We have this sort of large scale project that involves examining the use of machine learning and education. So rather than diving into building tools, which of course we're also working on, we also wanted to do a holistic survey and analysis of how machine learning is used in education. And we identified education experts and we sat with them and we talked through the papers with them. We were like, this paper's goal is to, let's say, predict student dropout, right? And the goal there would be not just to predict it, but also to hopefully do something about it so that students are not dropping out of schools. And so that's an admirable goal, that's a goal that all of us can get behind. But that problem has to be concretely formulated into some machine learning problem. And then you have to find the right data set and all that. And then now you have this prediction that you're doing around which students are going to drop out and hopefully you get to kind of translate that into some real world intervention. So just taking this student dropout risk example, we had this interview with someone at a large state university that also struggles a lot with student dropout. One of the things that they mentioned was, okay, this paper is predicting which students are likely to drop out. What can we do with that, right? You tell me that some student is at high risk of dropping out. That's terrible. In some sense, the deed is kind of done. At that point, you tell a student, hey, you're at high risk of dropping out. That's not necessarily useful to the student, right? And you tell the schools the student is dropping out. It doesn't necessarily tell them what can you do about it. And so what he said was something subtle, but I really appreciate it. He said, instead of predicting which students are going to drop out, why don't you predict, for instance, which students are likely to miss class? They've already missed some number of classes and maybe they're about to miss a third class or something. We know that if students are missing several classes, that's a sign that they might be kind of at risk of dropping out. But missing classes is a more actionable thing, right? We can tell students, hey, you know, I've noticed that you've been missing a lot of classes. I'm worried that you're going to miss more classes. What can we do here to support you to attend class? The point here is more subtle.  That target variable could be dropout or it could be something actionable like missing classes. And the second thing is something that they can more easily do something about. The latter, not as clear.


Hey, what's up yesterday? We talked about coachup. Why I want you to have your own website Why I want you to have your own brand and let's talk about that right now I'm gonna show you the easiest Possible solution to handle all of your online Website needs and there's a lot of them. There's millions of sites. I've used probably I think 12 different type of software in the past To handle all my websites all of my landing pages all of my payment pages and there's a lot of Distractions out there. I know there's like wicks square space Wordpress and a lot of other solutions out there that take a long time to figure out and my goal is very simple I am a coach.  You're not gonna want to do it the best solution I've come across if you look at all of my websites NeighborSoccerAcademy.com San Antonio SoccerCamps.com build my sports biz.com soccer entrepreneur.com I could go down the list of other sites I have they're all created on the same platform and it's called Kajabi It's K-A-J-A-B-I And if you shoot me a comment below, I will give you a 30-day free trial to Kajabi. I'm telling you it's the best thing out There it's literally drag-and-drop and they have really professional Templates you can use it's so easy all of the coaches that are in our consulting program They are starting to use that and it's gonna handle all of your payments We talked about yesterday in the video about CoachUp CoachUp is gonna allow you to sell blocks of sessions That is not gonna be the way you can have a successful business. You need to have a monthly membership set up With high higher-end commitments six to twelve months I teach you how to do this in our consulting program But having a website like Kajabi will handle all of the back-end work for you. This way you're not collecting cash Not collecting checks doing everything online and it will streamline your whole process With that being said yesterday we talked about having an online marketing strategy with emails Kajabi has a built-in email integration system that will allow you to send as many emails As you want so you can build an email list have control of that send emails every single day if you want if you're on my email newsletter Right now I send an email every single day for build my sports bits on this channel And that's something that's allowed us to massively grow what we do because we have every single day We have an email it's a daily consistent message. These are things I want for you as well for your private training business If you have any questions about Kajabi and you want to learn more about it I'll even get on a phone call with you. I'll talk to you about it I'll show you how it works. So if you want to reach out to me Simply go in the comments below just say hey Ben. I want to check out Kajabi and I'll send you a private link There so you can have free access to a 30-day trial again Don't let technology slow you down. Don't let it be an excuse Don't you don't want to say well, it's gonna take me too long to create a site Most coaches that I'm helping right now are using that it takes them under three hours to create an entire website So if you have that setup, you're gonna have again your own brand That's going to separate you from all the other coaches out there who are on coach up all the other coaches Who don't have websites and that positions you as the authority. I hope that helps. I'll see you on tomorrow's video


So, in the previous lecture we discussed the symmetric or unbiased random walk extensively and derived it is a symptotic form and then we also arrived at an expression in terms of real space and time variables by introducing the concept of diffusion coefficient. Subsequently, we gave a very brief introduction to the problem of what is called as random walk with the bias or it is also called asymmetric random walk which is basically a natural extension to the symmetric random walk that we discussed. There are many areas where asymmetric random walk is of considerable importance. For example, areas of importance could be or areas of relevance, transport of atoms or particles under external fields a simple example would be for example, the falling of a tiny dust particles. So, this is a problem of asymmetric if assume that there is a collision and random walk then the external force would introduce a certain asymmetry at each step. Some sense of direction there are other equally important cases such as for example, trends in the environmental variability of environmental parameters which is a matter of hot interest due to climate forcing for example, one expects temperature trends and all. And this is always superimposed with the other variabilities and randomness. So, in some ways this can also be although it will be too simplistic, but in a idealized way it can be called as a random walk with bias. There are other situations price of commodities and in physical sciences for example, growth and evaporation kinetics. There is always a forcing because of external conditions and that could again leads it to a problem of biased random walk. Then of course, in what is called as the gambler's ruin problems here a lucky gambler or unlucky gambler could have a certain trend say lucky or unlucky gambler. If it is totally neutral then it is equivalent to a symmetric random walk, but one has a streak of luck or misfortune then it will be a trend. Before any application one must first understand and formulate it in a way which will yield some results that can be discussed or held as a benchmark. The real problems could be much more complex. So, we take up a simple idealized problem and that is what I have shown here. You can see that there is a real line in which states are represented by sites indicated by numbers. So, there is a walker as earlier he starts from the origin and then executes random walk, but when he executes the random walk he he or she the random walker let us say he has landed at the m side. Now, we call it a symmetric if the transition probability from m to m plus 1 is not the same as the transition probability from m to m minus 1. So, if the former is p the latter is q all that we know is that p plus q equal to 1 and relatively p minus q need not be 0, but it could have some what is called as a bias factor. So, we now take up this problem in detail. So, let us therefore, postulate that the transition probability from state m to state let us say m plus 1 is not equal to same transition probability from m to m minus 1. So, let us denote this is origin here this is a state m minus 1 this is state m and this is state m plus 1 and this is p and this is q. So, p is the upper transition probability and q is the downwards transition probability and p plus q equal to 1 and we can say that p minus q is not equal to 0. We can call a factor p minus q equal to gamma in denote the gamma as a bias factor gamma equal to 0 it is a symmetric random work corresponds to symmetric random work. We can express also p and q in terms of now gamma because if you add the 2 by add we get also implies we can say p 2 p equal to 1 plus gamma or p will be 1 plus gamma by 2 and q will be similarly if you subtract 2 q will be 1 minus gamma so, q will be 1 minus gamma by 2. So, once we have bias factor we can express both the upward and the downward transition probabilities in terms of gamma. Now, it stands to reason by the same arguments that we have put forward in the case of symmetric random work that the occupancy probability w at a site m for an n plus 1th step should have come from transitions from m minus 1 with the factor p and transition from m plus 1 with the probability q and of course, from nowhere else because we continue to use the nearest neighbor transitions only. So, nearest neighbor model nearest neighbor transition probabilities transitions. So, we continue to use that then we can write them as earlier the equation for the occupancy probability. So, let us denote w n m as earlier, but if you want we can keep a superscript to be b for bias. So, right now I will write it as bias for the bias case as a occupancy probability at site m superscript bias just denotes for distinguishing from the previous case. Then as from following the argument that I mentioned the occupancy probability at the same site m at the n plus 1th step would come due to transition to the right from the at the n from the occupancy probability at the nth step at site m minus 1 and also would come by a transition from the right corresponding to the occupancy probability at the nth step at from the site and m plus 1. So, this is quite obvious now. So, all that we have to do is to solve it and we need an initial condition and as earlier we say that w to begin with thus walker was at the origin where delta now represents the chronicle delta. We can as earlier use the concept of generating functions define generating function g f or g m z will be since all states are accessible in principle. So, the sum will be over all states and it will be summed over the state or the site index and not the step index. So, this is site sum generating function where z now is a kind of a conjugate parameter that replaces the site, but keeps the memory of the site there and z as we mentioned could be any real number and the function g n z should exist in a small strips for some values continuous values of z. So, this is the definition. So, with this definition we can now work with the equation this equation here where the transition probabilities are given as a recurrence relation. So, we can multiply both sites by z to the power m and sum over multiply by z to the power m and sum over m let us call this as equation 1 and this as equation 2. So, then we we can easily see that the left hand side will become g of n plus 1 since we have multiplied by z to the power m it is only the index that changes g n plus 1 and the right hand side we will have now p here and we can easily see by following the same strategy that we adopted earlier that it can be written as m prime equal to minus infinity to infinity w n m z to the power m prime plus 1 plus q m prime equal to again minus infinity to infinity w n again here of course we will call m prime m prime, but z to the power m prime minus 1. So, this m prime was just new dummy index replacing m in the first equation on the right hand side the m prime was actually m minus 1 on the second equation the m prime was defined as m plus 1. So, that in both the cases we get w n m prime only. So, this now becomes a easy to move forward. So, we see that we get an equation g n plus 1 z equal to it will just come to p z plus q by z multiplied by g n z. We can easily see this equation because now the right hand side if you see you can take out the z out. So, the rest is simply g n of z similarly here also 1 by z if you take out the sum becomes just again g n z. So, it becomes p z plus q by z that is how we get this equation you can call it 3. Now, if we iterate this equation the following exactly the same steps using the initial condition iterate with n equal to 0 1 etcetera and use the initial condition which amounts to which implies g 0 z equal to 1. So, we get g n we get g n of z simply alpha z plus beta by z whole to the power n. So, since the g not equal to 1 is quite obvious because it was present only at the origin. So, all other z the powers they it does not exist all other coefficients do not exist that is why it becomes 1. So, you have now the general solution you can call it 4. Now, this is the generating function which is quite useful. Many results can be gotten as we have been seeing in many cases by just using the generating function alone. For example, we can easily note that at z equal to 1 g n 1 should be 1 because it is sum of all the probabilities which is true here. So, sorry it should be p and q not alpha beta p z plus q by z and when z equal to 1 p plus q is 1. So, g n 1 is 1. So, that sort of confirms that we are on the right track. So, we can now explicitly obtain the occupancy probabilities by expanding the generating function in powers of z using the binomial theorem as we did earlier. So, we will not repeat that derivation you can refer back to the method adopted in the case of unbiased random walk where we used a plus b to the power n equal to n c r a to the power r b to the power n minus r formula. So, similarly when we do this becomes sum say m equal to minus n to n n c n plus m by 2 p to the power n plus m by 2 then q to the power n minus m by 2 then z to the power m. So, this is the general expression for g and z expanded in terms of powers of z. So, as earlier we identify the coefficients of z to the power m identify the coefficients of z to the power m with w the occupancy probabilities since the subscript is n this will be w n and since it is z to the power m it will be at the site m as per the definition this as per the definition of g n. Then we get the formula w n with bias m is n c n plus m by 2 p to the power n plus m by 2 q to the power n minus m by 2 this is a actually formally the problem is solved. We can give it a slightly more transparent form in terms of gamma replace p and q with gamma using the relation p equal to 1 plus gamma by 2 and q was 1 minus gamma by 2 then we get w n with bias will be an expression which will have the form w n let us call it 0 without bias m and 1 plus gamma to the power n plus m by 2 into 1 minus gamma to the power n minus m by 2 where w n 0 this is occupancy probability for unbiased case and this we have derived an expression as 1 by 2 to the power n n factorial divided by n plus m by 2 factorial into n minus m by 2 factorial where these factorials have to be for integers which means if n is even m also should be even I mean if yes when n is even m will be even and when n is odd m will be odd that will be maintained this expression was our starting expression for symmetric random walk. So, the problem is fully and clearly obtained which makes it very clear that if gamma is 0 if there is no bias factor then the occupancy probability is same as for the unbiased case. So, that recoveries immediate in this. So, the next natural thing to do is to see the mean and the variance for this case for. So, mean and variance follows from the generating function as we saw or generating function g n z was p z plus q by z whole to the power n and we have seen it now several times that the mean what we call as m bar at nth step the mean at the nth step is given by g n prime to the evaluated at z equal to 1 and if you differentiate for example, here what we will get what is g n prime g n prime z is going to be n of p z plus q by z to the power n minus 1 and if you differentiate again this is going to be p and this will be minus q by z square. So, now if we set z equal to 1. So, g m prime 1 turns out to be if you put z equal to 1 and note that p plus q equal to 1 then the first term the n remains the first term becomes 1 and the second term becomes p minus q and in terms of the bias factor this is n gamma. So, we have the expression m bar mean equal to m bar is n gamma is an interesting result, but quite obvious now that is how the bias factor operates. In fact, another definition of the bias factor could be a measure of the mean displacement after several steps two things to be noted here the mean displacement is proportional to the number of steps gamma is a system parameter. So, it does not depend on n. So, it is proportional to the number of steps unlike the standard deviation which was going as square root of n and it is of course proportional to the bias factor. So, what it means is over superimposed by the random walk there is however a net trend in the direction of gamma positive. So, if gamma is positive here it is p minus q. So, p is greater than q that is if the forward jump is little more probable than the backward jump then on the whole the random walker tends to move in the forward direction towards the forward direction and gamma could be negative if q is more than p and then he would be moving in the opposite direction. So, that expected trend is reproduced by the mathematical formalism that we followed. Similarly, we can determine the variance which we simply mean short notation variance var which is defined as second derivative plus g prime 1 minus g prime 1 square. Here now one has to differentiate g n prime z once again it is a bit tedious, but very simple procedure to do. We will only give the results here it just turns out that this variance will become n into 1 minus gamma square or the standard deviation sigma equal to square root of 1 minus gamma square into n to the power half. If gamma is much less than 1 this will tend to n to the power half if gamma is far smaller than 1. So, if the bias factor is very weak then the standard deviation is almost undisturbed it remains the same at least to the order of gamma square same as that for the symmetric random walk. So, we can visualize this whole process as shifting of. So, the originally our random walker was here and slowly at some and after some steps the random walker will sort of would have moved with the mean which is now shifted and his standard deviation measure of the standard deviation would have been still this is after. So, I will join it for guiding the i after n steps this is m bar this could be sigma. So, there is a peak movement is seen unlike the symmetric case where only broadening takes place, but more or less the peak would remain at the origin itself. Thank you.


Hi, this is Pastor David Rosales of Calvary Chapel of the Chino Valley, California. In the Gospel of Luke, we have recorded a story given by Jesus concerning what happens after someone dies. It's the story of the rich man and Lazarus. The purpose behind this story is actually a warning concerning materialism and greed. The audience Jesus gives the story to is identified in chapter 15, where Luke tells us that Jesus is speaking to tax collectors, sinners, Pharisees and their scribes as well as his disciples and by inference his apostles. Luke tells us before Jesus gave the story that the Pharisees were lovers of money. He said this because Jesus had said you cannot serve God in mammon, which cause the Pharisees to sneer at him and to mock him. In other words, it cut them to their hearts. In light of this, Jesus spoke directly to them in parabolic form to address the folly of loving money and the wisdom of trusting God. And he did so by speaking of a certain unnamed rich man and contrasting him with a very destitute poor man named Lazarus. The point of the story was to show them and by virtue of application, all who would hear this story, how foolish trusting enriches actually is. Paul told us believers were not to trust in uncertain riches and concerning money. Solomon asked, will you set your eyes on that which is not? For riches certainly make themselves wings. They fly away like an eagle toward heaven. The Pharisees were guilty of loving money, so Jesus warns them and all who were listening to him about the future awaiting them. What good would their money do them when it no longer has any value? You know the story, the rich man dies as does the poor man Lazarus. They are both carried to their graves, but the grave isn't their final destination. Lazarus is carried to paradise, Abraham's bosom, but the rich man ends up in Hades. Jesus contrasted the fact that Lazarus was comforted with the rich man's crying out that he was in torment. At this point I will share about what happens when someone dies. There are many who think that when someone dies nothing actually happens. They believe that the body simply deteriorates and that is all. Others think when someone dies, if they're not believers they simply cease to exist. Others believe that they are reincarnated and others think that the soul simply sleeps until the resurrection and final judgment. Some think and teach that believers end up in a place they call purgatory. According to the Catholic Encyclopedia, purgatory is a place or condition of temporal punishment for those who departing this life in God's grace are not entirely free from venial faults or have not fully paid the satisfaction due to their transgressions. In the Catechism of the Catholic Church it is stated that purgatory is part of the Catholic doctrine of faith where a final purification occurs in order to achieve the holiness necessary to enter heaven. None of this is what the New Testament reveals about what happens after death. In this parable we see that Lazarus, a genuine believer, ends up in a place of comfort but the rich man who trusted in his riches and not God ends up in a place of torment. In the story we see that the lost man remembered his religious roots, became aware of his need for mercy, made it clear that he was in torment and that word speaks of agony, pain, grief. He even speaks of torture. Interestingly he was aware that Lazarus was being comforted but he himself tormented. He even said to Abraham, I'm tormented in this flame. By using the word flame he's saying I am in severe and continuous pain. Many do not believe in eternal punishment today. Some are teaching their churches and writing books that say that almost everybody will eventually end up in heaven. I did not believe this when I first got saved because if I did I wouldn't have witnessed to my parents. The fact is it is appointed for man to die once and then the judgment. It's interesting how in the story the rich man accepts his situation but asked Abraham to send Lazarus to warn his brothers. The reality of his eternity impacted him. His request was for his family to not suffer in the way that he himself was suffering. I wonder how many people would today say the same thing. The sad fact is the rich man had no excuse because he was aware of Moses and the prophets. He just never responded. They had enough to be aware of who Messiah was but rejected him even as the Pharisees who were listening to Jesus speak. At that moment we're doing Jesus made it clear there are two possibilities for the future. One comfort the other torment. We need to remember this. It should inspire us to live for the Lord to date to tell others how they can escape the future judgment. If you love your unsaved family and friends pray for them that they might come to Jesus before it is too late and share the gospel with them. This upcoming Sunday I will be teaching on this passage. I've called my message What Happens After Death. This is Pastor David Rosales of Calvary Chapel of the Chino Valley, California.