing I want to comment is about the repulsive part of the potential. So another way of modeling the repulsive part of the potential is by, instead of doing it non-local, and now that's why I'm inside the theme. This is non-local. Maybe I can do also the repulsive part local. What it means to do it locally. So I can assume that the potential, I have two separated parts, say, a repulsive part. Let me call it U-capital R, an attractive part. OK, there's a symbol that you have like this. And for the repulsive part, I can take something that is really, really, really very repulsive in the sense that maybe I can put a kind of a scanning parameter there, epsilon. I can assume that this U epsilon, well, is somehow, as a epsilon, goes to zero very close to a dirac at zero. This will mean that it's really very repulsive, hardcore repulsion in a sense. I want to think about it like this. So formally, what happens with that equation there? So let's separate the repulsive and the attractive part. So I have the repulsive, the force will be given by. The velocity field is this minus gradient UA, combo of rho. And now, yes, I set to put this as scaling parameter. Now this approximately, then if I put a dirac delta here, of course, I cannot do too well the gradient of the dirac. But what I'm going to put is the gradient on rho. I combine with the dirac. So formally, this should be minus gradient rho minus the gradient of UA, combo of rho. So somehow, if I do a very repulsive force, at least in this way, I recover for the repulsive part this term minus gradient rho. If I look now at the equation, I'll write it on the other side because I have the minus. So I will have minus divergence of rho v. So it's divergence of rho times the velocity field. OK. So this is what? This divergence of rho, gradient rho. And then from the other term, I get rho, gradient, the attractive part of the potential, combo of with rho. OK. So for those of you that were here yesterday in the talk of Juan Luis, and I'm sure that probably it appeared last week, I'm not going to do chak-chak. But I can write here like Laplace of rho squared and here 1 half. OK. And then the rest. OK. Yes. And then the first term is exactly the porous medium nonlinear diffusion, the genetic diffusion spawn in 2. Probably something like this appeared yesterday. But it's the local one. OK. But at least formally, you can recover from very strong repulsion this nonlinear diffusion. So I'm going to discuss a bit more these kind of models. And I will concentrate today precisely in a model like this, where I have the attractive part I will consider non-local. So I will forget from now on about the A. I will think UO is an attractive potential. While in the repulsive part, I'm going to assume that it comes from a local pressure function. So I can put something more general than just gradient of rho. I'm going to assume that I have the gradient of a function of rho. Directly from the particle system, even formally, I can recover only the power 2. OK. At least in that case. So the question is now, if I do this, if I model repulsion by this nonlinear diffusion and the attraction with this non-local convolution of this interaction energy, when does a balance between these two forces happen? And in which sense, it means that you have a balance. So I would look for a balance between the forces. Typically, it will give me to a kind of a stationary state. So my question is, do I have a stationary state or not? What can I say about that? OK. Now the next ingredient. These equations, in fact, for the experts in the room, they know perfectly that there are particular cases, at least formally, of being what is called a gradient flow of certain functional with respect to vast sustained distance. OK. I'm going to try to explain just a bit what it means this in practice. And I'm not going to get into the technicalities of the vast sustained distance, because it's not the objective of my talk. OK. But just to give you an idea why there is something like a gradient flow behind. So I'm already introducing this Lyapunov functional. Let's check that it is, in fact, this energy. I'm going to call it free energy, f of rho, which I'm going to write in the particular case of a power. So let's do a power. And then you see how it goes. So on the board, I'm going to use p of rho equals rho to the m. So here you will see that the right thing to do is 1 over m minus 1. The integral of rho to the m. And here you have 1 half double integral of u of x minus y rho x rho y. By the way, I didn't ask, is it large enough? OK, thanks. Good. So yeah, let's check that at least formally. This is a Lyapunov functional for that equation in the sense that it should decay in time among solutions of the PDE if everything in life is good. And we can take all kind of derivatives and integration by parts. So let's compute formally what is the derivative in time of f of rho. In principle, this is just a function defined on lm functions, l1 lm functions. And I'm assuming that they have undue enough properties such that this is well-defined for l1 functions. OK, let's not enter into the details yet. So I want just to compute formally what is the time derivative of f of rho, where here rho now is a solution of this PDE. OK, let's forget about the a, as we said. So this is the equation, the time I'm aiming at, because I want to use p of rho. OK, somebody could have that. So this is not the right thing to do. It's m over m minus 1. Sorry. OK, the constants are not important, but let's write the right constants. That's the p of rho that it has to be in order that I get this equation. But it should be written there. Probably I should. OK, so the thing is, let's first, yeah. So I'm starting from this equation. So I forget the other constants. That's why I got it wrong first. So let's forget about the other things. So I have d rho dt equals this. And let's compute the time derivative. But for that, the first thing I'm going to do is to rewrite this in a different way. I'm going to write it, again, like I had it written before, divergence of rho times something. And if you recover, what did you have to do in order to get here? You see this one is divergence of a gradient of rho to the m. So in order to recover rho gradient of something, you have to multiply and divide by the right constant, which is this one.   And here, I had just to write u comb of rho. So this and this are the same. So once I have written it like this, well, the first thing I'm going to realize is that all of this, I'm going to call it like this, and then I will explain what it means. I'm just going to call it like that. If you want right now, it's just a notation, which means variation of f with respect to rho. We will check that later. But nevertheless, I can write the equation in that form that is written there. d rho dt equals divergence rho gradient of the variation. Good. So at least, formally, what it means variation is that the time derivative of f of rho is going to give you d rho dt, the integral d rho dt, times the variation of f with respect to rho. This is if you want the definition of the variation. Or if you want, I can write it over here now. If you do some kind of perturbations of rho to compute this, you expect this to be an integral of what I'm calling the variation of f with respect to rho times phi for phi being such that rho plus epsilon phi is measured. So I need that the integral phi is 0. So you're doing just variations of f that preserves the mass of the density rho. You can compute what it is, and then you can realize that formally gives you an expression like that. And in fact, you recover what is the variation. The variation is exactly what I have written here. In this particular case, what I have written here between brackets. So that's the variation of this function. With respect to rho. OK, so that's why you have this formula over here. Now, once you have this formula over here, now it's just that you need to substitute the equation. d rho dt is minus divergence of rho gradient of the variation with respect to rho times the variation with respect to rho. You integrate by parts once and probably got the sign wrong somewhere because this is a plus. It's not a minus. So I integrate by parts now, and I get minus the integral rho. And then you have gradient of the variation of f with respect to rho. It's kind of product with gradient of the variation. So what you get is d square. OK, so the whole structure of the equation is in such a way that you have this kind of magic formula that at the end of the day, you have a derivative of f of rho. It's minus rho, the gradient of the variation square. This can be done with a general pressure law. And the relation between phi in the functional and p is written here. And yeah, this gives you the more general case when it's not a power. OK, so the main message is that for this kind of model, you have this Lyapunov functional. And then if you would like to obtain stable stationary states for this kind of PD, you would expect to have them as local means of that energy function. So what you are interested in, local minimizers of this functional. OK, so all of this just to tell you that this is the main objective of my two talks, I want to find properties on local minimizers or global minimizers if they exist. I can say they're global for functionals of that form. OK, so this problem, in fact, is quite classical in some particular cases. So what I want to know is precisely now, find the assumptions on the attractive part and the repulsive part in such a way that I have a local mean at least. And this is quite classical, as I said. And probably the first case in which this was widely discussed is for crystallization. But there, typically, the potentials are very single at zero. They are a kind of Leonard Jones potential, so they are not even locally interval. So I'm not discussing those cases. In fact, for me, I want to do it with densities, with L1 functions. So the minimal assumptions I'm going to put on you is that you is locally interval. So another very classical case is for semiconductors and in astrophysics, and also in math biology for chemotactic movement of cells where cells go up the gradient of certain chemical substance, then you end up in a problem like this for the particular case of the Newtonian potential. So you there is typically Newtonian potential either in two dimensions or in three dimensions. OK? And the classical cases are always with linear diffusion, which will corresponds to take here a roll of rho as the functional there. This is a comment I probably should have made. If you want to recover here linear diffusion, you see that m equals 1. You cannot get it so easily, but as a kind of limit. And if you do the limit as m goes to 1, you recover there the log. OK? So the function will be the integral of rho. There are other applications in which this question appears. So in mean field games, to find Cournot-Nash equilibria is one particular application of this for potential games. Also in fractional diffusion that you have heard so much during the last eight days, if you take you a potential more singular than the Newtonian up to local interability, in fact, this is nothing else than an inverse fraction of Laplacian. OK? And finally, there is also an interesting application for the eigenvalue distribution of random matrices, which is, again, a particular case here. Typically, it would be the log interaction, but in one dimension is a particular case of interest in that case. OK. So also I want to mention that this appears in also some problems in math biology. So one of the cases is what I said before, the chemotactive movement. And I want just to mention this because it's the most classical one and gives you a bit more of the modeling issues there. So just quite quickly, you will have typically an equation for the evolution of the cell density. So n is what it was wrote before, in a sense, because they have a density of cells. And you are assuming that the cells, they are just attracting each other. Why? They are attracting each other because they do it through the interaction via this chemical substance C. So you have another equation in principle for the chemical substance. This C gives you the concentration of that chemical. And then for that, you have, in principle, this kind of reaction diffusion equation where you have a source that is proportional to the number of cells. So if you do that and if you neglect the blue terms over there, you end up with solving this Laplace inverse of the density in order to get C. And if you write this in terms of the fundamental solution, you recover an equation of the previous form where the u is the Newtonian potential, in this case, in 2D. So it's a particular case, of course, is what is usually called a parabolic elliptic Keller-Siegel model. And typically, this is done with linear diffusion. But nonlinear diffusion has been also included by many people in the modeling side to model the size of the cells, to avoid overcrowding. Here you have just somebody playing around with a pipette with a chemical substance to which these cells are attracted to. And you see that's the kind of thing that you are trying to model when you have plenty. Another reason why I came to this question is also from math biology models. There are these models of swarming that they're not going to enter too much. But just to mention that it was somehow a motivation that triggered my attention. Because in those kind of models that they don't want to explain a lot, what you have is larger scale patterns that come from the movement of different animals that they're producing some coherent movement, a kind of flock or a kind of meal, like in this fish show that you have in the picture. The interesting thing is that many of these can be explained with basic mechanisms among those that action on revulsion. And some models that are just there, very basic models, they give you equations which are related to these ones with different potentials. So this to say that not only the Newtonian potential is interesting that appears for the case of the chemotactic movement, but they were using other potentials, like potentials behaving like modulus of x, either attractive or repulsive at 0, independently of the dimension, and with certain applications here. So it makes sense to look at different behaviors of the potential you are not just restrict to, say, the Newtonian case. OK, so I think it's enough for the motivation. And now let's get into a bit more mathematical details. So now the time after lunch is over. Now we get more into math details. OK, so I will concentrate on the case, on the particular case in which both the diffusion and the potential are homogeneous. So I'm going to take the particular case in which I have rho to the m as the diffusion, as I already wrote here. And let me start with discussing things about the particular case I'm going to do, which is I'm going to put also these homogeneous. I'm going to assume the u of x is modulus of x to the power k divided by k. OK, and here k in principle is going to be something between minus dimension and dimension. Dimension is d, no? Yes, OK? For me, k equals 0 means the log. And it's just a notation, as you want to take it, like this. The restrictions y, k between minus dimension and dimension I will explain them in a couple of slides. OK, let me start then, before discussing anything there, let me start by doing some computations with the f of rho. OK, I ensure that this computation will not surprise any of the experts in the room. But this is the first thing that you have to say to students that they haven't seen it. They haven't seen anything like this before. So the first thing that you have to do with this kind of energies is to look at how they change by dilations. OK? So let's take a density rho. It's just a given l1, lm density. And let's take any parameter lambda positive. Let's define the dilation rho lambda of x that preserves mass as lambda d rho of lambda x. And then let's compute f of rho lambda. Why in doing so? Because since I assume that both the diffusion and the non-local term are homogeneous, maybe I can work out the lambda in the computation. So let's see what is the dependence on lambda of f of rho lambda. So somehow I take a rho and looking at a kind of curve through rho, which is given by these dilations. And I see how the functional works there. OK, so let's do it. The substitute there, I compute. So help me with the change of variables. From the first time, I will have what? I'm going to try to do directly the change of variables. So what I have is rho of x to the power m. And then I will have a lambda to the dimension times m that was there when I put the rho lambda in changing variables. So I will do lambda x equals y. So then I will get minus d here. Do you agree with me? This is just changing variables. Y equals lambda x. I'm calling x again y. Good. Then from the second term, I have 1 over 2, double integral. Then here it's easier because essentially when I do change of variables both in x and in y, I will recover here an x over lambda, y over lambda. So I have a 1 over lambda that goes outside. So I will have lambda to the minus k. Do you agree with me? So you see, because they are homogeneous, I can get the lambdas out. And now we see something. We see that depending what's the balance between the m and the k, one term or the other will be dominant in a sense. So it's clear that if they are equal, so if I have d m minus 1 equals minus k, somehow I have the same homogeneity in both terms, that's the case I will call fair competition. In that case, what I have is that f of rolanda is, in fact, homogeneous. When I get lambda minus, well, it doesn't matter what I take out. Let's say that I take out lambda minus k. I forget about the m. I will have this property in that case. While if m is such that d times m minus 1 is larger than minus k, then this is an exercise for the students. You can check in that case that there is a global minimizer of this function as a function of lambda. It's a 1 lambda star such that you have a minimizer of this. So I mean, your function goes from 0. Well, it depends where the m is. So I don't want to enter in now different cases. It doesn't matter. There is a minimizer of the function for all cases. And you would expect somehow that, in some sense, I want to think about it that the diffusion overcomes the attraction or the possible aggregation due to attraction. So that's why I call it diffusion-dominated case. And of course, we have a third regime, no?  I will call it aggregation-dominated case. So let me discuss why these names a little bit. I know that I have some friends in the room that will not like some of the names here for some of the regimes. But let me try to convince you that they are good names. OK. So first, the diffusion-dominated regime. Well, I'm just writing in a bit different way. So dm has to be larger than d minus k over d or 1 minus k over d, as you prefer to, I prefer just to get the regime in terms of m. So in fact, for that case, in the particular case of k equals 0, you see k equals 0 would mean that I'm taking here the log. So for k equals 0 with the log here, if m simplifies to m larger than 1. And in fact, already that case, Calvea and myself, we studied this some years ago. And also, independently, Suhiyama did some works also in that case. And we were able to show at that time is that no matter what the initial data is, you have always L infinity bounds on the PDE, on the solution of the PDE, which are uniform in time on top. OK. So this will probably surprise some people here that know about the Keller-Siegel, but I will explain you what's the difference later on. Well, the standard Keller-Siegel, in fact, let's make this comment somewhere, probably here. For the classical Keller-Siegel, this corresponds to, say, dimension 2k equals 0 and m equals 1. OK, you just check with those numbers. It's exactly one of the cases of the fair competition, OK? Which is what I'm going to discuss also here. In the case of the fair competition, in fact, what you can, I will convince you that here you have in general a very similar situation as the classical Keller-Siegel. So for the non-experts in the room, let me explain to you what happened for the classical Keller-Siegel, what it was known there. In fact, it was known that here there is something that is called the critical parameter. And now for doing that, I'm going to put a parameter here. So I'm going to change just the functional. And instead of having one, I'm going to put here chi. Because I want to fix the mass of the density. I'm going to have unit mass. The L1 norm of rho is 1 in dealing with probability densities. So then I'm going to put a parameter chi in front of the attraction. Then in this classical Keller-Siegel, it was known that chi equals 8 pi is the critical parameter. In the sense that if chi is larger or less than this critical parameter, different things happen in the fair competition in this classical Keller-Siegel case. If chi is less than 8 pi, it was known that there is global assistance of solutions. While if chi is larger than 8 pi, the genetic thing is that there is blow up in finite time. For the critical, there are plenty of things known by now. But let me just say that there is global assistance of solutions. And they blow up, but in infinite time. Poor sand initial data. It's more complicated than this. But let me just say these three things today. In fact, also in the critical case, you have infinitely many stationary states. Sorry, it's a bit small probably. You will have it very soon in the slides. So you have infinitely many stationary states on some of them. And they have some basin of attraction too, apart from the ones that blow up in infinite time. So the situation is very complicated for the critical. The important thing is about this dichotomy. This dichotomy in terms of this critical parameter, the parameter is small. So if the interaction, the attraction is small, then you have global assistance. But if the attraction is large, then you have blow up in finite time. And if the attraction really gives you some particular, for very particular case, then you have exact compensation and you have stationary states. OK, so I will convince you that in fact, and I already advanced some of the results, this is exactly what happens for the whole fair competition case. Every time that you have this relation, as soon as k is negative at least. And finally, let me mention that you have also this aggregation-dominated case. And there, again, some particular cases were known. Essentially, these two works that I mentioned in there are for, again, the Newtonian case, taking k equals 0, or k equals Newtonian in several dimensions. And then they were able to show that independently of the parameter that you want, independently of chi, you may have, for any value of this chi, you may have either blow up for certain initial data or global assistance, meaning that there is no critical chi. Both things can coexist for any chi. OK?  OK? So don't think about aggregation-dominated as always giving you blow up. No. Just telling you that for any value of the parameter chi, you have always initial data for which you blow up in finite time. But this can coexist with other initial data which are spreading off, and this is globally. OK? Again, what the two works I mentioned in here are particular cases. So now what I'm going to show you in the last 10 minutes of this first part is a bit on the fair competition case. Let me see if I can finish that. And then I will concentrate on the diffusion-dominated case. OK, so let me see. There are probably two computations I can do even before starting with the fair competition case, which are interesting. I can do on the board to even clarify a bit more these different regimes. I will rewrite again the PDE here. So let me write the PDE here, d rho dt divergence. I mean, the constants are not that important at the end of the day. So rho gradient rho to the n minus 1. In fact, for this one, it will be n over n minus 1 here. That's rho gradient of modulus of x to the k divided by k comb of rho. OK, good. So let me do a computation here. So remember that this is also Laplace rho to the n plus divergence of rho gradient modulus of x to the k divided by k comb of rho. So also that you understand a bit what happens with the aggregation-dominated case. So let's compute formally that the constant disappears here. It gives you the Laplace rho to the n. In fact, I don't have the constants there, but follow this one. This one is correct. Good. So let's compute the evolution of the second moment here for this. So formally, I want to see this. I mean, I put the derivative respect to d inside if I can do this. And now let's iterate by parts, but let's write it directly from there. The Laplacian of the first term goes directly on the x square over 2 and gives me the dimension d times the integral of rho to the n. So that's the first term. Second term gives me minus the integral of x, because the gradient of x square over 2 gives me x. And then I iterate by parts already. And I have here rho. And then I have the gradient. So this is dotted with the gradient of ux minus y. So let's put what it is. Now let's work just a little bit here. This is what? This is, in fact, dot x dot x minus y to the x minus y to the k minus 1. Minus 2. Yes? OK. Rho x rho y. I'm just computing the gradient of modulus of x to the k, which gives me x modulus of x minus y to the k minus 2. Now I keep this the same. Now what I'm going to do here is to symmetrize this. So I change x by y here. OK. Since this is symmetric, this is symmetric. Here I will get y minus x, and here I get y. So I'm going to change 1 half of this by 1 half of symmetrizing. So you can convince yourself that what you get is minus 1 half, the double integral of x minus y dotted with x minus y, modulus of x minus y to the k minus 2, rho x rho y. You agree with me? So then here you get x minus y, x minus y squared. So you can add it to this one. And finally what you get is the integral of rho to the m minus 1 half, double integral of x minus y to the k, rho x rho y. And you see that you get the two terms of the free energy. And now if you want, I'm going to rewrite this. And believe me, if you do the algebra, this is d times m minus 1, 1 over m minus 1, the integral of rho to the m plus yes, here, OK. So here you will get, let me write the end of the computation, plus m minus 1 over 2, the double integral of modulus of x minus y to the k, rho x rho y. I think there should be a d. So in fact, you can see from here somehow, again, the exponent appearing. Because you choose exactly this relation dm minus 1 equals to minus k, OK?  So this computation to tell you that, again, in this particular case, in the case of the first competition, if you take the evolution of the second moment, you recover the free energy times a constant, OK? So we will see what are the implications of this. So let's leave this computation right now there. And let's see what is the implication of this. So let's concentrate, then, on the first competition case, where dm minus 1 equals minus k. Let me tell you what are the results that you can prove there. So the first thing is that, of course, you have this property under dilations, as I already said here. So if you have a stationary states, they will corresponds, or global minimizers, it doesn't matter. They will have zero energy, and they will correspond to the value of the optimizers of the zero energy for f. I will explain you from where they come later. So when do you have them, really? But a priori, from here, you just see that your minimizers will have zero energy. This is exactly what I mentioned to you that was known for the case of the classical Keller-Siegel. Plenty of people involved in part of this dichotomy. I hope not to have missed an important person. If I missed, I'm sorry, it should be included. So you have this dichotomy I mentioned. And now let me just point out that when k is negative, in the range, remember that k is always between minus dimension and dimension. So if k is negative, it's between minus dimension and zero, then just because of the relation that I have here, m is between 1 and 2. So your diffusion is nonlinear in the sense of porous medium case. While if k is positive, it's between zero and dimension, here you get diffusion, which is between zero and one. This is the reason if you want for the bound from above of being dimension, not to have an m which is less than zero. The bound from below on the minus dimension is precisely in this range to have here something which is a local interval. So should I stop now at the right time to stop? So let me stop here, and then I will continue discussing the fur competition case. Thanks.


I'm going to introduce to you today the Prisma 2020 R package for producing flow diagrams that have the possibility to be interactive. So why are flow diagrams important for evidence synthesis? Well they often deal with very complex sets of data, lots of methodological stages, many different numbers from different places, and lots of different records, sometimes tens of thousands and it's important to be able to keep track of all of those records. Flow diagrams do that very nicely. In the case of Prisma, this is the Prisma 2020 pre-print version of the flow diagram, and I'm going to describe the process of how the Prisma 2020 R package and Shiny packages, Shiny apps, work. So the main function is Prisma flow diagram, and it's based on graph biz and uses diagram R. In this code in this language, I use the term nodes for boxes and edges for arrows, and the package automatically connects the boxes with arrows. But for this case in Prisma 2020 I use explicit node locations, so I explicitly say where the boxes should go and another important factor is that the previous and other arms of the Prisma 2020 flow diagram are optional. So if you haven't integrated studies from previous reviews or if you haven't searched other sources of information, those arms can be dropped from the resultant flow diagram. It also has a what's called responsive location of the exclusion reasons node. So the box that has exclusion reasons in where each line is a different exclusion reason can be varying sizes depending on the number of exclusion reasons. And Prisma flow diagram, the function responsively moves the boxes around depending on how big that box is to a certain degree. So this is the flow diagram again, and on the left you can see the optional previous studies arm and on the right the optional other studies arm. So within the R package data can be read in from a template CSV file. Here's a screenshot of the CSV file and the data that can be changed by the user and that is read as different is in this red box. So the other columns are there for the user to understand which box the information relates to. There's also a template schematic that shows for the box column which box is which to make it easier. But users can change the box text. They can change the tool tips which are the text that appears when the mouse hovers over a tool when interactive when the interactive version is used. And the URL is the link that is used when the user clicks on an HTML version if the user specifies interactivity. And then the final column in this case n which was k in the original Prisma 2020 flow diagram is the number of studies or number of records at any step. You'll notice for two of the boxes there are multiple reasons. So where there are multiple reasons each reason is separated from its number by a comma and from the next number by a semicolon and the template shows you how to do that. It won't function if you don't enter the data in that format. So some of the challenges with this are that the vertical aligned text in these blue boxes is incompatible with graphics. So what we needed to do was to append that into the HTML using JavaScript using the packages HTML tools and HTML widgets and it adds text that is rotated through 90 degrees. And this is the function I won't go into detail but there's JavaScript in there. It embeds that JavaScript into the HTML after it's being produced. I also mentioned interactivity. There's a function SR flow interactive and it turns a static Prisma flow diagram into an interactive one. Why is interactivity important? Well it's helps to support full transparency in that it allows you to see the fate of each record. Normal flow diagrams show the number of total records going through each step but they don't show the fate of every single record. And full transparency allows you to see what happens to each record by examining a list of records at each step. It also facilitates data reuse and digital transparency and it makes particularly online communication very simple by explaining methods in as much detail as the user wants to see. So the user can click on a box and either see the methods or the data depending on what you want them to see. And the interactivity again uses JavaScript by appending href links into node elements and those links as I said before are specified in the data entry and tool tips are provided so that when the mouse goes over a bit more information pops up. So there's two levels of interactivity information provided in the tool tips and then information provided in whichever source you link to. There's also a shiny app as I mentioned. The beta testing version is up but it's likely to change over time. You can see that on the left you can specify which arm is included and down below you can enter the text as well for the values of N. At the moment this is all you can change. You can just change the N numbers in the shiny version. So some future developments are to add in the side panels. You'll notice there that the blue side panels aren't working because shiny doesn't support JavaScript. I also want to build interactivity in so that you can click on the nodes and be sent to URLs. We're also trying to build in flexible data entry so that in shiny you can either upload a CSV from the template or you can have manual data entry and to integrate the flow diagram with review management tools so this data automatically is populated from whichever review management tool you use. Thanks very much.


Last call today is the last final day for those who signed up for the ATC swap over at art venture to actually Come to the app and get your recipients address. There seems to be a lot of you who have disappeared I'm mailing mine out tomorrow Including the extra eight that I made to send out to randomly selected participants And if you never checked in that means you're not a participant anymore So you're not eligible to receive one So please follow through check your chat tab and reply to it. So we all know you got it


Welcome to Spotlight. I'm Joshua Leo. And I'm Christy Vaniragon. Spotlight uses a special English method of broadcasting. It is easier for people to understand, no matter where in the world they live. Park Place Oxford Street Luxury Tax Go directly to jail. Do not pass go. Do not collect $200. These are all parts of one of the world's most famous games, Monopoly. Today's Spotlight is on this game. Want to play? Monopoly is a board game. The game has a flat paper playing board. Players move small game pieces around this board. The players roll dice, solid squares with six sides. Each side has a number. The numbers represent the number of spaces a player moves to go around the game board. Each space on the board represents a different property. When a player lands on a property, he may decide to buy the property or not to buy it. But the idea of the game is to own as much property as you can. When another player lands on your property, that player must pay you money. It is like they are renting your property. There are many ways a player can make more and more money from his property. The idea is to monopolize or control much of the playing board. The more property you own, the bigger your monopoly. When one player controls most of the property, then he will have the most money. In the end, the person with the biggest monopoly wins the game. Monopoly was first sold in the United States in 1935. But it was invented a long time before that. In the 1900s, a woman named Lizzie Maggie created the first monopoly game. She called her game the Landlord's Game. Lizzie gave the property's names like Poverty Place. She used her game as a teaching tool. The point was to teach people about the problem of rich, large landowners. Lizzie was a Christian and she was particularly concerned about poor people. Over the years, the idea of Lizzie's game spread. Other people began making their own versions of the game. And they gave the properties their own names based on where they lived. The game was very popular among university economic students. They studied the economy. These students did not like the idea of big businesses replacing small businesses. They did not think this was democratic. They called these big businesses monopolies. They used the game to show the problems monopolies created. In the 1930s, the game arrived in Atlantic City, New Jersey, in the United States. A young teacher gave the properties the names of Atlantic City streets. The streets had names of U.S. states like Pennsylvania Avenue, Indiana Avenue, and New York Avenue. These names are the property names that many people play with today. The names remained popular because they included much of the nation. But by the 1930s, the point of the game had completely changed. At this time, the United States was experiencing the Great Depression. The U.S. economy was at its lowest. Many people were without jobs and without hope. At that time, a man named Charles Darrow enjoyed playing a version of Lizzie's game. He liked it so much that he designed a beautiful playing board. He called his version Monopoly. Charles took his Monopoly game to Parker Brothers. Parker Brothers was the most well-known game company in the USA. Charles wanted them to help him sell his game. The people at Parker Brothers rejected Charles' game. But Charles did not lose hope. Instead, he created 5,000 copies of his game. He brought them to a local toy store.  Then Parker Brothers was interested. They bought the game from Charles and the rest is history. Parker Brothers began selling Monopoly and they changed the point of the game. They used the game to bring glory to big businesses. When people play Monopoly today, they want to create Monopolies. Then they win the game. Many people today may not understand the first meaning of the game. Parker Brothers has sold over 275 million copies of Monopoly. It comes in more than 40 different languages. You can find the game in more than 100 different countries. Over the years, people have changed the playing board design along with the property names. But the rules remain the same. There is a London Monopoly board, a Thailand board and an Indonesian board. There are superhero boards, sports team boards and popular landmark boards. There is even a board representing my city, Grand Rapids, Michigan. Blind people have their own Monopoly playing board too. Their board uses Braille. These small raised points let blind people read the property names as they move around the board. People love playing the game Monopoly. And they have played the game in some very strange places, like underwater. Some people hold world records for playing Monopoly in these strange places. For example, the longest game in a tree house was 286 hours. The longest game underground lasted 100 hours. The longest game played upside down was 36 hours. The longest game of Monopoly ever was 1680 hours. That is 70 days of Monopoly playing. People have not always used Monopoly as just a game. During World War II, Monopoly helped captured soldiers. These British and American soldiers were in prison camps in Germany. Aid groups brought them food and mail. But sometimes they would also bring Monopoly games. The German soldiers trusted that the games were just games. But hiding inside the games were maps, real money and other materials. Cloth maps easily fit between small spaces cut into the game box. And the money hid under the game money. Just imagine the surprise of the German soldiers when they discovered the truth. Monopoly was helping their prisoners escape. Some people may think that Monopoly is just a fun game. And it is. But this game has its own special history that can teach us new things. It is important to remember that everything has a history. A history can give us special knowledge about ourselves, our culture and even about the games we play. The writer of this program was Rebecca Skipper. The producer was Michio Ozaki. The voices you heard were from the United States. You can listen to this program again and read it on the internet at www.radioenglish.net. This program is called The Monopoly Game. You can also leave your comments on our website or you can email us at radioenglish.net. You can also find us on Facebook. Just search for Spotlight Radio. We hope you can join us again for the next Spotlight program. Goodbye.


This second e-lecture about the phonological dialects of North America looks at these dialects, which are listed here, including the reference dialect which we already defined in the north. It looks at these dialects not in terms of their individual sound systems, but in terms of currently ongoing sound changes. Thus, we will define the phonology of North American English in the context of the recently published Atlas of North American English. In fact, it was published in 2005. Now, the Atlas of North American English is based on a large telephone survey of the urbanized areas of all English-speaking people in North America. It was conducted by the world's leading sociolinguist, William Labov, between 1992 and 2003. So this was the research period. Now, together with his co-workers Sharon Ash and Charles Boeberg, this is Sharon Ash, this is Charles Boeberg, and this of course is Labov himself. Together with them he interviewed a total of almost 800 subjects from something like 300 communities, including Canada and Alaska. The interviews were based on a variety of interview techniques to obtain different types of data, keywords, minimal pairs and so on. And to obtain reliable results, the data was examined acoustically and the resulting maps with their isoglosses were based on features such as formant analysis and other types of acoustic measurements. As a result, the Atlas of North American English provided a continental map of regional North American phonological dialects based on ongoing sound changes. Now, this dialect map and its numerous additional maps that trace the logic of these dialect definitions were published not only in book form but also on the CD-ROM and well, I can proudly say that we were the team here in Marburg that created the CD-ROM for Labov's team. The following main regional dialects were defined on this map. Now, first of all, we have the big region of Canada, this red isogloss then represented in green, the west. The blue isogloss is essentially the north and then we have the midlands or the midland variety and finally surrounded by the big south isogloss, the south. Now, these are the main phonological dialects. The other areas, for example, here you find an area inside the south which is called Texas south or another one over here towards Georgia, the inland south and so on and so forth. Now, central to the new definition of these dialect boundaries or isoglosses are recent developments in the North American vowel system that is simple and complex vocalic changes. Let us start with an overview of the most prominent simple sound shifts. Now, here's a selection of such sound changes more are discussed in the atlas itself and in the unit on the virtual linguistics compass English in North America. Let's look at them in detail. Now, the first one is the fronting of OO and it applies to keywords such as 2 or 2 and it is a feature that applies to all varieties that are listed here so it is a unifying feature across the entire North American continent so the result would be something like 2 becomes 2, 2. The second one would be O, the fronting of O in keywords such as go and we find that this feature is primarily realized in the Midland and in the South. Diphthongel A in words such as say can be found in a large number of varieties for example in Canada, in the North, in the Midland, not in the South but in the West so instead of saying say you would still have a diphthongel version such as say. Very prominent is the low back merger in words such as caught versus caught where the two vowels, the two low back vowels or and or merge to become identical in especially the Canadian dialect and of course in the West. Now the South does not realize this type of sound change but in the North and in the Midland we find transitional effects so some speakers do realize this type of sound shift others don't. The pin-pen merger, the in-end merger by contrast only applies to the South so you have words such as pin and pen which become identical. The glide deletion of I is another typical feature of the South where words such as five realize the vowel not as a diphthong but they delete the off glide and so five becomes five. Canadian raising is a feature that not only applies to Canada but also to the North and the key word would be something like house where the onset of the ow is raised towards o so house becomes host. And finally we have the Canadian shift which is a typical Canadian feature and it can be found in items such as pack which where the vowel is retracted so the result would be something like pack. Thus we can find some sound changes that unify the entirety of North America for example the fronting of oo. Others apply to large areas diphthongle A and the low back merger and then we have several ongoing sound changes that can be clearly associated with particular areas such as the South or the North. Furthermore there are additional regionally restricted sound shifts such as the short ass split in the North and North East or the southern drawl in the South. Some of these sound shifts even constitute the starting point of more complex system effects the so-called chain shifts. Two of them are very prominent in North America. The so-called northern city shift and the southern shift. So let's start with the northern city shift. This is a chain shift affecting the short vowels of the English spoken in the United States regions bordering the Great Lakes. It is triggered by the general raising of air in man and that and back and then it is followed by a fronting of awe, a lowering of awe and then quite interestingly the A in words such as get, yes and read is centralized so the result will be something like yes and read and get. This of course pushes the wedge out of the way the central vowel and backs it so that words such as but will become but. Let us listen to an example. Now here's a good friend of ours, Dan Spencer from Detroit in Michigan. In fact he uses the same teaching method that of the inverted classroom. Let's listen first. I welcome all users to this website on linguistics. My name is Dan and I speak American English. Let's now listen to the stages of the northern city shift. I said the first stage is the raising of air to air, clear cut raising of air. The fronting of awe, cut, well it is very much fronted and then the lowering of awe, cut. The backing of air in words such as yes, yes. And finally the backing and lowering of awe, the wedge as in but. So but will be but, but you hear the backing of awe. So this is a nice example of the northern city shift. The southern shift is triggered by the removal of eye from the low central position. So in most southern states of the United States, the triggering movement is a monofungalization of eye which we've already seen here. So this was our example of the glide deletion of eye and it applies to the southern states. Now when this monofungalization of eye to are takes place, we can also observe a slight shift of the monofungal nucleus towards the front as it enters the subsystem of long and in gliding vows. Let us represent all these changes on a map. Now the first dialect area which we looked at was Canadian and with its main features the fronting of awe, Canadian raising, Canadian shift and the low back merger. We didn't represent defungal eye here because we confined ourselves to the four main features. By the way we're using here the colors of the isoglosses that are used in the atlas of North American English. Now here's the west as our next big dialect area and we see represented in green here that the fronting of awe and the low back merger are two features that this and the defungal eye, in fact all these three features are shared with Canadian. In the north we find again the fronting of awe, Canadian raising shared with Canada, defungal eye like in Canada as well and here as a special feature the northern cities shift. The next is the midland a transitional area where we don't find the low back merger but the fronting of awe and awe and defungal eye. And finally the south which is specific due to its realization of the southern shift, no low back merger but it is unified with the other dialect areas by the fronting of awe and the fronting of awe. Let's listen to a speaker from the south. Here is a speaker from Jackson in Missouri. Let's listen to some examples first. So here you typically find the monothongization of eye. The two vowels in caught and caught are not merged. Then we typically have the fronting of zoo. And finally the in and merger we listed earlier on in words such as chin and pen you would find no difference between the two vowels chin, pen, chin, pen. Well let's summarize. Just like in England we have no uniform dialect situation in North America. Love of study and that of his co-authors Sharon Ash and Charles Bulberg have shown that the examination of ongoing sound changes allows us to define regions in North America that otherwise would have been separated either politically by means of their sheer distance or by social aspects such as prestige. To represent these sound changes and the North American vowel systems most adequately a transcription system other than the one used for the varieties of English seems indispensable. This system which takes into account the binary character of North American vowels will be introduced in the e-lecture the North American vowel system.


Early in the year, we couldn't play dead to John Wayne Western, so then we started getting better and because they work so hard, I'm happy for our school, our kids here, our community. It's a great thing to feel good about yourself and, you know, whatever happens is going to happen. You've got to play well for 32 minutes or however long it takes. Nobody thought we was going to be there and nobody thought we was going to get best possible for sure. We pulled it out and everybody thought it was over and then we just started playing with heart. We wanted it more, came out and got it done. To get to that overtime and we made some timely baskets and just having the fact to be the first team in Eastridge history to go to the All-A-State tournament is a very surreal moment for all of us and I'm glad I could do it with my best friends. It's definitely an honor just to represent school, family, you know, the community.  It's a great accomplishment for the team first in school history and I feel like no one thought we would be in the championship game and I feel like we proved a lot of people wrong and we're ready to go to Frankfurt. We've proven what we can do so far and we still haven't reached our full potential at all.


Now our digital scale model of the cell system moves into a little bit more complicated territory. What's that thing that roots you and I to the ground? It's gravity and every planet has it. So in this video, we're going to use the gravity values from that NASA planetary fact sheet data to help simulate what gravity might be like on other planets. Now remember, this is just a little model to simulate that. It's not going to be perfect. We just want to give a visual representation of it. And what's cool, if you got some interest in how to make a platformer in scratch, then this video is going to help you out because gravity is used in these platforms. And the cool thing is maybe your platformer can go to different planets.  But let's go code some gravity in just a sec. Hello world, Surfing Scratchy here, teacher, surfer, programmer. And on this channel, I help curious learners just like you along on your learning journeys. This video is part of a larger series on creating a digital scale model of the solar system in scratch. Go check the card in the top right hand corner right now and see those previous videos. And there's a link down in the description for a starter project to get yourself up and running with it. This video is all about simulating some gravity on each of our planets here on the screen based on data obtained from a NASA fact sheet. And I just want to make a quick shout out to FunArt Tutorials. Man, I hope I said that right. Let me know if I didn't because I checked out your how to make a platformer video that was very helpful. We're going to be using elements of this. So you know where the card is to go check that out. And quick disclaimer, I don't claim to be physicist in this video. I'm just using data obtained from a NASA fact sheet to just make an approximation of some gravity to simulate it visually. Hey, if we can get Neil deGrasse, Dyson, Neil Nye, or Derek Muller in here to perfect this, then hey, I'm all for it. And as always, I've got our blueprint set out here. Let's go execute it. All right, I'm just over here in the stage code area. And the first thing that we're going to do is create another state. And this is going to be called gravity. So let's just duplicate this code block and we'll set it to number three. For the three number key. And we need to create a new state variable. So I'm going to head over to variables, make one, call it state underscore gravity. I'm going to scroll up to where I'm initializing all those states to a bit of scroll down. And let's do it. Let's initiate it, call it gravity. Boom. And now that we've created that state variable, we need to make sure that we change the state to state underscore gravity. So now I'm going to go ahead and click the green flag and with any luck, as we press the third key on the keyboard, we should have all of our planets line up down the bottom here and we shouldn't see the distance sprite. Boom. That's what we're looking for. Okay. Now we're going to need a couple of sprites. So I'm just going to paint one. And this is going to be a ground simulating the planet's surface. Now obviously not all planets have a surface, but we're going to make the assumption that they do. And I'm just going to draw a rectangle. It's not going to have an outline. So I'm going to get rid of that just like that. And I'm going to drag it down. So it's just above the planets. We're going to make that our ground. You can change the height of this if you want, but I'm just going to leave it like that. The next sprite that we want to add, we're just going to choose one. You can import your own, but I found this dog in a space hat and I quite liked it. So we're going to have dot and dots a little bit big. So I'm just going to reduce dot size to about 70. Yeah, dots looking pretty good there. I'm just going to head back over to the planet distance sprite and grab this code block here when I receive state has changed. I'm just going to drag it on top of dot. I'm going to head into dot. And instead of state underscore distance, we want to be state underscore gravity. And I'm going to grab that same block and put it on the ground. So what that is going to do is only going to show dot and the ground when we're in the state of gravity. Okay, let's do a little bit of setup now. We need to create a couple of variables and a list. We need to create a gravity variable. We're going to create a wide velocity variable. If you're not sure what velocity or gravity is, go check the card in the top right corner. I've got a video that explains this.  And just like we've got the diameters, we need the gravities. I'm not really sure there's a plural for gravities, but you get the idea. And this gravities list is going to refer to all the different gravity measurements that we're going to obtain from that fact sheet. So let's go to that fact sheet right now. Okay, I've got the gravity fact sheet down here. Link below in the description for you to go and check it out as well. And I've got this column highlighted for our gravity for meters per second squared. We're not worried about the units here because our units are a little bit different on the screen. We're using pixels per frame, essentially. So we're just going to copy these values, open up a text editor, and we're going to create a new document. And I'm going to convert it to a plain text file so we can simply paste those values in. Now I'm going to save it as a text file. Just call it gravities. Cool. Now I'm going to head back over to scratch. I'm going to right click on our list and import. And I'm going to go to where I saved that, to gravities, open, and you'll see that our list is populated. So number one is going to refer to Mercury. I'll just give you a quick refresher on that. Here are our list of planets, and we've got a one-to-one mapping of all the locations. Now I'm just going to turn that off. And the first thing that we're going to do is we're going to grab the event when the selected planet has changed. And what we can do is set the gravity of that new planet to whichever one that we've selected. Let's get a set block. We're going to set the gravity. Let's scroll down to our list blocks, and we're going to need the item number and the item. We want the item number of the planet names, and the thing that we're looking for is the selected planet. And then we want the selected planet's index of gravities. So this is essentially going to give us the gravity value based on the selected planet. So the selected planet is currently Jupiter. The index of Jupiter is five, so I'm expecting a gravity value of 23.1. So let's click this to check it out, and there we go. Let's whack that block inside of there. And then when we click on a couple of different planets here, so we've got Pluto, and our gravity has changed to Pluto's gravity. Now we've got Mars' gravity. Okay, we're just about ready to get dot moving. So now let's drag out a when the green flag is clicked block. Put a forever loop down. Then we're going to create a custom block, and we're going to call it gravity. And then we're going to have an input and that input. I'm just going to call it acceleration, because I mean that's what gravity is. It's just the rate at which we accelerate. It's just a special name that we give to it. And let's go okay. Then we're going to call the gravity my block. Okay, great. Now it's time to construct our gravity function. Okay, so it's got it pretty crazy at the moment. Now we need to check if dot is touching the ground. So we'll put an if block in. We're touching the ground. And you want to repeat until we're not touching the ground, and we'll duplicate that code block just there. And then what we'll do is we're going to change the y value by one. So essentially what's happening here is dot's going to fall from the sky. It's going to touch the ground. We want to reverse the velocity. We want dot to go up. And after dot is no longer touching the ground, we want to set the y velocity back to zero. Okay, we want to make sure that we're only calling this gravity function. If our state is equal to the gravity state. So let's click the green flag and see where we're at. Going to head across to the gravity. You can see some funky business is going on here with dot. And the reason for that is we don't have run without screen refresh on. So let's right click, edit our block, and go run without screen refresh. We'll click okay, and our dot just sort of hovers above the ground. And that's good enough for now. Okay, and the way that we're going to show and visualize our gravity values here is we're going to get dot to jump. So inside of out, if we're touching the ground condition here, we're going to sense for a keyboard press. And let's just sense for when the key space is pressed. And what we can do here simply is just set the velocity to a value. And a value of around 15 seems to me some pretty nice jumping. So I'm going to press the green flag. I'm going to go across to it. And I'm going to press the spacebar. And you can see there that dot's having a hard time. And the reason for that is that we've got a pretty high acceleration value going on here. What we're going to change this to at the moment is negative one, because that's going to be our baseline. And then when I press the spacebar, you can see dot has a nice little jump here. So we've got our little test working, which is great, but we've got our values hard-coded in. So now we need to change it so we can map it to each of the gravities here in our list. We know that for a negative one value, that's mapped to the earth. So we can divide earth by earth. So if we divide earth gravity by earth gravity, we're going to end up at one. So let's go get a division block and let's hard code in earth's gravity at negative 9.8. Then we can go grab that gravity variable that we created earlier. And remember, this gravity variable has the current selected planet's gravity. And if we divide it by a negative number, then we're going to end up with a negative number. So if we click earth and we click this value, we should get negative one, which is great. Now let's click mercury. And I've got to be careful what I say here, because if I ask you if this number is going to be smaller than negative one, the answer would be wrong. It'd actually be a little bit bigger because negative 0.37 is actually larger than negative one. But it's kind of less gravity is what we're going for here. If we click on Jupiter, for instance, this is going to be a lot smaller. So let's whack that code block in there. And now to test it, I'm just going to click the green flag and see there's Jupiter's value and there's earth's value. And if I click mercury dot is going to try and leave the screen there. So that's looking pretty good. Now our work isn't quite done yet because for every gravity, we're hard coding in the wide velocity. And it'd be neat if our jump height was actually a little bit different for each planet. Now I'm just kind of playing around with these values a little bit. And what I arrived at was kind of switching these around to invert it. And we want it to be a positive number because this is a jump value now. So we're just going to divide earth's gravity by the selected gravity. And then because we like this 15 as a baseline, we know when earth is selected, this is going to be equal to one. We can multiply this by 15. But there is a slight problem with this code because if we go to a planet with really low gravity dot is just going to go off into space really quickly. And it's not going to look as nice as it could. It's going to be even worse for Pluto. So what we can do is just when the key space is pressed, we can just cap the velocity if it's greater than say 15 or 20, just like you see here. And now when I press the space bar, the gravity is looking pretty good. And I'll go over to Jupiter now and we press the space bar. You can see there's quite heavy gravity going on there for our large value.  And that's looking pretty nice, feeling pretty good there. Go to Pluto for our smallest gravity. And off goes dot and dot gently floats back down to our ground. The last thing I think we should do is when the state has changed, we should set dots, y to a positive value so the user can see dot drop in. And that's going to be pretty simple to do because all we need to do is go to an x and y. And the y that we want to go to, let's just make it 200. Okay, so now let's switch back to a different state. Here we are in the distance state and then we'll go back to the gravity state and you can see dot floats into our screen. And there you go. That's how we can do gravity. I've just gone ahead and reduced the size of our ground here. It's quite fun to play around with the ground just to watch dot go kind of up and down. Quite nice to play around with. An extension that you could do as well is change the color of the ground or the surface depending on which planet is selected. I'm not going to do that in this tutorial, but there's something for you to think about. All right, that's the end for this tutorial. Like I said earlier, I don't claim to be physicists. So this is just my approximation of these values. If you are in the know out there and you are pretty hardcore with your physics and you've got a better implementation of this, I'd love to hear from you. You know, post your solution down in the comments section. That would be awesome. I hope this video has given you some sort of visual reference point for the gravity values across the planets.


ᇽ ဒ ဒ ဘ စ တ လ ဉ ဴတ် ဘ ဠ ဒ ဴ ဒ ဒ တ းတးလရ ရ ငတ ဉ စ ဘ ္ ဃလ ရ ကလဝ ် ဠ ရ ပ် ပဘ ူတးရ နဏပရပန�ယ ဥဒ� here we will discuss about aggregate transformation. And what are the difference between SQL aggregate and SSIS aggregate? So let's start with aggregate transformation. So what is aggregate transformation? so it is used to perform aggregate operations on groups in a data set. Like we have a data set and it contains many columns and we want to do aggregate by any specific column then we can use aggregate transformation to do the same thing. The aggregate functions available are count, sum, average so these are the functions available in SQL Server as well as in SSIS. Aggregate transformation has one input and one or more than one output so let's move to our case study so this is our case study as we can see we have input table and it contains the information of phone number we have ID, phone type and phone number in ID, ID 1, 2, 3 in phone type business phone number, cell phone number, phone number so we have three type of phone numbers and we want to do the aggregation on ID and then phone type so first of all we want to do the aggregation on phone type second with the ID let's move to SQL Server management studio here we can see we have the same metadata with this phone aggregate table and we want to do the aggregate by using aggregate transformation so as we can see first of all we want to do aggregation with the phone type so we can execute our first query then we can see business phone has three count cell phone again has three count and home phone has four second we want to do the aggregation with ID then we can execute our second query here we can see ID 1 contain 2 ID 2 contain 3 and ID 3 contain 5 so we want to do this aggregation by SSIS so let's move to SSDT then we need to create one more practice right click on this SSIS practice create a new practice then we need to rename this practice with aggregate here we need to drag and drop our dataflow task so we can drag and drop then we need to double click on this dataflow task it will directly move to dataflow panel inside dataflow panel we need to configure our source transformation and destination so our source is OLEDB source so go to other sources then we can drag and drop our OLEDB source now we need to configure our OLEDB source so double click on this OLEDB source OLEDB source editor window will be open now we need to configure our connection manager so click on new here we have already made the connection so delete this connection and create a new connection click on new here we need to select our server name so this is our server name I am going to use window authentication so there is no need to use ID and password here we need to select our database name so database is SSIS test now we can check our connection connection succeed now click on OK so we have done with connection manager now we need to select the table so as we can see we have already typed the query so we can copy this query we need to change data access mode with SQL command here we need to paste the query now go to all columns we want all the columns so click on OK so we have done our source now we need to configure our transformation so our transformation is aggregate transformation inside this common we need to drag and drop aggregate transformation and connect with source now we need to double click on this aggregate here we have the columns so first of all we want to do the aggregation with phone type we need to select the phone type and select phone number so here we can see we have input columns output areas then operation so we want do the aggregation with phone type so our first operation is OK in our second operation we want count now click on OK so we have done our aggregation with phone type now we need to set up our destination so we don't want to load data any destination we want to just check our data so we need to drag and drop multicast go to on aggregate connect with multicast here we need to enable our data viewer so enable data viewer now I am going to execute these packages so as we can see phone type B, C and H 3, 3 and 4 now move to SQL Server Management Studio and execute our first query so once we execute our first query then we can see we are getting the same metadata as we are expected now we can stop our practice so here we can see it doesn't support any error output so here we can check we don't have any error output so aggregate transformation doesn't support error output next is so aggregate transformation has one output and in advance mode we can configure more than one output each will contain different aggregation so first we have done with phone type second we want to do the aggregation with id so double click on this aggregate so here we can see we have this advance so click on this advance as we can see we have only one aggregate here we can configure our second aggregate so we can click with aggregate 2 and this is for id so here we need to configure our second so this time we want to do the aggregate with id and we want to count with phone number so here we can change this phone number click on ok now we need to drag and drop one more multicast and here we can see we have one more output so we can select so this is for id and this is for phone type so here we need to enable data for id then we need to execute our package so as we can see this is for id and this is for phone type so we are getting the multiple aggregate at a single time so this is the difference between sequence over and ssis in ssis we can do multiple aggregate at a single time multiple aggregate at a single time we can also use aggregate to load unique data by applying group by to all columns so thank you so much for watching this video if you like this video please subscribe our channel to get many more videos thank you so much